Stimulated Raman scattering signals recordedby the use of an optical imaging techniqueEYNAS AMER,1,2,* PER GREN,1 AND MIKAEL SJÖDAHL1

1Division of Fluid and Experimental Mechanics, Luleå University of Technology, SE-971 87 Luleå, Sweden2Department of Engineering Physics and Mathematics, Faculty of Engineering, Zagazig University, Zagazig, Egypt*Corresponding author: eynas.amer@ltu.se

Received 28 April 2015; revised 5 June 2015; accepted 23 June 2015; posted 23 June 2015 (Doc. ID 239757); published 10 July 2015

In this paper, stimulated Raman scattering (SRS) signals have been recorded by an optical imaging technique thatis based on spatial modulation. A frequency doubled Q-switched Nd:YAG laser (532 nm) was used to pump apolymethyl methacrylate (PMMA) target. The frequency tripled (355 nm) beam from the same laser was used topump an optical parametric oscillator (OPO). The Stokes beam (from the OPO) was tuned to 631.27 nm so thatthe frequency difference between the pump and the Stokes beams fit the Raman active vibrational mode of thePMMA molecule (2956 cm−1). The pump beam has been spatially modulated with fringes produced in aMichelson interferometer. The pump and the Stokes beams were overlapped on the target resulting in a gainof the Stokes beam of roughly 2.5% and a corresponding loss of the pump beam through the SRS process.To demodulate the SRS signal, two images of the Stokes beam without and with the pump beam fringes presentwere recorded. The difference between these two images was calculated and Fourier transformed. Then, the gain ofthe Stokes beam was separated from the background in the Fourier domain. The results show that spatial modu-lation of the pump beam is a promising method to separate the weak SRS signal from the background. © 2015

Optical Society of America

OCIS codes: (290.5910) Scattering, stimulated Raman; (020.1670) Coherent optical effects.

http://dx.doi.org/10.1364/AO.54.006377

1. INTRODUCTION

Light interacting with matter will in general be scattered bothelastically (no energy exchange between the photon and theatom or molecule) and inelastically (energy exchange betweenthe photon and the atom or molecule). Inelastic scattering ofphotons is a process that intrinsically depends on the quantumstate of the interacting atoms or molecules. Many techniqueshave been developed that utilize inelastically scattered light tostudy specific species. Raman scattering is a versatile inelasticscattering process for specific species detection. Raman scatter-ing is associated with an energy exchange between a photon anda motion mode (i.e., vibration) of a molecule. The moleculecan either receive energy (Stokes scattering) or give away energy(anti-Stokes scattering), with Stokes scattering being moreprobable at thermodynamic equilibrium. Specific moleculeshave specific Raman frequencies, which serve as a fingerprintfor the molecules. Imaging methods based on spontaneousRaman scattering have been in existence for many years [1,2].However, the spontaneous Raman scattering signal is extremelyweak and this results in limited imaging speed. The weakRaman signal can be strongly enhanced by using nonlinear co-herent excitation. Two coherent Raman scattering (CRS) tech-niques named coherent anti-Stokes Raman scattering (CARS)

and stimulated Raman scattering (SRS) have been developed.The CARS signal is stronger than the spontaneous Ramansignal and imaging speeds up to video rate have been demon-strated [3,4]. The CARS signal, however, suffers from a strongnonresonant electronic background that limits its sensitivity.Unlike CARS, the SRS signal is free from the nonresonantbackground. In SRS, two laser beams referred to as the pumpbeam and Stokes beam, respectively, coincide on the sample.When the energy difference between the pump and Stokesbeams matches the molecular vibrational frequency of the sam-ple molecule, a nonlinear interaction occurs that is accompa-nied by an energy transfer from the pump beam to theStokes beam. The intensity of the pump beam experiences aloss called stimulated Raman loss (SRL), and the intensityof the Stokes beam experiences a gain called stimulatedRaman gain (SRG). When the energy difference betweenthe pump and Stokes beams does not match any vibrationalresonance of the sample molecule, there is no energy transferbetween the pump beam and the Stokes beam. Therefore, SRSis free from the nonresonant background and linearly depen-dent on the molecule concentration. Stimulated Raman scat-tering microscopy has been used as a label-free imagingtechnique in many biological and biomedical areas [5–7].

