The obtained interferograms and the results of their processing are given in Fig. 7 а-d. The dependence of IP period change on sample temperature is given in Fig. 7 е. As seen, with the temperature growing from 21 to 28 deg., the IP period changed from 1.8 mm to 0.7 mm, which corresponds to a change in angle 2φ (θmax shift) by 0.43 mrad. The experiment showed no change (within the measurements accuracy) in the IP period, measured before the start of measurements and after the sample cooled down to the room temperature. Thus, one can estimate the effect of temperature variation on parameters of polymeric hologram 1.2.mm thick with spatial frequency ν = 350 mm-1 as follows: with the temperature changing by 1К, the change in the diffraction angle (θmax shift) amounts to δθmax = 0.06 mrad, i. e. the

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Note that the temperature effect on parameters of polymeric reflection holograms, recorded on samples of Reoxan material (Sukhanov et al., 1984), demonstrates the magnitude of changes on the same order. With the temperature of Reoxan sample changing from 24 ºС to 29 ºС, the shift of λmax in the spectrum of reflected radiation is from 532.1 nm to 532.6 nm (spectral interval of reconstructing radiation, Δλ < 0.01 nm). Thus, the studied hologram (thickness 1 mm, ν > 3000 mm-1, spectral selectivity, Δλ = 0.15 nm), intended for the use as a

**4.3. The effect of ambient humidity variation on parameters of polymeric volume**

It has been established that a Difphen material sample (a disk 40 mm in diameter and 4 mm thick), when immersed in water in the temperature range (20 ÷ 30) ºС, takes up to 1.5% of water with respect to the sample weight in air-dry condition at relative humidity of the am‐ bient air Н ≈ 50%. Taking up moisture changes the average refractive index and thickness of

The effect of varying humidity of the ambient air on the polymeric hologram parameters was studied at an experimental stand of a design that provided for an enclosed volume around the hologram to maintain humidity ≈ 90% (much higher than normal conditions) and for conduct of long-time measurements (several hours). Fig. 8 shows the optical dia‐ gram of the stand (Fig. 8 а) and schematic drawing to illustrate possible changes in polymer‐

The stand was used to measure the angular selectivity contour of a hologram at a one-time fixation of all contour data. The hologram was illuminated with a divergent radiation beam; the intensity distribution of the diffracted radiation (angular selectivity contour) was record‐ ed by a CMOS matrix of a camera – the results of processing the experimental data are given in Fig. 9. The effect of varying humidity on hologram parameters was assessed by a change in the position, θmax, of the intensity maximum of diffracted radiation in a CMOS matrix during the process under study. Position θmax was detected with accuracy ± 1 pixel, which

*4.3.1. The method of assessment of the change in the space position of diffracted beam*

hologram under study has thermal shift 0.06 mrad/К.

**holograms**

narrowband spectral selector, had thermal shift δλmax = 0.1 nm/K.

the sample and, accordingly, characteristics of recorded holograms.

ic sample dimensions under moisture take-up (Fig. 8 b).

corresponded to angular resolution ≈ 0.02 mrad.

Before the experiment started, the hologram was set in the position, where the IP had the maximum period that provided the possibility under those conditions to process interfero‐ grams and perform quantitative measurements. To measure the temperature, a warm air jet was directed towards the hologram on the side 2 and the sample was heated up to tempera‐ ture Т = 32 ºС. The interferograms were shot in a stationary state of the scheme, with the sample cooling down after the action of warm air; the difference in readings Т1 and Т2 was within the measurements accuracy.

**Figure 7.** Changes of the period of the low-frequency interference pattern (IP) at variation of the temperature of poly‐ meric hologram grating with ν = 350 mm-1, recorded on a sample of Difphen material 1.2.mm thick: а, b – IP images at hologram temperature 21 ºС (а) and 27 ºС (b); с, d – processing of interferograms given in a and b, respectively; e – dependence of IP period, d, on sample temperature, dashed line illustrate the character of process.

#### *4.2.2. The experimental results*

The experiment was carried out under the following conditions: interfering beam diameter, D, 8–10 mm; angle between beams I1 and I2, 2θ, 10 deg.; λ = 488 nm; angular selectivity of the hologram under study, Δθ, 1.7 mrad; temperature variation interval 21–28 ºС.

The obtained interferograms and the results of their processing are given in Fig. 7 а-d. The dependence of IP period change on sample temperature is given in Fig. 7 е. As seen, with the temperature growing from 21 to 28 deg., the IP period changed from 1.8 mm to 0.7 mm, which corresponds to a change in angle 2φ (θmax shift) by 0.43 mrad. The experiment showed no change (within the measurements accuracy) in the IP period, measured before the start of measurements and after the sample cooled down to the room temperature. Thus, one can estimate the effect of temperature variation on parameters of polymeric hologram 1.2.mm thick with spatial frequency ν = 350 mm-1 as follows: with the temperature changing by 1К, the change in the diffraction angle (θmax shift) amounts to δθmax = 0.06 mrad, i. e. the hologram under study has thermal shift 0.06 mrad/К.

The forming interference pattern can be observed in each of propagating beams (I1 and I2) with a screen installed perpendicularly to the beam propagation. The IP was recorded using a CMOS matrix of a size that allowed recording the observed interference field in full and obtaining interferograms imaged in Fig.7а, b. The interferograms were shot at actual size si‐ multaneously with temperature control. The temperature sensors, mounted onto the sample on the side 1 (Т1) and on the side 2 (Т2) in close proximity to the observation area, allowed

Before the experiment started, the hologram was set in the position, where the IP had the maximum period that provided the possibility under those conditions to process interfero‐ grams and perform quantitative measurements. To measure the temperature, a warm air jet was directed towards the hologram on the side 2 and the sample was heated up to tempera‐ ture Т = 32 ºС. The interferograms were shot in a stationary state of the scheme, with the sample cooling down after the action of warm air; the difference in readings Т1 and Т2 was

**Figure 7.** Changes of the period of the low-frequency interference pattern (IP) at variation of the temperature of poly‐ meric hologram grating with ν = 350 mm-1, recorded on a sample of Difphen material 1.2.mm thick: а, b – IP images at hologram temperature 21 ºС (а) and 27 ºС (b); с, d – processing of interferograms given in a and b, respectively; e –

The experiment was carried out under the following conditions: interfering beam diameter, D, 8–10 mm; angle between beams I1 and I2, 2θ, 10 deg.; λ = 488 nm; angular selectivity of

dependence of IP period, d, on sample temperature, dashed line illustrate the character of process.

the hologram under study, Δθ, 1.7 mrad; temperature variation interval 21–28 ºС.

carrying out the control with accuracy 0.1 К.

52 Holography – Basic Principles and Contemporary Applications

within the measurements accuracy.

*4.2.2. The experimental results*

Note that the temperature effect on parameters of polymeric reflection holograms, recorded on samples of Reoxan material (Sukhanov et al., 1984), demonstrates the magnitude of changes on the same order. With the temperature of Reoxan sample changing from 24 ºС to 29 ºС, the shift of λmax in the spectrum of reflected radiation is from 532.1 nm to 532.6 nm (spectral interval of reconstructing radiation, Δλ < 0.01 nm). Thus, the studied hologram (thickness 1 mm, ν > 3000 mm-1, spectral selectivity, Δλ = 0.15 nm), intended for the use as a narrowband spectral selector, had thermal shift δλmax = 0.1 nm/K.

#### **4.3. The effect of ambient humidity variation on parameters of polymeric volume holograms**

#### *4.3.1. The method of assessment of the change in the space position of diffracted beam*

It has been established that a Difphen material sample (a disk 40 mm in diameter and 4 mm thick), when immersed in water in the temperature range (20 ÷ 30) ºС, takes up to 1.5% of water with respect to the sample weight in air-dry condition at relative humidity of the am‐ bient air Н ≈ 50%. Taking up moisture changes the average refractive index and thickness of the sample and, accordingly, characteristics of recorded holograms.

The effect of varying humidity of the ambient air on the polymeric hologram parameters was studied at an experimental stand of a design that provided for an enclosed volume around the hologram to maintain humidity ≈ 90% (much higher than normal conditions) and for conduct of long-time measurements (several hours). Fig. 8 shows the optical dia‐ gram of the stand (Fig. 8 а) and schematic drawing to illustrate possible changes in polymer‐ ic sample dimensions under moisture take-up (Fig. 8 b).

The stand was used to measure the angular selectivity contour of a hologram at a one-time fixation of all contour data. The hologram was illuminated with a divergent radiation beam; the intensity distribution of the diffracted radiation (angular selectivity contour) was record‐ ed by a CMOS matrix of a camera – the results of processing the experimental data are given in Fig. 9. The effect of varying humidity on hologram parameters was assessed by a change in the position, θmax, of the intensity maximum of diffracted radiation in a CMOS matrix during the process under study. Position θmax was detected with accuracy ± 1 pixel, which corresponded to angular resolution ≈ 0.02 mrad.

**Figure 9.** Processing of experimental results: а – the position of the angular selectivity contour maximum, θmax, in CMOS matrix at ambient humidity Н ≈ 40% (dot line) and Н ≈ 90% (solid line), δθmax is the position θmax shift (hologram with ν ≈ 450 mm-1); b – the relaxation of hologram grating at a sudden change in humidity from 85% to 50% (holo‐

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It shall be remembered that the recording of holograms under study took place, as a rule, at the ambient humidity Н ≈ (50 ÷ 60)%. With rising humidity, the growing of dimensions of a sample, rigidly fixed in a cartridge (Fig. 8 b, positions 3, 4), is accompanied by some defor‐ mation unlike the sample in a rigid framework and that in a free state (Fig. 8 b, positions 1 and 2, respectively). The sample, fixed in a rigid framework is as a rule a film one in silicate glass framework. When such sample takes up moisture, only the change in its thickness is considered (as, e. g., in the work Pandey et al., 2008). Here, side 1 of the sample is rigidly

**Ambience variation Hologram parameter variation**

**Table 6.** The effect of variation of ambient temperature and humidity on the parameters of polymeric volume

bending and the sample center shifting in space, as shown in Fig. 8 b, position 4.

The sample in a free state grows in size, when taking up moisture, along all three coordi‐ nates. The sample, rigidly fixed in a cartridge (Fig. 8 b, positions 3, 4), grows in volume, when taking up moisture, due to increasing thickness, with position of sides 1 and 2 of the sample changing relative to its center. At lesser deformations, the position of the sample center in space remains the same (Fig. 8 b, position 3). Yet, if the sample volume growth ex‐ ceeds the threshold deformation values determined by the sample geometry (the ratio of di‐ ameter to thickness), the performed calculations have revealed the possibility of the sample

Property Amount of change Parameter Amount of change Recording material Humidity, rel. % 5% θmax shift 0.03 mrad Difphen, ν ≈ 450 mm-1

> θmax shift 0.06 mrad Difphen, ν ≈ 350 mm-1 λmax shift 0.1 nm Reoxan ν > 3000 mm-1

gram with ν ≈ 350 mm-1), dashed line illustrate the character of process.

with the framework and never changes its position in space.

Temperature, К 1 К

hologram gratings about 1 mm thick.

**Figure 8.** а – optical diagram of experiment to assess the changes of hologram parameters under varying ambient humidity: RS – radiation source, Iinc is the incident (reconstructing) beam, Id is the diffracted beam, I0 is the zero-order diffraction beam, 2θ is the diffraction angle, ±δθ is the diffraction angle change, N is the readout of pixel number in CMOS matrix (in the arrow direction). b – polymeric sample growing in size upon taking up moisture: 1 – the sample is fixed in a rigid framework, 2 – the sample is in free state, 3, 4 – the sample is fixed in a cartridge, geometrical dimen‐ sions of a sample upon taking up moisture are dash lines, arrows show the size growth direction.

#### *4.3.2. The experimental results*

The experimental results are presented in Fig.9. Fig. 9 а shows the position θmax of a holo‐ gram at ambient humidity 40% and 90%. A change of position θmax in the present experi‐ ment corresponded to the increase of the diffraction angle and was as large as δθmax ≈ + 0.25 mrad. It is this value that characterizes the difference in hologram parameters in two stable states of the sample at different humidity.

The process of hologram relaxation (stabilization of its parameters) at a sudden drop of the ambient humidity from 85% to 50% is illustrated by Fig. 9 b. The stabilization of hologram parameters in changed conditions was accompanied by a change in the position of the selec‐ tivity contour maximum, which corresponds to a decrease of the diffraction angle and a shift of θmax by δθmax ≈ (0.10-0.18) mrad, fixed in 2.5 hours after the sudden variation of the hu‐ midity. As shown by results of experiments on different samples, position θmax, at a sudden drop of the ambient humidity from (85 ÷ 90)% to (40 ÷ 50)%, attains its steady state value, which remains later practically the same, in 2-3 hours (relaxation time is dependent on sam‐ ple properties), while θmax shifts by δθmax < 0.3 mrad.

Thus, one can estimate the change in the diffraction angle at humidity change of 5% (which accords with typical excursions of workroom humidity) to be (δθmax)5% < 0.03 mrad and rec‐ ommend to keep a polymeric hologram in stable conditions for at least two-three hours for stabilization of its internal structure. The effect of changing ambient temperature and hu‐ midity on the parameters of polymeric hologram gratings is given in Table 6.

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**Figure 9.** Processing of experimental results: а – the position of the angular selectivity contour maximum, θmax, in CMOS matrix at ambient humidity Н ≈ 40% (dot line) and Н ≈ 90% (solid line), δθmax is the position θmax shift (hologram with ν ≈ 450 mm-1); b – the relaxation of hologram grating at a sudden change in humidity from 85% to 50% (holo‐ gram with ν ≈ 350 mm-1), dashed line illustrate the character of process.

