## Sparse sampling for fast hyperspectral coherent anti-Stokes Raman scattering imaging |

Optics Express, Vol. 22, Issue 4, pp. 4021-4028 (2014)

http://dx.doi.org/10.1364/OE.22.004021

Acrobat PDF (1230 KB)

### Abstract

We demonstrate a method to increase the acquisition speed in coherent anti-Stokes Raman scattering (CARS) hyperspectral imaging while retaining the relevant spectral information. The method first determines the important spectral components of a sample from a hyper-spectral image over a small number of spatial points but a large number of spectral points covering the accessible spectral range and sampling the instrument spectral resolution at the Nyquist limit. From these components we determine a small set of frequencies needed to retrieve the weights of the components with minimum error for a given measurement noise. Hyperspectral images with a large number of spatial points, for example covering a large spatial region, are then measured at this small set of frequencies, and a reconstruction algorithm is applied to generate the full spectral range and resolution. The resulting spectra are suited to retrieve from the CARS intensity the CARS susceptibility which is linear in the concentration, and apply unsupervised quantitative analysis methods such as FSC^{3} [

© 2014 Optical Society of America

## 1. Introduction

2. C. L. Evans and X. S. Xie, “Coherent anti-Stokes Raman scattering microscopy: chemical imaging for biology and medicine,” Annu. Rev. Anal. Chem. **1**, 883–909 (2008). [CrossRef]

4. A. Zumbusch, W. Langbein, and P. Borri, “Nonlinear vibrational microscopy applied to lipid biology,” Progress in Lipid Research **52**, 615–632 (2013). [CrossRef] [PubMed]

2. C. L. Evans and X. S. Xie, “Coherent anti-Stokes Raman scattering microscopy: chemical imaging for biology and medicine,” Annu. Rev. Anal. Chem. **1**, 883–909 (2008). [CrossRef]

3. J. P. Pezacki, J. A. Blake, D. C. Danielson, D. C. Kennedy, R. K. Lyn, and R. Singaravelu, “Chemical contrast for imaging living systems: molecular vibrations drive CARS microscopy,” Nat. Chem. Biol. **7**, 137–145 (2011). [CrossRef] [PubMed]

5. C. L. Evans, E. O. Potma, M. Puoris’haag, D. Côté, C. P. Lin, and X. S. Xie, “Chemical imaging of tissue in vivo with video-rate coherent anti-Stokes Raman scattering microscopy,” Proc. Natl. Acad. Sci. U. S. A. **102**, 16807–16812 (2005). [CrossRef] [PubMed]

6. C. W. Freudiger, W. Min, B. G. Saar, S. Lu, G. R. Holtom, C. He, J. C. Tsai, J. X. Kang, and X. S. Xie, “Label-free biomedical imaging with high sensitivity by stimulated Raman scattering microscopy,” Science **322**, 1857–1861 (2008). [CrossRef] [PubMed]

9. D. Fu, F.-K. Lu, X. Zhang, C. Freudiger, D. R. Pernik, G. Holtom, and X. S. Xie, “Quantitative chemical imaging with multiplex stimulated Raman scattering microscopy,” Journal of the American Chemical Society **134**, 3623–3626 (2012). [CrossRef] [PubMed]

10. I. Pope, W. Langbein, P. Watson, and P. Borri, “Simultaneous hyperspectral differential-CARS, TPF and SHG microscopy with a single 5 fs Ti:Sa laser,” Opt. Express **21**, 7096–7106 (2013). [CrossRef] [PubMed]

11. L. Kong, M. Ji, G. R. Holtom, D. Fu, C. W. Freudiger, and X. S. Xie, “Multicolor stimulated Raman scattering microscopy with a rapidly tunable optical parametric oscillator,” Opt. Lett. **38**, 145–147 (2013). [CrossRef] [PubMed]

4. A. Zumbusch, W. Langbein, and P. Borri, “Nonlinear vibrational microscopy applied to lipid biology,” Progress in Lipid Research **52**, 615–632 (2013). [CrossRef] [PubMed]

1. F. Masia, A. Glen, P. Stephens, P. Borri, and W. Langbein, “Quantitative chemical imaging using hyperspectral coherent anti-Stokes Raman scattering microscopy,” Anal. Chem. (2013). DOI [CrossRef] .

