Chemical imaging with Fourier transform coherentanti-Stokes Raman scattering microscopy

Meng Cui, Joshua Skodack, and Jennifer P. Ogilvie*Department of Physics and Biophysics, University of Michigan, Ann Arbor, Michigan 48109 USA

*Corresponding author: jogilvie@umich.edu

Received 28 May 2008; revised 11 September 2008; accepted 26 September 2008;posted 1 October 2008 (Doc. ID 96680); published 24 October 2008

We report chemical imaging using Fourier transform coherent anti-Stokes Raman scattering (FTCARS)microscopy. Adding a passively phase-stable local field to amplify the weak FTCARS signal, we also de-monstrate interferometric FTCARS microscopy, permitting reduced incident power to be used for ima-ging. We discuss signal-to-noise considerations and the conditions necessary to effectively suppressbackground noise, allowing FTCARS microscopy that is limited by the shot noise of the detector. We alsodiscuss differences between the signal-to-noise obtainable by time and frequency domain coherent anti-Stokes Raman scattering (CARS) methods. © 2008 Optical Society of America

OCIS codes: 300.6230, 190.4810, 170.6920, 300.6310.

1. Introduction

Coherent anti-Stokes Raman scattering (CARS) mi-croscopy is a promising tool for label-free biologicalimaging that has attracted considerable recent at-tention [1–3] since its initial implementation in1982 [4]. To date, most CARS implementations haveutilized narrowband (picosecond) excitation andhave imaged single CARSmodes, typically exploitingthe C–H stretching region in a variety of biologicalstudies [5–7]. Extension of CARS microscopy to pro-vide spectrally-resolved images in the chemicallyrich fingerprint region (700–1800 cm−1) would openup the possibility of simultaneous imaging of multi-ple chemical species in complex samples. Towardsthis goal, multiplex CARS mixes narrowband andbroadband excitation [2,8]. An alternate approachhas been to use a single femtosecond laser with broadbandwidth to access the fingerprint region, obviatingthe need for the active synchronization of multiplelaser sources [9,10]. The challenge in using femtose-cond excitation is to obtain high spectral resolutionwhile suppressing nonresonant background signalsthat are stronger with shorter pulse excitation.

The Silberberg group has pioneered the use ofpulse-shaping in CARS microscopy, employing it toselectively image specific CARS modes [9,10]. Otherpulse-shaping schemes have included amplitudeshaping of pump and Stokes pulses [11], and spectralfocusing with chirped pulses [12–14]. Polarizationand phase shaping have permitted broadband spec-trally-resolved imaging [15–17]. Other recent single-laser implementations of CARS have combined nar-rowband pump with broadband Stokes excitation ob-tained by spectral broadening in a tapered orphotonic crystal fiber [18–20]. We recently demon-strated a single-laser, time-domain Fourier trans-form CARS (FTCARS) method that effectivelysuppresses nonresonant background signals whileproviding high spectral resolution images withinthe fingerprint regime [21].

Efforts to increase the sensitivity of CARS micro-scopy, necessary to address lower signal levels inthe fingerprint region, have employed heterodyne/interferometric methods that mix a local oscillator(LO) field with the weak CARS signal to provide am-plification and isolation of the resonant CARScomponent. While there have been a number of im-plementations of interferometric CARS spectroscopyand microscopy, the majority of these methods re-quire relatively complex experimental setups and

