Fast Raman Spectral Imaging Using Chirped Femtosecond Lasers Dan Fu 1, Gary Holtom 1, Christian Freudiger 1, Xu Zhang 2, Xiaoliang Sunney Xie 1 1. Department of Chemistry and Chemical Biology, Harvard University 2. School of Engineering and Applied Sciences, Harvard University Mathematical analysis for quantitative determination of concentrations of different species SRS spectroscopy has strict linear dependence on the chemical concentration. As a result, simple linear algebra analysis can be used for chemometric analysis. Assume that we have M molecule species in a given sample and they are inhomogeneously distributed. SRS signals for a total of K Raman bands at each sample point on a N N spatial grid are measured. At a representative pixel location (i, j), the concentration of species m is C m. If the Raman crosssection for each species at a certain Raman band k is σ k,m, we can write the SRS signal at each Raman shift as a linear sum of all the individual contributors: SRS k = m C m σ k,m P k (1) where P k comprises the multiplication of pump and Stokes power corresponding to the Raman band k as well as the scaling factor related to detection efficiency. The Raman cross-section σ m,k together with the power factor P k can be directly measured using pure solutions of each species at known concentration, resulting in a calibration matrix A: σ 1,1 P 1 σ 1,M P M A = (2) σ K,1 P 1 σ K,M P M Therefore, the SRS signal for the k Raman channels can be written in matrix form: SRS = A C + δ (3) where δ is the detection noise. Both SRS and δ are column vectors with K elements, while C is a column vector with M elements. For each pixel, the concentration of each species can be obtained by solving a set of K linear equations.
In case of spectral imaging, the number of Raman bands K is much larger than the number of species M. Thus the system is over-determined and the matrix is not invertible. A solution can be obtained through the ordinary least square operation: min C A C SRS (4) Because chemical concentration cannot be negative, there is an added constraint to the above equation: C m 0 for all m (5) For each pixel, a solution of M concentration can be obtained. This operation is repeated pixel by pixel, resulting in concentration maps for all the species. We used Matlab (Mathworks) for our SRS spectral imaging data analysis. SRS spectral imaging setup For SRS spectral imaging in the congested C-H stretching region from 2800 cm -1 to 3100 cm -1, we employed a Yb: KGW laser and a synchronously pumped optical parametric oscillator (OPO). The Yb: KGW laser outputs 76 MHz pulses trains centered at 1040 nm. The output has a full-width half maximum (FWHM) bandwidth of 9.3 nm and about 200 fs pulse duration. 1 W of the output is used as the Stokes beam and the rest (~6 W) is frequency doubled by a LBO crystal to 520 nm to pump a lithum niobate based OPO. The OPO is operated at close to zero dispersion. We tuned the OPO output to around 800 nm for use as the SRS pump beam. It has a FWHM bandwidth of over 15 nm. The Stokes beam is amplitude modulated by an EOM modulator (Thorlabs) driven at a quarter of the laser repetition frequency. Different glass blocks are used to chirp the pump and Stokes beams. A total length of 36 cm of NSF57 is used on the Stokes beam path. The total chirp is mostly from these glass blocks plus the dispersion from double passing the EOM. The optimal length of glass for pump beam is experimentally determined from obtaining the narrowest SRS peak and found to be 43 cm of NSF57. The two beams are spatially overlapping by adjusting a dichroic beamsplitter, and temporally overlapped by adjusting a motorized delay stage on the Stokes beam. The Raman shift is linearly related to the interpulse delay between the pump and the Stokes.
Figure S1: Schematic diagram of SRS spectral imaging using two broadband lasers. One of them is a Yb: KGW oscillator (Stokes beam), and the other is a synchronously pumped OPO (pump beam). The Stokes beam is amplitude modulated at 18.7 MHz by double passing an EOM modulator, a quarter-wave plate and a polarizing beamsplitter. The pump and Stokes beam are combined by a dichroic beamsplitter and sent to a laser scanning microscope (IX71/FV300, Olympus). The interpulse delay between the pump and the Stokes beam is adjusted through a motorized stage (Newport). SRS spectra calibration for the OPO laser system based SRS spectral imaging The SRS spectral imaging bandwidth is entirely determined by the bandwidth of the two lasers. For imaging based on the optical parametric oscillator (OPO) system, we operated the OPO in slightly positive dispersion regime to obtain a large output bandwidth. A typical output spectrum of the OPO is shown in Figure S2a. It has an optical FWHM bandwidth of more than 15 nm. The calibration of Raman frequency with respect to delay is very similar to that described in the SRS spectroscopy section except here we used cyclohexane and toluene as our Raman shift standards in the CH stretching region. We chose a 50: 50% mixture of toluene and cyclohexane as the calibration sample. The two peaks of cyclohexane at 2852.9 cm -1 and 2923.8 cm -1, and the peak of toluene at 3057.1 cm-1 are used as landmarks for Raman shift frequency (Figure S2b). By linearly fitting these Raman shifts against delay stage position, we obtain a calibration curve that gives the Raman frequency for any delay position (FigureS2c). We note that the OPO spectrum is not Gaussian shaped, therefore the SRS spectrum exhibit additional intensity variations besides that caused by pulse overlap. In order to normalize all intensity variations, we used a two photon absorbing sample and measured its spectrum. It is known that in this type of pump-probe imaging approach, two-photon
absorption also contributes to the signal. The dye Rhodamine 6G (R6G) has a large two-color two-photon absorption cross-section, much stronger than SRS at the wavelength range used. To a first approximation, we can assume that the R6G TPA cross-section does not change over the wavelength range used and the measured spectrum should reflect the cross-correlation of the pump and Stokes pulses. From the harmonic oscillator model, we can see that the SRS signal is also proportional to the cross-correlation of the two pulses, allowing us to use TPA spectrum to normalize intensity changes in the SRS spectrum. The measured TPA spectrum for 100mM R6G solution is shown in Figure S2d. Simply dividing the measured SRS Raman spectrum with the TPA spectrum gives the intensity normalized SRS spectrum. We note that for further chemometric analysis, this spectral normalization procedure is not necessary because the calibration SRS spectra are measured the same way as the sample, cancelling any spectral dependence. Figure S2: a. Pump beam spectrum from the OPO laser with a full-width half maximum bandwidth of 15-20 nm. b. Measured SRS signal of 50:50% cyclohexane/toluene mixture as a function of interpulse delay. c. Linear fitting of Raman shift to interpulse delay based on the three major Raman peaks. d. Two-photon absorption (TPA) spectrum of R6G using the same chirped laser pulses for excitation. The TPA spectrum is very broad. The tailing off at early and late delays reflect the smaller overlap of the two pulses at these delays. SRS spectral normalization is done by dividing measured SRS spectrum with the TPA spectrum.
SRS spectral imaging of polymer beads and mammalian cells Movie S1 (jp308938t_si_002.mpg): SRS spectral imaging of polymer bead mixture comprising melamine, polystyrene and PMMA at increasing Raman shift from 2767 cm -1 to 3095 cm -1 with 4.15 cm -1 increment for a total of 80 frames. Movie S2 (jp308938t_si_003.avi): Depth resolved SRS spectral imaging of two formaldehyde fixed HeLa cells with focal plane separated by 4 µm. The Raman shift is swept from 2810 cm -1 to 3088 cm -1 with 4.72 cm -1 increment for a total of 60 frames.