12. Y. Liu, Y. J. Lee, and M. T. Cicerone, “Broadband CARS spectral phase retrieval using a time-domain Kramers-Kronig transform,” Opt. Lett. **34**, 1363–1365 (2009). [CrossRef] [PubMed]

13. E. M. Vartiainen, H. A. Rinia, M. Müller, and M. Bonn, “Direct extraction of Raman line-shapes from congested CARS spectra,” Opt. Express **14**, 3622–3630 (2006). [CrossRef] [PubMed]

1. F. Masia, A. Glen, P. Stephens, P. Borri, and W. Langbein, “Quantitative chemical imaging using hyperspectral coherent anti-Stokes Raman scattering microscopy,” Anal. Chem. (2013). DOI [CrossRef] .

14. D. Zhang, M. N. Slipchenko, D. E. Leaird, A. M. Weiner, and J.-X. Cheng, “Spectrally modulated stimulated Raman scattering imaging with an angle-to-wavelength pulse shaper,” Opt. Express **21**, 13864–13874 (2013). [CrossRef] [PubMed]

1. F. Masia, A. Glen, P. Stephens, P. Borri, and W. Langbein, “Quantitative chemical imaging using hyperspectral coherent anti-Stokes Raman scattering microscopy,” Anal. Chem. (2013). DOI [CrossRef] .

15. Y. Ozeki, W. Umemura, Y. Otsuka, S. Satoh, H. Hashimoto, K. Sumimura, N. Nishizawa, K. Fukui, and K. Itoh, “High-speed molecular spectral imaging of tissue with stimulated Raman scattering,” Nature Photon. **6**, 845–851 (2012). [CrossRef]

^{−1}and 10 repetitions needed for sufficient signal-to-noise ratio, this corresponds to 0.03 hyperspectral frames per second (hfps). CARS imaging can reach similar speeds [2

2. C. L. Evans and X. S. Xie, “Coherent anti-Stokes Raman scattering microscopy: chemical imaging for biology and medicine,” Annu. Rev. Anal. Chem. **1**, 883–909 (2008). [CrossRef]

5. C. L. Evans, E. O. Potma, M. Puoris’haag, D. Côté, C. P. Lin, and X. S. Xie, “Chemical imaging of tissue in vivo with video-rate coherent anti-Stokes Raman scattering microscopy,” Proc. Natl. Acad. Sci. U. S. A. **102**, 16807–16812 (2005). [CrossRef] [PubMed]

## 2. Experimental

10. I. Pope, W. Langbein, P. Watson, and P. Borri, “Simultaneous hyperspectral differential-CARS, TPF and SHG microscopy with a single 5 fs Ti:Sa laser,” Opt. Express **21**, 7096–7106 (2013). [CrossRef] [PubMed]

17. T. Hellerer, A. M. Enejder, and A. Zumbusch, “Spectral focusing: High spectral resolution spectroscopy with broad-bandwidth laser pulses,” Appl. Phys. Lett. **85**, 25–27 (2004). [CrossRef]

19. W. Langbein, I. Rocha-Mendoza, and P. Borri, “Coherent anti-Stokes Raman micro-spectroscopy using spectral focusing: Theory and Experiment,” J. Raman Spectrosc. **40**, 800–808 (2009). [CrossRef]

^{−1}with a resolution of 10 cm

^{−1}is achieved by controlling the delay between pump and Stokes. The data discussed in this paper were taken over a (2400–3700) cm

^{−1}range with a 60× 1.27 NA water immersion objective (Nikon CFI Plan Apochromat IR

*λ*S series) and a 1.4 NA oil immersion condenser for signal collection in forward direction, with a resulting spatial resolution for the CARS susceptibility (full-width at half-maximum of the point-spread function amplitude) of 0.6 (2)

*μ*m in the lateral (axial) direction. The CARS light is discriminated by a pair of Semrock band-pass filters FF01-562/40 and then detected by a Hamamatsu H7422-40 photomultiplier. CARS hyperspectral images of a human osteosarcoma U2OS cell were acquired for IFDs in the range (2400–3700) cm

^{−1}with 5 cm

^{−1}steps. An example image at 2805 cm

^{−1}is shown in Fig. 1.