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However, the SRS signal-to-noise ratio is very small and thesignal can be buried in the laser noise [8,9]. One way to solvethis is to modulate the SRS signal temporally and detect themodulation using a lock-in technique. In previous studies ofSRS intensity [6,8,10], frequency [11] and spectrum [12] mod-ulations have been used to detect the signal. In this study, theSRS signal has been recorded by the use of an optical imagingtechnique that is based on spatial modulation. The spatialmodulation can be performed on either of the beams (thepump beam or the Stokes beam), and then, one can detect theeffect of this modulation on the other beam caused by SRS. Inthis study, for practical reasons, the pump beam has been spa-tially modulated. The spatial modulation was produced by aMichelson interferometer and this yielded parallel fringes. Twoimages of the Stokes beam without and with the pump beamfringes present were recorded. The difference between thesetwo images was calculated and Fourier transformed. Then,the gain of the Stokes beam (the SRS signal) was separated fromthe background in the Fourier domain. The experimental setupand procedure are described in Section 2. In Section 3,the theory explaining the procedure to separate the fringe-modulated SRS signal from the background is introduced.Finally the results and discussion are presented in Section 4.

2. EXPERIMENTAL SETUP AND PROCEDURE

The SRS signal has been measured by the use of an opticalimaging technique. An injection-seeded Q-switched Nd:YAGlaser system (Continuum PL 8000) was used as the source forboth the pump and Stokes beams. The laser system operates at10 Hz, and the pulse duration is 6 ns. The frequency tripled(355 nm) beam from the laser was used to pump an opticalparametric oscillator (OPO) (Continuum Sunlite EX OPO)with a tuning range from 445 to 1750 nm. The frequencydoubled (532 nm) beam from the same laser was used to pumpa polymethyl methacrylate (PMMA) target. The wavelengthshifted beam from the OPO was used as the Stokes beam.The frequency difference between the two beams (the pumpand Stokes beams) fit the Raman active vibrational mode ofthe PMMAmolecule (nominally 2956 cm−1). The PMMA tar-get was a cylinder with a diameter of 4.0 cm and a length of20.0 cm. The following two specific experimental setups havebeen used: the first setup was used to optimize the experimentalparameters and the second was used to record the SRS signal.Figure 1 shows the setup to optimize the experimental param-eters. In this setup, two heads of a computer controlled energymonitor (Ophir PE10 and PE25) have been used to monitorthe pulse energies, both before and after the target, respectively.Head 1 was used to measure the Stokes beam energy beforethe PMMA target, and head 2 was used to measure the Stokesbeam energy after the target. Hence, a ratio (Ri) of the Stokesbeam energy after and before the target can be calculated tocompensate for the change of the Stokes beam energy from shotto shot caused by the instability of the laser. R1 refers to a ratiowithout the pump beam present and R2 to a ratio with thepump beam present. The gain of the Stokes beam (SRG)was then calculated as �R2 − R1�∕R1. Two interference filters,namely, F1 and F2 (FL 632.8 nm, FWHM � 10 nm), havebeen positioned in front of head 1 and head 2, respectively,

to ensure that only the energy of the Stokes beam will be re-corded. Each recording represents an average of 1000 pulses.The pump beam energy at the target was 23 mJ and theStokes beam energy was 10.5 mJ. The beam diameter for boththe pump and Stokes beams was about 4 mm, which resulted ina power density of 30 and 14 MW∕cm2 for the pump andStokes beams, respectively. In general, the orientation of thebirefringent PMMA target, the polarizations of the two beams,and the wavelength of the Stokes beam need to be optimizedfor maximum gain. This optimization is detailed in the follow-ing subsections.

First, the optimum orientation of the PMMA cylinder inrelation to the polarization of the pump beam is considered.To investigate this, the Stokes beam in Fig. 1 was blockedand the polarization of the pump beam (532 nm) was kept ver-tically polarized. A camera imaging the scattered light from thePMMA was placed perpendicularly to the direction of thepump beam and images were acquired during multiple pulses.A typical result for a random orientation of the PMMA targetcan be seen in Fig. 2. Figure 2(a) shows the scattering patternthat appears from the scattered pump beam, and Fig. 2(b)shows the scattering pattern from the red and yellow wave-lengths that were generated by spontaneous Raman scattering.The Raman shifted wavelengths were acquired by putting a

Fig. 1. Setup for optimizing the experimental parameters. M,mirrors; F, interference filters for the Stokes beam.