0003-6935/08/315790-09$15.00/0© 2008 Optical Society of America

5790 APPLIED OPTICS / Vol. 47, No. 31 / 1 November 2008

lack phase stability between the CARS signal andLO [22–27]. Several implementations with passivephase stability have been demonstrated for narrow-band [28] and broadband CARS [15–17,29–32]. Bothphase stability and independent control of the LO in-tensity are desirable to optimize the CARS signal.We recently demonstrated both of these capabilitiesin an interferometric implementation of FTCARS[21] spectroscopy within the fingerprint region [29].Here we present imaging results obtained with theFTCARSmethod, and extend the work to perform in-terferometric FTCARS (IFTCARS) microscopy. InIFTCARS microscopy a LO is added coherently tothe FTCARS signal field with passive phase stabilityin a compact and robust setup. A single detectoris used to acquire broadband spectrally-resolvedimages over the bandwidth of the laser excitation(300–1500 cm−1). We discuss signal-to-noise ratio(SNR) considerations in FTCARS microscopy, andshow that the interferometric implementation effec-tively suppresses the background noise, allowing usto approach shot-noise-limited sensitivity at low ex-citation conditions.

2. Fourier Transform Coherent Anti-Stokes RamanScattering Microscopy

A. Fourier Transform Coherent Anti-Stokes RamanScattering Signal

The principle behind FTCARS has been discussedpreviously [21,29] and is mentioned only briefly here.As depicted in Fig. 1(c), an initial pump pulse (pulse1) excites Raman coherences that lie within its band-width. Pulse 2 probes these coherences after time de-lay τ, generating the CARS signal that can be readily

isolated via spectral filtering. Recording the CARSsignal as a function of τ allows the CARS spectrumto be obtained via Fourier transform of the time-domain data [21,29]. Essentially arbitrary spectralresolution can be obtained in FTCARS by scanninglonger τ delays. All CARS implementations mustdeal with a nonresonant (NR) background contribu-tion arising from the electronic response of themedium that can reduce chemical contrast. The in-stantaneous nature of the NR background meansthat it appears near τ ¼ 0. A significant benefit ofthe FTCARS method is that the NR backgroundcan be effectively separated in the time domain fromthe longer-lived vibrationally resonant contribution[21]. Other implementations of CARS microscopyand spectroscopy have also employed time delaysto discriminate between resonant and NR signals[33–37]. As well as the time-delay approach, polari-zation methods [38], pulse-shaping [10], and maxi-mum entropy [39] methods have also been used.

If the two excitation pulses in FTCARS are well-separated in time, the detected signal intensitycan be expressed as I ¼ I1 þ I2, where I1 and I2are the signal intensities generated by pulse 1 andpulse 2, respectively. I1 consists of resonant andNR contributions from pulse 1 and is independentof the time delay. I2 has three components: NR signalI2nr generated by pulse 2, resonant signal I2r gener-ated by pulse 2 only, and the resonant signal Ir12 fromcoherences created by pulse 1 and probed by pulse 2.This latter component is the only time-dependentterm. Note that we have neglected the NR signal gen-erated by the combination of pulses 1 and 2 since thisterm only contributes during their temporal overlap.The three I2 components interfere with each otherdue to their mutual coherence and time coincidenceat the detector. The first two components have a fixedrelative phase difference, allowing us to treat themas a single LO component Ilocal. Thus the overallFTCARS signal can be written as

IðτÞ ¼ I1 þ Ilocal þ Ir12

þ 2cffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiIlocalIr12

pcosðϕr12ðτÞ − ϕlocalÞ; ð1Þ

where c ≤ 1 is a constant accounting for the fact thatthe resonant and NR signals have different ampli-tude and phase profiles and, hence, may not haveperfect interference. The cosine term indicates theneed for relative phase stability between the signaland LO. Because ϕr12ðτÞ is derived from the phase ofχð3Þr ðτÞ and

ffiffiffiffiffiffiffiffiIr12

p∝ jχð3Þr ðτÞj, the last term in Eq. (1)

directly yields χð3Þr ðτÞ to within a constant phase fac-tor. The Fourier transform of IðτÞ yields the resonantCARS spectrum, provided the NR contribution with-in the pulse overlap region is windowed out. The firsttwo terms in Eq. (1), which carry no information, gen-erate background noise in the measurement. IFT-CARS is a straightforward extension of FTCARSin which an additional LO derived from the blue edgeof the laser spectrum is added for interference with

Fig. 1. Energy diagram of (a) single mode (picosecond) CARS;(b) multiplex CARS; (c) FTCARS signal generation: an initialbroadband pulse excites Raman coherences that are probed a de-lay τ later by a second broadband pulse. P: pump, S: Stokes, A:anti-Stokes.

