## Abstract

We report a unique triple-frequency symmetric subtraction scheme to effectively remove the nonresonant background in coherent anti-Stokes Raman scattering (CARS) microscopy. Theoretical and experimental studies show that this unique scheme has an optimal performance for high contrast vibrational imaging, particularly useful when the resonant signal was larger than or comparable to the nonresonant background.

© 2010 OSA

## 1. Introduction

First demonstrated by Duncan et al. at 1982 [1], coherent anti-Stokes Raman scattering (CARS) microscopy has received great interest as an emerging modality for biological and biomedical imaging in the past decades [1,2]. CARS technique is a third-order nonlinear optical process in which a pump beam at frequency ${\omega}_{p}$ and a Stokes beam at frequency ${\omega}_{s}$ are mixed to coherently interact with a sample. When the beat frequency (${\omega}_{p}-{\omega}_{s}$) between the two beams matches a particular Raman-active vibrational frequency ${\Omega}_{R}$ and the phase-matching condition is satisfied, a strong anti-Stokes signal at frequency ${\omega}_{as}=2{\omega}_{p}-{\omega}_{s}$ is radiated [3]. CARS microscopy has become a valuable tool for biomedical imaging due to its chemical selectivity for investigating label-free samples, three-dimensional sectioning ability as well as superior sensitivity over spontaneous Raman techniques. Despite all of its strengths, a major drawback of CARS is the existence of a nonresonant background mixed coherently with the resonant signal of interest which not only obscures the vibrational contrast of CARS images but also causes a redshift of the spectral peak, complicating spectral assignment for chemical bonds. The nonresonant contribution to the CARS signal originates from the third-order nonlinear susceptibility ${\chi}^{(3)}$ which consists of a resonant part ${\chi}_{R}^{(3)}$ and a nonresonant part ${\chi}_{NR}^{(3)}$. The resonant part is a complex quantity and represents the Raman response of molecular vibrations, while the nonresonant part depicts the electronic contributions to the third-order susceptibility from both the scatterers and surrounding media, and is essentially a real constant independent of the Raman shift in the limited spectral region of a single Raman band [3].

Various techniques have been developed to suppress the nonresonant contribution to the CARS signal, including epi-detection, polarization-sensitive detection, time-resolved detection, pulse shaping of excitation pulses, nonlinear interferometric CARS and multiplex CARS, etc [4–16]. These techniques are limited by either severe resonant signal attenuation or complicated implementation. Digital image processing has been recognized as a simple and robust method to remove the nonresonant background in CARS [17]. A technique of digitally subtracting the off-resonance image from the on-resonance one was first practised by Duncan et al. to image deuterated liposomes in CARS microscopy [18]. Li et al. [19] and Zimmerley et al. [20] recorded the difference and ratio images acquired at the peak and dip positions of a specific CARS band to obtain a high contrast of image. Dudovich et al. [21] used the image subtraction method with pulse-shaping techniques to realize background suppression by measuring the difference between the constructive interference and the destructive interference images. Three pulsed lasers have also been used to simultaneously compare CARS signals measured at different Raman shifts by frequency modulation (FM) [22] or a dual-pump scheme [23]. The dual-pump CARS employs a digital subtraction on the two simultaneously acquired images through the two excitation channels, while FM-CARS improves the sensitivity and reduces noise in digital subtraction with high-frequency repetition rates of the process. In this work, we report a unique triple-frequency symmetric subtraction scheme to effectively remove the nonresonant background in CARS microscopy. The theoretical mechanism behind the digital image processing which could yield background-free vibrational contrast for CARS imaging is also described and discussed. Further CARS experiments confirm the utility of the triple-frequency symmetric subtraction technique in practical CARS microscopy imaging.

