Abstract

Coherent Anti-Stokes Raman Scattering (CARS) microscopy is a valuable tool for label-free imaging of biological samples. As a major drawback quantification based on CARS images is compromised by the appearance of a nonresonant background. In this paper we propose and demonstrate a wide-field CARS vibrational phase imaging scheme that allows for nonresonant background suppression. Several CARS images at a few consecutive planes perpendicular to the propagation direction were recorded to reconstruct a phase map utilizing the iteration phase retrieval method. Experimental results verify that the CARS background is efficiently suppressed by the phase imaging approach, as compared to traditional CARS imaging without background correction. The proposed background correction method is robust against environmental disturbance, since the experimental implementation of the suggested detection scheme requires no reference beam.

© 2015 Optical Society of America

1. Introduction

Coherent Anti-Stokes Raman Scattering (CARS) microscopy is a powerful label-free imaging method providing contrast based on vibrational resonances [1,2]. The anti-Stokes radiation, resulting from inelastic scattering of the probe beam, is resonantly enhanced if the difference frequency of pump and Stokes pulses is tuned to a specific vibrational mode. Inevitably, the Raman resonant anti-Stokes radiation is superimposed by a nonresonant contribution arising from the electronic part of the polarization [315]. The latter can overwhelm a small Raman resonant CARS signal; in particular, if the samples are composed of a significant amount of water, where a strong nonresonant background over the whole image is obtained. To date, various approaches including Epi [3], polarization sensitive [4], time-resolved [5], spatial phase control CARS [6], quantum control based pulse chirping [79] and CARS phase imaging [1014] have been implemented in CARS microscopy to obtain the CARS image without the undesirable nonresonant background. Among CARS phase imaging, optical heterodyne detection schemes [1014] are of particular interest due to their intrinsic ability to retrieve Im(χ(3)), which is proportional to the Raman resonant signal. All these laser scanning methods, exploit the interference of the CARS field radiated by the molecules with a reference field generated by an external four-wave mixing (FWM) process. While these approaches feature a high accuracy, the use of an independent reference wave leads to an increase in the setup complexity making the measurement sensitive to external perturbations, such as vibrations, temperature changes, etc. In order to simplify the setup, single-beam configurations have been utilized for vibrational CARS imaging by appropriately modulating the spectral phase of the pulse, and consequently provide high-resolution background-free CARS images [1621]. Recently, wave-front sensors were also used to acquire the phase of the complex anti-Stokes amplitude without the necessity for a reference beam based on the optical homodyne detection on wide field CARS phase imaging [22,23]. However, this method demands highly accurate wave-front sensors.

Here, a reference-less extension of phase retrieval methods to wide field CARS microscopy allowing for background suppression is introduced and investigated. An iterative phase retrieval method [2433] is applied to perform phase reconstruction from the diffraction intensities recorded in different axial planes. This scheme relies on a simple experiment setup and thus is readily to implement and less sensitive to environmental disturbances because no reference beam is utilized as a major advantage over optical heterodyne detection schemes.

2. Method

The scheme of the wide-field CARS phase imaging microscopy setup is sketched in Fig. 1. The collimated Stokes and pump beams are superimposed spatially and temporally and are further weakly focused by the objective MO1 (magnification 10X, numerical aperture 0.3) onto the sample, which is located in the focal plane of objective MO1. The anti-Stokes radiation is generated by the pump and Stokes beams interacting with the sample via a four-wave-mixing (FWM) process. A 4f telescopic system MO2-L with 60 times magnification forms a CARS image at the detection plane. The whole field of view is 50μm × 50μm and the lateral resolution determined by the numerical aperture of MO2 is 458nm. Band-pass filters are inserted in front of the CMOS camera to block the pump and Stokes beams. For phase retrieval, a series of anti-Stokes far-field intensity patterns (I-M, I-M+1 ... I0 ... IM-1, IM) with an axial displacement mΔz (m = -M, -M + 1, …0,… M-1, M) from the image plane are recorded sequentially by moving the CMOS camera. Δz denotes the distance between neighboring planes.

 

Fig. 1 Schematic diagram of reference-less CARS phase imaging microscopy. Inset shows the mechanism of phase imaging from several intensities Im recorded for different axial planes.

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To remove the background, two z-stack intensities one in Raman resonant the other in nonresonant mode are acquired [22,23]. Energy-level diagrams of Raman resonant CARS and the nonresonant FWM background at the anti-Stokes frequency are displayed in Fig. 2(a). Resonant CARS radiation ECARSR is observed if the frequency difference between the pump and Stokes beams matches a molecular vibration (Raman resonant mode). In contrast, the nonresonant background ECARSNR requires no Raman resonance and is attributed to the electronic contribution of the polarization [2]. As outlined in Fig. 2(b), the Raman resonance adds a phase shift (vibrational phase response) to the anti-Stokes wave front as compared to the phase of the nonresonant response. This phase shift can be attributed to the imaginary part of the third order susceptibility Im(χ(3)).

 

Fig. 2 (a) Energy-level diagrams of Raman resonant CARS and nonresonant FWM background at the anti-Stokes frequency. (b) Principle of phase imaging: spatial phase alteration caused by a sample with spatially varying Raman resonant and nonresonant contributions [22].

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The total CARS field in the nonresonant mode is comprised of the nonresonant contributions from the sample and the surrounding medium that are described by the nonresonant third-order nonlinear susceptibility, represented by χ1NR and χ2NR. The total CARS field ECARSR in the Raman resonant mode is comprised of the Raman resonant CARS and nonresonant CARS contributions from both the sample and the surrounding medium. Thus, the electrical fields of the anti-Stokes radiation are given by:

ECARSNR(χ1NR+χ2NR)Ep2EsECARSR(χ1NR+χ2NR+Re(χ1R)+iIm(χ1R))Ep2Es
Here, χ1R denotes the Raman resonant part of the complex third-order nonlinear susceptibility of the sample. Ep and Es* express the pump and Stokes complex amplitude distributions, respectively. The vibrational phase (φχ) can be obtained by [22,23]:
φχ=φCARSRφCARSNR=Ang{ECARSRECARSNR}=Ang{χ1NR+χ2NR+Re(χ1R)+iIm(χ1R)χ1NR+χ2NR}
Here,ϕCARSR and ϕCARSNRdenote the phases of the Raman resonant and nonresonant anti-Stokes field. Equation (2) forms the basis for the wide-field CARS vibrational phase imaging to suppress the nonresonant contribution. Since χsampleNR and χbackgroundNR are real-valued, and only χsampleR is complex. φχ(x,y) equals to 0 at points (x, y) where there is no Raman resonant part; Raman resonant samples, however, will have φχ varying from 0 to π/2 depending on the ratio of the resonant and nonresonant contributions. Furthermore, the Raman resonant CARS signal can be extracted from the resonant CARS intensity by using the following equation [1013, 23]:
IbackgroundfreeICARSR(sinφχ)2
Here, Ibackground-free denotes the Raman resonant CARS intensity, i.e. without nonresonant background andICARSR=|ECARSR|2.

We note that the afore-mentioned concept of suppressing the nonresonant background using the phase shift φχ between Raman resonant and nonresonant mode has been well established [1013]. In this contribution we focus on applying an iterative method to retrieve the phases φCARSR and φCARSNR. This method is to the best of our knowledge first utilized for CARS microscopy. Here, a series of intensity patterns (I-M, I-M+1 ... I0 ... IM-1, IM) in the axial planes with the distance mΔz (m = -M, -M + 1, …0,… M-1, M) from the image plane are recorded sequentially by moving the camera. In the following, the framework of the iterative phase retrieval shall be introduced.