Fig. 2. Photos of the scattering pattern formed at the interactionvolume between the pump beam and the PMMA cylinder. (a) Thescattering pattern that appears from the scattered pump beam and(b) the scattering pattern that results from the scattered red andyellow wavelengths generated by spontaneous Raman scattering. Theexposure time of the camera is 15 s.

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notch filter in front of the camera blocking the green pumpbeam. The exposure time of the camera was 15 s, and the laserwas run at 10 Hz. As seen in the images, a typical pattern ofbright and dark regions appeared. Furthermore, the position ofthe dark and bright regions changes with the viewing direction,which is typical for Rayleigh scattering. This phenomenon isdue to birefringence in the PMMA, which rotates the polari-zation of the pump beam as it propagates through the target[13]. The dark regions in Fig. 2 therefore correspond to posi-tions where the local polarization of the beam is along the view-ing direction. To optimize the setup, the target was rotateduntil a continuous beam was imaged by the camera. At thisorientation, the polarization of the pump beam was alongone of the principal axes of the PMMA and the polarizationwill remain stationary throughout the target.

As a demonstration of the effect of the polarization of thepump and Stokes beams on the SRS signal generation, the twobeams were made to overlap in time and space at the PMMAtarget as shown in Fig. 1. Two different configurations weretested, where in both tests the nominally optimum Stokes beamwavelength of 631.27 nm was used. In the first configuration,the polarization of both beams was kept vertical and the ori-entation of the PMMA target was rotated. At the optimum ori-entation (one of the principal axes is vertical), a gain of about4% was recorded. When rotating the target by �90°, a gain ofabout 4% was again measured as the polarization of the twobeams again coincided with one of the principal axes. Whenrotating the target by �45°, the gain was reduced to about2.5%. This reduction in the gain is caused by de-couplingof the polarization of the two beams, as the SRS generationtakes place when the two beams are equally polarized [14].Therefore, as the two beams rotate at different speeds throughthe target, the nominal interaction length of the SRS willdecrease and as an effect the gain is reduced. As a second dem-onstration of the same phenomenon, the polarization of theStokes beam was kept constant along one of the principal axesof the PMMA and the polarization of the pump beam was ro-tated. When the polarization of the two beams coincided, again of 4.0% was again measured. Conversely, when the polari-zation of the two beams was set perpendicular, a minimum gainof about 0.8% was recorded. For the intermediate orientationof 45°, the gain was about 2.0%. It is obvious that the polari-zation of the two beams in relation to each other and to theprincipal axes of the target is crucial for the generation of SRS,and we retained this optimum configuration for the remainingexperiments. Finally, the SRG in the vicinity of the nominalStokes beam wavelength was measured. Seven measurementswith Stokes beam wavelengths ranging between 628 and635 nm were registered and plotted in Fig. 3. Each recordingrepresents an average of 1000 individual pulses. The error barsin the figure represent the standard error, which is mainly dueto the instability of the laser from shot to shot. Furthermore, aLorentian line shape was fitted to the data points. The profileshown in Fig. 3 corresponds to a line with maximum gain of4.0% at the wavelength 631.27 nm and a linewidth of 1.6 nm.We can now conclude that the nominal wavelength shift(631.27 nm) indeed results in maximum gain, and we contin-ued the experiments with this setting.

Once the experimental parameters had been optimized, theexperimental setup shown in Fig. 4 was used for detecting theSRS signal with the imaging technique. The pump beam(532 nm) was spatially modulated with fringes produced ina Michelson interferometer, where the fringe density was con-trolled by rotating mirrorsM5 andM6. The pump beam fringesand the Stokes beam were overlapped in time and space at thePMMA cylinder using the optimal settings from the previoussections. A photo of typical pump beam fringes is shown inFig. 5, where in Fig. 5(a), the whole PMMA target is shown,and in Fig. 5(b), an enlarged part is shown for a better view ofthe fringes. After the target, the two beams pass through thetelescope with a magnification of 3. After the telescope, thepump beam is reflected to a beam dump using the dichroicmirror M9, which is 100% reflective for 532 nm at an angle ofincidence of 45°. The Stokes beam was recorded using aPCO edge camera, which has a resolution of 2560 pixels ×2160 pixels, a pixel size of 6.5 μm × 6.5 μm, and a dynamic

Fig. 3. Optimization of the Stokes beam wavelength.