## 3. Results and discussion

*A*with a large spectral range and high spectral resolution is taken over a small number of spatial points. Singular value decomposition is used to determine the important spectra above the noise in

*A*. Then a number of important spectral points equal to the number of important spectra is determined to yield minimum deviation over

*A*in the spectra reconstructed from the important spectral points. Subsequently, hyperspectral data sets over large number of spatial points taken only at the important spectral points can be reconstructed.

### 3.1. Determination of important spectra and spectral points

*I*

_{C}) image

*A*with a spectral step size at the Nyquist-limit of the spectral resolution is acquired using either a coarse spatial sampling or a small region of the sample containing a representative ensemble of the chemical components present. The subsequent processing is done on the square root of

*I*

_{C}, which has a whitened shot noise [1

*S*×

*P′*) matrix with the elements

**d**

*, where*

_{s,p}*S*is the number of spectral points and

*P′*is the number of spatial points measured. The matrix

**d**is then factorized using a compact singular value decomposition (SVD) into

**d**=

**u**

*σ*

**v**

^{T}, where the (

*S*×

*S*) matrix

**u**is the rotation from the new spectral basis given by the singular spectra, to the old spectral basis given by the measured IFDs. The (

*S*×

*S*) matrix

*σ*is diagonal containing the singular values, and the (

*S*×

*P′*) matrix

**v**

^{T}contains the spatial images in the basis of the singular vectors. As example we use as hyperspectral data

*A*the data shown in Fig. 1 having

*S*= 261, but with a coarse spatial step of 1

*μ*m, containing only 1% of the spatial points of the frame, yielding

*P′*= 951.

*S*

_{max}of singular values not dominated by noise using the algorithm reported in [1

*σ*(see Fig. 2(a) with a linear dependence on the index

_{j,j}*j*for

*j*≥

*S*/2, and determine the largest index

*j*=

*S*

_{max}for which

*σ*is larger than

_{j,j}*S*

_{max}= 8. Components with

*j*>

*S*

_{max}are attributed to noise and we discard them by defining a

*σ̃*in which the diagonal values are set to zero for

*j*>

*S*

_{max}and define the noise-filtered data

**d̃**=

**u**

*σ̃*

**v**

^{T}.

*S*to

*S′*≪

*S*, we use only the most important

*S′*

_{max}≤

*S*

_{max}singular spectra, and determine their weights in the reconstruction by measurements at

*S′*≥

*S′*

_{max}spectral points.

*S′*

_{max}and the specific spectral points to be measured are determined from

**d̃**. In detail, we create a (

*S′*×

*P′*) matrix

**d̂**by selecting

*S′*out of the

*S*spectral points of

**d̃**, which are given by a vector

**s**= (

*s*

_{1},..,

*s*) of ascending spectral point indices, i.e.

_{S′}**d̂**

*=*

_{n,p}**d̃**

_{sn,p}with

*n*= 1

*..S′*. An approximation of the matrix

**d̃**can be obtained by determining the weights of the

*S′*

_{max}most important singular spectra using

**d̂**. To do this, we determine a

*S′*×

*S′*rotation matrix

**û**by taking the first

*S′*singular spectra of

**u**at the spectral points identified by

**s**, and using Gram-Schmidt orthogonalization of the resulting matrix in sequence of increasing singular spectrum index, i.e. decreasing importance. We then calculate a reduced matrix of coefficients

**â**such as

**d̂**=

**ûâ**. Having the coefficients of the singular spectra, we can reconstruct the data over all spectral points using the (

*S*×

*S′*) sub-matrix

**ũ**of

**u**containing the first

*S′*singular spectra. Similar to the SVD noise filtering, we restrict the reconstruction to