The iterative phase retrieval method (IPR) is displayed in the flowchart shown in Fig. 3. Starting with a random distribution, the phase is improved by repetitively propagating the wave between these diffraction patterns (I-M, I-M+1...I0...IM-1, IM). The propagation of the anti-Stokes field from the mth plane to (m + 1)th plane is achieved by the angular spectrum method [34]:

Om+1(x,y)=IFT{FT[Om]exp[ikΔz1(λκx)2(λκy)2]}
Here Om and Om + 1 denote the complex amplitude of the anti-Stokes fields (either resonant CARS field ECARSR or nonresonant CARS field ECARSNR) in the mth and (m + 1)th planes; Δz denotes the distance between neighbouring planes; κx and κy are the spatial coordinates in the frequency spectrum domain. The iterative phase retrieval is performed as follows:

 

Fig. 3 Flowchart of the iterative phase imaging.

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  • (1). Initialization of the object wave at the plane m (e.g. image plane) with Om = Im × exp(iφm0), with a random phaseφm0
  • (2). Propagation of Om(x, y) to the plane m + 1 using Eq. (4); the obtained wave is denoted Om + 1. Replacement of the amplitude of Om + 1 with Im+1
  • (3). Repetition of step (2) till m = M
  • (4). Propagation of OM to the plane m = -M, and replacement of the amplitude of O-M with IM
  • (5). Repetition of step (2) till image plane, and the obtained field is denoted with Om' whose phase is φm'
  • (6). Repetition of the iteration loop (2)–(5), until the phase difference φm'-φm of two consecutive iterations is smaller than a threshold value ε, that was set here to 1e−4φm

3. Experiment

3.1 Experiment setup

The experimental setup is schematically shown in Fig. 4. A frequency doubled continuous wave Neodymium-Vanadate laser at 532nm is used to pump a Coherent Mira HP Titanium-Sapphire laser (Coherent, USA) operating at a repetition rate of 76MHz in the picosecond modus, i.e. leading to 2-3ps pulses. The Titanium-Sapphire laser output is split into two beams: the first beam at a wavelength of 830nm is used directly as the Stokes beam, while the other beam is coupled into an optical parametric oscillator (OPO, APE, Berlin), generating the pump beam with a tunable range of 600–1000nm. For the CARS measurements the frequency difference between the pump and Stokes beams is tuned to match a Raman resonance of the sample, for example the polyethylene stretching vibration at 2845cm−1. The Stokes beam is directed through a telescope system L1-L2 which de-magnifies the output beam size by a factor of 5. Similarly, the pump beam is de-magnified 5 times by another telescope system L3-L4. Both beams are combined by a dichroic beamsplitter BS (Semrock FF750-SDi02-25x36) and temporally overlapped using a mechanic delay stage equipped with a retro-reflector. The joined laser beams are further directed into an objective lens MO1 (Olympus 10X Plan Fluorite Objective, 0.3 NA) and focused onto the sample. The CARS signal is generated and collected in forward direction by a telescope system comprising the objective MO2 (Olympus 40X Plan Fluorite Objective, 0.75 NA) and an achromatic lens L5 (focal length is 300mm). Dichronic filters (Semrock FF01-650/SP-25 and FF01-563/9-25) serve to filter the pump and Stokes beams. CARS images are acquired using a CMOS camera (Thorlabs DCC1645C).

 

Fig. 4 Schematic setup for CARS phase imaging.

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3.2 Phase imaging based on iterative phase retrieval (IPR) method

As test sample we used polyethylene beads (Cospheric LLC, USA) with the diameter 1-10μm, that are immersed in I2Zn solutions with a refractive index of 1.59. The latter is added to reduce the refractive index mismatch. First, the wavelength of the pump beam is tuned to 671.4nm to match the polyethylene Raman resonance at 2845cm−1. 12 resonant CARS images IiR are recorded displacing the detector by 2mm per step, as visualized in Fig. 5(a). In a second step, the pump wavelength is tuned to 675nm yielding a nonresonant frequency difference of 2776cm−1 (nonresonant mode), and 12 nonresonant CARS images IiNR are recorded - see Fig. 5(c). Using the iteration method described in the flowchart of Fig. 3, the resonant phase φCARSR and nonresonant phase φCARSNR over the field of view are retrieved after 200 iterations. The results are displayed in Fig. 5(b) and 5(d). Here it is assumed that the refractive index of the sample (and setup) is approximately the same for the CARS field on the resonant mode and nonresonant mode. The acquisition of 12 intensity images requires 1 minute while the iterative phase reconstruction from these intensity images takes 5 minutes on a computer with CPU 2.5GHz and RAM 6G. Such a long image acquisition time, which is mainly consumed by moving the camera to record the image at different planes, can be shortened by using a faster translation stage. The calculation time can be reduced by using a high-performance computer or GPU. From Fig. 5(d), it is evident that the larger part of the phase shift is caused by the difference in refractive index between the beads and the surrounding medium. Comparing Fig. 5(b) and 5(d), a small rise of the phase step is observed at the location of the beads for the resonant image. The desired vibrational phase image is obtained by subtracting the nonresonant CARS phase from the resonant CARS phase. The final result is shown in Fig. 5(e). Obviously, the polyethylene beads are highlighted and the background is suppressed. The dark ring around the beads are artifacts arising from the phase retrieval algorithm. Based on Eq. (3), the background-free image is calculated. The purely resonant image is depicted in Fig. 5(f). Comparing the intensity image in Fig. 5(a) and the background-free image in Fig. 5(f), the background has been significantly suppressed. For a quantification of the background suppression the line cross section [see Fig. 5(g)] shows that the nonresonant intensity is lowered from 0.4 to less than 0.004. It is found that the contrast of the background-free image has been improved by 100 times as compared to the original resonant intensity. Thus, the experimental results verify the efficient suppression of the CARS background.

 

Fig. 5 Phase imaging using the iterative phase retrieval (IPR) method. (a) and (c) are 6 of 12 intensities recorded in the resonant and nonresonant mode; (b) retrieved resonant phase image and (d) retrieved nonresonant phase image; (e) retrieved vibrational phase φCARSR-φCARSNR; (f) background-free intensity on the image plane; (g) intensity plot of the cross section outlined by a dashed line in (a) and (f).

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4. Conclusion

We have demonstrated the applicability of the reference-less phase retrieval method to wide-field CARS microscopy based on an iterative beam propagation method. This approach requires only CARS intensity images at a few consecutive planes perpendicular to the propagation direction, and no reference wave is needed. We found that the iterative method yields accurate results. The resulting phase information can be utilized to create high contrast CARS images, to remove the nonresonant background or to allow for the reconstruction of CARS images (~∣Imχ(3)2) that resemble the square of linear Raman microscopy maps.

Acknowledgments

This work was financially supported by the 'Europäischer Fonds für Regionale Entwicklung (EFRE)', the 'Thüringer Ministerium für Bildung, Wissenschaft und Kultur' (TMBWK, projects: B578-06001, 14.90 HWP and B714-07037), the ‘Carl Zeiss Stiftung’ and the Federal Ministry of Education and Research, Germany (FKZ: 13N10508), and the National Natural Science Foundation of China (NSFC) under Grants No. 61475187, 61275193, and 61275191. Juanjuan Zheng thanks the joint promotion program between Deutscher Akademischer Austausch Dienst (DAAD) and Chinese Academy of Science (CAS).