## 2. Theory of CARS background suppression by digital image processing

The CARS signal intensity is related to the third-order nonlinear susceptibility (${\chi}_{R}^{(3)}$ and ${\chi}_{NR}^{(3)}$) as follows [3]:

*A*is a constant related to the number of oscillators and the Raman cross-section for a single vibrational mode at ${\Omega}_{R}$,

*δ*denotes the beat frequency or the Raman shift, and $2\Gamma $ is the Raman linewidth (FWHM). Substituting Eq. (2) into Eq. (1), we obtain:

^{−1}where the spontaneous Raman line shape is close to a single vibrational mode. The resonant (second) term in Eq. (3) is symmetric about $\delta ={\Omega}_{R}$, while the mixed (third) term is anti-symmetric about the point (${\Omega}_{R}$, 0). The values of ${\Omega}_{R}$ and

*Γ*are chosen to be 2900 cm

^{−1}and 38 cm

^{−1}respectively by fitting the peak of the spontaneous Raman spectrum with a Lorentzian function, and $A/{\chi}_{NR}^{(3)}=55{\text{cm}}^{\text{-1}}$ is determined by measuring the peak and dip positions of the CARS spectrum [3].

#### 2.1 Comparison of CARS images on resonance and off resonance

In the method of subtracting the off-resonance image from the on-resonance image [17], the resulting image can be expressed as:

*δ*moves away from ${\Omega}_{R}$, the mixed term approaching zero is much slower than the resonant term does (Fig. 1(a)), especially when ${\chi}_{NR}^{(3)}$ is relatively large. If the off-resonance image is acquired at a region far enough from ${\Omega}_{R}$ for the mixed term to approach zero, the frequency difference may be too large for ${\chi}_{NR}^{(3)}$ to have a flat response, and thus other Raman bands inside the spectral region may interfere with the subtraction. As a result, this method is essentially more effective for strong scatterers where the resonant contribution dominates the CARS signal ($A/\Gamma >>{\chi}_{NR}^{(3)}$).

#### 2.2 Comparison of CARS images at the peak and dip positions

To determine the peak and dip positions of a CARS spectrum, we let the first-order derivative of ${\left|{\chi}^{(3)}\right|}^{2}$ be zero and solve the equation, which gives:

The resulting image is obviously not free of the nonresonant contribution, but when the resonant signal is insignificant compared with the nonresonant background ($A/\Gamma <<{\chi}_{NR}^{(3)}$), the result becomes $2{\chi}_{NR}^{(3)}A/\Gamma $. Assuming the nonresonant background from the scatterer is negligible and ${\chi}_{NR}^{(3)}$ is mainly from the surrounding medium (e.g., water), ${\chi}_{NR}^{(3)}$ can be measured from a pure nonresonant image of the surrounding medium and divided from the resulting image, yielding a resonant contrast proportional to the density of vibrational oscillators [18]. Under the same condition ($A/\Gamma <<{\chi}_{NR}^{(3)}$) the ratio image between the peak and dip positions gives a similar result $1+2A/({\chi}_{NR}^{(3)}\Gamma )$ [19]. Therefore, this method renders advantageous vibrational contrast for weak scatterers. On the other hand, the interference of the nonresonant background with the resonant signal is prominent when $A/\Gamma $ is comparable to ${\chi}_{NR}^{(3)}$. In addition, a prior knowledge of the peak and dip positions of the CARS spectrum is required.

#### 2.3 Triple-frequency symmetric subtraction scheme

Here, we propose a novel triple-frequency symmetric image subtraction scheme by utilizing respectively the symmetry and anti-symmetry of the resonant and the mixed terms in Eq. (3). The scheme is implemented by acquiring three images of the same sample region at $\delta ={\Omega}_{R}$ and $\delta ={\Omega}_{R}\pm \gamma $, respectively. The resulting image is then obtained by subtracting the two images at $\delta ={\Omega}_{R}\pm \gamma $ from the on-resonance image:

Through this simple operation, the nonresonant signal can be completely removed from the resulting image with the intensity being proportional to the square of the density of vibrational oscillators. Hence, when the symmetric shift $\gamma =\Gamma $, we obtain $\left|2{I}_{on}-({I}_{left}+{I}_{right})\right|\propto {A}^{2}/{\Gamma}^{2}$, while when *δ* is at the off-resonance region ($\gamma >>\Gamma $), the maximum signal level $\left|2{I}_{on}-({I}_{left}+{I}_{right})\right|\propto 2{A}^{2}/{\Gamma}^{2}$. It is worth noting that the off-resonance condition for this scheme is much more relaxed than that for the method of subtracting the two images on resonance and off resonance as the resonant term approaches zero much faster than the mixed term does.

