# Low frequency coherent Raman imaging robust to optical scattering

David R. Smith  Morgridge Institute for Research, Madison, WI  Jesse W. Wilson
Department of Electrical Engineering, Colorado State University, Fort Collins,
CO  Siddarth Shivkumar  Department of Physics, University of Ottawa, Ottawa,
Ontario K1N6N5, Canada  Hervé Rigneault  Aix Marseille Univ, CNRS, Centrale
Med, Institut Fresnel, Marseille, France.  Randy A. Bartels
<EMAIL_ADDRESS>Morgridge Institute for Research, Madison, WI
Department of Biomedical Engineering, University of Wisconsin, Madison, WI

###### Abstract

We demonstrate low-frequency interferometric impulsive stimulated Raman
scattering (ISRS) imaging with high robustness to distortions by optical
scattering. ISRS is a pump-probe coherent Raman spectroscopy that can capture
Raman vibrational spectra. Recording of ISRS spectra requires isolation of a
probe pulse from the pump pulse. While this separation is simple in non-
scattering specimens, such as liquids, scattering leads to significant pump
pulse contamination and prevent the extraction of a Raman spectrum. We
introduce a robust method for ISRS microscopy that works in complex scattering
samples. High signal-to-noise ISRS spectra are obtained even when the pump and
probe pulses pass through many scattering layers.

Coherent Raman, Raman spectroscopy, nonlinear optics, nonlinear microscopy

††preprint: AIP/123-QED

##  I Introduction

Chemical imaging is a powerful imaging modality in the biological sciences.
While fluorescent imaging with exogenous fluorescent probes or transgenically
expressed fluorescent proteins forms the workhorse for chemical imaging in
biological specimens [1], limitations of fluorescent imaging technologies have
driven the development of label-free imaging modalities. [2, 3, 4, 5, 6, 7, 8]
Of the many label-free imaging modalities, microscopy based on Raman
scattering remains particularly appealing due to the narrow Raman vibrational
spectroscopic lines that permit reliable identification of molecular species.

The vibrational frequency of materials and molecules offers a powerful means
to both identify them and probe their dynamics and interactions. [5] Spectral
features of the vibrational spectrum can be optically interrogated through
either direct dipole-allowed transitions with infrared Raman spectroscopy or
through inelastic Raman scattering. Raman scattering is often preferred
because infrared spectroscopy suffers from interference from water absorption,
broad spectral features, and low spatial resolution resulting from the use of
long optical wavelengths. [8] That said, while Raman microscopy with
spontaneous scattering is common for many applications, the weak Raman
scattering cross-section and incoherent nature of spontaneous Raman scattering
severely limit the rate of scattered signal detection—leading to long
integration times and poor sensitivity to low concentrations of Raman-active
molecules. Raman signals can be enhanced by stimulating the Raman transitions,
either by introducing near-field enhancements or by directly stimulating the
transitions with a Stokes laser field. Coherent Raman scattering (CRS) [2]
overcomes the weak Raman signals by invoking stimulated Raman scattering to
drive a much larger response, enabling video-rate CRS microscopy. Moreover, an
improved detection sensitivity for low concentration and weak Raman scattering
modes is obtained with techniques that leverage homodyne interference,
producing a linear dependence of the CRS signal on concentration [2, 9, 10].

Raman vibrational frequencies carry extremely valuable information for the
study of molecules and material systems. Vibrational frequencies,
$\Omega_{v}$, scale as a harmonic oscillator, $\Omega_{v}^{2}=k/m$. Thus,
strong binding, associated with a large value of the effective force constant
$k$, and low (reduced) mass, $m$, of the vibrational mode correspond to high
vibrational frequencies. The highest frequency modes are approximately
localized and correspond to hydrogen bonds due to the low hydrogen mass and
are used in investigations of water and lipids. The mid-band frequencies,
$\Omega_{v}\sim 400-1200$ cm-1, are extremely powerful for the identification
of particular molecules [2] and even for bacterial classification. [11] Recent
attention has focused on the largely neglected low-frequency vibrational
modes. [9] These modes are generally associated with large reduced mass and
correspond to vibrational motion that occurs over an extended region. Such
relevant motions include virus capsid vibrations, [12] deformations of
proteins, [13] and mechanical properties of solids, particularly for soft [14]
and two-dimensional materials. [15, 16]

However, implementation of Raman scattering at low vibrational frequencies
remains a persistent challenge [9] because inelastic scattering at small
offsets is difficult to measure, requiring low noise, narrow linewidth lasers,
multiple stages of monochromators, and extremely steep spectral edge filters.
The result is that imaging is extremely challenging. In this Letter, we
introduce a simple and robust technique that is suitable for imaging in
complex specimens. Our approach makes use of impulsive stimulated Raman
scattering (ISRS) to probe low-frequency vibrational modes with time-domain
spectroscopy.[9] In ISRS, a short pump pulse is used to drive the excitation
of vibrational coherences for vibrational frequencies lower than $\sim
1/\tau_{p}$, where $\tau_{p}$ is the pump pulse duration. [17] Because the
Raman interaction involves a change in molecular polarizability with
vibrational displacement, excitation of vibrational coherences produces an
effective time-varying perturbation to the linear optical susceptibility
denoted by $\delta\chi_{\rm eff}(t)$. [9] The Raman spectrum is obtained by
recording signals with a probe pulse that follows behind the pump pulse by a
delay of $\tau$. The recorded signals are derived from the temporal phase,
$\phi_{v}(t)$, accumulated by the probe pulse as it propagates through the
excited vibrational coherence. This recovered spectrum is continuous and spans
a range with a maximum frequency on the order of $1/\tau_{p}$ down to a
minimum frequency $1/\Delta\tau$ bounded by the range of pump-probe delay
$\Delta\tau$.

