a single - layer essentially thickness independent luminescent photoelastic coating ( lpc ) includes a polarizing maintaining luminescent dye and an excitation absorption dye . although a single luminescent and a single absorption dye is generally utilized with the invention , two or more luminescent and / or absorption dyes may be used . coatings according to the invention can be used to measure the full - field shear strain distribution and orientation . the inventive coating overcomes , or at least sharply reduces , thickness and adhesion related deficiencies in dual - layer strain sensitive coatings previously utilized . as defined herein , a “ polarizing maintaining luminescent dye ” is a dye that allows the coating to provide a luminescent signal responsive to a polarized optical excitation signal , where at least 5 % of the luminescent signal intensity maintains the polarization of the excitation signal . preferably , the coatings are at least 20 % to 30 % efficient in preserving polarization since the minimum strain resolution decreases with increasing polarization efficiency . an “ absorption dye ” is defined herein as a dye which absorbs the excitation signal , but does not emit significant electromagnetic radiation responsive to the excitation signal , such as dyes having a quantum yield of less than about 0 . 01 %. the absorption dye thus acts as an attenuator to limit the depth by which the excitation radiation can penetrate into the coating . by adjustment of the concentration of the absorption dye , the excitation penetration depth can be set . when the coating thickness that is greater than the penetration depth of the radiation is used , it has been found that the coating becomes essentially thickness independent . as used herein , the phrase “ penetration depth ” corresponds to a coating thickness sufficient to provide at least a 90 % attenuation , preferably 99 % attenuation , and most preferably 99 . 9 % attenuation of the excitation signal intensity . fig2 is a schematic depiction regarding operation of an essentially thickness independent coating according to the invention . the absorption dye molecules limit the penetration depth of the excitation radiation . the luminescent dye retains the polarization of the excitation radiation and emits a red shifted luminescent signal . the absorption dye preferably provides absorption in a band distinct from the luminescent signal emitted by the luminescent dye . this limits attenuation of the luminescent signal by the absorption dye which can undesirably reduce the luminescent signal level emitted from the coating . as used herein , “ band distinct ” corresponds to a spacing of the absorption and luminescent peaks of at least 25 nm , preferably at least 50 nm , and most preferably , at least 100 nm . the absorption dye is also preferably soluble in the non - polar solvents generally used to deliver the coating , which is desirable when wet processes such as spraying is used to deliver the coating . suitable absorption dye choices can include , for example , ruthenium - based absorption dyes , such as bis ( 2 , 2 ′: 6 ′, 2 ″- terpyridine ) ruthenium chloride . in one exemplary configuration , bis ( 2 , 2 ′: 6 ′, 2 ″- terpyridine ) ruthenium chloride ( a absorption dye ) and a perylene - based ( pe ) luminescent dye , such as n , n ′- bis ( 2 , 5 - di - tert - butylphenyl )- 3 , 4 , 9 , 10 perylenedicarboximide , are incorporated into an epoxy - based photoelastic overcoat . fig3 shows the absorption spectrum of the coating , with the ru - based dye providing the coating with strong absorption in the blue wavelengths near the wavelength of the excitation radiation λ ex to limit penetration depth of λ ex , but allowing the transmission in the red wavelengths where the luminescent dye emits to maximize signal intensity . the excitation radiation is generally referred to as being “ light ”. as used herein , the term “ light ” refers to electromagnetic radiation having wavelengths both within the visible spectrum and outside the visible spectrum . for example , the invention can generally be practiced with visible , infrared and / or ultraviolet light provided appropriate luminophores and detectors are provided . typical coating thickness is about 200 to 400 μm , but can be thicker or thinner than this typical range of thicknesses . as noted above , the luminescent dye is preferably polarizing preserving . examples of visible light luminescent polarizing preserving dyes are cyanine , rhodamine , coumarin , stilbene , perylene , rubrene , perylene diimide , phenylene ethynylene , and phenylene vinylene . the photoelastic polymer binder preferably comprises at least 20 wt . % of the coating layer , such as 30 %, 40 % 50 %, 60 or 70 % of the coating layer . the polymer binder provides photoelasticity and is preferably substantially optically transparent to the wavelength of excitation radiation used for measuring strain . examples of suitable polymer binders include , but are not limited to , epoxies , polyurethane , polyacrylate , cellulose acetate and poly ( dimethylsiloxane ). a variety of other optically