References and links

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

2. W. Min, C. W. Freudiger, S. Lu, and X. S. Xie, “Coherent Nonlinear Optical Imaging: Beyond Fluorescence Microscopy,” Annu. Rev. Phys. Chem. 62(1), 507–530 (2011). [CrossRef]   [PubMed]  

3. A. Volkmer, J. X. Cheng, and X. S. Xie, “Vibrational imaging with high sensitivity via Epi-detected Coherent Anti-Stokes Raman Scattering (E-CARS) microscopy,” Phys. Rev. Lett. 87(2), 023901 (2001). [CrossRef]  

4. J.-X. Cheng, L. D. Book, and X. S. Xie, “Polarization coherent anti-Stokes Raman scattering microscopy,” Opt. Lett. 26(17), 1341–1343 (2001). [CrossRef]   [PubMed]  

5. A. Volkmer, L. D. Book, and X. S. Xie, “Time-resolved coherent anti-Stokes Raman scattering microscopy: Imaging based on Raman free induction decay,” Appl. Phys. Lett. 80(9), 1505–1507 (2002). [CrossRef]  

6. V. V. Krishnamachari and E. O. Potma, “Focus-engineered coherent anti-Stokes Raman scattering microscopy: A numerical investigation,” J. Opt. Soc. Am. A 24(4), 1138–1147 (2007). [CrossRef]   [PubMed]  

7. S. A. Malinovskaya and V. S. Malinovsky, “Chirped-pulse adiabatic control in coherent anti-Stokes Raman scattering for imaging of biological structure and dynamics,” Opt. Lett. 32(6), 707–709 (2007). [CrossRef]   [PubMed]  

8. I. Rocha-Mendoza, W. Langbein, P. Watson, and P. Borri, “Differential coherent anti-Stokes Raman scattering microscopy with linearly chirped femtosecond laser pulses,” Opt. Lett. 34(15), 2258–2260 (2009). [CrossRef]   [PubMed]  

9. V. Patel, V. S. Malinovsky, and S. Malinovskaya, “Effects of phase and coupling between the vibrational modes on selective excitation in coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. A 81(6), 063404 (2010). [CrossRef]  

10. E. O. Potma, C. L. Evans, and X. S. Xie, “Heterodyne coherent anti-Stokes Raman scattering (CARS) imaging,” Opt. Lett. 31(2), 241–243 (2006). [CrossRef]   [PubMed]  

11. M. Jurna, J. P. Korterik, C. Otto, and H. L. Offerhaus, “Shot noise limited heterodyne detection of CARS signals,” Opt. Express 15(23), 15207–15213 (2007). [CrossRef]   [PubMed]  

12. M. Jurna, J. P. Korterik, C. Otto, J. L. Herek, and H. L. Offerhaus, “Background free CARS imaging by phase sensitive heterodyne CARS,” Opt. Express 16(20), 15863–15869 (2008). [CrossRef]   [PubMed]  

13. M. Jurna, J. P. Korterik, C. Otto, J. L. Herek, and H. L. Offerhaus, “Vibrational phase contrast microscopy by use of coherent anti-Stokes Raman scattering,” Phys. Rev. Lett. 103(4), 043905 (2009). [CrossRef]   [PubMed]  

14. C. L. Evans, E. O. Potma, and X. S. Xie, “Coherent anti-Stokes Raman scattering spectral interferometry: determination of the real and imaginary components of nonlinear susceptibility χ(3) for vibrational microscopy,” Opt. Lett. 29(24), 2923–2925 (2004). [CrossRef]   [PubMed]  

15. D. Akimov, S. Chatzipapadopoulos, T. Meyer, N. Tarcea, B. Dietzek, M. Schmitt, and J. Popp, “Different contrast information obtained from CARS and nonresonant FWM images,” J. Raman Spectrosc. 40(8), 941–947 (2009). [CrossRef]  

16. N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature 418(6897), 512–514 (2002). [CrossRef]   [PubMed]  

17. D. Oron, N. Dudovich, and Y. Silberberg, “Femtosecond phase-and-polarization control for background-free coherent anti-Stokes Raman spectroscopy,” Phys. Rev. Lett. 90(21), 213902 (2003). [CrossRef]   [PubMed]  

18. B. C. Chen and S. H. Lim, “Optimal laser pulse shaping for interferometric multiplex coherent anti-stokes Raman scattering microscopy,” J. Phys. Chem. B 112(12), 3653–3661 (2008). [CrossRef]   [PubMed]  

19. S. H. Lim, A. G. Caster, and S. R. Leone, “Fourier transform spectral interferometric coherent anti-Stokes Raman scattering (FTSI-CARS) spectroscopy,” Opt. Lett. 32(10), 1332–1334 (2007). [CrossRef]   [PubMed]  

20. B. von Vacano and M. Motzkus, “Time-resolving molecular vibration for microanalytics: single laser beam nonlinear Raman spectroscopy in simulation and experiment,” Phys. Chem. Chem. Phys. 10(5), 681–691 (2008). [CrossRef]   [PubMed]  

21. C. Müller, T. Buckup, B. von Vacano, and M. Motzkus, “Heterodyne single-beam CARS microscopy,” J. Raman Spectrosc. 40(7), 809–816 (2009). [CrossRef]  

22. P. Berto, D. Gachet, P. Bon, S. Monneret, and H. Rigneault, “Wide-Field Vibrational Phase Imaging,” Phys. Rev. Lett. 109(9), 093902 (2012). [CrossRef]   [PubMed]  

23. P. Berto, A. Jesacher, C. Roider, S. Monneret, H. Rigneault, and M. Ritsch-Marte, “Wide-field vibrational phase imaging in an extremely folded box-CARS scattering geometry,” Opt. Lett. 38(5), 709–711 (2013). [CrossRef]   [PubMed]  

24. G. Pedrini, W. Osten, and Y. Zhang, “Wave-front reconstruction from a sequence of interferograms recorded at different planes,” Opt. Lett. 30(8), 833–835 (2005). [CrossRef]   [PubMed]  

25. P. Almoro, G. Pedrini, and W. Osten, “Complete wavefront reconstruction using sequential intensity measurements of a volume speckle field,” Appl. Opt. 45(34), 8596–8605 (2006). [CrossRef]   [PubMed]  

26. P. Bao, F. Zhang, G. Pedrini, and W. Osten, “Phase retrieval using multiple illumination wavelengths,” Opt. Lett. 33(4), 309–311 (2008). [CrossRef]   [PubMed]  

27. Y. J. Liu, B. Chen, E. R. Li, J. Y. Wang, A. Marcelli, S. W. Wilkins, H. Ming, Y. C. Tian, K. A. Nugent, P. P. Zhu, and Z. Y. Wu, “Phase retrieval in x-ray imaging based on using structured illumination,” Phys. Rev. A 78(2), 023817 (2008). [CrossRef]  

28. F. Zhang, G. Pedrini, and W. Osten, “Phase retrieval of arbitrary complex-valued fields through aperture-plane modulation,” Phys. Rev. A 75(4), 043805 (2007). [CrossRef]  

29. F. Zhang and J. M. Rodenburg, “Phase retrieval based on wave-front relay and modulation,” Phys. Rev. B 82(12), 121104 (2010). [CrossRef]  

30. J. M. Rodenburg and H. M. L. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85(20), 4795–4798 (2004). [CrossRef]  

31. H. M. L. Faulkner and J. M. Rodenburg, “Movable Aperture Lensless Transmission Microscopy: A Novel Phase Retrieval Algorithm,” Phys. Rev. Lett. 93(2), 023903 (2004). [CrossRef]   [PubMed]  