#### 2.4 Numerical modeling of background-free CARS imaging with femtosecond laser excitation

The above derivations are based on the assumption that the bandwidths of pump and Stokes excitation light (e.g., picosecond pulses) are narrower than or comparable with the linewidth of the particular Raman vibrational band. In our CARS experiments, we employed the femtosecond pulses which have a FWHM bandwidth of ~100 cm^{−1} much larger than the Raman linewidth of biomolecules in tissue. Whether the broadband excitation significantly alters the behavior of the resonant, nonresonant and mixed components of the total CARS signal should be studied systematically. Here we apply the integration model [24] to numerically simulate the CARS signal under the broadband (~100 cm^{−1}) excitation. The femtosecond pulses used in this work have an intensity profile following sech^{2} function. Via Fourier transform, the pump and Stokes beams are assumed to be transform-limited pulses with hyperbolic secant spectral profiles:

*E*and

_{p0}*E*are the peak intensities of the pump and Stokes beams, ${\omega}_{p0}$ and ${\omega}_{s0}$ are the center frequencies of the two beams, and ${\Delta}_{p}$ and ${\Delta}_{s}$ are the FWHM bandwidths of the two beams, respectively. The third-order polarization in CARS interaction is written in an integration form:

_{s0}The resonant, nonresonant and total CARS signals are calculated by assuming ${\chi}^{(3)}={\chi}_{R}^{(3)}$, ${\chi}^{(3)}={\chi}_{NR}^{(3)}$ and ${\chi}^{(3)}={\chi}_{R}^{(3)}+{\chi}_{NR}^{(3)}$, respectively. The mixed component is obtained by subtracting the first two components from the total CARS signal. The calculated spectra of the three components and the CARS signal are shown in Fig. 2
. A great increase of the nonresonant signal can be observed and the resonant response curve is broadened, resulting in a more dispersive CARS spectrum compared with the spectrum calculated with monochromatic light in Fig. 1(b). However, the flat spectral response of the nonresonant component, the symmetry of the resonant component and the anti-symmetry of the mixed component are maintained, which provides the rationale for triple-frequency symmetric subtraction. The major influence is that the symmetric shift *γ* has to be much larger with broadband sources to yield the same resonant signal level as compared to that with narrowband sources.

## 3. CARS Experiments

To evaluate the utility of the triple-frequency symmetric subtraction scheme to effectively remove the nonresonant background in coherent anti-Stokes Raman scattering (CARS) microscopy, we have conducted the CARS measurements on cotton fibers. Details of our CARS microscopic system developed for vibrational imaging have been reported else [6–8]. Briefly, the output of a femtosecond Ti:Sapphire laser (wavelengths tunable from 700 to 1000 nm, 130 fs, 76 MHz repetition rate, horizontal polarization, Mira 900, Coherent Inc.) pumped by a Nd:YVO_{4} laser (10 W, Verdi, Coherent Inc.) was divided into two beams by a beam splitter. One of the laser beams worked as the pump beam, and the other was used to pump an OPO (wavelengths tunable from 1100 to 1600 nm, Coherent Inc.) to produce the Stokes beam. The Stokes beam was then combined collinearly with the pump beam through a dichroic mirror, coupled into a laser scanning confocal microscope (FV300, Olympus) and then focused onto the sample by a microscope objective (UPlanSApo 40×, N.A. 0.9, Olympus) for CARS generation. Synchronization of the two pulse trains to maximize the temporal overlap at the sample was achieved by an adjustable beam delay line along the pump light path. The CARS signals were collected by a condenser (UPlanSApo 20×, N.A. 0.75, Olympus) in the forward-direction and detected by a photomultiplier tube (R3896, Hamamatsu) through a short-pass filter set to eliminate the excitation light.