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the resonant signal. This allows control over the re-lative ratio between the resonant signal and the LOfor optimization of the SNR. This is particularly im-portant under low excitation conditions when the NRbackground is small.Closely related to both FTCARS and IFTCARS

is impulsive stimulated Raman scattering (ISRS)[40,41]. In ISRS, a pump pulse initiates vibrationalcoherences. After a certain time delay, a weakerpulse probes the coherences and is detected eitherin a transmission or reflection geometry. The differ-ence between this method and FTCARS is that theprobe (pulse 2) enters the detector in the pump-probemethod, whereas only the blue-shifted signal is de-tected in FTCARS due to spectral filtering. Thusin the pump-probe method, Ilocal is dominated bythe probe pulse. Because the intensity of the probepulse is many orders of magnitude larger thanI2nr, the signal contrast of the pump-probe methodis much smaller than in FTCARS. In IFTCARS,the amplitude of the LO can be controlled to maxi-mize the interferometric amplification of the signal.The high degree of fringe visibility achievable withFTCARS and IFTCARS produces signals that canbe directly digitized by a high speed data acquisitioncard without lock-in detection, making FTCARS sui-table for imaging applications.

B. Experimental Setup

The FTCARS setup is shown in Fig. 2. A 12 fs pulse(Femtolasers Synergy) centered at 790nm with arepetition rate of 75MHz provides the pump andprobe pulses. Both pulses traverse a long pass filterat 735nm (Omega Optical), and are dispersion-precompensated by a pair of chirped mirrors beforepassing into a scanning multiphoton microscope andbeing focused onto the sample via a NA 0.4 objectivelens. A short pass filter at 725nm is placed before thedetector to block the input laser light, allowing onlyblue-shifted components to enter the photomultipliertube detector (PMT) (Hamamatsu R636-10). Two di-mensional images are acquired one line at a time bydigitizing the PMT signal at 1MHz while simulta-neously scanning the line at 1kHz and the time delayat 1Hz. The time delay is accurately monitored by aHe–Ne fringe tracking scheme. Time-domain signalsfor each pixel in the line are reconstructed to obtainthe FTCARS spectra. The process is repeated untilthe entire image is scanned. The first 300 fs oftime-domain data is excluded from the Fourier trans-form to avoid NR background contributions. This isnecessary because our pulses are not transform-lim-ited but have a long-lived tail arising from a combi-nation of the sharp spectral feature imparted byspectral filtering and uncompensated third order dis-persion. This is expected to reduce the overallFTCARS signal by a factor of ∼1:5.

To control the amplitude of the LO for IFTCARS, areflective 4 f setup, as shown in Fig. 2b, is insertedinto the beam path after the interferometer, andthe long pass filter is moved to the pump arm of theinterferometer. At the Fourier plane, a linear neutraldensity (ND) filter is used to adjust the strength ofthe LO. A compensation glass slide on a rotary mountis employed to match the group delay of the LO withthat of the probe field. With such a design, both theprobe field and the LO travel through the same op-tics, ensuring passive phase stability. Compensationfor the group delay difference is important and can beadjusted by rotating the glass slide until maximizedoscillation visibility is achieved. We note that whilethe pump beam also traverses the 4 f setup, the pre-sence of the long pass filter in the arm of the inter-ferometer blocks the blue edge of the pump spectrumand allows spectral filtering of the interferometricsignal.