*S′*

_{max}≤

*S′*important spectra by setting in

**ũ**the singular spectra above

*S′*

_{max}to zero. The noise filtered reconstructed data is then given by

**d**

^{rec}=

**ũû**

^{−1}

**d̂**

*S′*

_{max}for the reconstruction, we have to consider that

*S*

_{max}was determined using the noise in a dataset with

*S*spectral components. Measuring only

*S′*spectral points, the noise is expected to be a factor of

**s**to minimize the influence of noise in the reconstruction. We accordingly determine

**s**by minimizing the error of the reconstructed hyperspectral image

*ε*= ||

**d̃**−

**d**

^{rec}||

_{F}/||

**d̃**||

_{F}, where ||.||

_{F}indicates the Frobenius norm, and

*S′*

_{max}=

*S*

_{max}is used to determine

**d**

^{rec}. For a typical number of

*S*in the order of 100, and

*S′*in the order of 10, the number of possible combinations in

**s**is

*S*!/(

*S′*!(

*S*−

*S′*)!) ∼ 10

^{13}, making it computationally unfeasible to find the exact minimum by calculating the error for each combination. We have therefore employed the following minimization algorithm. We start by choosing equidistant spectral points in

**s**, which corresponds to an under-sampling of the spectral resolution, and we choose the

**s**with minimum distance and centered in the spectral range. The minimization is then done by a random walk, choosing new spectral points

**s′**with

*s′*=

_{i}*s*+

_{i}*δ*using a random value

_{i}*δ*having a uniform distribution in the range

_{i}*s*

_{i}_{−1}−

*s*< 2

_{i}*δ*<

_{i}*s*

_{i}_{+1}−

*s*, i.e. covering half the distance to the adjacent spectral points, such that the ascending order is conserved. The new spectral points

_{i}**s′**are kept for subsequent steps only if the error improved. We limit the number of steps in the random walk, to 200 in the results shown here. We also investigated other minimization algorithms leading generally to similar or inferior results in terms of convergency and computational complexity. The error

*ε*of the reconstruction for equidistant spectral points,

*ε*

^{eq}, and for random walk optimized points,

*ε*

^{rw}, is shown in Fig. 2(b). The error reduces with increasing number of measured spectral points

*S′*approximately as

*ε*during the random walk minimization is shown in the inset of Fig. 2(b) for

*S′*=

*S*

_{max}= 8. Most of the improvement is realized within 10

^{3}steps. The standard deviation of

*ε*over 10 independent walks is generally below 0.2

*ε*, so that we can conclude that the minimization algorithm is sufficiently stable. Interestingly, the error for equidistant spectral points is typically only a factor of two larger than after random walk minimization, showing that the exact choice of the spectral points is in general not important for the retrieval.

*S′*

_{max}for the reconstruction is then determined taking into account the modification of the noise by multiplying the linear fit of the noise components in

*σ*(see solid line in Fig. 2) by the factor

### 3.2. Reconstruction of the spectra of a sparsely sampled hyperspectral image

**s**, a hyperspectral CARS intensity dataset

*B*is acquired at the

*S′*spectral points of

**s**over a large spatial region with a number of spatial points

*P*≫

*P′*. We used here the image shown in Fig. 1, for which

*P*= 95120, and we chose

*S′*=

*S*

_{max}= 8, for which we find

*S′*

_{max}= 4 (see Fig. 2). We format the data in

*B*as a

*S′*×

*P*matrix

**D̂**of

**D**

^{rec}=

**ũû**

^{−1}

**D̂**.

*I*

_{C}at the positions marked in Fig. 1 as obtained from the reconstruction algorithm (dashed lines) and directly measured and denoised (solid lines). The reconstruction reproduces the measured spectra up to small deviations, which are more important for the position #1 corresponding to a lipid droplet in the cell. We have verified that using

*S*

_{max}instead of

*S′*

_{max}components in the reconstruction results in a significantly increased noise in

**D**

^{rec}, as illustrated in Fig. 3(a) (gray line). The full datasets of the denoised and reconstructed

*I*

_{ref}in a non-resonant medium (the coverslip glass) to calculate the CARS ratio

*Ī*

_{C}=

*I*

_{C}/

*I*

_{ref}, which is then used to retrieve the imaginary part of the complex susceptibility

*Ī*

_{C}are shown in panels a), b) and c) of the hyperspectral movie Media 2, respectively.