**Figure 8.** а – optical diagram of experiment to assess the changes of hologram parameters under varying ambient humidity: RS – radiation source, Iinc is the incident (reconstructing) beam, Id is the diffracted beam, I0 is the zero-order diffraction beam, 2θ is the diffraction angle, ±δθ is the diffraction angle change, N is the readout of pixel number in CMOS matrix (in the arrow direction). b – polymeric sample growing in size upon taking up moisture: 1 – the sample is fixed in a rigid framework, 2 – the sample is in free state, 3, 4 – the sample is fixed in a cartridge, geometrical dimen‐

The experimental results are presented in Fig.9. Fig. 9 а shows the position θmax of a holo‐ gram at ambient humidity 40% and 90%. A change of position θmax in the present experi‐ ment corresponded to the increase of the diffraction angle and was as large as δθmax ≈ + 0.25 mrad. It is this value that characterizes the difference in hologram parameters in two stable

The process of hologram relaxation (stabilization of its parameters) at a sudden drop of the ambient humidity from 85% to 50% is illustrated by Fig. 9 b. The stabilization of hologram parameters in changed conditions was accompanied by a change in the position of the selec‐ tivity contour maximum, which corresponds to a decrease of the diffraction angle and a shift of θmax by δθmax ≈ (0.10-0.18) mrad, fixed in 2.5 hours after the sudden variation of the hu‐ midity. As shown by results of experiments on different samples, position θmax, at a sudden drop of the ambient humidity from (85 ÷ 90)% to (40 ÷ 50)%, attains its steady state value, which remains later practically the same, in 2-3 hours (relaxation time is dependent on sam‐

Thus, one can estimate the change in the diffraction angle at humidity change of 5% (which accords with typical excursions of workroom humidity) to be (δθmax)5% < 0.03 mrad and rec‐ ommend to keep a polymeric hologram in stable conditions for at least two-three hours for stabilization of its internal structure. The effect of changing ambient temperature and hu‐

midity on the parameters of polymeric hologram gratings is given in Table 6.

sions of a sample upon taking up moisture are dash lines, arrows show the size growth direction.

*4.3.2. The experimental results*

states of the sample at different humidity.

54 Holography – Basic Principles and Contemporary Applications

ple properties), while θmax shifts by δθmax < 0.3 mrad.

It shall be remembered that the recording of holograms under study took place, as a rule, at the ambient humidity Н ≈ (50 ÷ 60)%. With rising humidity, the growing of dimensions of a sample, rigidly fixed in a cartridge (Fig. 8 b, positions 3, 4), is accompanied by some defor‐ mation unlike the sample in a rigid framework and that in a free state (Fig. 8 b, positions 1 and 2, respectively). The sample, fixed in a rigid framework is as a rule a film one in silicate glass framework. When such sample takes up moisture, only the change in its thickness is considered (as, e. g., in the work Pandey et al., 2008). Here, side 1 of the sample is rigidly with the framework and never changes its position in space.

**Table 6.** The effect of variation of ambient temperature and humidity on the parameters of polymeric volume hologram gratings about 1 mm thick.

The sample in a free state grows in size, when taking up moisture, along all three coordi‐ nates. The sample, rigidly fixed in a cartridge (Fig. 8 b, positions 3, 4), grows in volume, when taking up moisture, due to increasing thickness, with position of sides 1 and 2 of the sample changing relative to its center. At lesser deformations, the position of the sample center in space remains the same (Fig. 8 b, position 3). Yet, if the sample volume growth ex‐ ceeds the threshold deformation values determined by the sample geometry (the ratio of di‐ ameter to thickness), the performed calculations have revealed the possibility of the sample bending and the sample center shifting in space, as shown in Fig. 8 b, position 4.

**Figure 10.** Diagram of experiment on observation of shifts of the diffracted beam (Id) during hologram reconstruction from side 1 (a) and side 2 (b) - deformation with a shift along the sample axis. Iinc is the incident (reconstruction) beam; I0 is the zero-order diffraction beam; О is the sample center without deformations; 1 and 2 are the sample sides; N is the CMOS matrix (the pixel number is counted in the arrow direction).

The presence of sample deformations due to its bending at taking-up the moisture has been detected in experiments on observation of the shift of the diffracted beam during reconstruc‐ tion of a hologram from either sample side. The experiment diagram is given in Fig. 10. Its implementation contains five stages. Fig. 11 gives the results of processing of the performed experiment and shows the change in position θmax in CMOS matrix at stages 1, 3, 5. Stage 1: the sample in steady state is mounted in a cartridge (at workroom humidity Н ≈ 50%), and angular selectivity contours are shot for several scores of minutes (Fig.11 – stage 1). Stage 2: enclosed volume is established around the sample (НОЕ) using a protective housing, where humidity Н ≈ 90% is maintained, the stage duration is about 20 hours. Stage 3: protective housing is removed, and selectivity contours are shot in automatic mode under hologram relaxation in conditions of workroom humidity (Fig. 11 – stage 3). Stage 4: the sample is kept in stable workroom conditions for about 20 hours. Stage 5: angular selectivity contours are shot for a hologram in steady state.

**Figure 11.** Results of experiment on observation of shifts of θmax during hologram reconstruction from side 1 (a) and side 2 (b): plots show the pixel number in CMOS matrix, N, corresponding to position θmax of a hologram at given in‐ stant of time in steady state (stages 1, 5) and out of the critical deformation (stage 3). Hologram with ν ≈ 450 mm-1.

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The present work discusses properties and specific features of volume holograms as well as results of original experiments that demonstrate unique potentiality of such holograms.

The results of examination of parameters are given for phase volume transmission hologram gratings that are of practical importance, and the hologram features are discussed, which are related to radiation propagation in media of great thickness with periodic structure on the

**5. Conclusion**

As seen from experimental data of Fig.11, position θmax in steady state of the hologram (stages 1 and 5) is stable and lies within measurement accuracy during reconstruction from both side 1 and side 2. However, position θmax at Н ≈ 90% (value N at t = 0 at stage 3) as compared to that at Н ≈ (40 ÷ 60)% demonstrates growth of the diffraction angle during hologram reconstruction from side 1 and decrease of the diffraction angle during recon‐ struction from side 2. Such situation may be due to the presence of sample deformations with a shift of its center in space (sample bending), as shown schematically on Fig. 10 a, b.

**Figure 11.** Results of experiment on observation of shifts of θmax during hologram reconstruction from side 1 (a) and side 2 (b): plots show the pixel number in CMOS matrix, N, corresponding to position θmax of a hologram at given in‐ stant of time in steady state (stages 1, 5) and out of the critical deformation (stage 3). Hologram with ν ≈ 450 mm-1.

## **5. Conclusion**

**Figure 10.** Diagram of experiment on observation of shifts of the diffracted beam (Id) during hologram reconstruction from side 1 (a) and side 2 (b) - deformation with a shift along the sample axis. Iinc is the incident (reconstruction) beam; I0 is the zero-order diffraction beam; О is the sample center without deformations; 1 and 2 are the sample sides; N is

The presence of sample deformations due to its bending at taking-up the moisture has been detected in experiments on observation of the shift of the diffracted beam during reconstruc‐ tion of a hologram from either sample side. The experiment diagram is given in Fig. 10. Its implementation contains five stages. Fig. 11 gives the results of processing of the performed experiment and shows the change in position θmax in CMOS matrix at stages 1, 3, 5. Stage 1: the sample in steady state is mounted in a cartridge (at workroom humidity Н ≈ 50%), and angular selectivity contours are shot for several scores of minutes (Fig.11 – stage 1). Stage 2: enclosed volume is established around the sample (НОЕ) using a protective housing, where humidity Н ≈ 90% is maintained, the stage duration is about 20 hours. Stage 3: protective housing is removed, and selectivity contours are shot in automatic mode under hologram relaxation in conditions of workroom humidity (Fig. 11 – stage 3). Stage 4: the sample is kept in stable workroom conditions for about 20 hours. Stage 5: angular selectivity contours are

As seen from experimental data of Fig.11, position θmax in steady state of the hologram (stages 1 and 5) is stable and lies within measurement accuracy during reconstruction from both side 1 and side 2. However, position θmax at Н ≈ 90% (value N at t = 0 at stage 3) as compared to that at Н ≈ (40 ÷ 60)% demonstrates growth of the diffraction angle during hologram reconstruction from side 1 and decrease of the diffraction angle during recon‐ struction from side 2. Such situation may be due to the presence of sample deformations with a shift of its center in space (sample bending), as shown schematically on Fig. 10 a, b.

the CMOS matrix (the pixel number is counted in the arrow direction).

56 Holography – Basic Principles and Contemporary Applications

shot for a hologram in steady state.

The present work discusses properties and specific features of volume holograms as well as results of original experiments that demonstrate unique potentiality of such holograms.

The results of examination of parameters are given for phase volume transmission hologram gratings that are of practical importance, and the hologram features are discussed, which are related to radiation propagation in media of great thickness with periodic structure on the order of the radiation wavelength. Practical recommendations are given to allow finding the phase modulation amplitude of "strong" hologram gratings by the value of diffraction effi‐ ciency and the shape of selectivity contour.

**Author details**

**References**

O.V. Andreeva, Yu.L. Korzinin and B.G. Manukhin

The National Research University of Information Technologies, Mechanics and Optics, Russia

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59

[1] Alekseev-Popov, A.V. (1981). *J. Technical Physics,* Vol.51(6), pp. 1275-1278, USSR

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[16] Malitson, I.H. (1963). A redetermination of some optical properties of calcium fluo‐

[18] Shcheulin, F.S. et al (2007). *Optics and Spectroscopy*, Vol.103(3,4), pp. 496; 664; 668; 673. [19] Shelby, R.M. (2002). Materials for holographic digital data storage, *Proceedings of*

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mo-refractive glass*. US Patent*. 6,673,497 B2.

[2] Angervaks, A.E. et al (2010, 2012) Holographic Prizm as a New Optical Element . *Op‐*

Experimental results are presented, which prove the existence of the effect of energy chan‐ nelizing by "strong" transmission hologram gratings when using a reconstruction radiation beam with non-uniform intensity distribution, and the experimental conditions are defined for the effect to be revealed. The energy propagation in such structures has been shown to be confined to area occupied by the interacting beams (zero-order and diffracted) upon at‐ taining φ1 = 0.5π, the first extremum of function η(φ1). An effect was found of beam bifurca‐ tion and emergence of two channels for radiation propagation during reconstruction of a "strong" hologram grating beyond Bragg angle.

Parameters are listed for recording media to produce volume holograms, they were devel‐ oped according to principles of recording media design, proposed in late 80s of the last cen‐ tury by S.I. Vavilov State Optical Institute specialists. The information is still topical as the last two decades saw mostly refinement, modification, and improvement of variants of vol‐ ume recording media manufactured in laboratory conditions.

The effect of ambient temperature and humidity was studied for parameters of polymeric hologram gratings about 1 mm thick with spatial frequency ~ (350 ÷ 450) mm-1, which were produced on Difphen material samples. The results allow estimating the change in the dif‐ fraction angle as ≈ 0.06 mrad at temperature variation by 1°К and as ≈ 0.03 mrad at relative humidity variation 5%. Despite the dependence of the values on the sample physical and mechanical properties, geometry and history, the estimates can be used to plan the working conditions for HOE on base of different polymers and to optimize the experimental condi‐ tions for handling polymer samples in information recording and reconstruction.

Experimental data were obtained to substantiate the assumption that taking-up of moisture can result not only in a change in thickness of a sample, rigidly fixed in a cartridge spatial, but also in its deformation, describable as "bending". Bending-type deformation was ob‐ served in conditions of high humidity on a sample with the diameter/thickness ratio of about 40:1. Thus, hologram gratings can be used to study deformation of materials under impact of ambient conditions.

The study of the temperature effect on parameters of polymeric hologram gratings em‐ ployed an original technique for observing hologram deformations with the help of low-fre‐ quency interference pattern. The obtained results demonstrated efficiency of the technique and high accuracy of detecting the changes of hologram parameters.

## **Acknowledgements**

The authors express their gratitude for participation in the experiments and assistance in preparation of the publication to А.А. Paramonov, S.А. Chivilikhin, D.А. Gomon, О.V. Ban‐ dyuk, V.V. Lesnichy, А.S. Zlatov, P.A. Kudriavcev.

## **Author details**

order of the radiation wavelength. Practical recommendations are given to allow finding the phase modulation amplitude of "strong" hologram gratings by the value of diffraction effi‐

Experimental results are presented, which prove the existence of the effect of energy chan‐ nelizing by "strong" transmission hologram gratings when using a reconstruction radiation beam with non-uniform intensity distribution, and the experimental conditions are defined for the effect to be revealed. The energy propagation in such structures has been shown to be confined to area occupied by the interacting beams (zero-order and diffracted) upon at‐ taining φ1 = 0.5π, the first extremum of function η(φ1). An effect was found of beam bifurca‐ tion and emergence of two channels for radiation propagation during reconstruction of a

Parameters are listed for recording media to produce volume holograms, they were devel‐ oped according to principles of recording media design, proposed in late 80s of the last cen‐ tury by S.I. Vavilov State Optical Institute specialists. The information is still topical as the last two decades saw mostly refinement, modification, and improvement of variants of vol‐

The effect of ambient temperature and humidity was studied for parameters of polymeric hologram gratings about 1 mm thick with spatial frequency ~ (350 ÷ 450) mm-1, which were produced on Difphen material samples. The results allow estimating the change in the dif‐ fraction angle as ≈ 0.06 mrad at temperature variation by 1°К and as ≈ 0.03 mrad at relative humidity variation 5%. Despite the dependence of the values on the sample physical and mechanical properties, geometry and history, the estimates can be used to plan the working conditions for HOE on base of different polymers and to optimize the experimental condi‐

Experimental data were obtained to substantiate the assumption that taking-up of moisture can result not only in a change in thickness of a sample, rigidly fixed in a cartridge spatial, but also in its deformation, describable as "bending". Bending-type deformation was ob‐ served in conditions of high humidity on a sample with the diameter/thickness ratio of about 40:1. Thus, hologram gratings can be used to study deformation of materials under

The study of the temperature effect on parameters of polymeric hologram gratings em‐ ployed an original technique for observing hologram deformations with the help of low-fre‐ quency interference pattern. The obtained results demonstrated efficiency of the technique

The authors express their gratitude for participation in the experiments and assistance in preparation of the publication to А.А. Paramonov, S.А. Chivilikhin, D.А. Gomon, О.V. Ban‐

tions for handling polymer samples in information recording and reconstruction.

and high accuracy of detecting the changes of hologram parameters.

dyuk, V.V. Lesnichy, А.S. Zlatov, P.A. Kudriavcev.

ciency and the shape of selectivity contour.