32. P. Gao, G. Pedrini, and W. Osten, “Phase retrieval with resolution enhancement by using structured illumination,” Opt. Lett. 38(24), 5204–5207 (2013). [CrossRef]   [PubMed]  

33. P. Gao, G. Pedrini, C. Zuo, and W. Osten, “Phase retrieval using spatially modulated illumination,” Opt. Lett. 39(12), 3615–3618 (2014). [CrossRef]   [PubMed]  

34. J. Zheng, Y. Yang, M. Lei, B. Yao, P. Gao, and T. Ye, “Fluorescence volume imaging with an axicon: simulation study based on scalar diffraction method,” Appl. Opt. 51(30), 7236–7245 (2012). [CrossRef]   [PubMed]  

References

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  1. C. L. Evans and X. S. Xie, “Coherent anti-stokes Raman scattering microscopy: chemical imaging for biology and medicine,” Annu Rev Anal Chem (Palo Alto Calif) 1(1), 883–909 (2008).
    [Crossref] [PubMed]
  2. W. Min, C. W. Freudiger, S. Lu, and X. S. Xie, “Coherent Nonlinear Optical Imaging: Beyond Fluorescence Microscopy,” Annu. Rev. Phys. Chem. 62(1), 507–530 (2011).
    [Crossref] [PubMed]
  3. A. Volkmer, J. X. Cheng, and X. S. Xie, “Vibrational imaging with high sensitivity via Epi-detected Coherent Anti-Stokes Raman Scattering (E-CARS) microscopy,” Phys. Rev. Lett. 87(2), 023901 (2001).
    [Crossref]
  4. J.-X. Cheng, L. D. Book, and X. S. Xie, “Polarization coherent anti-Stokes Raman scattering microscopy,” Opt. Lett. 26(17), 1341–1343 (2001).
    [Crossref] [PubMed]
  5. A. Volkmer, L. D. Book, and X. S. Xie, “Time-resolved coherent anti-Stokes Raman scattering microscopy: Imaging based on Raman free induction decay,” Appl. Phys. Lett. 80(9), 1505–1507 (2002).
    [Crossref]
  6. V. V. Krishnamachari and E. O. Potma, “Focus-engineered coherent anti-Stokes Raman scattering microscopy: A numerical investigation,” J. Opt. Soc. Am. A 24(4), 1138–1147 (2007).
    [Crossref] [PubMed]
  7. S. A. Malinovskaya and V. S. Malinovsky, “Chirped-pulse adiabatic control in coherent anti-Stokes Raman scattering for imaging of biological structure and dynamics,” Opt. Lett. 32(6), 707–709 (2007).
    [Crossref] [PubMed]
  8. I. Rocha-Mendoza, W. Langbein, P. Watson, and P. Borri, “Differential coherent anti-Stokes Raman scattering microscopy with linearly chirped femtosecond laser pulses,” Opt. Lett. 34(15), 2258–2260 (2009).
    [Crossref] [PubMed]
  9. V. Patel, V. S. Malinovsky, and S. Malinovskaya, “Effects of phase and coupling between the vibrational modes on selective excitation in coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. A 81(6), 063404 (2010).
    [Crossref]
  10. E. O. Potma, C. L. Evans, and X. S. Xie, “Heterodyne coherent anti-Stokes Raman scattering (CARS) imaging,” Opt. Lett. 31(2), 241–243 (2006).
    [Crossref] [PubMed]
  11. M. Jurna, J. P. Korterik, C. Otto, and H. L. Offerhaus, “Shot noise limited heterodyne detection of CARS signals,” Opt. Express 15(23), 15207–15213 (2007).
    [Crossref] [PubMed]
  12. M. Jurna, J. P. Korterik, C. Otto, J. L. Herek, and H. L. Offerhaus, “Background free CARS imaging by phase sensitive heterodyne CARS,” Opt. Express 16(20), 15863–15869 (2008).
    [Crossref] [PubMed]
  13. M. Jurna, J. P. Korterik, C. Otto, J. L. Herek, and H. L. Offerhaus, “Vibrational phase contrast microscopy by use of coherent anti-Stokes Raman scattering,” Phys. Rev. Lett. 103(4), 043905 (2009).
    [Crossref] [PubMed]
  14. C. L. Evans, E. O. Potma, and X. S. Xie, “Coherent anti-Stokes Raman scattering spectral interferometry: determination of the real and imaginary components of nonlinear susceptibility χ(3) for vibrational microscopy,” Opt. Lett. 29(24), 2923–2925 (2004).
    [Crossref] [PubMed]
  15. D. Akimov, S. Chatzipapadopoulos, T. Meyer, N. Tarcea, B. Dietzek, M. Schmitt, and J. Popp, “Different contrast information obtained from CARS and nonresonant FWM images,” J. Raman Spectrosc. 40(8), 941–947 (2009).
    [Crossref]
  16. N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature 418(6897), 512–514 (2002).
    [Crossref] [PubMed]
  17. D. Oron, N. Dudovich, and Y. Silberberg, “Femtosecond phase-and-polarization control for background-free coherent anti-Stokes Raman spectroscopy,” Phys. Rev. Lett. 90(21), 213902 (2003).
    [Crossref] [PubMed]
  18. B. C. Chen and S. H. Lim, “Optimal laser pulse shaping for interferometric multiplex coherent anti-stokes Raman scattering microscopy,” J. Phys. Chem. B 112(12), 3653–3661 (2008).
    [Crossref] [PubMed]
  19. S. H. Lim, A. G. Caster, and S. R. Leone, “Fourier transform spectral interferometric coherent anti-Stokes Raman scattering (FTSI-CARS) spectroscopy,” Opt. Lett. 32(10), 1332–1334 (2007).
    [Crossref] [PubMed]
  20. B. von Vacano and M. Motzkus, “Time-resolving molecular vibration for microanalytics: single laser beam nonlinear Raman spectroscopy in simulation and experiment,” Phys. Chem. Chem. Phys. 10(5), 681–691 (2008).
    [Crossref] [PubMed]
  21. C. Müller, T. Buckup, B. von Vacano, and M. Motzkus, “Heterodyne single-beam CARS microscopy,” J. Raman Spectrosc. 40(7), 809–816 (2009).
    [Crossref]
  22. P. Berto, D. Gachet, P. Bon, S. Monneret, and H. Rigneault, “Wide-Field Vibrational Phase Imaging,” Phys. Rev. Lett. 109(9), 093902 (2012).
    [Crossref] [PubMed]
  23. P. Berto, A. Jesacher, C. Roider, S. Monneret, H. Rigneault, and M. Ritsch-Marte, “Wide-field vibrational phase imaging in an extremely folded box-CARS scattering geometry,” Opt. Lett. 38(5), 709–711 (2013).
    [Crossref] [PubMed]
  24. G. Pedrini, W. Osten, and Y. Zhang, “Wave-front reconstruction from a sequence of interferograms recorded at different planes,” Opt. Lett. 30(8), 833–835 (2005).
    [Crossref] [PubMed]
  25. P. Almoro, G. Pedrini, and W. Osten, “Complete wavefront reconstruction using sequential intensity measurements of a volume speckle field,” Appl. Opt. 45(34), 8596–8605 (2006).
    [Crossref] [PubMed]
  26. P. Bao, F. Zhang, G. Pedrini, and W. Osten, “Phase retrieval using multiple illumination wavelengths,” Opt. Lett. 33(4), 309–311 (2008).
    [Crossref] [PubMed]
  27. Y. J. Liu, B. Chen, E. R. Li, J. Y. Wang, A. Marcelli, S. W. Wilkins, H. Ming, Y. C. Tian, K. A. Nugent, P. P. Zhu, and Z. Y. Wu, “Phase retrieval in x-ray imaging based on using structured illumination,” Phys. Rev. A 78(2), 023817 (2008).
    [Crossref]
  28. F. Zhang, G. Pedrini, and W. Osten, “Phase retrieval of arbitrary complex-valued fields through aperture-plane modulation,” Phys. Rev. A 75(4), 043805 (2007).
    [Crossref]
  29. F. Zhang and J. M. Rodenburg, “Phase retrieval based on wave-front relay and modulation,” Phys. Rev. B 82(12), 121104 (2010).
    [Crossref]
  30. J. M. Rodenburg and H. M. L. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85(20), 4795–4798 (2004).
    [Crossref]
  31. H. M. L. Faulkner and J. M. Rodenburg, “Movable Aperture Lensless Transmission Microscopy: A Novel Phase Retrieval Algorithm,” Phys. Rev. Lett. 93(2), 023903 (2004).
    [Crossref] [PubMed]
  32. P. Gao, G. Pedrini, and W. Osten, “Phase retrieval with resolution enhancement by using structured illumination,” Opt. Lett. 38(24), 5204–5207 (2013).
    [Crossref] [PubMed]
  33. P. Gao, G. Pedrini, C. Zuo, and W. Osten, “Phase retrieval using spatially modulated illumination,” Opt. Lett. 39(12), 3615–3618 (2014).
    [Crossref] [PubMed]
  34. J. Zheng, Y. Yang, M. Lei, B. Yao, P. Gao, and T. Ye, “Fluorescence volume imaging with an axicon: simulation study based on scalar diffraction method,” Appl. Opt. 51(30), 7236–7245 (2012).
    [Crossref] [PubMed]