The readout method of the Raman spectrum in ISRS impacts the sensitivity of
spectral detection. [9] The most common technique is to make use of a spectral
shift for detection, where spectral scattering from the time-dependent phase
modulation applied to the probe pulse by the transient effective linear
optical susceptibility leads to changes in power transmitted through a
spectral filter. [18, 19, 20, 21] Improved detection sensitivity can be
achieved by turning the probe pulse spectral shift into a change in arrival
time at a detector by applying additional spectral dispersion. [22] Methods
that detect the signal based on a spectral shift reduce the amplitude of the
low-frequency vibrational modes and impart a spectral filter on the relative
amplitudes of the Raman spectrum. To emphasize the low-frequency vibrational
modes and eliminate the spectral distortions imparted by frequency shift
detection, $\delta\chi_{\rm eff}(\tau)$ should be probed directly. [9]

Low frequency vibrations can be readily detected with ISRS methods where the
signal detection is directly proportional to the time-varying change in the
optical susceptibility induced by the forced Raman response. Several methods
have been explored for the direct measurement of $\delta\chi_{\rm eff}(t)$ to
obtain an undistorted Raman spectrum, which we call phase-sensitive ISRS (ps-
ISRS). ps-ISRS spectroscopy was originally implemented in a transient grating
geometry, [17] which allows for background-free measurements but relies on
direct measurement of the diffracted beam power, leading to limited detection
sensitivity. In the transient grating experiment, the amplitude of the
diffracted probe field is proportional to $\delta\chi_{\rm eff}(\tau)$, i.e.,
the susceptibility perturbation at the pump-probe delay $\tau$. However,
because the total scattered power is recorded, the Raman spectrum is
distorted. The direct amplitude of $\delta\chi_{\rm eff}(\tau)$ can be
obtained with Kerr lensing [23] and interferometric measurements. [24, 25, 26,
27] A comparison of the Raman spectral amplitudes has been demonstrated in a
Sagnac interferometer configuration and verified the access to low-frequency
vibrational spectral information when $\delta\chi_{\rm eff}(t)$ is directly
obtained. [24] The Sagnac interferometer configuration is intrinsically
stable, but has limited application for spectroscopic or imaging measurements.
A stable common path interferometer configuration is possible with a collinear
time-delayed probe and reference pulse configuration, [28, 29] which has been
demonstrated with spectral interferometry [25, 26, 27] and Fourier transform
interferometry. [30]

Figure 1: Common path interferometric ps-ISRS concept figure. a) Experimental
setup for ps-ISRS. The acousto-optic modulators, calcite crystals, and linear
polarizer are represented by the purple, green, and orange elements,
respectively. b) Conceptual figure that shows the interaction of the pump,
probe, and reference pulses with the sample, as well as the isolation of the
probe-reference pair and re-timing to produce pulse interference. The
interference produces signal current changes in a photodiode that are
proportional to the Raman-induced transient phase, $\phi(\tau)$, at the
arrival time, $\tau$, of the probe pulse. c) The relative arrival time of the
pump, probe, and reference pulses. d) Example Raman spectra measured in BGO
for ps-ISRS and spectral shift detection [31]. The improved low-frequency
Raman detection with ps-ISRS is evident.

##  II Concept

Unfortunately, the existing ps-ISRS methods are restricted to non-depolarizing
and non-scattering samples such as liquid-phase spectroscopy or transparent
crystals. In this Letter, we introduce a simple collinear interferometric
approach to ps-ISRS that is extremely stable and thus performs robustly in the
presence of strong scattering and depolarization effects, such as in cell
culture and tissues.

A conceptual schematic of the experimental system is shown in Fig. 1. A
modelocked ultrafast laser produces pulses that are passed through a spatial
light modulator pulse shaper for second and third order dispersion control.
The laser beam power is split into pump and probe pulses in an orthogonally
polarized Mach-Zenhder interferometer. The pump pulse intensity is modulated
by an acousto-optic modulator to allow for lock-in amplifier detection of the
Raman signal. A computer-controlled resonant delay scanner in the pump arm
enables rapid scanning of the relative pump-probe delay $\tau$. The probe
pulse arm is modified from a standard pump-probe experimental arrangement [19,
32, 21] in order to generate a probe-reference pulse pair with a birefringent
optical crystal. [29]

Birefringent crystals are used both as a pulse pair generator [29, 33, 19] and
a pulse retimer to create a common path collinearly propagating probe-
reference pulse pair with an extremely stable relative phase and a temporal
separation of $T$, as shown in Fig. 1b. The probe-reference pair is generated
by sending a linearly polarized probe pulse through a birefringent crystal
plate rotated so that the eigen-polarization axes are at 45 degrees with
respect to the input linear polarization of the probe pulse. Depending on the
cut of the crystal and the orientation of the optic axis, the relative delay
time, $T$, can be adjusted by rotating the birefringent crystal or by
adjusting the crystal thickness. The pulses are separated by a few picoseconds
and share a common propagation path.

To combine the probe-reference pulse pair with the pump pulse, the probe-
reference pair is projected onto the same linear polarization axis in the
polarizing beam splitter where the pulse pair is combined with the
orthogonally polarized pump pulse. The pulses are focused into the sample with
a high numerical aperture aspheric lens and recollimated with an identical
aspheric lens after passing through the specimen. The pump pulse is removed
from the collimated beams with a polarizer to isolate the probe-reference
pulse pair.

The coherent ISRS signal is contained in a phase perturbation, $\phi_{v}(t)$,
induced by the pump pulse. The reference pulse precedes the pump pulse,
accumulating a phase as it propagates through the optical system. This phase
accumulated by the reference pulse comes from the sample at equilibrium
because the vibrational coherences decay to equilibrium (over several
picoseconds), long before the next pulse in the oscillator pulse train arrives
($\sim 10$ ns). By contrast, the probe pulse arrives at a delay, $\tau$, after
the pump pulse and accumulates a phase identical to the reference pulse in
addition to a phase perturbation induced by Raman excitation by the pump
pulse. By placing the pump pulse in between the reference and probe pulses,
the relative phase between the probe and reference pulses is the accumulated
vibrational phase perturbation acquired by the probe pulse. After interacting
with the sample, the probe-reference pair is isolated from the pump pulse—for
example with a polarizer—then the probe-reference pulse pair is re-timed. In
this way, the relative phase is converted to an amplitude modulation through
interference between the probe and reference pulse so that the Raman signal is
detected with a simple photodiode.

This pulse pair is re-timed using a second birefringent crystal that is
oriented at –45 degrees to undo the probe-reference delay so that the probe
and reference pulses overlap in time, i.e., setting $T=0$. Because the probe-
reference pulse pair propagates along the same direction and are only
separated by a few picoseconds, $T\sim 6$ ps, the relative phase between these
two pulses is exceptionally stable—allowing very stable phase measurements of
the transient phase introduced by the pump pulse. The probe and reference
pulses are in the same spatial mode and polarization state; only half of the
power of the probe and reference pulses is overlapped in time and will
interfere (see Fig. 1 b)). In addition, the two pulses travel through exactly
the same optical path, and thus share the same spatial mode, making
interference between the beams robust to perturbations acquired with
propagation through optical scattering environments. To demonstrate the
robustness of our approach, we introduce controlled scattering to a sample by
adding layers of parafilm on the sample between the objective and the sample
of interest. For a more detailed description of the experimental setup, please
refer to the supplementary information.