58 Holography – Basic Principles and Contemporary Applications

"strong" hologram grating beyond Bragg angle.

impact of ambient conditions.

**Acknowledgements**

ume recording media manufactured in laboratory conditions.

O.V. Andreeva, Yu.L. Korzinin and B.G. Manukhin

The National Research University of Information Technologies, Mechanics and Optics, Russia

## **References**

**Chapter 3**

**White Light Reconstructed Holograms**

I would like to begin the chapter with two quotations, I came across during my study, I like very much and I am certain, they literally express holography, its properties, its beauty and its role today, at the beginning either of the 21st century or the third millenium, we have an

*"Holography is the only visual recording and playback process that can record our 3D world on a two-dimensional recording medium and playback the original object or scene to the unaided eyes, as a 3D image. The image demonstrates complete parallax and depth-of-field. The image floats in space ei‐ ther behind, in front, or straddling the recording medium."* – is the first one. It is hard to find its origin, since it can be found at the beginnings of many papers dealing with holography.

*"Since its first commercial usage in the 70's the demand has only increased with each passing year. Holography has found its applications in almost all industrial sectors including commercial and resi‐ dential applications. Next years might bring us to see a new world of holograms in every aspect. The use of holograms is the representation of a new visual language in communication and we are moving into the age of light as the media of the future. Holography will soon be an integral part of the light*

Well, people today come across the term *hologram* and can meet holograms on banknotes, various cards and products. A holographic technology comes along with advertisements, promotions,... People specialized in photonics [2], an interdisciplinary field dealing with uti‐ lizing photons, may know that holography is closely related to a special kind of light – laser light, which possesses a special property – *coherence*, i.e. all the light waves coming from a laser have the same properties. It is very important, because there are two basic physical

To record, i.e. to create a hologram, the phenomenon of *two-wave interference of light* is ap‐ plied. The term *hologram* tells us that all the information transported by light wave is record‐

> © 2013 Senderakova; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2013 Senderakova; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Additional information is available at the end of the chapter

Dagmar Senderakova

http://dx.doi.org/10.5772/53592

opportunity to be eye witnesses.

*age of information and communications."* [1]

light wave phenomena, enabling *holography*.

**1. Introduction**

## **White Light Reconstructed Holograms**

## Dagmar Senderakova

[21] Sidorovich, V.G. (1977), *Optics and Spectroscopy*, Vol.42(4), pp. 693-699

[22] Sidorovich, V.G. (2012), *Optics and Spectroscopy*, Vol.112(2), pp. 335-342

[25] Sukhanov, V.I. et al (1992). *Optics and Spectroscopy*, Vol.72(3), pp. 716-730

[28] Veniaminov, A.V. et al. (1991). *Optics and Spectroscopy,*. Vol.70, pp. 505-508

[29] Weber, M.J. (Ed) (2003). *Handbook of Optical Materials*, CRC Press LLC

[31] Zeldovich, B. et al. (1986). *Physics-Uspekhi,* Vol.149(3), pp. 511-549

[32] Zlatov, A.S. et al. (2010) , *J. Opt. Technol.,* Vol.77(12), pp. 22-24

[30] Yu, D. et al. (2010). *Optics Communs,* V.283, pp. 4219-4223

[24] Sukhanov, V.I. et al. (1984). Three dimensional hologram on Reoksan as narrow band

[26] Sukhanov, V.I. (1994). 3-Dimensional Deep Holograms and Materials for Recording

[27] Sukhanov, V.I. et al. (2007). *Proceedings of meeting "In Memorial of Yu.N Denisyuk "*,

[23] Steckman, G.J. et al. (1998), *Opt. Lett*., Vol.23(16), pp. 1310-1312

spectral selector, *Sov. Techn. Phys. Lett*., Vol.10, pp. 387-390

Them, *J. Opt. Technol.,* Vol.61(1), pp. 49-56

Sankt-Petersburg, pp. 262-276

60 Holography – Basic Principles and Contemporary Applications

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/53592

## **1. Introduction**

I would like to begin the chapter with two quotations, I came across during my study, I like very much and I am certain, they literally express holography, its properties, its beauty and its role today, at the beginning either of the 21st century or the third millenium, we have an opportunity to be eye witnesses.

*"Holography is the only visual recording and playback process that can record our 3D world on a two-dimensional recording medium and playback the original object or scene to the unaided eyes, as a 3D image. The image demonstrates complete parallax and depth-of-field. The image floats in space ei‐ ther behind, in front, or straddling the recording medium."* – is the first one. It is hard to find its origin, since it can be found at the beginnings of many papers dealing with holography.

*"Since its first commercial usage in the 70's the demand has only increased with each passing year. Holography has found its applications in almost all industrial sectors including commercial and resi‐ dential applications. Next years might bring us to see a new world of holograms in every aspect. The use of holograms is the representation of a new visual language in communication and we are moving into the age of light as the media of the future. Holography will soon be an integral part of the light age of information and communications."* [1]

Well, people today come across the term *hologram* and can meet holograms on banknotes, various cards and products. A holographic technology comes along with advertisements, promotions,... People specialized in photonics [2], an interdisciplinary field dealing with uti‐ lizing photons, may know that holography is closely related to a special kind of light – laser light, which possesses a special property – *coherence*, i.e. all the light waves coming from a laser have the same properties. It is very important, because there are two basic physical light wave phenomena, enabling *holography*.

To record, i.e. to create a hologram, the phenomenon of *two-wave interference of light* is ap‐ plied. The term *hologram* tells us that all the information transported by light wave is record‐

© 2013 Senderakova; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2013 Senderakova; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

ed. What does it mean – *all the information*? Let us repeat some basic terms [3]. Modelling light as a light wave *A*(*r*, *t*) depending on space (*r*) and time (*t*) means, that there are two main parameters – the *amplitude A*0 of a wave and its *phase Φ*

$$A = A\_0 \cos \mathcal{O}(\mathbf{r}, \ t) = A\_0 \cos \left(\omega t - \mathbf{k}. \mathbf{r} + \mathcal{O}\_0\right) \tag{1}$$

The value known as *intensity I* of light, is proportional to the energy per unit of surface and unit of time. It is very important to realise that the *time averaged light intensity* is a measura‐ ble value, only. Because of that it is said that both, light detection and light recording are

White Light Reconstructed Holograms http://dx.doi.org/10.5772/53592 63

It is just *holography*, which provides us with a method allowing to record both, the ampli‐ tude and phase information despite quadratic recording. Naturally, it is impossible when there is only one light wave. *Dennis Gabor* realized, that there is included the phase informa‐ tion in intensity interference pattern of two waves and it can be utilized in a new – *holograph‐*

When two light waves meet and are able to keep a constant phase difference at any point for a proper time interval (long enough to make a record), the interference pattern, i.e. a space redistribution of the resulted energy, can be recorded. Such a situation can come truth only for two coherent waves. Just because of that boom of practical holography started after laser

To reconstruct, i.e. to see what information is hidden in a hologram, another basic physical phenomenon is applied – *diffraction of light*. There are various types of holograms. Some of them can be reconstructed only by laser light. However, there is also a group of holograms, which can be reconstructed also using common sunlight or another source of *white light*, in which, all the visible spectrum is included. Naturally, that group takes the greatest interest among public and this chapter is going to deal just with such holograms, named here *white*

In the beginning, the basic properties of diffraction of light by a periodic structure are going to be noticed and correlation between diffraction and holographic reconstruction shown. At‐ tention is concentrated especially to the white light diffraction. Understanding of the princi‐ ples will help the reader to understand problems arising during white light reconstruction of a hologram and also give a hint how to proceed when recording a hologram to avoid such problems. Attention is going to be given to Denisyuk's holograms, image holograms

The last part of the chapter is focused on some applications of WLRH, especially public ones. To mention also a scientific application, one of our former works, dealing with deter‐

The simple fact that there are two groups of holograms, one of them reconstructed only by coherent light, another one by common white light, tells us that the secret must be hidden in the hologram recording process. To reveal the secret of recording, it would be usable to un‐ derstand phenomenon of light diffraction, which is the physical principle of hologram re‐

mination of index of refraction radial profile of a fibre is described briefly.

*quadratic*.

*ic* method of recording [4].

had been invented [5].

*light reconstructed holograms* (WLRH).

and Benton's rainbow holograms.

**2. How to record a WLRH**

construction.

where *r*(*x, y, z*) is a displacement vector determining a point in a space and *k*(*kx*, *ky, kz*) de‐ notes for a *wave vector,* determining direction of wave propagation. Its absolute value *k* = 2π/*λ* defines the *wave number*. *Φ*0 is the *initial phase* of the wave. The distance between the two neighbouring amplitude peaks of the same kind is *wavelength λ* [m]. *ω* [rad.s-1], is *an‐ gular frequency*, which is related to the linear *frequency*, *ν* [s-1], by the formula *ω = 2*π*ν*. It lasts *T* = *λ*/c seconds to pass the path *λ* at the speed c. Such a time interval is called *peri‐ od* and *T* = 1/*ν*.

A *wave front* is another useful term for us, else. It is the surface upon which the wave has equal phase. It is perpendicular to the direction of propagation, i.e. to the wave vector *k*.

For example, considering a wave propagating in the +*z* direction, the wave vector *k* is paral‐ lel to the *z*–axis everywhere. Because of that, wave fronts are parallel planes, perpendicular to the *z*–axis. Such a wave is known as a *plane wave*. When the *k*(*kx, ky, kz*) direction is general, the phase in a point determined by a displacement vector *r*(*x, y, z*) includes the scalar prod‐ uct of *k.r*.

Let us mention also a *spherical wave*

$$A(\mathbf{r}, t) = \frac{A\_0}{r} \cos(\alpha t - k.r + \varphi\_0) \tag{2}$$

which is irradiated from a point light source in homogeneous medium. In such a case wave fronts are centrally symmetrical spheres, so it is enough to consider only radial coordinate *r* of *spherical* ones. Moreover, *k* and *r* are parallel, so *k.r* = *kr*. Increasing distance from the source the surface of the sphere increases and amplitude *A0* decreases proportionally to 1/*r*.

It is more convenient to represent the light wave expression in a complex form

$$\mathbf{A} = A\_0 \mathbf{e}^{i\Phi} = A\_0 \cos\Phi + \mathbf{i}A\_0 \sin\Phi \tag{3}$$

As for light wave recording, one has to realize a special property of light waves. The instan‐ taneous amplitude *A*, which varies with both, time and space, cannot be measured experi‐ mentally in a direct way. The frequency of the *light wave* is too high for any known physical mechanism to reply to the changes of the instantaneous amplitude *A*. Any known detector or recording medium replies only to the incident energy. When denoting energy transferred by a wave as *E*, it can be got as square of the amplitude, i.e. *E* = (*A*0) 2 = *A.A\**, when using the complex representation, \*-symbol represents the complex conjugate quantity.

The value known as *intensity I* of light, is proportional to the energy per unit of surface and unit of time. It is very important to realise that the *time averaged light intensity* is a measura‐ ble value, only. Because of that it is said that both, light detection and light recording are *quadratic*.

It is just *holography*, which provides us with a method allowing to record both, the ampli‐ tude and phase information despite quadratic recording. Naturally, it is impossible when there is only one light wave. *Dennis Gabor* realized, that there is included the phase informa‐ tion in intensity interference pattern of two waves and it can be utilized in a new – *holograph‐ ic* method of recording [4].

When two light waves meet and are able to keep a constant phase difference at any point for a proper time interval (long enough to make a record), the interference pattern, i.e. a space redistribution of the resulted energy, can be recorded. Such a situation can come truth only for two coherent waves. Just because of that boom of practical holography started after laser had been invented [5].

To reconstruct, i.e. to see what information is hidden in a hologram, another basic physical phenomenon is applied – *diffraction of light*. There are various types of holograms. Some of them can be reconstructed only by laser light. However, there is also a group of holograms, which can be reconstructed also using common sunlight or another source of *white light*, in which, all the visible spectrum is included. Naturally, that group takes the greatest interest among public and this chapter is going to deal just with such holograms, named here *white light reconstructed holograms* (WLRH).

In the beginning, the basic properties of diffraction of light by a periodic structure are going to be noticed and correlation between diffraction and holographic reconstruction shown. At‐ tention is concentrated especially to the white light diffraction. Understanding of the princi‐ ples will help the reader to understand problems arising during white light reconstruction of a hologram and also give a hint how to proceed when recording a hologram to avoid such problems. Attention is going to be given to Denisyuk's holograms, image holograms and Benton's rainbow holograms.

The last part of the chapter is focused on some applications of WLRH, especially public ones. To mention also a scientific application, one of our former works, dealing with deter‐ mination of index of refraction radial profile of a fibre is described briefly.

## **2. How to record a WLRH**

ed. What does it mean – *all the information*? Let us repeat some basic terms [3]. Modelling light as a light wave *A*(*r*, *t*) depending on space (*r*) and time (*t*) means, that there are two

where *r*(*x, y, z*) is a displacement vector determining a point in a space and *k*(*kx*, *ky, kz*) de‐ notes for a *wave vector,* determining direction of wave propagation. Its absolute value *k* = 2π/*λ* defines the *wave number*. *Φ*0 is the *initial phase* of the wave. The distance between the two neighbouring amplitude peaks of the same kind is *wavelength λ* [m]. *ω* [rad.s-1], is *an‐ gular frequency*, which is related to the linear *frequency*, *ν* [s-1], by the formula *ω = 2*π*ν*. It lasts *T* = *λ*/c seconds to pass the path *λ* at the speed c. Such a time interval is called *peri‐*

A *wave front* is another useful term for us, else. It is the surface upon which the wave has equal phase. It is perpendicular to the direction of propagation, i.e. to the wave vector *k*.