Fig. 4. Experimental setup for imaging the SRS signal. M, mirrors;B.S, beam splitter; F, absorbing filter set.

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range of 16 bits. The field of view is 5.5 mm × 4.7 mm. Anabsorbing filter set F, with total optical density of 6, was usedto ensure that no part of the pump beam passes to the cameraand to reduce the Stokes beam energy for camera protection.

This experiment was performed and evaluated as follows.Two intensity images of the Stokes beam were required.The first image (I r ) was recorded without the pump beampresent, and the second image (I g ) was recorded with the pumpbeam present. These images may in principle be single-shotimages, but in the results that follow, they are the average in-tensity of 128 pulses each. The difference between these twoimages was calculated and Fourier transformed. Then, the gainof the Stokes beam was separated from the residual backgroundin the Fourier domain. The final gain image was then obtainedfrom an inverse Fourier transform of the filtered signal.The theory explaining the procedure to separate the fringe-modulated SRS signal from the background is introduced inthe next section.

3. THEORY

Consider a general Stokes beam Es � Aseiφs and two planepump beams Ep� � Apei2π�σz z�σx x−νt�, where AS and Ap arethe amplitudes of the Stokes beam and pump beam, respec-tively, ϕs is the phase of the Stokes beam, the σ’s are spatialfrequencies, � indicates a propagation direction relative tothe given z-axis, and ν is the temporal frequency (see Fig. 6for an illustration).

Under the assumption of SRG, the propagating Stokes wavemay be expressed as

E � Es � αEp�Es � αEp−Es; (1)

where α is the amplitude interaction strength that determinesthe Raman gain. The parameter α depends in general on theRaman cross section and the number of Raman active

molecules the light interacts with during its propagation.The Raman interaction strength α is the carrier of image infor-mation in this problem. It will be assumed to be weak, i.e.,jαj ≪ 1, so that the small moderations caused by the gaindo not change the propagation. Upon detection, we get theirradiance I � hjE j2iΔt , where Δt indicates the pulse durationand is assumed to be significantly longer than 1∕ν, theoscillation period of the optical wave. Typically, Δt is in theorder of nanoseconds. This will generate three types of terms.The first type,

I 1 � I s�1� 2jαj2I p�; (2)

gives the sum of the individual irradiance terms and is an effectfrom self-interference solely. The second type,

I2 � I s�2jαjhcos�2π�σzz � σxx − νt� � ϕs�iΔt�2jαjhcos�2π�σzz − σxx − νt� � ϕs�iΔt�; (3)

describes the temporal average of two propagating waves thatwill become zero upon recording, and the third type,

I3 � I sI pjαj2�ei4πσx x � e−i4πσx x� � 2I sI pjαj2 cos�4πσxx�;(4)

is the standing wave interference term. We may thus express thedetected intensity as

I g � I 1 � I 3 � I s � 2jαj2I sI p � 2jαj2I sI p cos�4πσxx�:(5)

If we for a moment assume that I s and I p are constants, Eq. (5)may be rewritten as

I g � I s � 2Jα � 2Jα cos�4πσxx�; (6)

where Jα is proportional to the intensity interaction strengthjαj2, and this is the gain signal of interest. In general, Jα de-pends on the local distribution of stimulated molecules andmay be assumed to be spatially band limited to within [−B, B].It should also be noted that the strength of Jα depends linearlyon the pump beam (I p) and Stokes beam (I s) intensities.Taking the spatial Fourier transform of Eq. (6) results inthe following expression:

I g�S� � I s�S� � 2Jα�S� � Jα�S − 2σx� � Jα�S � 2σx�; (7)

where S is a spatial frequency coordinate. The four lobes inEq. (7) represent the spatial spectrum of the Stokes beam cen-tered at S � 0 and the spatial spectrum of Jα centered at S � 0and S � �2σx , respectively. The three lobes associated with

Fig. 5. (a) Photo of the pump beam fringes interacting with thePMMA target and (b) an enlarged part of the photo.