The interferometric signal for ISRS spectroscopy emerges from the fact that
the pump pulse excites a non-equilibrium time-varying change in effective
linear optical susceptibility, $\delta\chi_{\rm eff}(t)$, imparting a
transient phase modulation on a time-delayed probe pulse. The reference pulse
can be arranged to arrive before the pump pulse so that the only phase that it
accumulates is from the optical system and the specimen at thermal
equilibrium. The pump pulse-induced phase perturbation, $\phi_{v}(t)=k_{\rm
pr}\,\ell\,\delta\chi_{\rm eff}(t)/2n_{0}$, is then the only phase shift
acquired between the probe and reference pulses. Here, $\ell$ is the focal
interaction length, $n_{0}$ is the sample refractive index at thermal
equilibrium, and $k_{\rm pr}=2\,\pi/\lambda$ is the free-space wavenumber for
a pulse with center wavelength $\lambda$. The fact that the probe and
reference pulses are common path means that all accumulated scattering,
aberrations, and depolarizations are identical for both beams. This produces
an extremely stable signal that prevents many forms of technical noise.

Figure 2: ps-ISRS data from multiple samples with low frequency Raman
vibrations. The left column shows the time-resolved signal for each sample and
the right column shows the corresponding Raman spectrum.

The phase modulation due to the excited vibrational coherence can be expressed
as a linear superposition of the phase modulation from each excited
vibrational mode as $\delta\phi^{v}(\tau)=\sum_{v}\delta\phi_{0}^{v}\
h_{v}(\tau)$, and depends on the arrival time $\tau$ of the probe pulse after
the excitation induced by the pump and is summed over the contribution of each
vibrational mode, denoted with a superscript $v$. Each vibrational mode is
excited through an impulsive forced Raman response that is driven by the pump
pulse, leading to a damped causal oscillation [10, 9],
$h_{v}(t)=\Theta(t)\,\exp(-\Gamma_{v}\ t/2)\,\sin(\Omega_{v}t)$. Here
$\Theta(t)$ is the Heavyside step function that ensures causality and
$\Gamma_{v}$ is the damping rate of the mode at the vibrational frequency
$\Omega_{v}$. The induced vibrational phase perturbation
$\delta\phi_{0}^{v}=g_{f}\,\mathrm{Im}[\chi^{(3)}_{\mathrm{V}R}(\Omega_{v})]\,\Gamma_{v}\,\tilde{D}(\Omega_{v})\,\bar{p}_{\rm
pu}$ scales linearly with the average power of the pump pulse, $\bar{p}_{\rm
pu}$, and the molecular concentration, $N$, which becomes clear when we note
that
$\mathrm{Im}[\chi^{(3)}_{\mathrm{V}R}(\Omega_{v})]=N\,(\partial\alpha/\partial
Q)^{2}_{0}/6\epsilon_{0}\,\Gamma_{v}\,\Omega_{v}$. The amplitude of the Raman-
induced phase modulation is also proportional to the power spectral density
(PSD) of the pulse intensity profile at the vibrational frequency $\Omega_{v}$
[31, 34], $\tilde{D}(\Omega)=\mathcal{F}\\{I(t)\\}/I_{0}\,\tau_{0}$. Here
$I_{0}$ is the peak pulse intensity and $\tau_{0}=\int I(t)/I_{0}\,dt$ is a
measure of the pulse duration. In the limit of an impulsive pump pulse,
$I(t)=I_{0}\,\delta(t)$, then the excitation PSD,
$\tilde{D}(\Omega)\rightarrow 1$, so that the forced Raman response is the
impulse for vibrational excitation. Here, we assume that the temporal
duration, $\tau_{p}$, and the temporal intensity, $I(t)$, of the pump, probe,
and reference pulses are all identical. The coherent Raman excitation that
drives the vibrational phase perturbation also depends on the focusing
conditions, which are encapsulated in the focusing parameter
$g_{f}=12\,\pi\,\ell/(n^{2}\,\epsilon_{0}\,c\,\nu_{R}\,\mathcal{A}_{f}\,\lambda)$,
where $\mathcal{A}_{f}$ is the focal beam cross sectional area, $\nu_{R}$ is
the laser repetition rate frequency, and $\lambda$ is probe pulse center
wavelength.

Figure 3: a) A composite image of the three low-frequency Raman-active optical
phonon modes in an anthracene crystal. b) The Raman spectrum of the crystal at
a single pixel centered in the orange square shown in a). c–e) Individual
images of the three Raman modes indicated in b). f) The signal-to-noise ratio
(SNR) of the three Raman vibrational modes of a BGO crystal with scattering
layers added between the sample and the excitation objective. A high SNR is
indicated for $>10$ scattering lengths. g) A comparison of the Raman spectrum
of BGO for zero and 12 scattering layers shows high quality spectra extracted
even under conditions of strong optical scattering.

##  III Results

In our experiment, the probe-reference pulse pair, with a total average power
of $\bar{p}_{\rm pr}$, is isolated from the pump pulse using polarizer to
block the pump pulse. Then, half of the probe and reference pulse average
power is adjusted to interfere in a compact, collinear interferometer using an
angle-tuned birefringent crystal. The relative phase of probe and reference
pulses are adjusted to be in quadrature so that the total power of the
interfering pulses is $\bar{p}_{\rm int}=\bar{p}_{\rm
pr}\left\\{1+\sin[\delta\phi^{v}(\tau)]\right\\}/2$ , leading to a signal
power incident on the detector of $\bar{p}_{\rm
sig}(\tau)=\delta\phi^{v}(\tau)\ \bar{p}_{\rm pr}/2$, with a background power
equal to the total average probe pulse train power $\bar{p}_{\rm
bkg}=\bar{p}_{\rm pr}$. In the shot noise limit, the signal-to-noise ratio
(SNR) for a detection integration time of $\Delta t$ reads
$\mathrm{SNR}=(\delta\phi^{v}/2)\ \Upsilon\ \sqrt{\Delta t}$, where
$\Upsilon=\sqrt{\mathcal{R}\ \bar{p}_{\rm pr}/e}$, $\mathcal{R}$ is the
detector responsivity, and $e$ is the elementary charge. Provided that the
total probe power exceeds approximately 2 mW, the shot noise limit is valid
for lock-in detection that is able to largely avoid the laser intensity
fluctuation noise. Because both the signal power and SNR depend linearly on
$\delta\phi^{v}$, this collinear interferometric method is sensitive to low
Raman vibrational frequencies, and is limited where the impulsive Raman
excitation strength, $\tilde{D}(\Omega_{v})$, becomes too low, which occurs
when the vibrational period is on the order or larger than the pump pulse
duration.