For example, considering a wave propagating in the +*z* direction, the wave vector *k* is paral‐ lel to the *z*–axis everywhere. Because of that, wave fronts are parallel planes, perpendicular to the *z*–axis. Such a wave is known as a *plane wave*. When the *k*(*kx, ky, kz*) direction is general, the phase in a point determined by a displacement vector *r*(*x, y, z*) includes the scalar prod‐

which is irradiated from a point light source in homogeneous medium. In such a case wave fronts are centrally symmetrical spheres, so it is enough to consider only radial coordinate *r* of *spherical* ones. Moreover, *k* and *r* are parallel, so *k.r* = *kr*. Increasing distance from the source the surface of the sphere increases and amplitude *A0* decreases proportionally to 1/*r*.

As for light wave recording, one has to realize a special property of light waves. The instan‐ taneous amplitude *A*, which varies with both, time and space, cannot be measured experi‐ mentally in a direct way. The frequency of the *light wave* is too high for any known physical mechanism to reply to the changes of the instantaneous amplitude *A*. Any known detector or recording medium replies only to the incident energy. When denoting energy transferred

 j

00 0 *AA A* e cos i sin F *A* = = F+ F (3)

2

= *A.A\**, when using the

(2)

0 0 ( , ) cos( . ) *A A t t kr*

It is more convenient to represent the light wave expression in a complex form

i

by a wave as *E*, it can be got as square of the amplitude, i.e. *E* = (*A*0)

complex representation, \*-symbol represents the complex conjugate quantity.

*r* **r** = -+ w

*A*= *A*0cos*Φ*(*r*, *t*)= *A*0cos(*ωt* −*k***.***r* + *Φ*0) (1)

main parameters – the *amplitude A*0 of a wave and its *phase Φ*

62 Holography – Basic Principles and Contemporary Applications

*od* and *T* = 1/*ν*.

uct of *k.r*.

Let us mention also a *spherical wave*

The simple fact that there are two groups of holograms, one of them reconstructed only by coherent light, another one by common white light, tells us that the secret must be hidden in the hologram recording process. To reveal the secret of recording, it would be usable to un‐ derstand phenomenon of light diffraction, which is the physical principle of hologram re‐ construction.

#### **2.1. Diffraction – the physical principle of hologram reconstruction**

Firstly - it is said that any deviation from rectilinear propagation of light that cannot be ex‐ plained because of reflection or refraction is included into diffraction. Such a deviation can be met when light either passes through or reflects from a structure, i.e. a space distribution either of the transmittance, or the refractive index.

Telling more precisely - diffraction is the spreading of waves from a wave-front limited in extent, occurring either when a part of the wave-front is removed by an obstacle, or when all, but a part of the wave-front is removed by an aperture or a stop. The Fraunhofer theory of diffraction, which is interesting for us from the point of view of hologram re‐ construction, is concerned with the angular spread of light leaving an aperture of arbitra‐ ry shape and size [3].

**Figure 1.** To the principle to solve scalar diffraction problems

(*x* − *x*0)2→ *x* 2 −2*xx*0 and (*y* − *y*0)2→ *y* 2 −2*y y*0

and integral (4) turns into

(,,)

l

*AP*

*xyz*

=

To calculate the integral (4), two approximations for *r*2 are used – Fresnel's approximation and Fraunhofer's ones. For the purposes of this chapter, let us mention Fraunhofer's aproxi‐

( ) { ( )} 2 2

A holographic record can be regarded as a record of a general structure. The light diffraction theory (5) gives us a detail description of light diffraction at a regular plane grating. It is

*x y k xx yy k z Axy x y*

exp i i exp i , ,0 d d

2 *S*

**Figure 2.** Diffraction by a plane grating (*d* – grating interval, *b* – slit width)

ï ï î þ è ø òò

*z z z*

widely used, especially in spectroscopy (looking for various wavelengths).

ì ü æ ö + - + ï ï = -+ í ý ç ÷

0 0

White Light Reconstructed Holograms http://dx.doi.org/10.5772/53592 65

(5)

000 0 0

mation: *x0, y0, « z*, i.e. next mathematical approximation is used to express the phase

Secondly – remember that a hologram is, in fact, a two-wave interference pattern recorded, i.e. a kind of structure of intensity distribution. It depends on the type of recording medium and related light-matter interaction mechanism, which of its optical properties distribution follows the interference pattern intensity distribution.

And thirdly – when reconstructing a hologram, it has to be illuminated with light that either passes through or reflects from the hologram. Now, it seems to be obvious to put the equal sign between reconstruction and diffraction.

An introduction to phenomenon of light diffraction and related basic relations can be found in any basic book of optics/photonics, e.g. [3] and even in [6]. Let us show briefly some basic results, related to white light reconstructed holograms.

For the readers, taking a deeper interest - exact solutions of diffraction problems are given by solving Maxwell's equations. However, well-known Kirchhoff's scalar theory gives very good results if period of diffraction structure does not approach a wavelengths size and am‐ plitude vector does not leave a plane.

Let the plane (*x*0*, y*0 ) is the plane of a structure and diffraction is observed in the plane (*x, y*). To find resulting amplitude *A*P in *P*(*x*, *y*), amplitudes of spherical waves from all the point sources in the plane of the structure have to be summed (Fig. 1). The idea is expressed by Kirchhoff's diffraction integral

$$A\_P(\mathbf{x}, y, z) \sim \iint\_S \frac{A\_0(\mathbf{x}\_0, y\_0)}{r\_2} \exp\left\{-\mathrm{i}k r\_2\right\} d\mathbf{x}\_0 dy\_0 \tag{4}$$

where the distance *r*2 = [(*x* - *x*0) 2 + (*y* - *y*0) 2 + *z*2 ] 1/2 and *S* is size of the illuminated structure. The experimentally observable interference pattern is given by

$$I(\mathbf{x}, \; \; y, \; z) \sim \mathbf{A}\_P(\mathbf{x}, \; \; y, \; z) \mathbf{J} \mathbf{A}\_P(\mathbf{x}, \; \; y, \; z) \mathbf{J}^\* \mathbf{J}$$

**Figure 1.** To the principle to solve scalar diffraction problems

To calculate the integral (4), two approximations for *r*2 are used – Fresnel's approximation and Fraunhofer's ones. For the purposes of this chapter, let us mention Fraunhofer's aproxi‐ mation: *x0, y0, « z*, i.e. next mathematical approximation is used to express the phase

$$(\infty - x\_0)^2 \rightharpoonup x^2 - 2\pi x\_0 \quad \text{and} \quad (y - y\_0)^2 \rightharpoonup y^2 - 2\, y \, y\_0$$

and integral (4) turns into

**2.1. Diffraction – the physical principle of hologram reconstruction**

either of the transmittance, or the refractive index.

64 Holography – Basic Principles and Contemporary Applications

follows the interference pattern intensity distribution.

results, related to white light reconstructed holograms.

sign between reconstruction and diffraction.

plitude vector does not leave a plane.

Kirchhoff's diffraction integral

where the distance *r*2 = [(*x* - *x*0)

ry shape and size [3].

Firstly - it is said that any deviation from rectilinear propagation of light that cannot be ex‐ plained because of reflection or refraction is included into diffraction. Such a deviation can be met when light either passes through or reflects from a structure, i.e. a space distribution

Telling more precisely - diffraction is the spreading of waves from a wave-front limited in extent, occurring either when a part of the wave-front is removed by an obstacle, or when all, but a part of the wave-front is removed by an aperture or a stop. The Fraunhofer theory of diffraction, which is interesting for us from the point of view of hologram re‐ construction, is concerned with the angular spread of light leaving an aperture of arbitra‐

Secondly – remember that a hologram is, in fact, a two-wave interference pattern recorded, i.e. a kind of structure of intensity distribution. It depends on the type of recording medium and related light-matter interaction mechanism, which of its optical properties distribution

And thirdly – when reconstructing a hologram, it has to be illuminated with light that either passes through or reflects from the hologram. Now, it seems to be obvious to put the equal

An introduction to phenomenon of light diffraction and related basic relations can be found in any basic book of optics/photonics, e.g. [3] and even in [6]. Let us show briefly some basic

For the readers, taking a deeper interest - exact solutions of diffraction problems are given by solving Maxwell's equations. However, well-known Kirchhoff's scalar theory gives very good results if period of diffraction structure does not approach a wavelengths size and am‐

Let the plane (*x*0*, y*0 ) is the plane of a structure and diffraction is observed in the plane (*x, y*). To find resulting amplitude *A*P in *P*(*x*, *y*), amplitudes of spherical waves from all the point sources in the plane of the structure have to be summed (Fig. 1). The idea is expressed by

{ } 000

2 (,) ( , , )~ exp i

> 2 + *z*2 ]

*Axy xyz kr dx dy*

*S*

2 + (*y* - *y*0)

experimentally observable interference pattern is given by

*I*(*x*, *y*, *z*) ~ *AP*(*x*, *y*, *z*). *AP*(*x*, *y*, *z*) \* .

2 00

1/2 and *S* is size of the illuminated structure. The

*r* - *P* òò *A* (4)

$$\begin{aligned} A\_P(\mathbf{x}, y, z) &= \\ \mathbf{x} &= \frac{\mathbf{i}}{\lambda z} \exp\left\{-\mathrm{ik}\left(z + \frac{\mathbf{x}^2 + y^2}{2z}\right)\right\} \iint\_S A\_0(\mathbf{x}\_0, y\_0, \mathbf{0}) \, \frac{\exp\left\{-\mathrm{ik}\left(\mathbf{x} x\_0 + y y\_0\right)\right\}}{z} \, \mathrm{d}\mathbf{x}\_0 \, \mathrm{d}y\_0 \end{aligned} \tag{5}$$

A holographic record can be regarded as a record of a general structure. The light diffraction theory (5) gives us a detail description of light diffraction at a regular plane grating. It is widely used, especially in spectroscopy (looking for various wavelengths).

**Figure 2.** Diffraction by a plane grating (*d* – grating interval, *b* – slit width)

The grating is an ensemble of single equal slits, parallel to each other and having the same distance between each other.

There are two parameters, which define the grating – the *slit width* (*b*) and the *grating interval* (*d*) – distance between centres of any two adjacent slits (Fig. 2.). Symbols *θ*i and *θ* denote angles of incident and diffracted waves respectively.

Diffraction at such a grating is, in fact, the interference of many "diffractions" by single slits. The number of interfering "diffractions" depends on the number *N* of illuminated slits. A detailed calculating of (5) results in the angular intensity distribution

*I* ~ *AP*.(*AP*) \*

and it's normalized value can be get in the form

$$I\_R = I\_{R1} I\_{R2} = \frac{I(\theta, \lambda, b, d)}{bI\_0} = \left\{ \frac{\sin\left[ (kb/2)\sin\theta \right]}{(kb/2)\sin\theta} \right\}^2 \left\{ \frac{\sin\left[ (kld/2) \left( \sin\theta + \sin\theta\_i \right) \right]}{\sin\left[ (kd/2) \left( \sin\theta + \sin\theta\_i \right) \right]} \right\}^2 \tag{6}$$

The angle *θ* appeared because of the Fraunhofer's approximation, where *x*/*z* ~ sin*θ*. In fact, relation (6) expresses *N*-wave interference (*I*R2) modulated by diffraction at a single slit (*I*R1). Practically usable is especially the condition for interference maxima

$$\frac{kd}{2}(\sin\theta + \sin\theta\_i) = m\pi, \quad \left| m \right| = 0, 1, 2, 3, \dots \tag{7}$$

angle of refraction *θ*. To get the intensity maximum in passing light, the condition (7) has to

Moreover, because of the thickness of the grating, all the waves irradiated along the *z*-axis

The condition has to be satisfied for all the *z* coordinates. It is possible only for *θ* = ±*θ*i that

Concluding this paragraph, let us try to describe the diffraction phenomenon using holo‐

interfere (Fig.4a). The interference pattern that will work as a grating can be expressed in the

 lë û = == (9)

> j**1 2** (11)

+ = *m* (8)

White Light Reconstructed Holograms http://dx.doi.org/10.5772/53592 67

= = (10)

( ) 0 sin sin *i nd* qql

( ) ( ) 0 02 1 0 – – – , 0, 1, 2, ... *AC BD n n z z cos cos m where m i* é ù qq

0 2 sin , 0, 1, 2, ... *i nd m m*

( ) ( ) 1 2 *w w* ~ exp i , ~ exp i

j

form, which corresponds with the amplitude transmission *t* of produced grating

 l

leads to the well known Bragg's law for X-ray reflection from a crystal

q

used also to describe diffraction at optical volume gratings.

graphic terms. Two coherent plane waves

should be in phase in direction of the angle *θ*, i.e.

**Figure 3.** Diffraction by a volume grating (*h* – thickness, *n* – index of refraction)

be fulfilled, i.e.

where *k =* 2π*n*/*λ*0, *n* – refractive index of the space of diffraction, *λ*0 – wavelength in vacuum and *m* – order of diffraction. It is obvious that real values of *m* can be achieved only when grating constant *d* > *λ*0/*n* = *λ*. For simplicity, only one-dimensional (*x*) structure distribution was considered.

Study in the region of X-rays contributed to the phenomenon of diffraction. The short wave‐ lengths of X-rays are not well suited for diffraction by optical gratings. They are, however, conveniently close to the spacing of atoms in crystal lattices, which therefore provide excel‐ lent three-dimensional diffraction gratings for X-rays. It was shown, that the diffraction pat‐ tern is intimately connected with the arrangement and spacing of atoms within a crystal, so that X-rays can be used for determining the lattice structure [3].