Fig. 6. Schematic illustrating the propagation of the pump beamfringes.

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the gain signal will be separated provided that σx > B. In thatcase, one of the sidelobes, for example, Jα�S − 2σx�, may beisolated using a rectangular window. The image jJαj is thenrestored from the Fourier transform (shifting to the origin isoptional), which is the standard technique in single-shot fringeprojection [15]. In essence, the technique is the spatial corre-spondence to lock-in detection using temporal intensity modu-lation [11]. However, the dominating spectrum in Eq. (7) isI s�S�, which cannot be assumed to be band limited in general.Frequency components from I s�S� may therefore leak in to thewindow of Jα�S − 2σx� and deteriorate the estimation of jJαj.To reduce the influence from I s�S�, a reference image ofthe Stokes beam without the pump beam fringes (I r) is re-quired. From the two images I g and I r , a difference imageΔI � I g − I r is calculated where the Stokes background isnulled apart from a small error ΔI s that is mainly associatedwith shot-to-shot instabilities of the laser. The Fourier trans-form of ΔI then becomes

ΔI�S� � ΔI s�S� � 2Jα�S� � Jα�S − 2σx� � Jα�S � 2σx�:(8)

As ΔI s�S� is significantly reduced in amplitude as compared toI s�S� and its components are assumed to originate from shot-to-shot instabilities, its spectrum will be dominated by low fre-quency components. Therefore, if the spectrum of Jα�S − 2σx�is moved appropriately far away from the origin, jJαj may beestimated free from the cross talk of the other lobes. In thefollowing work, we will investigate the procedure leading toEq. (8) to separate the SRS signal from the Stokes beambackground.

4. RESULTS AND DISCUSSION

The different steps for isolating the SRS signal image are visu-alized in Figs. 7 and 8 for two different fringe densities. In bothexperiments, the mean power density of the pump beam at thetarget was 18 MW∕cm2 and the power density of the Stokesbeam was 14 MW∕cm2. In the first experiment, the fringespacing at the target was set to 0.55 mm, and in the secondexperiment, the fringe spacing was reduced to 0.28 mm.These numbers were measured from the burn pattern acquiredat the target and imaged in an optical microscope. The resultsshown in Fig. 7 are the results from the coarser fringe density,while those in Fig. 8 are the results from the finer fringes.Images of the pump beam fringes with spacings of 0.55 and0.28 mm are shown in Figs. 7(a) and 8(a), respectively.These figures show that the fringes were not optimum. Thereason for this is that the cross sectional spatial distributionof the pump beam (532 nm) is the residual after producingthe frequency tripled 355 nm beam used to pump theOPO, as sketched in Figs. 1 and 4. As a result, the cross sectionof the pump beam will vary not only harmonically over theimage, but also in relation to position. Figures 7(b) and 8(b)show the images of the pump beam fringes at spacings of 0.55and 0.28 mm, respectively, in the presence of filter set F placedin front of the camera. The figures are completely black, whichemphasizes that the pump beam along with all spontaneousRaman and other disturbances have been filtered out. The im-ages shown in Figs. 7(c), 7(d), 8(c), and 8(d) are the images of