The ps-ISRS spectrum of the low-frequency optical phonon Raman spectrum in BGO
is shown in Fig. 3d in comparison to a spectral shift measurement. The
increased amplitude at low vibrational frequencies is apparent in the
interferometric measurement. Because the pump-probe delay $\tau$ can be
controlled independently of the separation between the probe and reference
pulses, which is a fixed delay $T$, there are three zones for the ps-ISRS
experimental system, each of which is illustrated in Fig. S2. We define the
time-frame so that $t=0$ occurs at the center of the pump pulse The first
pulse to arrive is denoted the reference pulse that is incident at at a time
$t=\tau-T$ and the probe pulse arrives at a time $\tau$. Zone I occurs when
$\tau<0$, so that both the probe and reference pulses arrive before the pump
pulse. In this region, there is no pump-induced transient phase acquired
between the probe and reference pulses, so we have a null signal. Zone II is
where we pull the Raman spectra; this temporal signal provides a pure Raman
spectrum because only the probe pulse accumulated the Raman-induced phase
shift. In Zone III, the spectrum is distorted because the interference signal
is determined by the phase shift acquired by the probe and reference pulses,
i.e., $\phi(\tau)-\phi(T-\tau)$.

Inteferometric ps-ISRS spectra from several samples displaying low-frequency
Raman modes are shown in Fig. 2. While the chloroform and tetrabromoethane are
liquid samples and do not suffer depolarization, the cadmium tungstate is a
birefringent crystal and induces a depolarization between the pump pulse and
the probe-reference pulse pair. The time-domain traces are shown on the left
column, whereas the Raman spectra shown in the right column is computed from
the power spectral density of the time-domain trace after isolation of the
signal that contains only the Raman transients away from the cross phase
modulation feature near time zero. [27] The observed Raman spectral modes
match known Raman spectral lines of these three samples.

Hyperspectral Raman images of anthracene crystals for three low-frequency
Raman-active optical phonon modes are shown in Fig. 3. The Raman spectrum of
the optical phonon modes is shown in Fig. 3b. Images for the three phonon
modes marked in the spectrum are shown in Fig. 3c-e, whereas a composite image
is displayed in Fig. 3a. The complex morphology of the crystals produces
scattering that distorts the beams and degrades the Raman signal. However, we
see that high-quality images are obtained with the common-path interferometric
readout because the probe and reference pulses maintain identical spatial and
polarization modes.

To quantitatively evaluate the effect of optical scattering on ps-ISRS with
common-path interferometric detection, we captured Raman spectra as we added
layers of optical scattering material. For each measurement, the Raman signal
and the noise were estimated from the temporal trace, from which we computed
the SNR. To introduce optical scattering, layers of parafilm were added on the
front of the BGO sample, thus introducing scattering before Raman excitation
by the pump pulse and spectral scattering of the probe pulse. Results are
shown in Fig. 3f, displaying the SNR as a function of the number of scattering
layers added between the sample and the excitation objective. The data show
two regions of SNR decay as a function of the number of scattering lengths,
indicated by dashed lines in the figure. The Raman spectra for the highest and
lowest SNR data are shown in Fig. 3g.

##  IV Discussion

Imaging of low-frequency vibrational modes with coherent Raman remains a
challenging prospect. Here we introduce a new imaging strategy for a wide
bandwidth of Raman vibrational frequencies, spanning from very low frequencies
($<300$ cm-1) to frequencies well within the fingerprint region $>1000$ cm-1.
Our new strategy relies on a pump-probe geometry using ps-ISRS excitation of a
vibrational coherence by a short pump pulse that is electronically non-
resonant with the specimen. Such short pulse excitation is capable of exciting
vibrational frequencies with periods that are longer than the pump pulse
duration. [31] As a result, short laser pulses with carefully maintained
dispersion compensation are critical for ISRS excitation. After excitation of
the vibrational coherence, the readout of the signal with a probe pulse plays
a crucial role in the vibrational frequencies that are observed. The
conventional strategy is to use a spectral edge filter to convert the spectral
scattering driven by the transient phase modulation acquired by the probe
pulse when propagating through the vibrational coherence into a change in
probe pulse power transmitted through the spectral filter. [19, 35]
Unfortunately, this simple strategy renders ISRS largely insensitive to low-
frequency vibrations. [9] By reading out the phase directly through
interferometry, we directly detect the time domain-forced Raman response,
providing sensitive detection of the low-frequency Raman vibrational modes.

Aside from the high sensitivity to low-frequency vibrational modes (e.g.,
terahertz Raman), we have demonstrated that our common-mode strategy for the
detection of the transient Raman phase modulation produces high SNR data even
in the face of optical scattering. This resilience of our signal detection to
optical scattering follows from two properties that we acquire by generating
the probe-reference pair in a suitably oriented birefringent crystal. The
first property is that the probe and reference pulses are common path. Because
of this common path propagation, any scattering that is encountered is common
to both the probe and reference pulse beams. As a result, the beams are
guaranteed to still interfere. Indeed, even depolarization is not a problem,
as the spatial modes of the probe and reference beams are identical—ensuring
stable interference even after becoming severely distorted, as they are
distorted identically.

Of course, common path perturbations are only relevant if the relative phase,
scattering, and depolarization are stable for the duration of the integration
time over which the interference is acquired. The relative stability of the
probe and reference pulses is guaranteed by the fact that there is very little
perturbation of the refractive index of the specimen that can occur on the
timescale of a few picoseconds other than the non-equilibrium vibrational
coherence dynamics that are excited with the pump pulse.