It was Max von Laue who first suggested that a crystal might behave towards a beam of Xrays rather as does a ruled diffraction grating to ordinary light. It is interesting, that at the time it was not certain either crystals really were such regular arrangements, or X-rays were short-wavelength electromagnetic radiation [3]. W. L. Bragg proved the idea in 1912.

It can be derived in a simply way taking into account the result for plane grating and the influence of a thickness *h* of the grating (Fig. 3). Let us consider angles of incidence *θ*i and

**Figure 3.** Diffraction by a volume grating (*h* – thickness, *n* – index of refraction)

The grating is an ensemble of single equal slits, parallel to each other and having the same

There are two parameters, which define the grating – the *slit width* (*b*) and the *grating interval*

Diffraction at such a grating is, in fact, the interference of many "diffractions" by single slits. The number of interfering "diffractions" depends on the number *N* of illuminated slits. A

0 i

ë û + ï î þ î þ

q

The angle *θ* appeared because of the Fraunhofer's approximation, where *x*/*z* ~ sin*θ*. In fact, relation (6) expresses *N*-wave interference (*I*R2) modulated by diffraction at a single slit (*I*R1).

where *k =* 2π*n*/*λ*0, *n* – refractive index of the space of diffraction, *λ*0 – wavelength in vacuum and *m* – order of diffraction. It is obvious that real values of *m* can be achieved only when grating constant *d* > *λ*0/*n* = *λ*. For simplicity, only one-dimensional (*x*) structure distribution

Study in the region of X-rays contributed to the phenomenon of diffraction. The short wave‐ lengths of X-rays are not well suited for diffraction by optical gratings. They are, however, conveniently close to the spacing of atoms in crystal lattices, which therefore provide excel‐ lent three-dimensional diffraction gratings for X-rays. It was shown, that the diffraction pat‐ tern is intimately connected with the arrangement and spacing of atoms within a crystal, so

It was Max von Laue who first suggested that a crystal might behave towards a beam of Xrays rather as does a ruled diffraction grating to ordinary light. It is interesting, that at the time it was not certain either crystals really were such regular arrangements, or X-rays were

It can be derived in a simply way taking into account the result for plane grating and the influence of a thickness *h* of the grating (Fig. 3). Let us consider angles of incidence *θ*i and

short-wavelength electromagnetic radiation [3]. W. L. Bragg proved the idea in 1912.

q

ì é ùé ü ì + ù ü ï ë ûë ï ï û ï == = í ý í ý ï ï ï é ù

(sin sin , 0,1,2,3,... ) 2 *i*

and *θ* denote

(6)

( )( ) ( )( )

q

q

i

 q

 q

2 2

+= = *m m* (7)

(*d*) – distance between centres of any two adjacent slits (Fig. 2.). Symbols *θ*i

( ) ( )

(, ,,) sin 2 sin sin 2 sin sin . 2 sin sin 2 sin sin *R RR I bd k b Nkd*

*bI k b kd*

detailed calculating of (5) results in the angular intensity distribution

Practically usable is especially the condition for interference maxima

that X-rays can be used for determining the lattice structure [3].

qqp

angles of incident and diffracted waves respectively.

66 Holography – Basic Principles and Contemporary Applications

and it's normalized value can be get in the form

*kd*

q l

distance between each other.

1 2

*I II*

was considered.

*I* ~ *AP*.(*AP*) \*

angle of refraction *θ*. To get the intensity maximum in passing light, the condition (7) has to be fulfilled, i.e.

$$md\left(\sin\theta + \sin\theta\_i\right) = m\mathcal{Z}\_0\tag{8}$$

Moreover, because of the thickness of the grating, all the waves irradiated along the *z*-axis should be in phase in direction of the angle *θ*, i.e.

$$(AC - BD)n\_0 = n\_0(z\_2 - z\_1) \left[ \cos \theta\_i - \cos \theta \right] \\
= m\lambda\_{0'} \quad \text{where } \left| m \right| \\
= 0, \ 1, \ 2, \dots \tag{9}$$

The condition has to be satisfied for all the *z* coordinates. It is possible only for *θ* = ±*θ*i that leads to the well known Bragg's law for X-ray reflection from a crystal

$$\text{m}\,2md\sin\theta\_i = m\mathbb{X}\_{0^\prime} \quad \left| m \right| = 0, 1, 2, \dots \tag{10}$$

used also to describe diffraction at optical volume gratings.

Concluding this paragraph, let us try to describe the diffraction phenomenon using holo‐ graphic terms. Two coherent plane waves

$$w\_1 \sim \exp(\mathrm{i}\varphi\_1), \qquad w\_2 \sim \exp(\mathrm{i}\varphi\_2) \tag{11}$$

interfere (Fig.4a). The interference pattern that will work as a grating can be expressed in the form, which corresponds with the amplitude transmission *t* of produced grating

$$\mathbf{t} = \left(\mathbf{w}\_1 + \mathbf{w}\_2\right) \left(\mathbf{w}\_1 + \mathbf{w}\_2\right)^\* = \left|\mathbf{w}\_1\right|^2 + \left|\mathbf{w}\_2\right|^2 + \mathbf{w}\_1 \mathbf{w}\_2^\* + \mathbf{w}\_1^\* \mathbf{w}\_2 \tag{12}$$

Let us suppose the grating to be very thin and illuminated by a plane wave *w0* in the *z* axis direction (Fig. 4b). The phases of all the waves can be expressed as

$$
\sigma\_j = k \alpha \sin \phi\_{j\prime} \quad j = 0, 1, 2 \tag{13}
$$

Taking into account *θi*

= 2sin(-*α*/2), as relations (16).

ed at various angles *θ*j

= 0, the condition (7) for intensity maximum turns into

= = *m m* ( ) (18)

+= = *m m* (19)

== = (20)

. When considering reconstruction as a diffraction, *m* =1. The angle *θ*

, they will be diffract‐

(*λ*0j) will cause various po‐

White Light Reconstructed Holograms http://dx.doi.org/10.5772/53592 69

sin .2sin / 2 , 0,1,2,3,...

The relation (18) gives the same angles of propagation sin*θA* = 0, sin*θB* = 2sin(*α*/2), and sin*θC*

Now we posses all the knowledge to realize what kind of problems can be met when recon‐ structing a hologram using white light and even to find a way to avoid them. There are two important results that had been derived above – relation (7) expressing the conditions for existence of a diffracted wave of the order *m* at a plane grating that can be rewritten into:

( ) 0 sin sin , 0,1,2,3,... *i dn*

The second one is the same kind of relation, valid for a volume grating - relation (10)

0 2 sin 2 sin , 0, 1, 2, ... *i nd nd m m*

Let us consider white light reconstruction of a *plane hologram*, which deals with the relation

sitions of the reconstructed object (Fig. 5.) Naturally, it results in "a blurred" reconstructed object both, horizontally and vertically. However, looking at Fig. 5, it could have occurred to us that if the distance between the object and hologram would have been smaller a less blur‐

 ql

(19). It is obvious that when using waves with various wavelengths *λ*j

**Figure 5.** White light reconstruction – the scheme and white light & HeNe laser reconstruction

of diffraction depends on the wavelength *λ*0j and various angles *θ*j

red reconstruction could be obtained (image holograms).

qql

q

 a

**2.2. How to avoid problems arising during white-light reconstruction**

q

The light wave *w* passing the grating consists of three parts

$$\mathbf{w} = \mathbf{w}\_0 \mathbf{t} = \mathbf{w}\_0 \left( \left| \mathbf{w}\_1 \right|^2 + \left| \mathbf{w}\_2 \right|^2 \right) + \mathbf{w}\_0 \mathbf{w}\_1 \mathbf{w}\_2^\* + \mathbf{w}\_0 \mathbf{w}\_1^\* \mathbf{w} = \mathbf{w}\_A + \mathbf{w}\_B + \mathbf{w}\_C \tag{14}$$

The phases of three waves in (14) are

$$\begin{aligned} \, \, \varphi\_A = kx \sin \phi\_0, \quad \, \varphi\_B = kx \left( \sin \phi\_0 + \sin \phi\_1 - \sin \phi\_2 \right), \quad \, \varphi\_C = kx \left( \sin \phi\_0 - \sin \phi\_1 + \sin \phi\_2 \right) \end{aligned} \tag{15}$$

**Figure 4.** Diffraction as holography. *a* - 2-wave interference produces a grating; *b* - diffraction at the grating

Supposing *φ0* = 0, *φ1* = *α*/2 and *φ2* = -*α*/2 one can obtain phases

$$
\varphi\_A = 0, \quad \varphi\_B = 2k\pi \sin\{\alpha/2\}, \quad \varphi\_\odot = 2k\pi \sin\{-\alpha/2\} \tag{16}
$$

Let us compare (16) to the light diffraction at a plane grating with the grating interval *d*. The grating interval in our case is

$$d = \lambda / 2\sin(\alpha/2) \tag{17}$$

Taking into account *θi* = 0, the condition (7) for intensity maximum turns into

( )( ) 2 2

direction (Fig. 4b). The phases of all the waves can be expressed as

j

The light wave *w* passing the grating consists of three parts

The phases of three waves in (14) are

68 Holography – Basic Principles and Contemporary Applications

 fj

j

( ) 2 2

 f

Supposing *φ0* = 0, *φ1* = *α*/2 and *φ2* = -*α*/2 one can obtain phases

 j

j

grating interval in our case is

=+ + = + + + \* *\* \**

Let us suppose the grating to be very thin and illuminated by a plane wave *w0* in the *z* axis

sin , 0,1,2 *j j*

( ) ( ) 0 012 012 sin , sin sin sin , sin sin sin *A B C*

**Figure 4.** Diffraction as holography. *a* - 2-wave interference produces a grating; *b* - diffraction at the grating

*d* = l aj

Let us compare (16) to the light diffraction at a plane grating with the grating interval *d*. The

 a

 f

 f  f

*1 2 1 2 1 2 12 12 t w w w w w w ww ww* (12)

= = + + + =++ *\* \* w wt w w w www www w w w 0 0 1 2 012 01 A B C* (14)

 j

= = +- = -+ *kx kx kx* (15)

= = *kx j* (13)

 f

 a

/ 2sin / 2 ( ) (17)

*A B* = = 0, 2 sin / 2 , 2 sin / 2 *kx* ( ) *C* = - *kx* ( ) (16)

 f

 f

$$
\sin \theta = m.2 \sin \left( a \,\prime \,\, \mathcal{D} \right), \quad \left| m \right| = 0, 1, 2, 3, \dots \tag{18}
$$

The relation (18) gives the same angles of propagation sin*θA* = 0, sin*θB* = 2sin(*α*/2), and sin*θC* = 2sin(-*α*/2), as relations (16).

#### **2.2. How to avoid problems arising during white-light reconstruction**

Now we posses all the knowledge to realize what kind of problems can be met when recon‐ structing a hologram using white light and even to find a way to avoid them. There are two important results that had been derived above – relation (7) expressing the conditions for existence of a diffracted wave of the order *m* at a plane grating that can be rewritten into:

$$m\left(\sin\theta + \sin\theta\_i\right) = m\mathbb{X}\_{0'} \quad \left|m\right| = 0, 1, 2, 3, \dots \tag{19}$$

The second one is the same kind of relation, valid for a volume grating - relation (10)

$$2md\sin\theta = 2md\sin\theta\_i = m\mathbb{1}\_{0^\prime} \quad \left| m \right| = 0, 1, 2, \dots \tag{20}$$

Let us consider white light reconstruction of a *plane hologram*, which deals with the relation (19). It is obvious that when using waves with various wavelengths *λ*j , they will be diffract‐ ed at various angles *θ*j . When considering reconstruction as a diffraction, *m* =1. The angle *θ* of diffraction depends on the wavelength *λ*0j and various angles *θ*j (*λ*0j) will cause various po‐ sitions of the reconstructed object (Fig. 5.) Naturally, it results in "a blurred" reconstructed object both, horizontally and vertically. However, looking at Fig. 5, it could have occurred to us that if the distance between the object and hologram would have been smaller a less blur‐ red reconstruction could be obtained (image holograms).

**Figure 5.** White light reconstruction – the scheme and white light & HeNe laser reconstruction

Moreover, not only a colour blur appears. It is also a *space blur* present. Both, lens and holo‐ gram create an image, so hologram is often compared to a lens. So-called *hologram formula*

$$\frac{1}{R\_2^{(r,v)}} + \frac{1}{R\_1} = \frac{1}{R\_1} \left( 1 + \frac{\lambda\_2}{\lambda\_1} \right) - \frac{\lambda\_2 / \lambda\_1}{L\_1} \pm \frac{1}{L\_2} = \frac{1}{f\_{\text{H}}^{(\text{r,v})}} \tag{21}$$

ours of nature to adequate tonal values in black and white, the French physicist Gabriel Lippmann conceived a method to record and reproduce colour images directly through the wavelengths from the lighted object. He introduced a photographic colour process that de‐ manded no colorants, dyes, or pigments, based on light waves interference principles, too.

White Light Reconstructed Holograms http://dx.doi.org/10.5772/53592 71

**Figure 6.** Principle of Lippmann's colour photography. a - colour photography (1-object, 2-lens, 3-image); b - twowave interference (*w*1 and *w*2-interfering waves, 1-photographic glass plate, 2-photographic emulsion, 3-mercury mir‐

He used a photographic emulsion between a photographic glass plate and a mercury mirror (Fig. 6a). The glass plate and emulsion are nearly transparent. Light waves coming from the object reflect from the HG-mirror (*w*1) and interfere with coming light waves (*w*2) – Fig. 6b. Since the Hg index of refraction prevails the emulsion index of refraction *n*, standing waves are created [3]. The interference pattern consists of *nodes*-surfaces and *loops*-surfaces, i.e. dark and bright interference surfaces that are recorded in the fine grain emulsion. Fig. 6b demonstrates a simple section of the interference surfaces to evaluate their spacing *λ*0/2*n*,

It can be derived in a very simply way, when realizing the phase difference Δ*Φ*(*z*) between

If Δ*Φ*(*zm*) = 2*m*π, where *m* = 0, 1, 2,... interference maximum is located at *zm*. It follows for the spacing between two adjacent maxima the value Δ*z* = *zm+1* – *zm* = *λ*0/2*n*. For simplicity, to point the principle, only, the angle between interfering plane waves was taken to be π.