the Stokes beam being recorded during the experiment for thetwo different fringe densities. Specifically, Figs. 7(c) and 8(c) arethe images of the Stokes beam recorded without the pumpbeam present (I r) and Figs. 7(d) and 8(d) are the images ofthe Stokes beam recorded with the pump beam present (I g ).The small gain generated by the SRS process taking place be-tween the (c) and (d) images is drowned in the overall intensityvariation. However, when calculating the difference images(ΔI ), which are shown in Figs. 7(e) and 8(e), the modulationin terms of fringes appears. Hence, an energy transfer from thepump beam fringes to the Stokes due to SRS takes place. In thecross sections shown in Figs. 7(f ) and 8(f ), it can be seen thatthe position and spacing of the difference image fringes roughlycoincide with the position and spacing of the pump beamfringes. These cross sections of the fringes were calculated as anaverage from Y � 2.7 mm to Y � 3.0 mm in the respectiveimage as a representative part of the image. That modulationfringes so clearly appear in the difference image indicates thatthe assumption of stable laser conditions is fulfilled to a greatextent. Some variation in the recording conditions, however, ispresent and manifested by a small residual intensity variationapart from the fringes. Comparing the fringes shown in (a) and(e) images, it can be seen that the difference image fringes dropoff toward the edges of the beam. The reason for this is that theSRS signal is produced in proportion to I pI s, where I p is thepump beam intensity and I s is the Stokes beam intensity [6],[see Eqs. (5) and (6)]. The fringes are therefore only producedin the area where there is a substantial overlap between the twobeams. This effect is clearly shown in Figs. 7 and 8 where theposition of the fringes in the (e) images coincide roughly withthe overlapping area between (a) and (c) images. Figures 7(g)and 8(g) show a cross section of the magnitude of the Fouriertransform of each difference image [see Eq. (8)]. The spatialfrequencies are given in relation to the object coordinatesystem. The lobes representing the gain signal [Jα in Eq. (8)]are centered in the neighborhood [2σx in Eq. (8)] of about�1.80 mm−1 and �3.60 mm−1 in Figs. 7(g) and 8(g), respec-tively, which corresponds to a fringe spacing of 0.55 mm and0.28 mm for the two cases considered, respectively. It is clearthat the positions of these lobes correspond to the carrier fre-quency of the pump beam fringes and that a higher carrier fre-quency moves the lobes out further away from the central lobe.As discussed in Section 2, the gain signal (Jα) with a spatialband limit within [−B, B] will be separated from the centralbackground peak provided that σx > B, where 2σx is the spatialfrequency of the pump beam fringes. From Fig. 7(g), the widthof the gain signal (2B) is 1.44 mm−1 and 2σx is 1.80 mm−1

�σx ≈ B�; hence, significant overlap is present between the loberepresenting the gain signal and the central lobe wherefore theycannot be separated unambiguously. Conversely, Fig. 8(g)shows that the carrier frequency is high enough to separatethe two lobes. The width of the gain signal (2B) is 1.26 mm−1

and 2σx is 3.60 mm−1 �σx > B�; additionally, a simple rectan-gular window may be used to filter out the interesting gain sig-nal. Maximizing the separation between the gain lobe and thecentral lobe is the key feature to optimize the outputs of thetechnique. The way to fulfill this condition is to produce a highenough fringe density in the plane of the object. The window

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shown as a red box around one of the gain lobes in Figs. 7(g)and 8(g) is the rectangular window used to filter out the infor-mation of interest. The width of this window is 1.44 mm−1 inFig. 7(g) and 1.26 mm−1 in Fig. 8(g), which gives a poor spatialresolution in the gain image compared to the spatial resolutionin the original image. As the main purpose of this study isto show that it is possible to separate the SRS signal from thebackground using the spatial modulation method, the

resolution provided here is sufficient. As a final note on theFourier spectra, estimation of the magnitude of the gain israther difficult because of the high noise level. However,the gain magnitude will roughly be about 2.5% (IP is18 MW∕cm2) compared to the gain of 4% measured in thecalibration setup of Fig. 1 (IP is 30 MW∕cm2) as the expectedgain scales linearly with the pump beam intensity. Although themagnitude of the estimated gain is somewhat unreliable, the

Fig. 7. (a) Image of the pump beam fringes with spacings of 0.55 mm, (b) image of the pump beam fringes in the presence of the filter set F, (c)and (d) images of the Stokes beam without and with the pump beam fringes, respectively, (e) a difference image between the (d) and (c) images,(f ) cross sections of the pump beam fringes in (a) and the difference image fringes in (e) (an average from Y � 2.7 mm to Y � 3.0 mm), (g) crosssection of the magnitude of the Fourier transform for the difference image in (e), and (h) gain image of the Stokes beam produced from the spatialfrequency content within the window marked by a red rectangle in (g). IP is 18 MW∕cm2, and I S is 14 MW∕cm2.

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gain itself is adequate to provide a sufficient lobe in the Fourierspectrum representing the gain image. The gain images thatwere generated from an inverse Fourier transform of the infor-mation within the windows in Figs. 7(g) and 8(g) are presentedin Figs. 7(h) and 8(h), respectively. These images represent themagnitude of the reconstructed images. The intensity in theseimages corresponds roughly to the positions of the sharp fringesin the difference images [Figs. 7(e) and 8(e)] and the areas of

overlap between the pump beam fringes and the Stokes beam.It is also clear that areas where no modulation has taken placeare dark. Therefore, high contrast SRS images may be con-structed from a small modulation provided the signal-to-noiseratio is sufficient.