The combination of the temporal and common-mode interferometric stability
ensures extremely stable and high-sensitivity detection of the vibration-
induced phase shift. The robustness of our approach is demonstrated by
introducing controlled scattering to a sample by adding layers of parafilm on
the sample between the objective and the sample of interest. The scattering
introduced by the parafilm layers was characterized by measuring power
transmission through a blank sample as more layers of parafilm were added. The
power transmitted through the scattering layers decreases exponentially with
the number of scattering layers. The scattering length, defined as when the
optical power decreases by $1/e$, was found to be $\ell_{s}=1.29$ parafilm
layers. Figure 3f shows the SNR for the three main vibrational modes of BGO as
a function of scattering length of parafilm added to the sample. Panel (g) of
Figure 3 shows the time-resolved signal and the Raman spectrum (inset) of BGO
with no scattering layers (orange) and the signal with the maximum number of
scattering layers used (blue), which is 12 layers of parafilm, or 9.34
scattering lengths. This result shows the robustness of the interferometric
Raman technique, with the SNR of the BGO modes remaining high after 9.34
scattering lengths. The incident optical powers at the sample were
$p_{pu}=37.8$ mW and $p_{pr}=38.95$ mW for the pump and probe, respectively.
After passing through the sample, objectives, retiming crystal and analyzing
polarizer, the probe power incident on the detection photodiode was
$p_{pr}=8.6$ mW with no scattering present. The probe power incident on the
detection photodiode was measured to be $p_{pr}=7.7$ $\mu$W with 12 parafilm
layers (9.34 scattering lengths).

Because we have constructed this system based on orthogonally polarized pump
and probe-reference pulses, we are limited to vibrational modes with a more
symmetric character, and we may have reduced sensitivity to asymmetric modes.
The spectral resolution of this strategy is limited to $\sim 1/T$ for methods
that rely on power spectral estimation, e.g. the FFT or multitaper
computation. However, the use of model-based estimation, e.g. LP-SVD, can
circumvent this spectral resolution limitation. The lower bound of the
vibrational frequency is limited by the scan range of the probe-reference
pair. For Zome II, the lower bound is $\tilde{\nu}=(c\,T)^{-1}\sim 7$ cm-1,
but this can be extended arbitrarily with synthetic aperture scanning [25],
where the probe and reference pulse pair both follow the pump pulse, at the
cost of the loss of frequencies with vibrational periods that are an integer
multiple of $T$. Application of LD-SVD methods are expected to further improve
this lower bound.

##  V Conclusions

We have developed a new and versatile method for low-frequency coherent Raman
imaging. Balanced detection could eliminate the need for the acousto-optic
modulator for beam intensity modulation, which will drastically reduce the
spectral dispersion burden of the system. Such an approach would allow for
easier use of high numerical aperture objective lenses that also carry a high
dispersion. Right now, the relatively low numerical aperture and off-axis
aberrations of the aspheres have limited our ability to image in complex
samples, and the long working distance makes thin samples such as two-
dimensional materials challenging to image. Future advances will explore
additional strategies to simplify the imaging approach.

###### Acknowledgements.

We are grateful for the help of Dekel Raanan and Maor Asher for crystal
synthesis as well as Dan Oron for helpful discussions and assistance with
sample. We are grateful for funding from DE-FOA-0002603 (Bartels). Alicia
Williams from the Morgridge Institute provided scientific editing support.
ANR-21-ESRS-0002 IDEC, EU ICT 101016923 CRIMSON, EU EIC 101099058 VIRUSONG, EU
ERC 101052911 (Rigneault). NIH 5 R21GM135772-02 (Wilson and Bartels)

##  Appendix A Appendixes

##  Appendix B ps-ISRS experimental system

The experimental layout for the system is provided in Fig. 4. The key to a
robust ps-ISRS imaging is the production of common-path probe and reference
pulses.[28, 29, 36] This pulse pair is generated in the experimental system
that builds on a pump-probe experimental system using a Mach-Zehnder
interferometer.[21] In addition, because we are using an ISRS interaction with
broad-bandwidth ultrafast pulses, careful dispersion management is required.
Pulses are generated in a Ti:sapphire laser (KM Labs Halcyon, $\sim~{}600$ mW
average power, $\sim 18$ fs pulses, 94 MHz repetition rate). The output laser
beam is collimated and then directed into a pulse shaper constructed from a
folded Martinez stretcher with a flat mirror and a transmission spatial light
modulator (SLM) placed at the focal plane of the lens (the Martinez Fourier
plane). [37, 38] Details of the pulse compression protocol can be found in the
supplemental information in our recent split-spectrum ISRS paper. [21]

After passing through the pulse shaper, the beam is split into pump and probe
(reference) pulses with a low-dispersion polarizing beam splitter (ATFilms,
PBS1005-GVD). The relative power in the two arms is controlled by a half-wave
plate placed before the beam splitter. An acousto-optic modulator (AOM)
crystal resides in each arm of the pump-probe interferometer. In the pump arm,
the pump pulse is passed through an AOM that imparts a sinusoidal intensity
modulation onto the pump pulse train for lock-in detection. The pump pulses
are modulated at several MHZ to allow for detection of the signal through
lock-in detection at an offset frequency where intensity noise fluctuations
from the laser are low. The AOM in probe arm is left passive and is required
to balance the spectral dispersion in the two interferometer arms. The pump
and probe pulses are recombined with a second low-dispersion polarizing beam
splitter. A reflective optical delay line in the pump pulse arm is used to
control the relative arrival time, $\tau$, of the pump and probe pulses. The
pump-probe delay is rapidly scanned with a resonant scanner delay line
(Peregrine, Mesa Photonics) that is capable of performing 20 ps delay scans at
60 Hz. The full delay is scanned with a triangle pattern that produces full
ps-ISRS signal traces at a rate of 120 Hz. A full Raman spectrum is obtained
in $\sim$8.3 ms. The Raman spectrum is obtained from the temporal trace by
either estimating the spectrum of the temporal trace with a fast Fourier
transform through linear prediction singular value decomposition. [25, 33, 39]

Figure 4: Experimental layout. a) Pump-probe experimental layout with an
ultrafast pulse laser, and ultrafast pulse shaper, and a orthogonal, linearly
polarized Mach-Zehnder interferometer. b) Illustration of the oriented
uniaxial crystal that is used to produce a very stable probe-reference pulse
pair from a single probe pulse. The pulse pair never propagates in free space
ans are only delayed by a few picoseconds. Thus, the relative phase stability
is extremely robust. c) When the pump pulse and probe-reference pulse pair are
recombined on the output polarizing beam splitter, the probe-reference pulses
are projected onto the same linear polarization direction that is
perpendicular the the linearly polarized pump pulse direction. d) After the
probe and reference pulses are re-timed, we have a set of three pulses, where
the middle pulse comes from the interference of the probe and reference pulses
and the two satellite pulses are the residual pulses projected onto the
analyzer polarization direction.