**D**is the noise filtered data taken at full spectral and spatial resolution. Figure 4 shows the spatial dependence of the spectral error for

*S*

_{max}/

*S*+

*ρ*)

^{−1}where

*ρ*=

*P′/P*is the fraction of spatial positions in dataset

*A*compared to

*B*, For the example shown here we have

*S*

_{max}= 8,

*S*= 261,

*ρ*= 0.01 resulting in a 25 fold increase in acquisition speed. In our analysis it is required that

*ρP*≫

*S*for a correct SVD-based noise filtering procedure. In typical situations where samples of a given chemical variety are imaged over a large set of replica, such as in high throughput screening, dataset

*A*needs to be acquired only once, such that the speedup is effectively only limited by

*S/S′*, which is 33 in the present case. In absolute terms it is typically sufficient to measure at 5–10 spectral points to reconstruct most of the chemical information obtainable in a full spectral scan.

## 4. Conclusion

*S*×

*P*) into two smaller matrices of (

*S*×

*P′*) and (

*S′*×

*P*), with

*S′*≪

*S*and

*P′*≪

*P*. We demonstrated that the acquisition time for a human osteosarcoma U2OS cell was reduced by a factor of 25 without significant loss of information. This method, combined with state of the art CARS microscopes, is expected to enable real-time chemical imaging and high-throughput high-content label-free microscopy. The method is suited also for other coherent vibrational microscopy techniques such as stimulated Raman scattering, and in general for hyperspectral imaging techniques with sequential spectral acquisition.

## Acknowledgments

## References and links

1. | F. Masia, A. Glen, P. Stephens, P. Borri, and W. Langbein, “Quantitative chemical imaging using hyperspectral coherent anti-Stokes Raman scattering microscopy,” Anal. Chem. (2013). DOI [CrossRef] . |

2. | C. L. Evans and X. S. Xie, “Coherent anti-Stokes Raman scattering microscopy: chemical imaging for biology and medicine,” Annu. Rev. Anal. Chem. |

3. | J. P. Pezacki, J. A. Blake, D. C. Danielson, D. C. Kennedy, R. K. Lyn, and R. Singaravelu, “Chemical contrast for imaging living systems: molecular vibrations drive CARS microscopy,” Nat. Chem. Biol. |

4. | A. Zumbusch, W. Langbein, and P. Borri, “Nonlinear vibrational microscopy applied to lipid biology,” Progress in Lipid Research |

5. | C. L. Evans, E. O. Potma, M. Puoris’haag, D. Côté, C. P. Lin, and X. S. Xie, “Chemical imaging of tissue in vivo with video-rate coherent anti-Stokes Raman scattering microscopy,” Proc. Natl. Acad. Sci. U. S. A. |

6. | C. W. Freudiger, W. Min, B. G. Saar, S. Lu, G. R. Holtom, C. He, J. C. Tsai, J. X. Kang, and X. S. Xie, “Label-free biomedical imaging with high sensitivity by stimulated Raman scattering microscopy,” Science |

7. | Y. Ozeki, F. Dake, S. Kajiyama, K. Fukui, and K. Itoh, “Analysis and experimental assessment of the sensitivity of stimulated Raman scattering microscopy,” Opt. Express |

8. | B. G. Saar, C. W. Freudiger, J. Reichman, C. M. Stanley, G. R. Holtom, and X. S. Xie, “Video-rate molecular imaging in vivo with stimulated Raman scattering,” Science |

9. | D. Fu, F.-K. Lu, X. Zhang, C. Freudiger, D. R. Pernik, G. Holtom, and X. S. Xie, “Quantitative chemical imaging with multiplex stimulated Raman scattering microscopy,” Journal of the American Chemical Society |