0 0 2 2 () ( ) 2 *z nh h z z nh z*

( )

D = +-- = - é ù ë û (23)

 p

 l

ror, *n*(*h*)-refractive index (thickness) of the emulsion.

which depends on the wavelength *λ*0.

two plane waves meeting at the coordinate *z*

j p

l

similar to the *lens formula* can be derived, too. A hologram also can be characterised by its *focal length f*H. It depends on the wavelength of light when either recording (*λ*1), or recon‐ structing (*λ*2), object distance from the hologram (*R*1) and distance of the source of both, ref‐ erence (*L*1) and reconstructing (*L*2) beam from the hologram [7]. Paraxial approximation is supposed, all the distances are measured perpendicularly to the plane of hologram and indi‐ ces (signs) *r* (±→-), *v* (±→+) in (21) are related to *real* and *virtual* reconstruction.

In fact, the relation (21) defines a space blur (various *R*2j) because of various wavelengths *λ*0j. Remembering of various horizontal and vertical resolution of a human eye, it gives us an‐ other hint – to try to limit a possibility of the reconstruction *in whole* (Benton's holograms).

Now, let us take an interest in *volume holograms*, where results obtained for diffraction at a volume grating were obtained. Ideally there are only two diffraction grating order numbers relevant – *m* = 0, 1. Intensity of higher diffraction grating orders diminish to zero because of mutual interference and the condition (20) turns into

$$2nd\sin\theta\_j = 2nd\sin\theta\_{ij} = \mathcal{I}\_{0j} \tag{22}$$

It is a very interesting and for WLRH important result. According to the relation (22) there is an unambiguous relation among the grating period *d*, wavelength *λ*0j and angle *θ*j = *θ*ij. That means – when reconstructing by white light there is the only special angle for every wave‐ length. This way, the *volume hologram* picks from the white-light spectrum different recon‐ struction angle for every wavelength, i.e. prepares time coherent light for reconstruction (Denisyuk's hologram). It depends on the method of hologram recording if the reconstruct‐ ed object is observed either in single colours or colourfully.

#### **2.3. Denisyuk's holograms**

Let us proceed following the history of holography and start with Denisyuk's holograms. In 1962, Yuri Denisyuk combined holography with 1908 Nobel Laureate Gabriel Lippmann's work in natural color photography [8]. Denisyuk's approach produced a white-light reflec‐ tion hologram which, for the first time, could be viewed in light from an ordinary incandes‐ cent light bulb [9].

To explain the principle briefly, at least: Isaac Newton found out colours produced by a very thin layer due to interference of light. Colours in butterflies are the result of interference phenomena, too. And in 1886, when the photography was still struggling to transfer the col‐ ours of nature to adequate tonal values in black and white, the French physicist Gabriel Lippmann conceived a method to record and reproduce colour images directly through the wavelengths from the lighted object. He introduced a photographic colour process that de‐ manded no colorants, dyes, or pigments, based on light waves interference principles, too.

Moreover, not only a colour blur appears. It is also a *space blur* present. Both, lens and holo‐ gram create an image, so hologram is often compared to a lens. So-called *hologram formula*

> 2 21 (,) (r,v) 2 H 11 1 1 2 1 11 1 1 1 *r v R f RR L L* l

è ø (21)

= = (22)

= *θ*ij. That

 ll

similar to the *lens formula* can be derived, too. A hologram also can be characterised by its *focal length f*H. It depends on the wavelength of light when either recording (*λ*1), or recon‐ structing (*λ*2), object distance from the hologram (*R*1) and distance of the source of both, ref‐ erence (*L*1) and reconstructing (*L*2) beam from the hologram [7]. Paraxial approximation is supposed, all the distances are measured perpendicularly to the plane of hologram and indi‐

In fact, the relation (21) defines a space blur (various *R*2j) because of various wavelengths *λ*0j. Remembering of various horizontal and vertical resolution of a human eye, it gives us an‐ other hint – to try to limit a possibility of the reconstruction *in whole* (Benton's holograms).

Now, let us take an interest in *volume holograms*, where results obtained for diffraction at a volume grating were obtained. Ideally there are only two diffraction grating order numbers relevant – *m* = 0, 1. Intensity of higher diffraction grating orders diminish to zero because of

> ql

It is a very interesting and for WLRH important result. According to the relation (22) there is

means – when reconstructing by white light there is the only special angle for every wave‐ length. This way, the *volume hologram* picks from the white-light spectrum different recon‐ struction angle for every wavelength, i.e. prepares time coherent light for reconstruction (Denisyuk's hologram). It depends on the method of hologram recording if the reconstruct‐

Let us proceed following the history of holography and start with Denisyuk's holograms. In 1962, Yuri Denisyuk combined holography with 1908 Nobel Laureate Gabriel Lippmann's work in natural color photography [8]. Denisyuk's approach produced a white-light reflec‐ tion hologram which, for the first time, could be viewed in light from an ordinary incandes‐

To explain the principle briefly, at least: Isaac Newton found out colours produced by a very thin layer due to interference of light. Colours in butterflies are the result of interference phenomena, too. And in 1886, when the photography was still struggling to transfer the col‐

0 2 sin 2 sin *j ij j nd nd*

an unambiguous relation among the grating period *d*, wavelength *λ*0j and angle *θ*j

q

l

æ ö += + - ±= ç ÷

ces (signs) *r* (±→-), *v* (±→+) in (21) are related to *real* and *virtual* reconstruction.

mutual interference and the condition (20) turns into

70 Holography – Basic Principles and Contemporary Applications

ed object is observed either in single colours or colourfully.

**2.3. Denisyuk's holograms**

cent light bulb [9].

**Figure 6.** Principle of Lippmann's colour photography. a - colour photography (1-object, 2-lens, 3-image); b - twowave interference (*w*1 and *w*2-interfering waves, 1-photographic glass plate, 2-photographic emulsion, 3-mercury mir‐ ror, *n*(*h*)-refractive index (thickness) of the emulsion.

He used a photographic emulsion between a photographic glass plate and a mercury mirror (Fig. 6a). The glass plate and emulsion are nearly transparent. Light waves coming from the object reflect from the HG-mirror (*w*1) and interfere with coming light waves (*w*2) – Fig. 6b. Since the Hg index of refraction prevails the emulsion index of refraction *n*, standing waves are created [3]. The interference pattern consists of *nodes*-surfaces and *loops*-surfaces, i.e. dark and bright interference surfaces that are recorded in the fine grain emulsion. Fig. 6b demonstrates a simple section of the interference surfaces to evaluate their spacing *λ*0/2*n*, which depends on the wavelength *λ*0.

It can be derived in a very simply way, when realizing the phase difference Δ*Φ*(*z*) between two plane waves meeting at the coordinate *z*

$$
\Delta\varphi(z) = \frac{2\pi}{\lambda\_0} n \left[ h + (h - z) - z \right] = \frac{2\pi}{\lambda\_0} 2n \left( h - z \right) \tag{23}
$$

If Δ*Φ*(*zm*) = 2*m*π, where *m* = 0, 1, 2,... interference maximum is located at *zm*. It follows for the spacing between two adjacent maxima the value Δ*z* = *zm+1* – *zm* = *λ*0/2*n*. For simplicity, to point the principle, only, the angle between interfering plane waves was taken to be π.

This way the processed photographic emulsion became a layer where beside an image also vol‐ ume gratings with various grating intervals, related to the local wavelength, were recorded.

However, as mentioned above, such a reconstruction is a monochromatic one, only (Fig. 8).

White Light Reconstructed Holograms http://dx.doi.org/10.5772/53592 73

To produce colourful hologram, one needs three lasers generating on three basic wave‐ lengths (red, green, blue) to record such a hologram. Each of the waves creates own interfer‐ ence structure (Fig. 9). After illuminating such a hologram with white light, each structure helps to reconstruct the object wave in related wavelength. The reconstruction can be seen in

**Figure 9.** A colourful hologram recording (1-object, 2-recording medium, 3-optics to spread light, 4-mirror, 5-semi‐

Yu. N. Denisyuk presented his technique as a generalized form of Lippmann photography, or as a colour-dependent optical element. This technique, using reflection holography and the white-light reconstruction technique, seems to be the most promising one as regards the

Writing on white-light reconstructed holograms it is necessary to take into account that de‐ pending on the relation between the thickness *h* of the recording medium and the average

grams – *thin* and *thick*, i.e. *volume* ones. They are characterized by a parameter *Q*

¯ of the recorded holographic structure fringes, there are defined two types of holo‐

three colours and thanks to sophisticated activity of our brain as colourful.

**Figure 8.** Yu. Denisyuk reconstructed from a hologram and alive [11]

What about colour holograms?

transparent mirrors)

**2.4. Image hologram**

spacing *d*

actual recording of colour holograms [12].

Taking into account the former paragraph (2.2), it is obvious that after the photograph is il‐ luminated by white light, the image in its original colours can be observed because of dif‐ fraction of white light at such a structure.

It is hardly imaginable that in the late 1800s such an advanced photographic technique was already conceived and realized. The resemblance with volume holography, published in 1962 by Yuri Denisyuk, is striking. Lippmann photography actually is the ancestor of vol‐ ume reflection holography or Denisyuk holography, which is sometimes also referred to as Denisyuk-Lippmann-Bragg holography.

Yu. Denisyuk, inspired by the ingenious Lippmann's colour photography technique did ex‐ tensive theoretical analysis and experimented with mercury lamp sources since 1958 and even enlisted colleagues to develop a special thick, high-resolution, and relatively sensitive photographic emulsion to record the wave pattern in depth [10].

Later, realizing the potential of wave-front reconstruction, devised a different approach to record a hologram. A laser beam illuminated an object through a photographic plate (refer‐ ence beam) interfered with light reflected from the object (object beam) to produce a holo‐ gram in the layer of the photographic emulsion (Fig. 7a).

Reconstruction can be performed by sunlight or another white-light source lighting the hologram. If the direction is the same as when recording, the Bragg's diffractive reflection provides us with a monochromatic reconstructed image of the object in the wavelength used when recording the hologram (e.g. Fig. 7b). Fig. 7c demonstrates a possible two-beam exper‐ imental set-up.

**Figure 7.** Denisyuk's 1-beam holographical set-up. *a* – recording (1-object, 2-recording medium, 3-reference beam, 4 object beam), *b* – reconstruction (1-hologram, 2-reconstructing beam, 3-reconstructed wave, 4-holographic image), *c* – 2-beam set-up (1-object, 2-recording medium, 3-reference beam, 4-object beam, 5-beam splitter, 6-mirror).

However, as mentioned above, such a reconstruction is a monochromatic one, only (Fig. 8). What about colour holograms?

To produce colourful hologram, one needs three lasers generating on three basic wave‐ lengths (red, green, blue) to record such a hologram. Each of the waves creates own interfer‐ ence structure (Fig. 9). After illuminating such a hologram with white light, each structure helps to reconstruct the object wave in related wavelength. The reconstruction can be seen in three colours and thanks to sophisticated activity of our brain as colourful.

**Figure 8.** Yu. Denisyuk reconstructed from a hologram and alive [11]

**Figure 9.** A colourful hologram recording (1-object, 2-recording medium, 3-optics to spread light, 4-mirror, 5-semi‐ transparent mirrors)

Yu. N. Denisyuk presented his technique as a generalized form of Lippmann photography, or as a colour-dependent optical element. This technique, using reflection holography and the white-light reconstruction technique, seems to be the most promising one as regards the actual recording of colour holograms [12].

#### **2.4. Image hologram**

This way the processed photographic emulsion became a layer where beside an image also vol‐ ume gratings with various grating intervals, related to the local wavelength, were recorded.

Taking into account the former paragraph (2.2), it is obvious that after the photograph is il‐ luminated by white light, the image in its original colours can be observed because of dif‐

It is hardly imaginable that in the late 1800s such an advanced photographic technique was already conceived and realized. The resemblance with volume holography, published in 1962 by Yuri Denisyuk, is striking. Lippmann photography actually is the ancestor of vol‐ ume reflection holography or Denisyuk holography, which is sometimes also referred to as

Yu. Denisyuk, inspired by the ingenious Lippmann's colour photography technique did ex‐ tensive theoretical analysis and experimented with mercury lamp sources since 1958 and even enlisted colleagues to develop a special thick, high-resolution, and relatively sensitive

Later, realizing the potential of wave-front reconstruction, devised a different approach to record a hologram. A laser beam illuminated an object through a photographic plate (refer‐ ence beam) interfered with light reflected from the object (object beam) to produce a holo‐

Reconstruction can be performed by sunlight or another white-light source lighting the hologram. If the direction is the same as when recording, the Bragg's diffractive reflection provides us with a monochromatic reconstructed image of the object in the wavelength used when recording the hologram (e.g. Fig. 7b). Fig. 7c demonstrates a possible two-beam exper‐

**Figure 7.** Denisyuk's 1-beam holographical set-up. *a* – recording (1-object, 2-recording medium, 3-reference beam, 4 object beam), *b* – reconstruction (1-hologram, 2-reconstructing beam, 3-reconstructed wave, 4-holographic image), *c* – 2-beam set-up (1-object, 2-recording medium, 3-reference beam, 4-object beam, 5-beam splitter, 6-mirror).

fraction of white light at such a structure.

72 Holography – Basic Principles and Contemporary Applications

Denisyuk-Lippmann-Bragg holography.

imental set-up.

photographic emulsion to record the wave pattern in depth [10].

gram in the layer of the photographic emulsion (Fig. 7a).