3. Results and Discussion

A. Fourier Transform Coherent Anti-Stokes RamanScattering Results

A typical time-domain FTCARS signal is shown inFig. 3 for the solvent 2-propanol. The large NR signalis evident near zero delay, while the dominant modenear 800 cm−1 is apparent at longer delays (shown inthe inset). In Fig. 4 we show FTCARS images of asample of 15 μm polystyrene beads imaged with4mW of power in each pulse. Figure 4(a) showsthe NR signal obtained from a single pulse. While

Fig. 2. (a) Experimental setup of standard FTCARS. The laser isa 12 fs Ti:sapphire oscillator centered at 790nm. BS: beam splitter,LP: long-pass filter, SP: short-pass filter, Obj: objective lens. A He–Ne fringe tracking system (not shown) provides accurate monitor-ing of the time delay. For IFTCARS, the optical arrangementshown in (b) is added after the interferometer, and the long-passfilter (LP) is moved to filter the pump arm only. RM: return mirror,CM: curved mirror, gr: grating, ND: linear ND filter, EM: end mir-ror (Fourier plane), cg: compensation glass.

5792 APPLIED OPTICS / Vol. 47, No. 31 / 1 November 2008

the chemical contrast provided by NR signals is lim-ited, we note that it may also find applications fornoninvasive imaging [42]. In Fig. 4(b) we showspectrally-resolved images of a single bead, acquiredwith 7ms=pixel exposure time with 16 cm−1 spectralresolution. Higher spectral resolution is readily ob-tained by scanning longer τ delays. We show the cor-responding FTCARS spectrum for a single pixel inthe bead in Fig. 4(c). Figure 5 shows a larger imageof 15 μm polystyrene beads embedded in PMMA andimaged under the same acquisition conditions.

B. Interferometric Fourier Transform Coherent Anti-StokesRaman Scattering Results

At relatively high excitation (>3mW), the NR signalfrom pulse 2 provides a large enough LO to amplifythe weak FTCARS signal interferometrically, allow-ing shot-noise-limited detection. However, ideal ima-ging conditions for biological samples must employthe lowest possible incident intensity. Under suchconditions the NR background may no longer provideadequate signal amplification. Here IFTCARS can beemployed to optimize the imaging conditions. We de-monstrate this fact in Fig. 6, which compares inter-ferometric and standard FTCARS line scans takenon a 4 μm polystyrene bead, acquired with 13pJ(1mW) pulses in 4 s. Figure 6(a) employs IFTCARS,while Fig. 6(b) shows the corresponding image usingstandard FTCARS (where the added LO has beenblocked). The τ delay range for these images is∼2100 fs, yielding ∼16 cm−1 spectral resolution. Un-der the same experimental conditions, IFTCARS pro-duces a bright resonant image at the expectedspectral peak position for polystrene within the spec-tral resolution of the measurement. Figure 6(c) com-pares the power spectrum for a single pixel in theimage, demonstrating the considerable improvementmade with the addition of the LO. We note that theexcitation conditions and image acquisition time of

the IFTCARS data are highly competitive with otherrecent spectrally-resolved CARS approaches [16,36].

In FTCARS, phase instabilities between pulse 1and 2 are not a significant source of noise. Pulse 1generates the long-lived Raman coherences, whilepulse 2 probes these coherences. CARSmodes we canimage have frequencies of 400–1500 cm−1, or equiva-lently, wavelengths of 25–6:7 μm. Since we use a He–Ne fringe tracking system to determine the timedelay between pulses 1 and 2, optical pathlengthfluctuations between the two arms of the interferom-eter are accounted for with an error of ≪6:3nm.Thus pathlength fluctuations are accounted for tobetter than λ=1000 for even the highest frequencymode, indicating that this is not a significant source

Fig. 3. Time-domain data of 2-propanol using standard FTCARSspectroscopy. Incident pulse energies were 300pJ and acquisitiontime was 1 s. The ratio of resonant to NR signal field is 1:20, asmeasured from the Fourier transform of the time-domain data.

Fig. 4. (a) Nonresonant background image of 15 μm polystyrenebeads in water (4mW in each beam, 512 × 512 pixels, 10 μs expo-sure time per pixel); (b) FTCARS image of a single polystyrenebead from the sample shown in (a) (4mW in each beam, 36 × 36pixels, 7ms exposure time per pixel, spectral resolution of16 cm−1); (c) FTCARS spectrum from a single pixel within the beadin image (b).