To enable ps-ISRS detection, the probe pulses are temporally split into a pair
of orthogonally-polarized probe and reference pulses. The probe and reference
pulses are created by sending the linearly polarized probe pulse into the
birefringent crystal (10mm thick calcite, Newlight Photonics) with the crystal
rotated so that the axis of the linear polarization of the probe pulse is at
45 degrees with respect to the eigen-polarization axes of the ordinary and
extraordinary polarization directions. [28, 29, 36, 25, 38, 26, 19, 30] The
group velocity of the pulses that are projected onto the ordinary and
extraordinary polarization directions differ, leading time delay accumulated
through propagation through the uniaxial birefringent crystal. The rotation
angle of the optical axis of the crystal can be adjusted to fine-tune the
relative delay and the relative phase between the probe and reference pulses.
Then the probe-reference pair is combined with the pump pulse in the
polarizing beam splitter, the pulses are projected on the same linear
polarization with equal amplitude. The pump pulse is orthogonally polarized to
the probe-reference pair. An identical birefringent crystal is placed in pump
arm to mach the dispersion between the arms.

The combined and orthogonally polarized pump and probe-reference pulses are
focused into the with a low-dispersion aspheric lens (40x/0.6 NA, Newport).
Typical pump/probe powers at the focus are $p_{pu}=38\textrm{ mW}$,
$p_{pr}=19.5\textrm{ mW}$, and $p_{ref}=19.5\textrm{ mW}$. After passing
through the sample, the beams are collimated with a matching asphere. Once the
probe-reference pulse pair is isolated with a polarizer, the time-delay is
collapsed with a birefringent crystal oriented in the opposite direction of
the original probe-reference pulse pair generator. The relative delay between
the pulses is set to zero by adjusting the crystal angle to tune the relative
delay to zero. The crystal angle is fine-tuned to adjust the relative phase so
to $\pi/2$ or $-\pi/2$ to provide optimal sensitivity to the small phase shift
accumulated by the probe pulse. After passing through an analyzing polarizer,
the pulses interfere and convert the phase shift accumulated by the probe
pulse to an amplitude modulation of the pulse interference. Note that because
the probe and reference pulses were polarized along the same direction, each
pulse is projected onto the ordinary and extraordinary polarization
directions, so that half of the field amplitude for each pulse is further
delayed in time. This is illustrated in Fig. 4d). The ps-ISRS signal is
detected by an amplified photodiode (Thorlabs, PDA36A2) that is directed into
a lock-in amplifier (Zurich Instruments, HF2LI).

Figure 5: a) Three zones of probe-reference pulse delays pump probe
interferometry. In zone I, the probe and the reference pulses arrive before
the pump pulse. Thus the probe and reference beams experience the same thermal
equilibrium phase, so there is zero phase difference between these pulses, and
thus no signal. In zone II, the reference pulse arrives before the pump pulse.
Next the pump pulse arrives and excites the Raman vibrational coherence that
are proved by the probe pulse. Thus, the phase difference that produces the
signal is from non-equilibrium phase perturbation induced by the pump pulse.
Finally, in zone III, both the reference pulse and the probe pulse arrive
after the pump pulse. The phase difference depends on the difference in the
non-equilibrium phase probed by reference and probe pulses. b) The power
spectrum estimated from Zone II gives the Raman spectrum. The probe and
reference pulses are linearly polarized along the same direction and
perpendicular to the linear pump polarization. c) Illustrates Zone I where
both probe and reference pulses arrive before the pump pulse. d) Illustrates
Zone II where the pump pulse arrives in-between the probe and reference
pulses. e) Illustrates Zone IIII where the probe and references pulses arrive
after the pump pulse.

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Two-Layer Dispersion of Air Pollutants: Optimal Measure and Control

PhD Research Proposal in Mathematics

by

Eeshwar Prasad Poudel

MSc Mathematics, TU

Devdaha-2, Rupandehi, Nepal

Supervisor: Dr. Shreeram Khadka
Associate Professor, Central Department of Mathematics
Tribhuvan University, Kirtipur, Kathmandu, Nepal
Co-supervisor: Dr.Jeevan Kafle
Assistant Professor, Central Department of Mathematics
Tribhuvan University, Kirtipur, Kathmandu, Nepal

Submitted to

University Grants Commission (UGC)
Sanothimi,Bhaktapur,Npal

December 2023

Two Layer Dispersion of Air Pollutants: Optimal Measure and Control
Abstract:
Air pollution is a mixture of harmful solid particles, gases and other
pollutants in the air. It is one of the biggest problems in both developed and
developing countries. Nowadays, More than 90% of the world population is
exposing unhealthy air. Long-term health effects from air pollution include
heart disease, lungs cancer, and respiratory diseases such as emphysema. Air
pollution can also cause long-term damage to people’s nerves, brain, kidneys,
liver, and other organs. Some scientists suspect air pollutants cause birth
defects. So, to make the lives of almost all of the things i.e; both living
and non living better, mitigation of air pollution is essential. Different
researchers have suggested their way of mitigating air pollutants.
Mathematical modeling concern to this issue also has been developed. Which is
widely applied to assess how air pollutants impact on human and ecological
health. Air pollution consists of dense particles in lower layer and loose
particles in upper layer. The region up to 200m from the ground remained
substantially polluted. Beyond 200m from the ground, pollutant concentration
decreased up to 800m and remained unchanged until the one kilometer mark. So,
In this work, a two-layered pollution model is planning to develop including
turbulent effect which can better describe pollution dispersion, optimal
measure, and control of air pollution. Additionally, the two-layer pollution
equation for advection and diffusion will also develop to analyze the
pollutants concentration. Since the model parameter such as eddy diffusivity,
and wind profile are different in lower and the upper layer, it is more
appropriate to study them separately by adopting the fundamental approaches of
the two-layer model. The model illustrates that there is fundamentally
different simulation results observed in the upper and lower layer by
variation of model parameters. The validation of the expected model will be
accomplished using parameter analyses through available laboratory and field
data. The insights of this work will directly contribute to environmental
sustainability by mitigating pollutants concentration, especially in the core
urban areas. Moreover, the work is also applicable for the researcher and
academia to select the optimal measurement techniques and way forward for
controlling the pollution level in the atmosphere.
Keywords: Advection, Diffusion, Turbulence, Concentration of pollutants,
Diffusivity
1\. Background
The term air pollution refers to the contamination of the air as a result of
the presence of compounds in the atmosphere that are hazardous to human health
and the health of other living things, or that affect the environment or
materials. Air pollution has increased recently as a result of both
anthropogenic and natural causes [1]. The major contributors of air pollution
are both point and non-point sources including vehicular emissions. Figure (1)
illustrates one of the most polluting sources due to trends toward increased
industrialization and urbanization. As a result, we became interested in
atmospheric pollution and used the advection diffusion model to examine the
pollutant dispersion in atmospheric air at various heights, from various
emission sources, with various wind speeds, and at various rates of diffusion.
The advection diffusion equation is a well-known example of a major partial
differential equation and is used in many environmental engineering and
industrial applications, particularly in the investigation of transport
processes of air pollutants [7]. To comprehend the effects of air pollution on
both human and ecological health, mathematical modeling is frequently used.
Air pollution has different behavior above and below from the height level of
emission source. A two-layered model of air pollution may consists of model
parameters like air density, temperature, humidity, concentration, eddy
diffusivity, wind speed, Pressure and turbulent effect realizing that they are
different in the lower and upper layers111https://www.dtn.com/what-are-
meteorological-parameters/. By incorporating the turbulent effect in the two-
layer model, we can describe more about pollution concentration, its optimal
measure, and control of air pollution. Mountains can be useful as natural
protection obstacles to mitigate air pollution whereas we can make artificial
protective obstacles to mitigate as well as divert air pollution. In reality,
upper layer have observed turbulent effect. This important aspect will be
incorporated in the new model.