Writing on white-light reconstructed holograms it is necessary to take into account that de‐ pending on the relation between the thickness *h* of the recording medium and the average spacing *d* ¯ of the recorded holographic structure fringes, there are defined two types of holo‐ grams – *thin* and *thick*, i.e. *volume* ones. They are characterized by a parameter *Q*

$$Q = \frac{2\pi\lambda\_0\hbar}{n\overline{d}^2} \tag{24}$$

there by a projecting lens (Fig. 10a). When reconstructing in white light the reconstruction is observed in various (rainbow) colours from various directions at the same place (Fig. 10c.). When the image coincides with the hologram plane, it is perfectly sharp. Naturally, projec‐ tion of a 3D object has 3D properties, too. In practice, display holograms up to around 2 cm in depth can be acceptable. This type of hologram is called an *open-aperture* hologram [14]. However, such a simple method is used mostly for approximately "2D" objects like medals,

A more detailed estimation of the image blur can be found in [15]. It can be shown that if the source used to reconstruct the hologram is located at the same position as the reference source used to record it and has very nearly the same wavelength, the blur Δ*xR2* of the recon‐

Similarly, if the source used to reconstruct the hologram has a mean wavelength *λ2* very nearly equal to *λ1*, the wavelength used to record the hologram, and a spectral bandwidth Δ*λ2*, the transverse image blur Δ*xR2* due to the finite spectral bandwidth of the source of re‐

> l l

( ) ( ) 2 2 21 2 2 / / *R L* D= D *x x LR*

It follows from (25) and (26) that if the interbeam angle and the depth of the object are small,

When a real 3D object is recorded the well-known Benton's method [16], which allows us to get rid of vertical blur of the reconstructed image, has to be used. The Benton (rainbow) hologram is a transfer transmission hologram, which reconstructs a bright, sharp, mono‐ chromatic image when illuminated with white light [17]. Benton holograms are produced by means of an optical technique that sacrifices the vertical parallax of the holographic image in favour of a sharp monochromatic reconstruction by a white light point source. In other words - the physical basis of this method is to reduce the amount of information on the hologram. The vertical parallax is eliminated. The method relays on the fact that human be‐ ings have two eyes in horizontal position, i.e. people are less sensitive to vertical parallax.

In fact, it is a hologram of a hologram. The first (master) hologram H1 of the object O is pro‐ duced (Fig. 11a). The object and reference waves are directed around the horizontal plane.

Then, H1 is masked with a narrow horizontal slit S and wave 1, conjugated to the reference wave 2 from Fig. 11a is used to reconstruct the free part of H1. The conjugate wave [6] of the

The image blur increases with the depth of the image and the interbeam angle.

it is possible to use an extended white-light source to view the image.

2 12 2 (/) *R L* D= D *x RL x* (25)

(26)

White Light Reconstructed Holograms http://dx.doi.org/10.5772/53592 75

coins, photos, and so on.

**2.5. Benton's holograms**

structed image along the *x* axis for a source size Δ*xL2* is

constructing wave, located at *xL2* can be shown to be

introduced in [13]. *Q* < 1 corresponds to thin gratings, while *Q* > 1 corresponds to volume gratings. Moreover the objects around us can be defined as either 2D or 3D objects.

It is obvious that Denisyuk's method of holography is applicable to any object and the re‐ cording media suitable to create a volume hologram. Moreover, it represents a reflection holography, i.e. the reconstructed wave seems like reflection of the reconstructing wave from the hologram. When recording, the reference beam and the object beam come from op‐ posite sides of the recording medium. Because of that, when reconstructing, observer and the source of the reconstructing wave are on the same side of the hologram. The next two paragraphs are dealing with so-called *transmission thin holograms*.

Let us remember of the physical principle of reconstruction of a hologram. It is diffraction of either transmitted or reflected incident, i.e. reconstructing light. Due to that, the white-light reconstruction of transmission thin holograms brings a possible colour and space *blur* of the reconstructed image (Fig. 5). The illustrative Fig.5 gives us a hint to decrease the object – hologram distance when recording the hologram as much as possible to avoid the colour blur. It would be the best to decrease the distance to zero. However, the reference beam must not be blocked.

**Figure 10.** Image holography. *a* – experimental set-up (1-laser & collimator, 2-beam splitter, 3-mirror, 4-hologram, 5 ground glass, 6-object, 7-projecting lens; *b* - objects, *c* - reconstruction

There is a simple possibility to put the recorded object (Fig. 10b) even "into" the recording medium and not to restrict the reference wave while recording the hologram – to *project* it there by a projecting lens (Fig. 10a). When reconstructing in white light the reconstruction is observed in various (rainbow) colours from various directions at the same place (Fig. 10c.).

When the image coincides with the hologram plane, it is perfectly sharp. Naturally, projec‐ tion of a 3D object has 3D properties, too. In practice, display holograms up to around 2 cm in depth can be acceptable. This type of hologram is called an *open-aperture* hologram [14]. However, such a simple method is used mostly for approximately "2D" objects like medals, coins, photos, and so on.

A more detailed estimation of the image blur can be found in [15]. It can be shown that if the source used to reconstruct the hologram is located at the same position as the reference source used to record it and has very nearly the same wavelength, the blur Δ*xR2* of the recon‐ structed image along the *x* axis for a source size Δ*xL2* is

$$
\Delta \mathbf{x}\_{R2} = (R\_1 / L\_2) \Delta \mathbf{x}\_{L2} \tag{25}
$$

Similarly, if the source used to reconstruct the hologram has a mean wavelength *λ2* very nearly equal to *λ1*, the wavelength used to record the hologram, and a spectral bandwidth Δ*λ2*, the transverse image blur Δ*xR2* due to the finite spectral bandwidth of the source of re‐ constructing wave, located at *xL2* can be shown to be

$$\left| \Delta \mathbf{x}\_{\mathbb{R}2} \right| = \left( \mathbf{x}\_{12} \;/ \, L\_2 \right) \mathbf{R}\_1 \left( \Delta \boldsymbol{\uplambda}\_2 \;/ \, \boldsymbol{\uplambda}\_2 \right) \tag{26}$$

The image blur increases with the depth of the image and the interbeam angle.

It follows from (25) and (26) that if the interbeam angle and the depth of the object are small, it is possible to use an extended white-light source to view the image.

#### **2.5. Benton's holograms**

0 2 2 *h Q nd* pl

introduced in [13]. *Q* < 1 corresponds to thin gratings, while *Q* > 1 corresponds to volume

It is obvious that Denisyuk's method of holography is applicable to any object and the re‐ cording media suitable to create a volume hologram. Moreover, it represents a reflection holography, i.e. the reconstructed wave seems like reflection of the reconstructing wave from the hologram. When recording, the reference beam and the object beam come from op‐ posite sides of the recording medium. Because of that, when reconstructing, observer and the source of the reconstructing wave are on the same side of the hologram. The next two

Let us remember of the physical principle of reconstruction of a hologram. It is diffraction of either transmitted or reflected incident, i.e. reconstructing light. Due to that, the white-light reconstruction of transmission thin holograms brings a possible colour and space *blur* of the reconstructed image (Fig. 5). The illustrative Fig.5 gives us a hint to decrease the object – hologram distance when recording the hologram as much as possible to avoid the colour blur. It would be the best to decrease the distance to zero. However, the reference beam

**Figure 10.** Image holography. *a* – experimental set-up (1-laser & collimator, 2-beam splitter, 3-mirror, 4-hologram, 5-

There is a simple possibility to put the recorded object (Fig. 10b) even "into" the recording medium and not to restrict the reference wave while recording the hologram – to *project* it

ground glass, 6-object, 7-projecting lens; *b* - objects, *c* - reconstruction

gratings. Moreover the objects around us can be defined as either 2D or 3D objects.

paragraphs are dealing with so-called *transmission thin holograms*.

74 Holography – Basic Principles and Contemporary Applications

must not be blocked.

= (24)

When a real 3D object is recorded the well-known Benton's method [16], which allows us to get rid of vertical blur of the reconstructed image, has to be used. The Benton (rainbow) hologram is a transfer transmission hologram, which reconstructs a bright, sharp, mono‐ chromatic image when illuminated with white light [17]. Benton holograms are produced by means of an optical technique that sacrifices the vertical parallax of the holographic image in favour of a sharp monochromatic reconstruction by a white light point source. In other words - the physical basis of this method is to reduce the amount of information on the hologram. The vertical parallax is eliminated. The method relays on the fact that human be‐ ings have two eyes in horizontal position, i.e. people are less sensitive to vertical parallax.

In fact, it is a hologram of a hologram. The first (master) hologram H1 of the object O is pro‐ duced (Fig. 11a). The object and reference waves are directed around the horizontal plane.

Then, H1 is masked with a narrow horizontal slit S and wave 1, conjugated to the reference wave 2 from Fig. 11a is used to reconstruct the free part of H1. The conjugate wave [6] of the original object wave is reconstructed and the real holographic image HI serves as an object to record the second hologram H2 (the part *a)* in Fig. 11b). The part *b)* of Fig. 11b demon‐ strates the view to the process of recording H2 from the side. The 3D object, represented by reconstructed HI straddles the plane of medium to record H2 and a converging reference wave 3 is now inclined in the vertical plane.

One cause of image blur is the finite wavelength spread in the image. The maximum wave‐ length spread observed when the rainbow hologram is illuminated with white light can be

where *θ* is the angle between object and reference waves when recording H2, *L* is the dis‐ tance between H1 and H2, *D* is eye pupil diameter and *b* is the slite S width. The eyes of the person viewing the image are supposed to be placed in the position, where the image of the slit is formed. The relation (27) leads to the image blur due to wavelength spread of about

( ) 0 ~ / *zDb L*

where *z*0 reprezents the H2-to-image distance generally, when the image does not straddle

Another cause of image blur is the finite size of the source used to illuminate the hologram. If the source has the angular subtense *ΩS*, as viewed from the hologram, the resultant image

**Figure 12.** White light reconstruction of Benton's hologram "*Holography Blocks*" (made of tens of 1 inch transparent

( ) 0 ~2 / *diff*

 l

acrylic cubes) photographed from two directions to demonstrate its 3D property [20].

d

0 ~ *S S* d

max ( ) *Db L* (27)

White Light Reconstructed Holograms http://dx.doi.org/10.5772/53592 77

D + (28)

*z* W (29)

*z Lb* + (30)

( ) ~ / sin / / D +

 lq

l d

l

the H2 plane. With *z*0 → 0 the image blur (28) also goes to zero.

A final cause of image blur is diffraction at the slit

estimated as

blur is approximatelly

When viewing such a hologram in the same monochromatic light as the recording one, the holographic image from H2 that straddles the plane of H2 is reconstructed. However, while recording H2 the width of the slit S limited the vertical parallax of the object and it will be limited when observing the reconstruction, too. That means, there is a small interval of an‐ gles in vertical direction that allows observing the reconstruction of H2, i.e. the perspective information in vertical axis is lost. The horizontal parallax is much more wider, given by the width of H1 determined by the length of the slit S.

**Figure 11.** Principle of Benton's rainbow hologram. *a* – object O, hologram H1, object wave 1, reference wave 2; *b* – hologram H1, slit S, reconstructing wave 1, reconstructed wave 2 as a new object wave, holographic image HI, refer‐ ence wave 3, hologram H2; *c* – hologram H2, reconstructing white light 1, colour reconstructed waves 2 related to vari‐ ous angles α.

It seems like a kind of limitation, but remember – when recording H2, the reference wave 3 was inclined in the vertical plane. This way, the hologram H2, which is a set of arbitrary gra‐ tings with horizontal fringes in principle, became a dispersion element for vertical angle var‐ iations. That provides the hologram H2 with colour dispersion. With a white-light source, located approximately in the convergence point of 3 (Fig. 11c), the reconstruction is dis‐ persed in the vertical plane to form a continuous spectrum (hence the term "rainbow"). An observer whose eyes are positioned at any part of this spectrum then sees a sharp, three-di‐ mensional image of the object in the corresponding colour. In [18] is presented an optical system that permits both steps of the recording process to be carried out with a minimum of adjustment.

The image reconstructed from a rainbow hologram is free from speckle, because it is illumi‐ nated with incoherent light. However, it is not free from blur. A more detailed analyse of rainbow holograms can be found in [19].

One cause of image blur is the finite wavelength spread in the image. The maximum wave‐ length spread observed when the rainbow hologram is illuminated with white light can be estimated as

$$\left(\left(\Delta\right)\_{\text{max}} \sim \lambda / \sin\theta \,/\left(D + b\right) / L\right.\tag{27}$$

where *θ* is the angle between object and reference waves when recording H2, *L* is the dis‐ tance between H1 and H2, *D* is eye pupil diameter and *b* is the slite S width. The eyes of the person viewing the image are supposed to be placed in the position, where the image of the slit is formed. The relation (27) leads to the image blur due to wavelength spread of about

$$
\delta\_{\Lambda\dot{\varkappa}} \sim z\_0 \left( D + b \right) / L \tag{28}
$$

where *z*0 reprezents the H2-to-image distance generally, when the image does not straddle the H2 plane. With *z*0 → 0 the image blur (28) also goes to zero.