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of noise in FTCARS. More serious than phase stabi-lity between pulses 1 and 2 is the need for phase sta-bility between the probe and LO. Since the probe andLO traverse the same optical path (they do not traveldifferent arms of the interferometer), they have pas-sive phase stability. To quantify the phase stability,we have performed spectral interferometry [43] tomeasure the relative phase between the LO and NRsignal generated by the probe in a solution of 2-propanol. This measurement required inserting anextra piece of glass in the probe beam at the Fourierplane [shown in Fig. 2(b)] to produce a 1:7ps delaybetween the LO and the probe. Based on this mea-surement, we find an RMS phase stability of λ=350over a period of several minutes, indicating that thepassive phase stability of the method is morethan robust enough on the time scales relevant forimaging.

C. Noise Considerations in Fourier Transform CoherentAnti-Stokes Raman Scattering

Whether or not a stronger LO can increase the SNRdepends on the noise character of the system. Threetypes of noise are present in the time-domainFTCARS measurement: laser noise, detector noise,and electronic noise. Ti:sapphire oscillators areknown to have amplitude fluctuations around 0Hzon the order of 1%. This type of noise has a lineardependence on the input light power, and is oftensuppressed by shifting the signal to higher frequen-cies by fast scanning and the use of balanced detec-tors. For low light measurements and high dataacquisition bandwidth, this type of noise is oftenmuch smaller than the noise from the detector, asis the case in our FTCARS measurements. Mostlow light linear detectors (PMTs, avalanche photo-diodes (APDs)) have three noise components: darkcurrent, shot noise, and Johnson noise, where the lat-ter component is much weaker than the first two and

can, in most cases, be neglected. The dark noise pre-sents a constant background signal while the shotnoise can be described by

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2qIs▵f

p, where Is is the

current (proportional to the incident light intensity

Fig. 5. FTCARS images of 15 μm polystyrene beads embedded inPMMA. The image is acquired with 4mWpower in each beamwitha data acquisition time of 7ms=pixel. The spectral resolution is16 cm−1. The top row of images show amaximum contribution fromthe PMMA near 820 cm−1, while the lower row corresponds to thedominant polystyrene peak near 1000 cm−1 in agreement with theRaman reported spectra. The upper row has been multiplied by afactor of 4 to show the weaker PMMA signal on the same scale asthe polystyrene.

Fig. 6. (a) Line scan through a 4 μm polystyrene bead taken withIFTCARS. The image is acquired with 1mW power in each beamwith a data acquisition time of 4 s and spectral resolution of16 cm−1. (b) Corresponding standard FTCARS line scan (addedLO is blocked). (c) Comparison of FTCARS spectra at pixel 75in the two images.

5794 APPLIED OPTICS / Vol. 47, No. 31 / 1 November 2008

I when operating in the linear regime), q is the ele-mentary charge, and ▵f is the bandwidth. Hence thetotal noise can be written as aþ b

ffiffiffiI

p, where a is the

overall background noise including dark currentnoise from the detector and electronic noise and b isa constant describing shot noise. Increasing or de-creasing data acquisition time may lower or raiseboth a and b proportionally, and the ratio betweenbackground noise and shot noise is conserved. Ide-ally, the dark noise originates only from the dark cur-rent of the detector. In FTCARS however, there canbe leakage from imperfect filters, electronic noise,and the NR signal generated by the first pulse. Allof these components increase the background noisefloor. Interferometric FTCARS suppresses this back-ground noise by increasing the LO field. As we cansee from Eq. (1), like the shot noise, the signal am-plification is linearly proportional to the square rootof the intensity of the LO. The signal-to-noise ratio isthus,