Due to the broadband of femtosecond pulses, the broad Raman bands are preferred for our experiment as their spectral features can be resolved by broadband excitations. The CH stretching band of cellulose at 2800~3000 cm^{−1} in cotton fibers has a large Raman linewidth (~76 cm^{−1}). The cotton fibers consisting of polymer chains of cellulose were imaged in water environment. Then microcrystalline cellulose (MCC, Avicel PH 101) was imaged without water, serving as a smaller and weaker scatterer. CARS spectra of cotton in water and dry MCC were also measured by fixing the pump beam frequency at 11933 cm^{−1} while varying the Stokes beam frequencies. The average powers of the pump and Stokes beams on the samples are 10 and 5 mW, respectively. Within the frequency range of spectrum measurement, the intensity and the bandwidth of the Stokes beam as well as the detection efficiency are not uniform. To eliminate the effect from these factors, we first obtained the CARS spectrum of MgF_{2} which has no visible Raman mode in the spectral range and exhibits a highly uniform nonresonant response. The intensities of the MgF_{2} spectrum were normalized to the maximum intensity, and all the spectra measured afterwards were divided by this reference spectrum for calibration. The acquired images were also normalized through dividing the image by the reference MgF_{2} intensity at the corresponding frequency.

## 4. Results and discussion

Figure 3
shows the comparison of CARS spectra of cotton fibers immersed in water and dry MCC. The corresponding spontaneous Raman spectra were acquired on a microRaman spectrometer system (inVia, Renishaw, UK). The red-shifted peaks and the dips at the blue end are clearly visible. The measured CARS spectra are less dispersive than the simulated curve in Fig. 2(b), indicating a limited influence of broadband excitation. Triple-frequency symmetric subtraction was applied to CARS imaging of cotton in water with the symmetric shift *γ* varying from 8 cm^{−1} to 100 cm^{−1}. According to Eq. (7), the resonant signal increases with *γ* until reaching an optimum value at the off-resonance region. Contrast of a resulting image is defined as the intensity ratio of the bright object region to the background region. The ratio contrast also increases with the resonant intensity as the background intensity is almost the same across different symmetric shifts as shown in Fig. 4
. Both contrast and the resonant intensity saturate at about 80~100 cm^{−1}. Beyond this region the background intensity is affected by the increasing resonant signal from the broad OH stretching band of water at 3000~3600 cm^{−1}.

The triple-frequency symmetric subtraction scheme on CARS imaging was tested using two different samples (i.e., cotton fibers in water; dry MCC) at symmetric Raman shifts of 30 cm^{−1} (which is close to *Γ*), and of 80 cm^{−1} (which approaches the off-resonance region), respectively. The effect of triple-frequency symmetric subtraction scheme on CARS contrast enhancement has been demonstrated with the results compared with the on-resonance image and the resulting image of the ‘peak minus dip’ method. Figure 5
shows the comparison of CARS images (CH stretching band of cellulose at ~2900 cm^{−1}) of cotton fibers in water: (a) normal CARS on resonance; (b) triple-frequency subtraction at symmetric shift of 30 cm^{−1}; (c) triple-frequency subtraction at symmetric shift 80 cm^{−1}, and (d) ‘peak minus dip’ image. The corresponding intensity profiles along the sampling lines indicated in the CARS images [Figs. 5((a) to (d))] are shown in Figs. 5((e) to (h)), respectively. The conventional on-resonance CARS image [Fig. 5(a)] has a signal-to-background contrast of ~3.5:1 limited by nonresonant contributions mainly from the water environment. The resulting image from ‘peak minus dip’ method [Fig. 5(d)] gives an improved image contrast (~15:1) by a simple digital subtraction between the two CARS images acquired at the peak and dip positions of the CARS spectrum. However, the contrast is still limited by a nonresonant background. On the other hand, the resulting image from triple-frequency symmetric subtraction at symmetric shift of 30 cm^{−1} [Fig. 5(b)] has a much higher signal-to-background contrast (~20:1) than the ‘peak minus dip’ image, but suffers from an attenuation of the resonant intensity. The scheme at symmetric shift of 80 cm^{−1} [Fig. 5(c)] further enhances the contrast as the resonant intensity is significantly raised with a larger symmetric shift while the nonresonant background remains at the same level, thereby achieving a 13-fold improvement in image contrast as compared to the on-resonance image, and a 3-fold contrast improvement as compared to the ‘peak minus dip’ imaging. The above results confirm the superior performance of the triple-frequency symmetric subtraction scheme for effective suppression of the nonresonant background in CARS imaging. Although the theoretical calculations of this unique scheme proposed yields background-free vibrational contrast regardless of the symmetric shift values, in practice, the contrast enhancement achieve increases for the larger symmetric shift until signal saturation in the presence of a nonzero background as anticipated by Eq. (7).