Another cause of image blur is the finite size of the source used to illuminate the hologram. If the source has the angular subtense *ΩS*, as viewed from the hologram, the resultant image blur is approximatelly

$$
\delta\_{\mathbb{S}} \sim z\_0 \Omega\_{\mathbb{S}} \tag{29}
$$

A final cause of image blur is diffraction at the slit

original object wave is reconstructed and the real holographic image HI serves as an object to record the second hologram H2 (the part *a)* in Fig. 11b). The part *b)* of Fig. 11b demon‐ strates the view to the process of recording H2 from the side. The 3D object, represented by reconstructed HI straddles the plane of medium to record H2 and a converging reference

When viewing such a hologram in the same monochromatic light as the recording one, the holographic image from H2 that straddles the plane of H2 is reconstructed. However, while recording H2 the width of the slit S limited the vertical parallax of the object and it will be limited when observing the reconstruction, too. That means, there is a small interval of an‐ gles in vertical direction that allows observing the reconstruction of H2, i.e. the perspective information in vertical axis is lost. The horizontal parallax is much more wider, given by the

**Figure 11.** Principle of Benton's rainbow hologram. *a* – object O, hologram H1, object wave 1, reference wave 2; *b* – hologram H1, slit S, reconstructing wave 1, reconstructed wave 2 as a new object wave, holographic image HI, refer‐ ence wave 3, hologram H2; *c* – hologram H2, reconstructing white light 1, colour reconstructed waves 2 related to vari‐

It seems like a kind of limitation, but remember – when recording H2, the reference wave 3 was inclined in the vertical plane. This way, the hologram H2, which is a set of arbitrary gra‐ tings with horizontal fringes in principle, became a dispersion element for vertical angle var‐ iations. That provides the hologram H2 with colour dispersion. With a white-light source, located approximately in the convergence point of 3 (Fig. 11c), the reconstruction is dis‐ persed in the vertical plane to form a continuous spectrum (hence the term "rainbow"). An observer whose eyes are positioned at any part of this spectrum then sees a sharp, three-di‐ mensional image of the object in the corresponding colour. In [18] is presented an optical system that permits both steps of the recording process to be carried out with a minimum of

The image reconstructed from a rainbow hologram is free from speckle, because it is illumi‐ nated with incoherent light. However, it is not free from blur. A more detailed analyse of

wave 3 is now inclined in the vertical plane.

76 Holography – Basic Principles and Contemporary Applications

width of H1 determined by the length of the slit S.

ous angles α.

adjustment.

rainbow holograms can be found in [19].

**Figure 12.** White light reconstruction of Benton's hologram "*Holography Blocks*" (made of tens of 1 inch transparent acrylic cubes) photographed from two directions to demonstrate its 3D property [20].

$$
\delta\_{\rm diff} \sim 2\lambda \left( z\_0 + L \right) / b \tag{30}
$$

However, this can be neglected unless the width of the slit is very small.

Concluding this part, I would like to memory the inventor of this kind of holography, Ben‐ ton S. A., and include the reconstruction of his *Holography Blocks*, the transmission rainbow hologram that he made of tens of 1 inch transparent acrylic cubes (1975). The pictures (Fig. 12) were photographed from his hologram from the left and from the right to demonstrate its 3D property by R. L. van Renesse and published in his monograph written in remem‐ brance of Steve Benton after he passed away, in 2003 [20].

It was soon realized that holograms might be used as security features on valuable docu‐ ments and products and this way classical hologram became the first of a manifold of dif‐ fractive structures developed to thwart counterfeiting. Many of these diffractive structures can no longer be called holograms in the strict sense and some of them are no longer made by laser interference techniques, but created by advanced electron beam lithographic techni‐

White Light Reconstructed Holograms http://dx.doi.org/10.5772/53592 79

These holograms, i.e. diffractive elements provide a powerful obstacle to counterfeiting. One can meet holograms either on various goods itself or in the packaging of products, on bank‐ notes, various types of cards, and so on. For example - almost all credit cards carry a holo‐ gram, which is a good sign that security holography has proven to be very effective. There

*Holographic labels* are firmly affixed on the desired place of a product to verify its genuine‐ ness. Such labels cannot be copied, altered, either adapted or manufactured in an easy way. Moreover, hidden information can be embedded, visible at special circumstances, only. To increase the uniqueness of holographic labels, there are used another specific techniques, e.g. custom etching and overwriting of labels. To give some examples, holographic labels are used in various kinds of cards, artwork, banknotes, bank checks, product packaging for

*Holographic stickers* (*HS*) – most of them are self adhesive, providing authentication, security and protection against counterfeit, too. To increase their security level, various techniques are used. Let us mention some of them, like laser beam engraved dots (*dot-matrix HS*), dou‐ ble-exposed hologram of two objects from two directions (*flip-flop HS*) that displays two im‐ ages from two different viewing angles), combinations of holograms, micro-information included, visible only by magnifier (*micro text/image HS*). Locally different thickness of the hologram layer gives reconstruction in various colours. A hidden text or image invisible to the naked eye but visible by means of a laser reader, serial numbers, overprinting left after

the sticker is peeled off, are next examples of holographic stickers security increasing.

To minimise counterfeiting in holograms various methods during recording are used. It is possible to include hidden information or make the image so complicated that it is not worth to duplicate it, considering the time and money involved [1]. However, hidden infor‐ mation is of great value only if the cheater cannot find it or duplicate it. So, effective use of hidden information or any kind of complex images requires some sort of relatively simple

Another possibility profits from using variable processing parameters, like randomly changed exposure, development time or other processing parameters to produce variable shrinkage all over the hologram. This results into a hologram whose colour varies from point to point and when using a monochromatic source - laser the brightness changes dra‐

Holograms are not easy to counterfeit either if variable information like serial numbers, en‐ coded personal information or dates are included or they are made of some special materi‐

als. Combined countermeasures can be another effective approach, too.

are various kinds of holographic labels and stickers [1].

brand protection, alcohol, cosmetics, and so on.

and inexpensive reading device or decoding device.

matically with the shrinkage of the film.

ques [21].

## **3. Some applications of WLRH**

This paragraph consists of two parts. The first one mentions some situations briefly, at least, when anyone can meet white light reconstructed holograms. For those, taking an interest, there is great amount of Internet information accessible now, even pointing to details related to methods and technologies to produce WLRH.

Naturally, there are many scientific applications of WLRH, too. To solve the problem of com‐ mercial application can, also, be considered as a scientific application. I decided to use the sec‐ ond part to present short information, at least, on one of our former works, which was published in Slovak, only. It is focused on using the phase-shifting image holographic interfer‐ ometry to study an optical fibre refractive index radial distribution. The image holography was used for us to be able to profit from possible magnification of the studied region.

### **3.1. Popular WLRH applications**

When considering current applications of holographic technology enabling white light holo‐ gram reconstruction, i.e. displaying and viewing holograms using a common white light source, consumer products and advertising materials have to be mentioned firstly [1].

Security and product authentication seem to be the most popular growing areas for the use of holograms, especially of white-light reconstructed holograms. Why is it so?

Generally speaking, holograms can reconstruct one of two waves used to record them, when illuminated by the second one. That means optical reconstruction of 3D space from a 2D re‐ cord. After four milestones in history of holography, represented by D. Gabor (father of hol‐ ography), Yu. N. Denisyuk (invented volume reflection holography), E. N. Leith and J. Upatnieks (invented off-axis holography), and S. Benton (invented rainbow holography), the subsequent development of the micro-embossing technique allowed their mass replica‐ tion [21].

For example a very popular variation became the *embossed hologram*. Such holograms are easily produced in mass quantity and at a very low cost. The holographic structure is re‐ corded on a light sensitive medium (a photo-resistor), which can be processed by etching and a microscopic relief is created. By electro-deposition of a metal (nickel) on the relief a stamper is made and its surface relief is copied by impressing it onto another material (e.g. polyester base film, thermoplastic film).

It was soon realized that holograms might be used as security features on valuable docu‐ ments and products and this way classical hologram became the first of a manifold of dif‐ fractive structures developed to thwart counterfeiting. Many of these diffractive structures can no longer be called holograms in the strict sense and some of them are no longer made by laser interference techniques, but created by advanced electron beam lithographic techni‐ ques [21].

However, this can be neglected unless the width of the slit is very small.

brance of Steve Benton after he passed away, in 2003 [20].

**3. Some applications of WLRH**

78 Holography – Basic Principles and Contemporary Applications

**3.1. Popular WLRH applications**

polyester base film, thermoplastic film).

tion [21].

to methods and technologies to produce WLRH.

Concluding this part, I would like to memory the inventor of this kind of holography, Ben‐ ton S. A., and include the reconstruction of his *Holography Blocks*, the transmission rainbow hologram that he made of tens of 1 inch transparent acrylic cubes (1975). The pictures (Fig. 12) were photographed from his hologram from the left and from the right to demonstrate its 3D property by R. L. van Renesse and published in his monograph written in remem‐

This paragraph consists of two parts. The first one mentions some situations briefly, at least, when anyone can meet white light reconstructed holograms. For those, taking an interest, there is great amount of Internet information accessible now, even pointing to details related

Naturally, there are many scientific applications of WLRH, too. To solve the problem of com‐ mercial application can, also, be considered as a scientific application. I decided to use the sec‐ ond part to present short information, at least, on one of our former works, which was published in Slovak, only. It is focused on using the phase-shifting image holographic interfer‐ ometry to study an optical fibre refractive index radial distribution. The image holography was

When considering current applications of holographic technology enabling white light holo‐ gram reconstruction, i.e. displaying and viewing holograms using a common white light source, consumer products and advertising materials have to be mentioned firstly [1].

Security and product authentication seem to be the most popular growing areas for the use

Generally speaking, holograms can reconstruct one of two waves used to record them, when illuminated by the second one. That means optical reconstruction of 3D space from a 2D re‐ cord. After four milestones in history of holography, represented by D. Gabor (father of hol‐ ography), Yu. N. Denisyuk (invented volume reflection holography), E. N. Leith and J. Upatnieks (invented off-axis holography), and S. Benton (invented rainbow holography), the subsequent development of the micro-embossing technique allowed their mass replica‐

For example a very popular variation became the *embossed hologram*. Such holograms are easily produced in mass quantity and at a very low cost. The holographic structure is re‐ corded on a light sensitive medium (a photo-resistor), which can be processed by etching and a microscopic relief is created. By electro-deposition of a metal (nickel) on the relief a stamper is made and its surface relief is copied by impressing it onto another material (e.g.

used for us to be able to profit from possible magnification of the studied region.

of holograms, especially of white-light reconstructed holograms. Why is it so?

These holograms, i.e. diffractive elements provide a powerful obstacle to counterfeiting. One can meet holograms either on various goods itself or in the packaging of products, on bank‐ notes, various types of cards, and so on. For example - almost all credit cards carry a holo‐ gram, which is a good sign that security holography has proven to be very effective. There are various kinds of holographic labels and stickers [1].

*Holographic labels* are firmly affixed on the desired place of a product to verify its genuine‐ ness. Such labels cannot be copied, altered, either adapted or manufactured in an easy way. Moreover, hidden information can be embedded, visible at special circumstances, only. To increase the uniqueness of holographic labels, there are used another specific techniques, e.g. custom etching and overwriting of labels. To give some examples, holographic labels are used in various kinds of cards, artwork, banknotes, bank checks, product packaging for brand protection, alcohol, cosmetics, and so on.

*Holographic stickers* (*HS*) – most of them are self adhesive, providing authentication, security and protection against counterfeit, too. To increase their security level, various techniques are used. Let us mention some of them, like laser beam engraved dots (*dot-matrix HS*), dou‐ ble-exposed hologram of two objects from two directions (*flip-flop HS*) that displays two im‐ ages from two different viewing angles), combinations of holograms, micro-information included, visible only by magnifier (*micro text/image HS*). Locally different thickness of the hologram layer gives reconstruction in various colours. A hidden text or image invisible to the naked eye but visible by means of a laser reader, serial numbers, overprinting left after the sticker is peeled off, are next examples of holographic stickers security increasing.

To minimise counterfeiting in holograms various methods during recording are used. It is possible to include hidden information or make the image so complicated that it is not worth to duplicate it, considering the time and money involved [1]. However, hidden infor‐ mation is of great value only if the cheater cannot find it or duplicate it. So, effective use of hidden information or any kind of complex images requires some sort of relatively simple and inexpensive reading device or decoding device.

Another possibility profits from using variable processing parameters, like randomly changed exposure, development time or other processing parameters to produce variable shrinkage all over the hologram. This results into a hologram whose colour varies from point to point and when using a monochromatic source - laser the brightness changes dra‐ matically with the shrinkage of the film.

Holograms are not easy to counterfeit either if variable information like serial numbers, en‐ coded personal information or dates are included or they are made of some special materi‐ als. Combined countermeasures can be another effective approach, too.

To show another ways of WLRH using, let us remember that in the beginning, holograms, a kind of "windows with a memory" with unfamiliar properties, were regarded as similar to daguerreotypes, photography predecessors [22]. Like early photography, holography was expected to develop technically and become cheaper, more capable and widespread. Where possible, people worked to realize these expectations of progress, especially for trade show displays. A pulse ruby laser had been developed to enable recording a human portrait in a darkened room to create static 3D human scenes for advertising. While such holograms at‐ tracted interest their display requirements (laser) made them too unwieldy to be sold or even displayed outside the laboratories.

promotional purpose. This type of holography can be found as a part of some either pure or

White Light Reconstructed Holograms http://dx.doi.org/10.5772/53592 81

There is a special interest focused to optical fibres all over the world. They became of great importance as parts of many photonic devices and various methods are used to study their properties. Radial profile of fibre optical thickness, i.e. of its refractive index is one of the most important fibre characteristics. Many papers arise contemporary. Mostly they are based on classic interferometric microscopy of a fibre located in a wedge shaped layer of an immerse liquid. When applying optical imaging, methods are limited by the diffractive reso‐ lution *λ*/2*n.*sin*θ*, where *n* is the refractive index of the object space, *θ* is the angle related en‐ trance aperture of the objective. The limit follows from the Rayleigh criterion, applicable in the Fraunhofer approximation. Taking into account a conception of near-field optics it

The experimental method elaborated in our paper is based on double-exposure phase-shift‐ ing interferometry. Moreover, the image holographic interferometry was used to profit from both the advantages - lower demands on optical quality of all the set-up elements and also the possibility of white-light reconstruction and magnifying the object size. Moreover, phase-shifting interferometry allows determining both, the size and direction of optical path changes. Fig. 13 demonstrates the experimental set-up. The laser beam is divided into colli‐ mated waves, object (*o*) and reference (*p*) ones. The object V is projected on the recording medium with a proper magnification and hologram H is recorded. To apply the phase-shift‐ ing interferometry the wedge K inclines the reference beam between two expositions. V rep‐ resents two states of the object – either a glass cell filled with glycerine (*nK* = 1,4534 ± 0.0005) and the fibre embedded into it, or the glass cell filled with glycerine without the fibre.