SNR ¼ 2cffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiIlocalIr12

p

aþ bffiffiffiI

p <2c

ffiffiffiffiffiffiffiffiIr12

p

b; ð2Þ

where I is the total incident intensity that can be ap-proximated as Ilocal. From Eq. (2), we can see that theupper limit of the SNR is 2c

ffiffiffiffiffiffiffiffiIr12

p=b, which is inde-

pendent of the background noise a. This limit isachieved when the shot noise is much greater thanbackground noise. In this regime, the detection isshot-noise limited.To better characterize the SNR within the fre-

quency range of our experiments, we first performednoise measurements under the same conditions asthose used for imaging. Varying the incident inten-sity, we digitized the PMT signal using a high speeddata acquisition card (PCI6110) at a sampling ratehigher than twice the bandwidth of the detection sys-tem. The averaged amplitude of the Fourier trans-form around 100Hz represented the noise at agiven incident intensity, which is close to the actualsignal measured. (Note that the detection frequencyis determined by the speed at which we scan our timedelay.) From these data we obtained values of a ¼3:1� 0:2 × 10−13 W and b ¼ 9:0� 0:4 × 10−7 W1=2 forthe parameters in Eq. (2) under typical FTCARS ex-perimental conditions. Normalizing for the numberof data samples available, we plot the noise as a func-tion of LO power in Fig. 7. Two regimes are clearlyseen: the regime in which background noise domi-nates (LO < 1pW) and the shot-noise-limited regime(LO > 100pW). Thus the SNR will saturate with in-creasing LO power due to the fact that the signal andshot noise both scale the same way with LO. Thismeans that arbitrarily increasing the LO will notfurther enhance the SNR.To explore the dependence of the FTCARS signal

amplitude on several experimental parameters, wecalculate the time-domain FTCARS signal as out-lined previously [29]. The relative size of the reso-nant to NR background, is set by matching the

resonant to NR signals calculated for FTCARS tothe measured ratio determined from FTCARS dataon 2-propanol (shown in Fig. 3). The spectral resolu-tion is set to 10 cm−1, corresponding to a maximumtime delay of 3ps. We assume transform-limited in-put pulses of 12 fs in duration, centered at 790nmand perform spectral filtering with a constant se-paration of 5nm between long and short pass filters.As with the experimental data, we window out thefirst 300 fs of the time-domain data before takingthe Fourier transform to yield the FTCARS spec-trum. We vary several parameters to study their ef-fect on the FTCARS signal: the long pass filter edgewavelength, the power ratio between the two pulses,and the frequency of the Raman mode excited. Theresults are summarized in Fig. 8. As expected, thecalculations show that the resonant signal level is re-duced for higher frequency modes, since fewer fre-quency combinations can excite the given mode.However, this is partly compensated by the fact thatthe larger blue shift of the higher frequency modesmeans that the signal passes the combination of longpass and short pass filters more efficiently than forlower frequency modes, resulting in a resonant sig-nal level that is almost flat over the entire 600 cm−1,demonstrating the very broad effective bandwidth ofthe FTCARS method. The choice of long pass filterwavelength also influences the relative efficiencywith which different modes can be excited. In the ab-sence of an external LO, the signal is linearly depen-dent on pulse 1 and quadratically dependent on pulse2, with the quadratic dependence arising from inter-ference between the resonant signal and the NRbackground generated by pulse 2. Thus as expected,the second pulse should be stronger than the firstpulse for optimum excitation, as shown in Fig. 8(b).

With the addition of a LO, as in IFTCARS, thesecond pulse need no longer be stronger than thefirst pulse to obtain a high SNR. To estimate the

Fig. 7. Total noise versus LO power. Two regimes are clearlyseen: a background noise regime (LO < 1pW) and the shot noiseregime (LO < 100pW). The actual LO used in the interferometricFTCARS images shown in Fig. 6 is 38pW as indicated. At very lowexcitation power where the NR background is small, standardFTCARS results in operation within the background noise regime,degrading the SNR.