Figure 6
shows the comparison of CARS images of dry MCC at the CH stretching band of ~2900 cm^{−1}: (a) normal CARS on resonance; (b) triple-frequency subtraction at symmetric shift of 30 cm^{−1}; (c) triple-frequency subtraction at symmetric shift of 80 cm^{−1}, and (d) ‘peak minus dip’ image. The corresponding intensity profiles along the sampling lines indicated in the CARS images [Figs. 6((a) to (d))] are shown in Figs. 6((e) to (h)), respectively. The conventional on-resonance CARS image [Fig. 6(a)] shows the presence of a nonresonant contributions (mainly arising from coverslip) comparable to the resonant signal level ($A/\Gamma ~{\chi}_{NR}^{(3)}$), resulting in a poor signal-to-background contrast (~2:1). At a symmetric shift of 80 cm^{−1} [Fig. 6(c)], triple-frequency symmetric subtraction renders a 5-fold improvement on the on-resonance image and 2-fold improvement on the ‘peak minus dip’ image. Again, the above results reinforce the superiority of the triple-frequency symmetric subtraction scheme for effective suppression of the nonresonant background in CARS imaging.

Nevertheless, we also note that the contrast enhancements in CARS imaging for the weaker Raman scatterers is relatively less prominent as compared to the strong Raman scatterers using the triple-frequency subtraction scheme. This tendency, in fact, agrees with the implications of Eq. (7) that the resulting processed image intensity depends on the square of $A/\Gamma $. One notes that the resulting images of the triple-frequency subtraction scheme may suffer from an intensity attenuation of weak scatterers due to the quadratic dependence of the resulting image intensity on $A/\Gamma $. Under this condition ($A/\Gamma <<{\chi}_{NR}^{(3)}$), difference image at the peak and dip positions could provide a better approach to digitally removing the nonresonant background. Another limitation of triple-frequency symmetric subtraction scheme is that it is essentially more effective for an isolated Raman band without the interference of other nearby vibrational modes. This requires the chosen symmetric frequency shift to be smaller than the distance between the resonant Raman band and a neighboring band, which may be hardly applicable in spectrally crowded regions. On the other hand, the optimum value of symmetric shift is determined by both the Raman linewidth and the excitation bandwidth used as previously indicated. Consequently, the broadband source (femtosecond pulses) used in this work is limited by its low spectral resolution and picosecond pulses are believed to be a better excitation source for implementing the triple-frequency subtraction scheme as picosecond excitation is able to resolve the spectral features of typical Raman bands with a Raman linewidth of 10~20 cm^{−1}. Finally, digital image processing techniques remove the nonresonant contribution digitally from the intensity values of each pixel of the acquired image, rather than inherently suppressing the nonresonant signal during the generation or detection process, resulting in a relatively low detection sensitivity compared with the “hardware” techniques using dedicated excitation and detection schemes. The sensitivity is also limited by the accumulated noise from multiple images, which requires a proper filtering during image processing. To further improve the detection sensitivity in a practical system, the proposed triple-frequency subtraction scheme can be implemented in a frequency modulation manner with the resulting images to be measured using three excitation channels and lock-in detection instead of the simple image subtraction.

## 4. Conclusions

Amongst the various techniques aiming to remove the nonresonant background in CARS microscopy, digital image processing offers a simple and robust approach to obtain images with enhanced vibrational contrast. In this work, we comprehensively assess the strengths and limitations of the two well-established image processing methods by deriving the theoretical models. We propose a triple-frequency symmetric subtraction scheme to yield background-free vibrational contrast in CARS imaging. Numerical simulations are also carried out to validate the proposed method under broadband femtosecond excitation. The CARS experimental results show that triple-frequency symmetric subtraction scheme has a superior performance when the resonant signal is larger than or comparable to the nonresonant background. It is believed that the theoretically sound triple-frequency symmetric subtraction method has the potential to become a simple and practical routine operation in CARS imaging for various biomedical and biological systems.

## Acknowledgments

This work was supported by the Biomedical Research Council, the National Medical Research Council, and the Faculty Research Fund from the National University of Singapore.

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