2014 (1)

2013 (2)

2012 (2)

2011 (1)

W. Min, C. W. Freudiger, S. Lu, and X. S. Xie, “Coherent Nonlinear Optical Imaging: Beyond Fluorescence Microscopy,” Annu. Rev. Phys. Chem. 62(1), 507–530 (2011).
[Crossref] [PubMed]

2010 (2)

V. Patel, V. S. Malinovsky, and S. Malinovskaya, “Effects of phase and coupling between the vibrational modes on selective excitation in coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. A 81(6), 063404 (2010).
[Crossref]

F. Zhang and J. M. Rodenburg, “Phase retrieval based on wave-front relay and modulation,” Phys. Rev. B 82(12), 121104 (2010).
[Crossref]

2009 (4)

C. Müller, T. Buckup, B. von Vacano, and M. Motzkus, “Heterodyne single-beam CARS microscopy,” J. Raman Spectrosc. 40(7), 809–816 (2009).
[Crossref]

I. Rocha-Mendoza, W. Langbein, P. Watson, and P. Borri, “Differential coherent anti-Stokes Raman scattering microscopy with linearly chirped femtosecond laser pulses,” Opt. Lett. 34(15), 2258–2260 (2009).
[Crossref] [PubMed]

M. Jurna, J. P. Korterik, C. Otto, J. L. Herek, and H. L. Offerhaus, “Vibrational phase contrast microscopy by use of coherent anti-Stokes Raman scattering,” Phys. Rev. Lett. 103(4), 043905 (2009).
[Crossref] [PubMed]

D. Akimov, S. Chatzipapadopoulos, T. Meyer, N. Tarcea, B. Dietzek, M. Schmitt, and J. Popp, “Different contrast information obtained from CARS and nonresonant FWM images,” J. Raman Spectrosc. 40(8), 941–947 (2009).
[Crossref]

2008 (6)

M. Jurna, J. P. Korterik, C. Otto, J. L. Herek, and H. L. Offerhaus, “Background free CARS imaging by phase sensitive heterodyne CARS,” Opt. Express 16(20), 15863–15869 (2008).
[Crossref] [PubMed]

C. L. Evans and X. S. Xie, “Coherent anti-stokes Raman scattering microscopy: chemical imaging for biology and medicine,” Annu Rev Anal Chem (Palo Alto Calif) 1(1), 883–909 (2008).
[Crossref] [PubMed]

B. von Vacano and M. Motzkus, “Time-resolving molecular vibration for microanalytics: single laser beam nonlinear Raman spectroscopy in simulation and experiment,” Phys. Chem. Chem. Phys. 10(5), 681–691 (2008).
[Crossref] [PubMed]

B. C. Chen and S. H. Lim, “Optimal laser pulse shaping for interferometric multiplex coherent anti-stokes Raman scattering microscopy,” J. Phys. Chem. B 112(12), 3653–3661 (2008).
[Crossref] [PubMed]

P. Bao, F. Zhang, G. Pedrini, and W. Osten, “Phase retrieval using multiple illumination wavelengths,” Opt. Lett. 33(4), 309–311 (2008).
[Crossref] [PubMed]

Y. J. Liu, B. Chen, E. R. Li, J. Y. Wang, A. Marcelli, S. W. Wilkins, H. Ming, Y. C. Tian, K. A. Nugent, P. P. Zhu, and Z. Y. Wu, “Phase retrieval in x-ray imaging based on using structured illumination,” Phys. Rev. A 78(2), 023817 (2008).
[Crossref]

2007 (5)

2006 (2)

2005 (1)

2004 (3)

J. M. Rodenburg and H. M. L. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85(20), 4795–4798 (2004).
[Crossref]

H. M. L. Faulkner and J. M. Rodenburg, “Movable Aperture Lensless Transmission Microscopy: A Novel Phase Retrieval Algorithm,” Phys. Rev. Lett. 93(2), 023903 (2004).
[Crossref] [PubMed]

C. L. Evans, E. O. Potma, and X. S. Xie, “Coherent anti-Stokes Raman scattering spectral interferometry: determination of the real and imaginary components of nonlinear susceptibility χ(3) for vibrational microscopy,” Opt. Lett. 29(24), 2923–2925 (2004).
[Crossref] [PubMed]

2003 (1)

D. Oron, N. Dudovich, and Y. Silberberg, “Femtosecond phase-and-polarization control for background-free coherent anti-Stokes Raman spectroscopy,” Phys. Rev. Lett. 90(21), 213902 (2003).
[Crossref] [PubMed]

2002 (2)

N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature 418(6897), 512–514 (2002).
[Crossref] [PubMed]

A. Volkmer, L. D. Book, and X. S. Xie, “Time-resolved coherent anti-Stokes Raman scattering microscopy: Imaging based on Raman free induction decay,” Appl. Phys. Lett. 80(9), 1505–1507 (2002).
[Crossref]

2001 (2)

A. Volkmer, J. X. Cheng, and X. S. Xie, “Vibrational imaging with high sensitivity via Epi-detected Coherent Anti-Stokes Raman Scattering (E-CARS) microscopy,” Phys. Rev. Lett. 87(2), 023901 (2001).
[Crossref]

J.-X. Cheng, L. D. Book, and X. S. Xie, “Polarization coherent anti-Stokes Raman scattering microscopy,” Opt. Lett. 26(17), 1341–1343 (2001).
[Crossref] [PubMed]

Akimov, D.

D. Akimov, S. Chatzipapadopoulos, T. Meyer, N. Tarcea, B. Dietzek, M. Schmitt, and J. Popp, “Different contrast information obtained from CARS and nonresonant FWM images,” J. Raman Spectrosc. 40(8), 941–947 (2009).
[Crossref]

Almoro, P.

Bao, P.