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enhancement obtainable, we consider the experi-mental conditions corresponding to Fig. 6. Here a to-tal LO of 38pW was used in IFTCARS, whereas thestandard FTCARS produced a NR background (orLO) of only 4pW. Leakage through the filters pro-duced a background signal power of 22 pW. UsingEq. (2) we predict a SNR enhancement of ∼2 inthe signal field amplitude (or ∼4 in the signal inten-sity) with the addition of the LO, consistent with ourexperimentalresults. This magnitude of LO was chosen to operateas close to the shot-noise limit as possible while tak-ing into account the finite dynamic range of the 12 bitdata acquisition electronics. Further increasing theLO without the need to consider the dynamic rangeof the data acquisition is expected to give at most a30% improvement in SNR. We note that a recent pa-per has discussed the capability of achieving shot-noise-limited detection of heterodyne CARS signalsusing a variety of detectors [26]. They find that forlower gain detectors, such as photodiodes, hetero-dyne CARS shows a large degree of enhancementover nonheterodyne detection, while the enhance-ment is more modest for PMT detection. Our choice

of PMT is motivated by the high gain and quantumefficiency that allows shot-noise-limited operation atlower signal levels that are well-separated from theregime where laser noise becomes significant.

Another important parameter for optimizing theIFTCARS signal is the interference contrast constantc, which depends on the relative spectral profiles ofthe signal and LO. To investigate the effect of usingthe blue edge of the laser pulse (as in interferometricFTCARS) and the NR signal (as in standardFTCARS), we calculated the interference strengthfor these two cases relative to interference using anideal LO with spectral characteristics that matchedthe signal. Using the same assumptions as in the pre-viously discussed FTCARS calculation, the interfer-ence contrast in both cases is within 5% of theoptimum value for an 800 cm−1 mode and within 25%for a 1400 cm−1 mode. Thus, despite the fact that theNR signal has a long tail extending past 685nm, thedifference between employing the NR signal and theblue edge of the laser pulse as the LO is negligible, inagreement with our experimental observations. Thebenefit of IFTCARS comes from the ability to adjustthe magnitude of the LO, rather than its spectralcharacteristics.

One extreme situation is where the LO added isgreater than 1nW, providing a total signal that isstrong enough to be detected by Si detectors, whosequantum efficiency is higher than that of a PMT inthe near infrared region. This is equivalent to theconventional pump-probe technique, in which no fil-ters are placed before the sample and the entire blueedge of the probe pulse enters the detector. At thissignal level, laser noise becomes significant and a ba-lanced detector is required to cancel the laser ampli-tude fluctuations. Given that only background noiseand shot noise are left, we can conclude that, at best,the SNR should remain the same as the shot-noise-limited value 2c

ffiffiffiffiffiffiffiffiIr12

p=b, where b is determined by

the Si detector used. In the conventional pump-probetechnique, no attempt is made to adjust the ratio be-tween the LO and the signal field. Maximizing Ir12requires a strong probe pulse, while obtaining highersignal contrast requires a weak LO and, hence, aweak probe pulse. With the flexibility of interfero-metric CARS setup, however, the ratio between thefirst pulse and second pulse can be optimized whileindependently choosing the LO to overcome the back-ground noise while remaining within the dynamicrange of the data acquisition electronics.

4. Time and Frequency Domain Considerations

Initial Fourier transform measurements were re-ported to have a “multiplex advantage” over scan-ning monochromator measurements [44]. The originof this advantage is the following: for a measurementtime T, during which time N measurements aremade, a Fourier transform method can measureN=2 frequencies, each of which has N=2 times longerdata accumulation time than does a scanning mono-chromator that measures N=2 frequencies one at a

Fig. 8. (a) Dependence of the FTCARS resonant signal amplitudeon the frequency of the CARSmode for different choices of the long-pass filter wavelength. (b) Dependence of the FTCARS resonantsignal amplitude on the frequency of the CARSmode to be excited.Several different relative power ratios between pulses 1 and 2ðP1=P2Þ are shown.