transparent photoelastic materials can be used with the invention , such as polycarbonate or polymethylmethacrylate . preferred materials are optically transparent in the wavelength range of interest , provide high polarization sensitivity , provide high optical sensitivity , have low surface roughness , have low viscosity or alterable viscosity with additives , have good adhesion qualities , and have reasonable curing times and conditions . the strain - optic sensitivity of the coating is represented by the strain - optic sensitivity constant k which defines a fundamental property of the photoelastic material itself , and is independent of the coating thickness or the length of the light path . in order to translate measured intensity data fringe orders in a photoelastic coating into strains or stresses in the coated test object , it is necessary to introduce the strain - optic sensitivity constant of the coating . the strain - optic sensitivity constant k is dimensionless and for typical photoelastic polymers used in the stress or strain analysis of structural materials , varies from 0 . 05 to about 0 . 15 , with the larger coefficients corresponding to the more optically sensitive materials . although a larger strain - optic sensitivity constant k is generally preferred , the invention generally only requires a coating which provides a strain - optic sensitivity constant of at least 0 . 001 , which is primarily provided by the photolelastic polymer binder . there is also a curing epoxy generally added which may have photoelastic properties , but the photolelastic polymer binder component is generally at least ten times greater . for example , the strain - optic coefficient of the coating is generally between about 0 . 75 and 0 . 125 when the bgm polymer is photolelastic polymer binder , the actual value depends on the specific coating mixture used . the structure for the bgm monomer is shown below as structure 1 . formula weight : 312 . 37 g - mol − 1 , mp . − 15 ° c . density : 1 . 19 g - ml viscosity ( 25 ° c .) 2000 - 3000 cps . another exemplary photoelastic polymer material which can be used with the invention is formed from the curing of the bisphenol - a glycerolate diacrylate monomer . the structure for this monomer is shown in structure 2 . this monomer is quite viscous and can be cured by typical acrylate initiators . this epoxy monomer is an acrylate ester and generally shares properties with other acrylate coatings . use of this epoxy monomer can produce an easily applied acrylate coating which has reduced flow after air brush deposition . the structure for the bisphenol - a glycerolate diacrylate monomer is shown below as structure 2 . in one embodiment , a specific photoelastic coating formulation can include bisphenol - a glycerolate diacrylate ( 40 - 60 %), chloroform ( 20 - 30 %), toluene ( 10 - 20 %) and benzoin ethyl ether ( 1 - 8 %), where all values are listed in % by weight . the epoxy coating can be applied to the luminescent undercoat and cured by exposure to uv light for about 1 hour at ambient temperature . although not required to practice the invention , the inventors , not seeking to be bound by theoretical aspects regarding the invention , provide the following . for a conventional dual layer coating where luminescent molecules are dispersed in a separate layer underneath a top photoelastic layer , the governing equations are : i i avg = 1 + ϕ ⁢ ⁢ sin ⁡ ( δ ) ⁢ sin ⁡ ( 2 ⁢ α - 2 ⁢ θ ) , ⁢ where ( 1 ) δ = 2 ⁢ π ⁢ ⁢ kh ⁢ ⁢ γ λ * ( 2 ) λ * = λ ex ⁢ λ em λ ex + λ em ( 3 ) however , for single layer lpc coatings according to the invention , the governing equations are different because the luminescent molecules are dispersed throughout the photoelastic layer as opposed to in a layer underneath the photoelastic layer . thus , both the relative luminescence and the retardation become thickness dependent . the relative intensity of excitation , i ex , at a given depth , y , is modeled using beer &# 39 ; s law as shown in eq . 4 below : where a is the absorbitivity . equation 5 models the effect the excitation attenuation has on the measured intensity response at a specific depth : i ⁡ ( y ) i avg = e - ay ⁡ ( 1 + ϕ ⁢ ⁢ sin ⁡ ( 2 ⁢ π ⁢ ky ⁢ ⁢ γ λ * ) ⁢ sin ⁡ ( 2 ⁢ α - 2 ⁢ θ ) ) . ( 5 ) where the relative retardation , δ , also depends on the thickness . integrated over a depth h , the result is : i i avg = 1 - e - ah a + ϕ ⁡ ( h * γ - e - ah ⁢ h * γ ⁢ ( cos ⁢ γ ⁢ ⁢ h h * + ah * γ ⁢ sin ⁢ γ ⁢ ⁢ h h * ) 1 + ( ah * γ ) 2 ) ⁢ sin ⁡ ( 2 ⁢ α - 2 ⁢ θ ) . ( 6 ) h * = λ * 2 ⁢ π ⁢ ⁢ k . ( 7 ) because both the luminescent and absorption dye are distributed throughout the coating , the osr of the single - layer coating is different compared to the theoretical sin ( δ ) response of the dual - layer coating . fig4 is a plot of the osr with respect to strain as governed by eq . 6 ( h *= 0 . 40 μm , a = 0 . 