Berto, P.

Bon, P.

P. Berto, D. Gachet, P. Bon, S. Monneret, and H. Rigneault, “Wide-Field Vibrational Phase Imaging,” Phys. Rev. Lett. 109(9), 093902 (2012).
[Crossref] [PubMed]

Book, L. D.

A. Volkmer, L. D. Book, and X. S. Xie, “Time-resolved coherent anti-Stokes Raman scattering microscopy: Imaging based on Raman free induction decay,” Appl. Phys. Lett. 80(9), 1505–1507 (2002).
[Crossref]

J.-X. Cheng, L. D. Book, and X. S. Xie, “Polarization coherent anti-Stokes Raman scattering microscopy,” Opt. Lett. 26(17), 1341–1343 (2001).
[Crossref] [PubMed]

Borri, P.

Buckup, T.

C. Müller, T. Buckup, B. von Vacano, and M. Motzkus, “Heterodyne single-beam CARS microscopy,” J. Raman Spectrosc. 40(7), 809–816 (2009).
[Crossref]

Caster, A. G.

Chatzipapadopoulos, S.

D. Akimov, S. Chatzipapadopoulos, T. Meyer, N. Tarcea, B. Dietzek, M. Schmitt, and J. Popp, “Different contrast information obtained from CARS and nonresonant FWM images,” J. Raman Spectrosc. 40(8), 941–947 (2009).
[Crossref]

Chen, B.

Y. J. Liu, B. Chen, E. R. Li, J. Y. Wang, A. Marcelli, S. W. Wilkins, H. Ming, Y. C. Tian, K. A. Nugent, P. P. Zhu, and Z. Y. Wu, “Phase retrieval in x-ray imaging based on using structured illumination,” Phys. Rev. A 78(2), 023817 (2008).
[Crossref]

Chen, B. C.

B. C. Chen and S. H. Lim, “Optimal laser pulse shaping for interferometric multiplex coherent anti-stokes Raman scattering microscopy,” J. Phys. Chem. B 112(12), 3653–3661 (2008).
[Crossref] [PubMed]

Cheng, J. X.

A. Volkmer, J. X. Cheng, and X. S. Xie, “Vibrational imaging with high sensitivity via Epi-detected Coherent Anti-Stokes Raman Scattering (E-CARS) microscopy,” Phys. Rev. Lett. 87(2), 023901 (2001).
[Crossref]

Cheng, J.-X.

Dietzek, B.

D. Akimov, S. Chatzipapadopoulos, T. Meyer, N. Tarcea, B. Dietzek, M. Schmitt, and J. Popp, “Different contrast information obtained from CARS and nonresonant FWM images,” J. Raman Spectrosc. 40(8), 941–947 (2009).
[Crossref]

Dudovich, N.

D. Oron, N. Dudovich, and Y. Silberberg, “Femtosecond phase-and-polarization control for background-free coherent anti-Stokes Raman spectroscopy,” Phys. Rev. Lett. 90(21), 213902 (2003).
[Crossref] [PubMed]

N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature 418(6897), 512–514 (2002).
[Crossref] [PubMed]

Evans, C. L.

Faulkner, H. M. L.

J. M. Rodenburg and H. M. L. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85(20), 4795–4798 (2004).
[Crossref]

H. M. L. Faulkner and J. M. Rodenburg, “Movable Aperture Lensless Transmission Microscopy: A Novel Phase Retrieval Algorithm,” Phys. Rev. Lett. 93(2), 023903 (2004).
[Crossref] [PubMed]

Freudiger, C. W.

W. Min, C. W. Freudiger, S. Lu, and X. S. Xie, “Coherent Nonlinear Optical Imaging: Beyond Fluorescence Microscopy,” Annu. Rev. Phys. Chem. 62(1), 507–530 (2011).
[Crossref] [PubMed]

Gachet, D.

P. Berto, D. Gachet, P. Bon, S. Monneret, and H. Rigneault, “Wide-Field Vibrational Phase Imaging,” Phys. Rev. Lett. 109(9), 093902 (2012).
[Crossref] [PubMed]

Gao, P.

Herek, J. L.

M. Jurna, J. P. Korterik, C. Otto, J. L. Herek, and H. L. Offerhaus, “Vibrational phase contrast microscopy by use of coherent anti-Stokes Raman scattering,” Phys. Rev. Lett. 103(4), 043905 (2009).
[Crossref] [PubMed]

M. Jurna, J. P. Korterik, C. Otto, J. L. Herek, and H. L. Offerhaus, “Background free CARS imaging by phase sensitive heterodyne CARS,” Opt. Express 16(20), 15863–15869 (2008).
[Crossref] [PubMed]

Jesacher, A.

Jurna, M.

Korterik, J. P.

Krishnamachari, V. V.

Langbein, W.

Lei, M.

Leone, S. R.

Li, E. R.

Y. J. Liu, B. Chen, E. R. Li, J. Y. Wang, A. Marcelli, S. W. Wilkins, H. Ming, Y. C. Tian, K. A. Nugent, P. P. Zhu, and Z. Y. Wu, “Phase retrieval in x-ray imaging based on using structured illumination,” Phys. Rev. A 78(2), 023817 (2008).
[Crossref]

Lim, S. H.

B. C. Chen and S. H. Lim, “Optimal laser pulse shaping for interferometric multiplex coherent anti-stokes Raman scattering microscopy,” J. Phys. Chem. B 112(12), 3653–3661 (2008).
[Crossref] [PubMed]

S. H. Lim, A. G. Caster, and S. R. Leone, “Fourier transform spectral interferometric coherent anti-Stokes Raman scattering (FTSI-CARS) spectroscopy,” Opt. Lett. 32(10), 1332–1334 (2007).
[Crossref] [PubMed]

Liu, Y. J.

Y. J. Liu, B. Chen, E. R. Li, J. Y. Wang, A. Marcelli, S. W. Wilkins, H. Ming, Y. C. Tian, K. A. Nugent, P. P. Zhu, and Z. Y. Wu, “Phase retrieval in x-ray imaging based on using structured illumination,” Phys. Rev. A 78(2), 023817 (2008).
[Crossref]

Lu, S.

W. Min, C. W. Freudiger, S. Lu, and X. S. Xie, “Coherent Nonlinear Optical Imaging: Beyond Fluorescence Microscopy,” Annu. Rev. Phys. Chem. 62(1), 507–530 (2011).
[Crossref] [PubMed]

Malinovskaya, S.

V. Patel, V. S. Malinovsky, and S. Malinovskaya, “Effects of phase and coupling between the vibrational modes on selective excitation in coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. A 81(6), 063404 (2010).
[Crossref]

Malinovskaya, S. A.

Malinovsky, V. S.

V. Patel, V. S. Malinovsky, and S. Malinovskaya, “Effects of phase and coupling between the vibrational modes on selective excitation in coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. A 81(6), 063404 (2010).
[Crossref]

S. A. Malinovskaya and V. S. Malinovsky, “Chirped-pulse adiabatic control in coherent anti-Stokes Raman scattering for imaging of biological structure and dynamics,” Opt. Lett. 32(6), 707–709 (2007).
[Crossref] [PubMed]

Marcelli, A.

Y. J. Liu, B. Chen, E. R. Li, J. Y. Wang, A. Marcelli, S. W. Wilkins, H. Ming, Y. C. Tian, K. A. Nugent, P. P. Zhu, and Z. Y. Wu, “Phase retrieval in x-ray imaging based on using structured illumination,” Phys. Rev. A 78(2), 023817 (2008).
[Crossref]

Meyer, T.