10. | I. Pope, W. Langbein, P. Watson, and P. Borri, “Simultaneous hyperspectral differential-CARS, TPF and SHG microscopy with a single 5 fs Ti:Sa laser,” Opt. Express |

11. | L. Kong, M. Ji, G. R. Holtom, D. Fu, C. W. Freudiger, and X. S. Xie, “Multicolor stimulated Raman scattering microscopy with a rapidly tunable optical parametric oscillator,” Opt. Lett. |

12. | Y. Liu, Y. J. Lee, and M. T. Cicerone, “Broadband CARS spectral phase retrieval using a time-domain Kramers-Kronig transform,” Opt. Lett. |

13. | E. M. Vartiainen, H. A. Rinia, M. Müller, and M. Bonn, “Direct extraction of Raman line-shapes from congested CARS spectra,” Opt. Express |

14. | D. Zhang, M. N. Slipchenko, D. E. Leaird, A. M. Weiner, and J.-X. Cheng, “Spectrally modulated stimulated Raman scattering imaging with an angle-to-wavelength pulse shaper,” Opt. Express |

15. | Y. Ozeki, W. Umemura, Y. Otsuka, S. Satoh, H. Hashimoto, K. Sumimura, N. Nishizawa, K. Fukui, and K. Itoh, “High-speed molecular spectral imaging of tissue with stimulated Raman scattering,” Nature Photon. |

16. | S. Qaisar, R.M. Bilal, W. Iqbal, M. Naureen, and S. Lee, “Compressive sensing: from theory to applications, a survey,” J. Communications and Network |

17. | T. Hellerer, A. M. Enejder, and A. Zumbusch, “Spectral focusing: High spectral resolution spectroscopy with broad-bandwidth laser pulses,” Appl. Phys. Lett. |

18. | I. Rocha-Mendoza, W. Langbein, and P. Borri, “Coherent anti-Stokes Raman microspectroscopy using spectral focusing with glass dispersion,” Appl. Phys. Lett. |

19. | W. Langbein, I. Rocha-Mendoza, and P. Borri, “Coherent anti-Stokes Raman micro-spectroscopy using spectral focusing: Theory and Experiment,” J. Raman Spectrosc. |

**OCIS Codes**

(300.6230) Spectroscopy : Spectroscopy, coherent anti-Stokes Raman scattering

(180.4315) Microscopy : Nonlinear microscopy

**ToC Category:**

Microscopy

**History**

Original Manuscript: November 22, 2013

Revised Manuscript: February 3, 2014

Manuscript Accepted: February 3, 2014

Published: February 13, 2014

**Virtual Issues**

Vol. 9, Iss. 4 *Virtual Journal for Biomedical Optics*

**Citation**

Francesco Masia, Paola Borri, and Wolfgang Langbein, "Sparse sampling for fast hyperspectral coherent anti-Stokes Raman scattering imaging," Opt. Express **22**, 4021-4028 (2014)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-22-4-4021