0056 μm − 1 ). for a set thickness , the osr increases with strain , then peaks and decreases , resulting in a multi - valued strain function . as the coating thickness is increased , the initial region of the osr curves of fig4 converge onto each other , indicating a penetration depth or threshold thickness in which the theoretical osr is essentially independent of thickness . fig5 shows the theoretical difference in strain ( or strain error ) resulting from thickness variations for a coating with a 99 % absorption depth of 360 μm . equation 6 is simplified when h approaches a penetration depth such that e − ah approaches zero : i i avg * = 1 + ϕ ⁡ ( γ η 1 + ( γ η ) 2 ) ⁢ sin ⁡ ( 2 ⁢ α - 2 ⁢ θ ) , ( 8 ) the nondimensional parameter η is a coating characteristic relating the absorptivity per unit depth to the photoelastic depth , η = ah * = a ⁢ λ * 2 ⁢ π ⁢ ⁢ k ( 9 ) and i * avg is the averaged intensity over 180 ° analyzer angle . for the case of an optically thick coating , the peak osr of 0 . 5 occurs when η = γ . in terms of osr ( represented by δ in eq . 10 ), the shear strain in the subfringe region is : γ = η - η ⁢ 1 - 4 ⁢ ( δ / ϕ ) 2 2 ⁢ ( δ / ϕ ) . ( 10 ) advantages of coatings according to the invention compared to traditional photoelastic techniques using thicker coatings and surface contouring may include : 1 . more uniform emission signal at oblique viewing angles , 2 . higher spatial resolution , especially near edges , 3 . simpler post - processing by eliminating phase unwrapping and fringe counting , 4 . less substrate reinforcement , and 5 . lower coating residual strains . the invention is expected to have a variety of applications . coatings according to the invention can be used on virtually all solid materials , including , but not limited to , metallic , ceramic , plastic and composite specimens . the present invention is further illustrated by the following specific examples , which should not be construed as limiting the scope or content of the invention in any way . to test the single - layer concept , aluminum bar specimens — both primed black and unprimed — were sprayed - coated with varying concentrations of the absorption dye within the lpc , ranging from 0 % to 0 . 5 % ru - based absorption dye by weight . the specimen dimensions were 38 . 1 × 3 . 18 × 304 . 8 mm . for each individual specimen , the lpc was sprayed in a manner to create four stepwise regions of increasing thickness from below 100 μm to above 300 μm . the thickness was measured using a contact eddy - current probe . two sample tests were conducted . the first test was an intensity test to demonstrate the effect of the absorption dye on the overall measured luminescent intensity with respect to coating thickness . the second test was a tensile test in which the specimens were subjected to a maximum tensile load 16 . 7 kn , and the osr was measured . for each test , a blue led lamp ( 465 nm center wavelength ) was used to excite the coating . the luminescence was measured , in a darkened environment , with a 16 - bit digital charged - couple device ( ccd ) camera fitted with a bandpass interference filter ( 550 nm center wavelength ) and an f - mount zoom lens . for the osr tests , wavelength - matched polarization and retardation optics were fitted with the blue led lamp to create circular polarized light , and an analyzing optic was placed in front of the ccd emission filter . the optical sensitivity of the coating is ˜ 0 . 1 . at any given load state , including an unloaded state , a sequence of four images were acquired at 45 ° analyzer angle intervals . the images for the unloaded state were used to correct the unloaded signal offset due to residual strains in the coating or unpolarized luminescent reflections . a full description of the general lpc analysis process is described in hubner , j . p ., ifju , p . g ., schanze , k . s ., liu , y ., chen , l ., and el - ratal , w ., “ luminescent photoelastic coatings ,” proceedings of the 2003 sem annual conference and exposition , paper # 263 , june 2003 . fig6 shows the effect of the absorption dye on the measured luminescent intensity from the coating . plotted is the centerline intensity , normalized relative to the ccd full - well capacity , for two black - primed specimens . the thickness of the coating for both specimens increases from left to right as shown . for the 0 . 0 % ru - based adsorption dye specimen , the normalized intensity relative to the ccd full - well capacity increases with increasing coating thickness as indicated by the three distinct steps between the four regions . the gradual roll - off in intensity along a specific region is due to the spatially varying excitation field . the relative change in the intensity for each step is nearly proportional to the relative change in thickness , showing little absorption of the excitation by the luminescent dye or photoelastic coating . contrastingly , the normalized intensity for the 0 . 5 % ru - based absorption dye specimen is relatively constant across the third and fourth regions with a slight drop in the second region . the only clear step in the data is between 85 and 205 μm , indicating that the coating is near optically thick at greater thicknesses . the absorptivity of the 0 . 5 % ru - based absorption dye lpc is 0 . 0074 μm − 1 . this corresponds to a transmission ratio , t , of 3 % or an absorbance , a , of 1 . 