D. Akimov, S. Chatzipapadopoulos, T. Meyer, N. Tarcea, B. Dietzek, M. Schmitt, and J. Popp, “Different contrast information obtained from CARS and nonresonant FWM images,” J. Raman Spectrosc. 40(8), 941–947 (2009).
[Crossref]

Min, W.

W. Min, C. W. Freudiger, S. Lu, and X. S. Xie, “Coherent Nonlinear Optical Imaging: Beyond Fluorescence Microscopy,” Annu. Rev. Phys. Chem. 62(1), 507–530 (2011).
[Crossref] [PubMed]

Ming, H.

Y. J. Liu, B. Chen, E. R. Li, J. Y. Wang, A. Marcelli, S. W. Wilkins, H. Ming, Y. C. Tian, K. A. Nugent, P. P. Zhu, and Z. Y. Wu, “Phase retrieval in x-ray imaging based on using structured illumination,” Phys. Rev. A 78(2), 023817 (2008).
[Crossref]

Monneret, S.

Motzkus, M.

C. Müller, T. Buckup, B. von Vacano, and M. Motzkus, “Heterodyne single-beam CARS microscopy,” J. Raman Spectrosc. 40(7), 809–816 (2009).
[Crossref]

B. von Vacano and M. Motzkus, “Time-resolving molecular vibration for microanalytics: single laser beam nonlinear Raman spectroscopy in simulation and experiment,” Phys. Chem. Chem. Phys. 10(5), 681–691 (2008).
[Crossref] [PubMed]

Müller, C.

C. Müller, T. Buckup, B. von Vacano, and M. Motzkus, “Heterodyne single-beam CARS microscopy,” J. Raman Spectrosc. 40(7), 809–816 (2009).
[Crossref]

Nugent, K. A.

Y. J. Liu, B. Chen, E. R. Li, J. Y. Wang, A. Marcelli, S. W. Wilkins, H. Ming, Y. C. Tian, K. A. Nugent, P. P. Zhu, and Z. Y. Wu, “Phase retrieval in x-ray imaging based on using structured illumination,” Phys. Rev. A 78(2), 023817 (2008).
[Crossref]

Offerhaus, H. L.

Oron, D.

D. Oron, N. Dudovich, and Y. Silberberg, “Femtosecond phase-and-polarization control for background-free coherent anti-Stokes Raman spectroscopy,” Phys. Rev. Lett. 90(21), 213902 (2003).
[Crossref] [PubMed]

N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature 418(6897), 512–514 (2002).
[Crossref] [PubMed]

Osten, W.

Otto, C.

Patel, V.

V. Patel, V. S. Malinovsky, and S. Malinovskaya, “Effects of phase and coupling between the vibrational modes on selective excitation in coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. A 81(6), 063404 (2010).
[Crossref]

Pedrini, G.

Popp, J.

D. Akimov, S. Chatzipapadopoulos, T. Meyer, N. Tarcea, B. Dietzek, M. Schmitt, and J. Popp, “Different contrast information obtained from CARS and nonresonant FWM images,” J. Raman Spectrosc. 40(8), 941–947 (2009).
[Crossref]

Potma, E. O.

Rigneault, H.

Ritsch-Marte, M.

Rocha-Mendoza, I.

Rodenburg, J. M.

F. Zhang and J. M. Rodenburg, “Phase retrieval based on wave-front relay and modulation,” Phys. Rev. B 82(12), 121104 (2010).
[Crossref]

J. M. Rodenburg and H. M. L. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85(20), 4795–4798 (2004).
[Crossref]

H. M. L. Faulkner and J. M. Rodenburg, “Movable Aperture Lensless Transmission Microscopy: A Novel Phase Retrieval Algorithm,” Phys. Rev. Lett. 93(2), 023903 (2004).
[Crossref] [PubMed]

Roider, C.

Schmitt, M.

D. Akimov, S. Chatzipapadopoulos, T. Meyer, N. Tarcea, B. Dietzek, M. Schmitt, and J. Popp, “Different contrast information obtained from CARS and nonresonant FWM images,” J. Raman Spectrosc. 40(8), 941–947 (2009).
[Crossref]

Silberberg, Y.

D. Oron, N. Dudovich, and Y. Silberberg, “Femtosecond phase-and-polarization control for background-free coherent anti-Stokes Raman spectroscopy,” Phys. Rev. Lett. 90(21), 213902 (2003).
[Crossref] [PubMed]

N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature 418(6897), 512–514 (2002).
[Crossref] [PubMed]

Tarcea, N.

D. Akimov, S. Chatzipapadopoulos, T. Meyer, N. Tarcea, B. Dietzek, M. Schmitt, and J. Popp, “Different contrast information obtained from CARS and nonresonant FWM images,” J. Raman Spectrosc. 40(8), 941–947 (2009).
[Crossref]

Tian, Y. C.

Y. J. Liu, B. Chen, E. R. Li, J. Y. Wang, A. Marcelli, S. W. Wilkins, H. Ming, Y. C. Tian, K. A. Nugent, P. P. Zhu, and Z. Y. Wu, “Phase retrieval in x-ray imaging based on using structured illumination,” Phys. Rev. A 78(2), 023817 (2008).
[Crossref]

Volkmer, A.

A. Volkmer, L. D. Book, and X. S. Xie, “Time-resolved coherent anti-Stokes Raman scattering microscopy: Imaging based on Raman free induction decay,” Appl. Phys. Lett. 80(9), 1505–1507 (2002).
[Crossref]

A. Volkmer, J. X. Cheng, and X. S. Xie, “Vibrational imaging with high sensitivity via Epi-detected Coherent Anti-Stokes Raman Scattering (E-CARS) microscopy,” Phys. Rev. Lett. 87(2), 023901 (2001).
[Crossref]

von Vacano, B.

C. Müller, T. Buckup, B. von Vacano, and M. Motzkus, “Heterodyne single-beam CARS microscopy,” J. Raman Spectrosc. 40(7), 809–816 (2009).
[Crossref]

B. von Vacano and M. Motzkus, “Time-resolving molecular vibration for microanalytics: single laser beam nonlinear Raman spectroscopy in simulation and experiment,” Phys. Chem. Chem. Phys. 10(5), 681–691 (2008).
[Crossref] [PubMed]

Wang, J. Y.

Y. J. Liu, B. Chen, E. R. Li, J. Y. Wang, A. Marcelli, S. W. Wilkins, H. Ming, Y. C. Tian, K. A. Nugent, P. P. Zhu, and Z. Y. Wu, “Phase retrieval in x-ray imaging based on using structured illumination,” Phys. Rev. A 78(2), 023817 (2008).
[Crossref]

Watson, P.

Wilkins, S. W.

Y. J. Liu, B. Chen, E. R. Li, J. Y. Wang, A. Marcelli, S. W. Wilkins, H. Ming, Y. C. Tian, K. A. Nugent, P. P. Zhu, and Z. Y. Wu, “Phase retrieval in x-ray imaging based on using structured illumination,” Phys. Rev. A 78(2), 023817 (2008).
[Crossref]

Wu, Z. Y.

Y. J. Liu, B. Chen, E. R. Li, J. Y. Wang, A. Marcelli, S. W. Wilkins, H. Ming, Y. C. Tian, K. A. Nugent, P. P. Zhu, and Z. Y. Wu, “Phase retrieval in x-ray imaging based on using structured illumination,” Phys. Rev. A 78(2), 023817 (2008).
[Crossref]

Xie, X. S.