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### References

- F. Masia, A. Glen, P. Stephens, P. Borri, W. Langbein, “Quantitative chemical imaging using hyperspectral coherent anti-Stokes Raman scattering microscopy,” Anal. Chem. (2013). DOI. [CrossRef]
- C. L. Evans, X. S. Xie, “Coherent anti-Stokes Raman scattering microscopy: chemical imaging for biology and medicine,” Annu. Rev. Anal. Chem. 1, 883–909 (2008). [CrossRef]
- J. P. Pezacki, J. A. Blake, D. C. Danielson, D. C. Kennedy, R. K. Lyn, R. Singaravelu, “Chemical contrast for imaging living systems: molecular vibrations drive CARS microscopy,” Nat. Chem. Biol. 7, 137–145 (2011). [CrossRef] [PubMed]
- A. Zumbusch, W. Langbein, P. Borri, “Nonlinear vibrational microscopy applied to lipid biology,” Progress in Lipid Research 52, 615–632 (2013). [CrossRef] [PubMed]
- C. L. Evans, E. O. Potma, M. Puoris’haag, D. Côté, C. P. Lin, X. S. Xie, “Chemical imaging of tissue in vivo with video-rate coherent anti-Stokes Raman scattering microscopy,” Proc. Natl. Acad. Sci. U. S. A. 102, 16807–16812 (2005). [CrossRef] [PubMed]
- C. W. Freudiger, W. Min, B. G. Saar, S. Lu, G. R. Holtom, C. He, J. C. Tsai, J. X. Kang, X. S. Xie, “Label-free biomedical imaging with high sensitivity by stimulated Raman scattering microscopy,” Science 322, 1857–1861 (2008). [CrossRef] [PubMed]
- Y. Ozeki, F. Dake, S. Kajiyama, K. Fukui, K. Itoh, “Analysis and experimental assessment of the sensitivity of stimulated Raman scattering microscopy,” Opt. Express 17, 3651–3658 (2009). [CrossRef] [PubMed]
- B. G. Saar, C. W. Freudiger, J. Reichman, C. M. Stanley, G. R. Holtom, X. S. Xie, “Video-rate molecular imaging in vivo with stimulated Raman scattering,” Science 330, 1368–1370 (2010). [CrossRef] [PubMed]
- D. Fu, F.-K. Lu, X. Zhang, C. Freudiger, D. R. Pernik, G. Holtom, X. S. Xie, “Quantitative chemical imaging with multiplex stimulated Raman scattering microscopy,” Journal of the American Chemical Society 134, 3623–3626 (2012). [CrossRef] [PubMed]
- I. Pope, W. Langbein, P. Watson, P. Borri, “Simultaneous hyperspectral differential-CARS, TPF and SHG microscopy with a single 5 fs Ti:Sa laser,” Opt. Express 21, 7096–7106 (2013). [CrossRef] [PubMed]
- L. Kong, M. Ji, G. R. Holtom, D. Fu, C. W. Freudiger, X. S. Xie, “Multicolor stimulated Raman scattering microscopy with a rapidly tunable optical parametric oscillator,” Opt. Lett. 38, 145–147 (2013). [CrossRef] [PubMed]
- Y. Liu, Y. J. Lee, M. T. Cicerone, “Broadband CARS spectral phase retrieval using a time-domain Kramers-Kronig transform,” Opt. Lett. 34, 1363–1365 (2009). [CrossRef] [PubMed]
- E. M. Vartiainen, H. A. Rinia, M. Müller, M. Bonn, “Direct extraction of Raman line-shapes from congested CARS spectra,” Opt. Express 14, 3622–3630 (2006). [CrossRef] [PubMed]
- D. Zhang, M. N. Slipchenko, D. E. Leaird, A. M. Weiner, J.-X. Cheng, “Spectrally modulated stimulated Raman scattering imaging with an angle-to-wavelength pulse shaper,” Opt. Express 21, 13864–13874 (2013). [CrossRef] [PubMed]
- Y. Ozeki, W. Umemura, Y. Otsuka, S. Satoh, H. Hashimoto, K. Sumimura, N. Nishizawa, K. Fukui, K. Itoh, “High-speed molecular spectral imaging of tissue with stimulated Raman scattering,” Nature Photon. 6, 845–851 (2012). [CrossRef]
- S. Qaisar, R.M. Bilal, W. Iqbal, M. Naureen, S. Lee, “Compressive sensing: from theory to applications, a survey,” J. Communications and Network 15, 443–456 (2013).
- T. Hellerer, A. M. Enejder, A. Zumbusch, “Spectral focusing: High spectral resolution spectroscopy with broad-bandwidth laser pulses,” Appl. Phys. Lett. 85, 25–27 (2004). [CrossRef]
- I. Rocha-Mendoza, W. Langbein, P. Borri, “Coherent anti-Stokes Raman microspectroscopy using spectral focusing with glass dispersion,” Appl. Phys. Lett. 93, 201103 (2008). [CrossRef]
- W. Langbein, I. Rocha-Mendoza, P. Borri, “Coherent anti-Stokes Raman micro-spectroscopy using spectral focusing: Theory and Experiment,” J. Raman Spectrosc. 40, 800–808 (2009). [CrossRef]

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