Figure 1: An illustration of the primary sources of air pollution, with a
focus on the variables that the wind most frequently affects as it transports
pollutants through the atmosphere [19]

2\. Problem Statement
There are substantial evidences that air pollutants impacts human health,
damages flora and fauna, non-living environment including soil and building
materials [9]. The global climate change is mainly caused by the atmospheric
pollutants including $CO_{2}$, CFCs, $NO_{x}$ and $CH_{4}$. It is one of the
serious concern of both developing and developed countries [19]. Environmental
problems like deforestation, toxic material release, solid waste, air
pollution, and many others have attracted more attention than ever due to
ongoing urban expansion and population rise [2]. Urban air pollution has
become such a major issue that it is now necessary to receive scientific and
reliable information from the perspective of human and ecological health
safety. The potentially toxic trace element such as Hg, Cd, Pb and Zn are
major toxic chemicals that are one of the serious issues from the human and
ecological point of view. The haphazard development activities and rapid
urbanization including unmanaged industrialization are some of the major
causes of air pollutants in developing countries like Nepal. Additionally, the
major air pollutants in the core urban areas of the region are PM10, PM2.5,
aerosols, dust particles,tropospheric ozone etc. Precisely, Nepal is ranked as
one of the most polluted nation in the world by the World Air Quality
Report222https://www.iqair.com/nepal. However, the research revealed that the
amount of air pollution that Nepal was determined to be with a PM2.5 yearly
average of $44.46$ g/m3, down from $54.15$ g/m3 in $2018$, when Nepal was
still placed eighth. The amount of PM2.5 in the air in Kathmandu is very high,
especially during the dry winter months (December). Urban Kathmandu air
quality during this month can be described as extremely unhealthy [14]. Some
other metropolitan cities like Biratnagar, Birgunj etc also have similar air
pollution related issues in Nepal. Thus these issues should be solved for the
sustainability of urban development and management. To anticipate pollutant
concentrations, mathematical advection diffusion models is the most beneficial
since this quickly produce findings and provide meaningful information [3].
3\. Literature Review and Research Gaps
Taylor [2] established the modeling notion of diffusion. The main outcome of
these investigations was the identification of the Gaussian nature of the
average cross wind concentration. The foundation for the eventual development
of atmospheric diffusion theory was established from the theoretical and
experimental perspective. Additionally, Sutton [15] explained the methodology
utilized to create the Gaussian diffusion theory. Hanna et al. [10] referenced
two fundamental elements to explain the turbulent diffusion process that leads
to the Gaussian model. Gradient transport, also referred to as eddy diffusion,
is a theory that applies differential volume to a mass balance. The eddy
diffusion model and statistical theory of turbulence both provide the same
outcome. Hanna and Paine [8] explained about the convective nature of the
dispersion of buoyant plumes from towering stacks. Schnelle [12] highlighted
that any created atmospheric diffusion model shall specify that the
concentration should be exactly proportional to the source strength and
inversely related to the average wind speed. Park and Baik [2] explained that
power functions of vertical height in an unbounded space after the advection
diffusion equation for a source with a small area.
Similarly, Gayal et al. [20] studied the pollution dispersion with low wind
convective circumstances. Modeling based study were available from the
developing and developed countries for getting insights on the diffusion of
air pollutants. For instance, the ground level concentrations of SO2 owing to
point sources in Delhi were forecast using the Gaussian plume model and two
low wind models. In populated locations like Delhi, India, there are
frequently low wind conditions. Low wind speeds (less than $2$ m/s) made it
difficult for Gaussian models to predict concentrations. Pramod et al. [2]
have used crosswind-integrated concentrations to create a generalized
analytical model for the dispersion of a pollutant produced from a continuous
source in the atmospheric boundary layer. The resulting two-dimensional
steady-state advection-diffusion equations explained about the eddy
diffusivity as a function of vertically height and downwind path length from
the source, as well as for height above the ground as a generalized function
of horizontal wind speed. Romao et al. [6] investigated any errors in the
solution of 3D convection diffusion equation using finite difference
techniques.
The aforementioned results highlighted that the quality of atmospheric air has
been seriously deteriorating in last few decades. However there are very
limited studies focusing on the quality of air especially from the developing
counties. Precisely, there are negligible scientific publication focusing on
the quality of air by using two layer mathematical model. Thus this research
gap motivates me to develop new two layer air pollution model to increase the
quality of air from the developing countries like Nepal.

4\. Research Objectives
The following are the main specific objective of this research proposal:
Ob-I: To gain knowledge of two-layer air pollution dispersion. Formulation of
new two-layer air pollution model by incorporating the turbulence effect and
carrying out simulation in different situations.
Ob-II: We perform the simulation of concentration of pollutants by variation
of height, emission sources, eddy diffusivity, and wind profile by adopting
the fundamental approaches of the two-layer pollution model.
Ob-III: With proper validation of the new model through laboratory and field
data found in existing literature , possible optimal measures and control of
air pollution levels to an agreed standard at least cost are analyzed and
suggested.
Ob-IV: Finding exact and numerical solutions to the reduced model, model
performance is explained through parameter analyses .
5.Theoretical/ Conceptual Framework
The advection diffusion model, which simulates the physical procedures
involved in pollutant dispersion, is used to characterize the distribution of
air pollutants. The following equation, which is time dependent, can be used
to express the dispersion of pollutants [1, 2]:

$\displaystyle\frac{\partial c}{\partial t}+u\frac{\partial c}{\partial
x}+v\frac{\partial c}{\partial y}+w\frac{\partial c}{\partial
z}=\frac{\partial}{\partial x}\left(D_{x}\frac{\partial c}{\partial
x}\right)+\frac{\partial}{\partial y}\left(D_{y}\frac{\partial c}{\partial
y}\right)+\frac{\partial}{\partial z}\left(D_{z}\frac{\partial c}{\partial
z}\right)+S+R$ (1)

where $c$ = $c$($x,y,z$) is the concentration of pollutants at any location
($x,y,z$) at time $t$. $u$, $v$, and $w$ are mean wind velocity for downwind
($x$), crosswind ($y$), and vertical wind ($z$) directions respectively.
$D_{x}$, $D_{y}$, and $D_{z}$ are the respective diffusivity in the downwind
($x$), crosswind ($y$) and vertical ($z$) direction. S is the source term and
R is removal term [1, 2, 5].
The proposed work aim to formulate of new two-layer air pollution model by
incorporating the turbulence effect and carrying out simulation by using
appropriate numerical method in different situations.
6\. Expected Findings
The proposed work aim to formulate the new two-layer air pollution model by
incorporating the turbulence effect and carry out simulation by using
appropriate numerical method in different situations. The proposed research
work investigates the different types of models, their effectiveness and
relevancy. We will focus our study in one and two-layer models developed by
different mathematicians. Basically our interest is to study the effect of
turbulence on different flow parameters . Such models will be studied with the
help of simulation. Expected outcomes will be able to describe the relevance
of one and two-layer model.
7\. Novelty and Level of Contribution of the Study
With several anticipated results, the proposed research work concentrated on
two-layered air pollution model including turbulent effect and carrying out
simulation in different situations. The insights of this work will directly
contribute to environmental sustainability by mitigating the pollutants
concentration, especially in the core urban areas like Kathmandu.
Additionally, the work is also applicable for the researcher and academia to
select the optimal measurement techniques and way forward for controlling the
pollution level in the atmosphere.
The outcome of this research work will be substantially able to quickly impact
the international scientific community dealing with two-layered air pollution.
From the Nepalese perspective, this research will enhance further competence
of the national experts/researchers of the multidisciplinary field. We will
conduct workshops/conferences in the field of air pollution with the
researchers, academicians, policymakers, government authorities, and other
stakeholders to discuss such issues and bring fruitful solutions to the
problems of this field.
8\. Organisation of the Study
The research activities will be executed as follows to meet the specified
objectives within the estimated time frame.
WP-I. First-year: Focus on the study of the related journals, their
developments and literature reviews in details. During the time, simulation
results is carried out in the case of single layer of air pollution.
simulation results developed is validated with the suitable data from the
available literature and field data.
WP-II. Second-year: The study mainly dedicates on understanding and
constructing new two-layer air pollution model by incorporating the turbulence
effect and carrying out simulation in different situations. The new
mathematical model and numerical simulation techniques will be analyzed in
detail using the parameter analysis. Exact and analytical solutions will be
constructed to the mechanically and geometrically simplified and reduced
systems. Such analysis and solutions will help to gain deeper insights into
the model system. Manuscripts for possible paper publications will be
prepared.
WP-III.. Third-year: The simulation results obtained at WP-I, WP-II will be
compared and validated with laboratory and/or field data. The model and the
simulation tool developed is implemented to the real flow situation in nature
with the data found in the literature and/or by establishing collaboration
with relevant researchers (e.g., from other countries). Finalizing the
research project and submitting the reports.
9.Expected Outputs (Publications)
The goal of the study is to publish 3-4 papers within the study timeline. The
results will be disseminated at relevant national and international
conferences, symposiums, workshops, and seminars. The research activity also
seeks to establish national and international collaborations for further
research and exchanges. During the research period, international
relations/collaborations/exchange programs may be established/acquired to
enhance the modelling, simulation and/or experimental aspects of the research,
e.g., with suitable universities and research institutes abroad.
10\. Limitation and Delimitation
In our case, it is not possible to set up actual laboratory experiment which
shows air pollution. We will try to visit such laboratories if possible and we
will try to perform experiment. We will depend upon the existing literature
for numerical analysis. It may take further more time for mathematical
verification of the data obtained and to develop the improved model.
11\. Ethical / Safety Issues
The research work will be ethically original. Secondary data and results used
form existing literature will be acknowledged through citations and
references. We will try to verify mathematically the experimental data
obtained by researchers of the concerned field. We will try to participate in
a related laboratory work for experiment and try to achieve the reliable and
accurate data.

12\. Association to National Priority
According to the National Priorities for Research Funding prepared by the
university grant commission, this proposed research falls in the category of
Science and Technology as it contains different aspects of mathematics,
biology and fluid dynamics. This proposed work is closely related with
environmental science as well as public health and will be useful for the
large number of citizens of our country who are suffering from the diseases
due to air pollution. As we have realized this is an important problem not
properly addressed yet and we hope our research work will be a small step
towards this field. After publishing our work, the researchers can further
extend this work in their field for the goodness of public health and
environment science. More researchers will follow us to extend our work and
will be a contribution for the nation.

13\. Grant Chart and Detailed Budget
The tentative budget to carry out the proposed research work is as tabulated
below.

Table 1: Item wise whole budget

S.N. | Item | Cost
---|---|---
| Personal Cost |
| (i) Reference books and journals | Rs.235000
1. | (ii) Stationery |
| (iii) Conference and workshop |
| Laboratory Cost |
2. | (i) Lab equipment | Rs.150000
| (ii) Computer and Software |
| Field Cost |
3. | (i) Travel costs (Fellow and Assistant) | Rs. 150000
| (ii) Rental cost |
| (iii) Daily allowance (Fellow and Assistant) |
| (iv) Safety materials and other materials for field visits |
| Office Cost |
4. | (i) (i) Office Equipment | Rs. 120000
| (ii) Communication |
| Facilities and Administrative Cost |
| (i) Institutional Overhead Cost (as per the rule of | Rs. 120000
| the institution: 10 % of total budget) |
| (ii) Project Accounting and Auditing |
5. | (iii) Administrative Travel Cost |
| (iv) Proposal Preparation Cost |
| (v) Documentation and Publication Cost |
| Total Cost (NPR) | Rs. 775000

Table 2: Yearly Breakdown of the Total Budget S.N. | Item | Cost
---|---|---
1. | First Year | Rs. 275000
2. | Second Year | Rs. 250000
3. | Third Year | Rs. 250000
| Total Cost (NPR) | Rs. 775000

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