W. Min, C. W. Freudiger, S. Lu, and X. S. Xie, “Coherent Nonlinear Optical Imaging: Beyond Fluorescence Microscopy,” Annu. Rev. Phys. Chem. 62(1), 507–530 (2011).
[Crossref] [PubMed]

C. L. Evans and X. S. Xie, “Coherent anti-stokes Raman scattering microscopy: chemical imaging for biology and medicine,” Annu Rev Anal Chem (Palo Alto Calif) 1(1), 883–909 (2008).
[Crossref] [PubMed]

E. O. Potma, C. L. Evans, and X. S. Xie, “Heterodyne coherent anti-Stokes Raman scattering (CARS) imaging,” Opt. Lett. 31(2), 241–243 (2006).
[Crossref] [PubMed]

C. L. Evans, E. O. Potma, and X. S. Xie, “Coherent anti-Stokes Raman scattering spectral interferometry: determination of the real and imaginary components of nonlinear susceptibility χ(3) for vibrational microscopy,” Opt. Lett. 29(24), 2923–2925 (2004).
[Crossref] [PubMed]

A. Volkmer, L. D. Book, and X. S. Xie, “Time-resolved coherent anti-Stokes Raman scattering microscopy: Imaging based on Raman free induction decay,” Appl. Phys. Lett. 80(9), 1505–1507 (2002).
[Crossref]

J.-X. Cheng, L. D. Book, and X. S. Xie, “Polarization coherent anti-Stokes Raman scattering microscopy,” Opt. Lett. 26(17), 1341–1343 (2001).
[Crossref] [PubMed]

A. Volkmer, J. X. Cheng, and X. S. Xie, “Vibrational imaging with high sensitivity via Epi-detected Coherent Anti-Stokes Raman Scattering (E-CARS) microscopy,” Phys. Rev. Lett. 87(2), 023901 (2001).
[Crossref]

Yang, Y.

Yao, B.

Ye, T.

Zhang, F.

F. Zhang and J. M. Rodenburg, “Phase retrieval based on wave-front relay and modulation,” Phys. Rev. B 82(12), 121104 (2010).
[Crossref]

P. Bao, F. Zhang, G. Pedrini, and W. Osten, “Phase retrieval using multiple illumination wavelengths,” Opt. Lett. 33(4), 309–311 (2008).
[Crossref] [PubMed]

F. Zhang, G. Pedrini, and W. Osten, “Phase retrieval of arbitrary complex-valued fields through aperture-plane modulation,” Phys. Rev. A 75(4), 043805 (2007).
[Crossref]

Zhang, Y.

Zheng, J.

Zhu, P. P.

Y. J. Liu, B. Chen, E. R. Li, J. Y. Wang, A. Marcelli, S. W. Wilkins, H. Ming, Y. C. Tian, K. A. Nugent, P. P. Zhu, and Z. Y. Wu, “Phase retrieval in x-ray imaging based on using structured illumination,” Phys. Rev. A 78(2), 023817 (2008).
[Crossref]

Zuo, C.

Annu Rev Anal Chem (Palo Alto Calif) (1)

C. L. Evans and X. S. Xie, “Coherent anti-stokes Raman scattering microscopy: chemical imaging for biology and medicine,” Annu Rev Anal Chem (Palo Alto Calif) 1(1), 883–909 (2008).
[Crossref] [PubMed]

Annu. Rev. Phys. Chem. (1)

W. Min, C. W. Freudiger, S. Lu, and X. S. Xie, “Coherent Nonlinear Optical Imaging: Beyond Fluorescence Microscopy,” Annu. Rev. Phys. Chem. 62(1), 507–530 (2011).
[Crossref] [PubMed]

Appl. Opt. (2)

Appl. Phys. Lett. (2)

J. M. Rodenburg and H. M. L. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85(20), 4795–4798 (2004).
[Crossref]

A. Volkmer, L. D. Book, and X. S. Xie, “Time-resolved coherent anti-Stokes Raman scattering microscopy: Imaging based on Raman free induction decay,” Appl. Phys. Lett. 80(9), 1505–1507 (2002).
[Crossref]

J. Opt. Soc. Am. A (1)

J. Phys. Chem. B (1)

B. C. Chen and S. H. Lim, “Optimal laser pulse shaping for interferometric multiplex coherent anti-stokes Raman scattering microscopy,” J. Phys. Chem. B 112(12), 3653–3661 (2008).
[Crossref] [PubMed]

J. Raman Spectrosc. (2)

C. Müller, T. Buckup, B. von Vacano, and M. Motzkus, “Heterodyne single-beam CARS microscopy,” J. Raman Spectrosc. 40(7), 809–816 (2009).
[Crossref]

D. Akimov, S. Chatzipapadopoulos, T. Meyer, N. Tarcea, B. Dietzek, M. Schmitt, and J. Popp, “Different contrast information obtained from CARS and nonresonant FWM images,” J. Raman Spectrosc. 40(8), 941–947 (2009).
[Crossref]

Nature (1)

N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature 418(6897), 512–514 (2002).
[Crossref] [PubMed]

Opt. Express (2)

Opt. Lett. (11)

S. H. Lim, A. G. Caster, and S. R. Leone, “Fourier transform spectral interferometric coherent anti-Stokes Raman scattering (FTSI-CARS) spectroscopy,” Opt. Lett. 32(10), 1332–1334 (2007).
[Crossref] [PubMed]

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Phys. Chem. Chem. Phys. (1)

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Phys. Rev. A (3)

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[Crossref]

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[Crossref]

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[Crossref]

Phys. Rev. B (1)

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[Crossref]

Phys. Rev. Lett. (5)

H. M. L. Faulkner and J. M. Rodenburg, “Movable Aperture Lensless Transmission Microscopy: A Novel Phase Retrieval Algorithm,” Phys. Rev. Lett. 93(2), 023903 (2004).
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Figures (5)

Fig. 1
Fig. 1 Schematic diagram of reference-less CARS phase imaging microscopy. Inset shows the mechanism of phase imaging from several intensities Im recorded for different axial planes.
Fig. 2
Fig. 2 (a) Energy-level diagrams of Raman resonant CARS and nonresonant FWM background at the anti-Stokes frequency. (b) Principle of phase imaging: spatial phase alteration caused by a sample with spatially varying Raman resonant and nonresonant contributions [22].
Fig. 3
Fig. 3 Flowchart of the iterative phase imaging.
Fig. 4
Fig. 4 Schematic setup for CARS phase imaging.
Fig. 5
Fig. 5 Phase imaging using the iterative phase retrieval (IPR) method. (a) and (c) are 6 of 12 intensities recorded in the resonant and nonresonant mode; (b) retrieved resonant phase image and (d) retrieved nonresonant phase image; (e) retrieved vibrational phase φ CARS R - φ CARS NR ; (f) background-free intensity on the image plane; (g) intensity plot of the cross section outlined by a dashed line in (a) and (f).

Equations (4)

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E CARS NR ( χ 1 NR + χ 2 NR ) E p 2 E s E CARS R ( χ 1 NR + χ 2 NR +Re( χ 1 R )+iIm( χ 1 R ) ) E p 2 E s
φ χ = φ CARS R φ CARS NR =Ang{ E CARS R E CARS NR }=Ang{ χ 1 NR + χ 2 NR +Re( χ 1 R )+iIm( χ 1 R ) χ 1 NR + χ 2 NR }
I backgroundfree I CARS R ( sin φ χ ) 2
O m+1 ( x,y )=IFT{ FT[ O m ]exp[ ikΔz 1 ( λ κ x ) 2 ( λ κ y ) 2 ] }

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