5796 APPLIED OPTICS / Vol. 47, No. 31 / 1 November 2008

time. With the wide use of multiplex CCD detectorsthis advantage is no longer applicable: a detectorwithN=2 channels can accumulate signal in each fre-quency channel over the full duration of the mea-surement, making the available measurement timeequivalent for time and frequency domain methods.It is of interest to consider how the ideal SNRscompare for time and frequency domain experimentsunder shot-noise-limited conditions in which anamount of resonant signal Ir12 has been generated.Subsection 3.C provided an estimate of the SNR ob-tainable with shot-noise-limited IFTCARS. In a shot-noise-limited multiplex CARS experiment, the SNRwill be given by Ir12=ðb

ffiffiffiffiffiffiffiffiIr12

p Þ ¼ ffiffiffiffiffiffiffiffiIr12

p=b, which is

roughly equivalent to the SNR obtainable by IFT-CARS [see Eq. (2)]. A heterodyne-detected imple-mentation of multiplex CARS will do no better thanIFTCARS: the addition of a larger LO increases theshot noise as rapidly as it amplifies the signal, mak-ing heterodyne detection useful only when the addi-tion of a LO is necessary to reach the shot-noise-limited regime.Practically, the noise characteristics of the differ-

ent detectors used in time and frequency domainmeasurements must also be considered. The higherquantum efficiency of CCD detectors over PMTs canoffer some improvement (approximately a factor of 2)in SNR for shot-noise-limited CARS imaging. Wealso note that while FTCARS requires only a singledetector, avoiding spectrometer losses, this benefit isoffset by losses due to imperfect filters, and the factthat the resonant signal that is not sufficiently blue-shifted with respect to the probe is rejected in ourspectral filtering method. Other considerations im-portant for biological imaging must include samplephotodamage. Koester et al. have studied photodam-age in cells using 75 fs–3:2ps pulse durations [45].They have found that photodamage scales nonli-nearly with incident intensity, providing motivationfor using longer pulses. The pixel dwell timemay alsobe a consideration for minimizing photodamage. Byrapidly scanning one line in the image while scan-ning the time delay, FTCARS returns multiple timesto make measurements at a given sample position,but has a shorter dwell time at each measurement.Depending on the dominant photodamage mechan-ism, this could provide an advantage over spectraldomain methods that have longer consecutive dwelltimes at a given sample position. Further photodam-age studies to assess the effects of dwell time andshorter pulse durations are currently underway.

5. Conclusions

We have presented chemical imaging using FTCARSmicroscopy and have discussed the experimentalconsiderations necessary for optimizing FTCARSimages. We have demonstrated interferometricFTCARS imaging, which is a variant of the FTCARSapproach with the flexibility to control the LO toreach the shot-noise-limited regime. Different frommany other heterodyne CARS methods, IFTCARS

has passive phase stability, greatly simplifying theexperiment. We performed signal-to-noise analysisto discuss the effect of the LO, finding that it can sup-press the background noise arising from detectordark current noise and electronic noise, improvingthe SNR under low excitation conditions. In theory,further increase in the LO is expected to give a minorimprovement in the SNR. In practice, however, theamount of LO that can be employed is limited bythe dynamic range of the data acquisition electronics.Based on the amount of LO, interferometric FTCARSis a hybrid method that stands between FTCARS (noadded LO) and pump probe spectroscopy (maximumamount of LO) techniques. The flexibility of inter-ferometric FTCARS makes it possible to optimizethe ratio between pump and probe and the amountof LO separately, promising to yield the highest pos-sible SNR (limited by shot noise only) with low re-quirement on the dynamic range of the dataacquisition electronics.

The authors gratefully acknowledge funding fromthe National Science Foundation (NSF) (grant0721370), the NSF-funded Frontiers in Optical Co-herent and Ultrafast Science (FOCUS) Center, theAlfred P. Sloan Foundation and the American Chemi-cal Society Petroleum Research Fund.

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