5 at 205 μm . not clearly visible in fig6 is the spatial roll - off of intensity for the 0 . 5 % ru - based absorption dye concentration , which is the same relative amount as the 0 . 0 % ru - based absorption dye case . unprimed specimens displayed similar thickness independent characteristics , but the working threshold thickness was greater due to the luminescent reflection off the metallic surface . the consequence of creating an optically thick coating is lower detected emission and thus increased exposure times to use the full dynamic range of the ccd camera . lpc exposure times range between 5 to 90 s depending on coating absorptivity , coating thickness , led placement and power , ccd placement and sensitivity , and lens selection . the following techniques were found to increase the signal - to - noise characteristics of the measurement : 1 . increasing the exposure time , 2 . increasing the number of analyzer angles , 3 . increasing the number of images acquired per load and analyzer image , and 4 . increasing spatial pixel averaging , at the expense of spatial resolution . fig7 shows the osr ( the amplitude of eq . 8 ) with respect to thickness for three specimens ( 0 . 0 %, 0 . 25 %, and 0 . 5 % ru - based absorption dye ). the applied shear strain ( via tensile loading ) was 2600 με . clearly , osr for the specimen without the absorption dye is thickness dependent . for the other two specimens , increasing the ru - based absorption dye concentration decreases the osr . however , osr is thickness independent ( within the noise bounds ) once a threshold thickness is achieved . the working threshold thickness of the lpc is roughly 250 and 200 μm for the 0 . 25 % and 0 . 5 % specimens , respectively , which is lower than the 99 % absorption level . the error bars indicate a 2σ deviation ( 95 % confidence ) of the sample pixel population . the osr at 2600 με for the 0 . 0 % ( 300 μm ), 0 . 25 % and 0 . 5 % specimens were 0 . 127 , 0 . 106 and 0 . 084 , respectively . thus , increasing the absorption dye concentration decreases the optical strain response . this is also expected as shown in eqs . 8 and 9 . if the absorption dye is increased , the absorptivity , a , increases which in turn increases the nondimensional parameter , 72 . a significant finding of the osr measurements is that the strain - dependent response of the single - layer coating is effectively thickness independent once a threshold thickness is achieved . advantages of the single - layer coating include : 1 . thickness independent strain response for optically thick coatings ( target absorbance of ˜ 1 . 7 ( about 98 % absorbance ), 2 . increase in the maximum subfringe strain level due to the distribution of the luminescent dye throughout the coating instead of underneath the coating , 3 . elimination of compliance and adhesion issues due to improper application / cure or modulus mismatch between multiple layer coatings , 4 . and easier coating preparation and application . fig8 ( a ) and ( b ), and fig9 show results from a single layer coating tested on specimens with non - uniform strain fields . fig8 ( a ) and 8 ( b ) are scanned images indicating the maximum shear strain and principal direction distribution for an aluminum isotropic open - hole tension specimen . the 2024 - t6 aluminum specimen was 6 . 4 mm thick and 38 . 1 mm wide . the ratio of the hole diameter to specimen width was 1 : 3 . a tensile load of 19 . 2 kn was applied in the vertical direction . for fig8 ( a ), white and light - gray regions ( up to 5000 microstrain ) near the left and right of the hole indicate high strain areas , and black and dark - gray regions above and below the hole indicate low strain areas . for fig8 ( b ), white , gray and black correspond to + 30 , 0 and − 30 degrees , respectively ( 0 degrees is vertical ). clearly present are the stress concentrations on both sides of the hole as well as regions of shielded stress above and below the hole . high stress regions radiate out as lobes along diagonal axes as expected . fig9 provides shear strain results from a comparison test on an anisotropic material . the unidirectional composite specimen was made of as4 / 3501 - 6 ( 24 plies ). the ratio of hole diameter to specimen width was 1 : 4 ; the maximum load was 4 . 5 kn . instead of the shear strain contours radiating from the hole at approximately 45 °, the high stress regions radiate out in the vertical directions from the sides of the hole . additionally , the maximum shear strain is not along the horizontal axis passing through the center of the hole , but rather , located just above and below this axis . this is due to the compliant shear planes associated with the unidirectional laminate . the maximum shear strain is approximately four times higher than the average shear strain across the axis of minimum area . this invention can be embodied in other forms without departing from the spirit or essential attributes thereof and , accordingly , reference should be had to the following claims rather than the foregoing specification as indicating the scope of the invention .