Finally, higher fringe densities have been investigated.Figures 9 and 10 show the results at fringes spacing of 0.24and 0.21 mm, respectively. Images of the pump beam fringes

Fig. 8. (a) Image of the pump beam fringes with spacings of 0.28 mm, (b) image of the pump beam fringes in the presence of the filter set F, (c)and (d) images of the Stokes beam without and with the pump beam fringes, respectively, (e) a difference image between the (d) and (c) images,(f ) cross sections of the pump beam fringes in (a) and the difference image fringes in (e) (an average from Y � 2.7 mm to Y � 3.0 mm), (g) crosssection of the magnitude of the Fourier transform of the difference image in (e), and (h) gain image of the Stokes beam produced from the spatialfrequency content within the window marked by a red rectangle in (g). IP is 18 MW∕cm2, and I S is 14 MW∕cm2.

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Fig. 9. (a) Image of the pump beam fringes with spacings of 0.24 mm, (b) a difference image between the images of the Stokes beam with andwithout the pump beam fringes, and (c) cross section of the magnitude of the Fourier transform for the difference image in (b). IP is 18 MW∕cm2,and IS is 14 MW∕cm2.

Fig. 10. (a) Image of the pump beam fringes with spacings of 0.21 mm, (b) a difference image between the images of the Stokes beam with andwithout the pump beam fringes, and (c) cross section of the magnitude of the Fourier transform for the difference image in (b). IP is 18 MW∕cm2,and IS is 14 MW∕cm2.

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with spacings of 0.24 and 0.21 mm are shown in Figs. 9(a)and 10(a), respectively. The difference images of the Stokesbeam with and without the pump beam present for the twofringes spacing are shown in Figs 9(b) and 10(b), respectively.The fringe modulation due to the SRS process can be clearlyseen in the figures. The corresponding cross sections of themagnitude of the Fourier transform for the difference imagesin Figs. 9(b) and 10(b) are shown in Figs. 9(c) and 10(c),respectively. The lobes representing the gain signal (Jα) arecentered in the neighborhood of about �4.14 mm−1 and�5.0 mm−1 in Figs. 9(c) and 10(c), respectively, which corre-sponds to a fringe spacing of 0.24 and 0.21 mm, respectively.These figures show that at higher fringe densities the gain lobesmoved further away from the central lobe but the gain signal-to-noise ratio decreased as the fringe densities increased; thus, itwas difficult to separate the gain signal from background noise.This effect most likely originates from a small misalignmentbetween the Stokes beam and the pump beam caused by point-ing instability of the laser. Such an effect was more pronouncedin the case of large fringe density. Therefore, the nominal in-teraction length of the SRS will decrease, and as an effect, thegain will be reduced. Hence, the spatial modulation techniquedepends strongly on the optimization of the fringe density inthe object plane. The fringe density should be high enough toseparate the gain lobes from the center lobe as well as produce ahigh enough gain signal-to-noise ratio.

5. CONCLUSION

The SRS signal has been recorded by the use of an optical im-aging technique that is based on spatial modulation. Two laserbeams (the pump and Stokes beams) were overlapped in timeand space in a solid PMMA cylinder resulting in a gain of theStokes beam through the SRS process of about 4.0% at a pumpbeam intensity of 30 MW∕cm2 and a Stokes beam intensity of14 MW∕cm2. The pump beam was spatially modulated withfringes produced in a Michelson interferometer. To demodu-late the SRS signal, two images of the Stokes beam without andwith the pump beam present were recorded. The difference be-tween these two images was calculated and Fourier trans-formed. Then, the gain of the Stokes beam was separatedfrom the background in the Fourier domain. In this case, amaximum gain of 2.5% was estimated. The efficient separationof the SRS signal lobe from the background lobe dependsstrongly on the optimization of the fringe density in the objectplane. Overall, the results showed that spatial modulation ofthe pump beam is a promising method to separate the weakSRS signal from the background. This technique can be appliedto pin-point specific species and record their spatial and tem-poral distribution.

Funding. Bio4Energy.

Acknowledgment. Bio4Energy is a strategic research

environment established by the Swedish government.

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