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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 6 — Mar. 12, 2012
  • pp: 6042–6051
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Superresolution four-wave mixing microscopy

Hyunmin Kim, Garnett W. Bryant, and Stephan J. Stranick  »View Author Affiliations


Optics Express, Vol. 20, Issue 6, pp. 6042-6051 (2012)
http://dx.doi.org/10.1364/OE.20.006042


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Abstract

We report on the development of a superresolution four-wave mixing microscope with spatial resolution approaching 130 nm which represents better than twice the diffraction limit at 800 nm while retaining the ability to acquire materials- and chemical- specific contrast. The resolution enhancement is achieved by narrowing the microscope’s excitation volume in the focal plane through the combined use of a Toraldo-style pupil phase filter with the multiplicative nature of four-wave mixing.

© 2012 OSA

Introduction

Our understanding of nanoscale chemical systems is hampered by the absence of chemical imaging tools with the requisite resolution. The properties of these chemical systems are generally determined and governed by the degree of coupling between the components that comprise them and the resulting level of complexity, e.g., chemical and physical heterogeneity, phase, and morphology. More often than not, the degree to which we can harness a particular material property into a new technology is based largely on our knowledge and understanding of that system at or below the size scale of the components that comprise it. As important technology sectors such as alternative energy, advanced electronics, and health care exploit the unique properties of nanosystems, chemical imaging with greater and greater resolving power will continue to grow in importance.

The pursuit of higher resolution optical microscopy is much broader and diverse than chemical imaging alone. A number of superresolution (SR) techniques based on florescent microscopy have been developed for applications in life and materials science. Optical superresolution techniques fall into three general categories: optical bandwidth expansion, point spread function (PSF) engineering, and post recovery of optical bandwidth. Optical bandwidth expansion involves the extraction of higher spatial frequency information through the use of high numerical optics, e.g., solid emersion lens, or through spatial modulation techniques like structured illumination microscopy [1

1. W. Lukosz, “Optical systems with resolving powers exceeding the classical limit,” J. Opt. Soc. Am. A 56(11), 1463–1472 (1966). [CrossRef]

4

4. M. G. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198(2), 82–87 (2000). [CrossRef] [PubMed]

] to achieve resolution improvements of a factor of two and better. Point spread function engineering has been used to alter the illumination conditions and thus the Rayleigh criterion to theoretically allow for unlimited resolution [5

5. G. T. Francia, “Super-gain antennas and optical resolving power,” Nuovo Cim. 9(S3), 426–438 (1952). [CrossRef]

]. An example of a point spread function engineered superresolution technique is stimulated emission depletion microscopy (STED) [6

6. M. Dyba and S. W. Hell, “Focal spots of size λ/23 open up far-field fluorescence microscopy at 33 nm axial resolution,” Phys. Rev. Lett. 88(16), 163901 (2002). [CrossRef] [PubMed]

]. STED is a focus-engineered fluorescent microscopy technique that works by actively controlling the centroid of the emission through the depletion of the fluorescence from the outer circumference of a diffraction limited spot. The technique has achieved sub-50 nm scale optical resolution in the as-measured data [7

7. R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, “Spherical nanosized focal spot unravels the interior of cells,” Nat. Methods 5(6), 539–544 (2008). [CrossRef] [PubMed]

]. Lastly, there are those techniques that require post recovery of superresolution. These techniques can range from deconvolution algorithms [8

8. W. Richardson, “Bayesian-based iterative method of image restoration,” J. Opt. Soc. Am. A 62(1), 55–59 (1972). [CrossRef]

] to those that augment the microscopes spatial frequency channels (x, y, z) with the temporal channel [9

9. I. Cox and C. Sheppard, “Information capacity and resolution in an optical system,” J. Opt. Soc. Am. A 3(8), 1152–1158 (1986). [CrossRef]

]. These superresolution techniques include photo-activated localization microscopy (PALM) [10

10. E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006). [CrossRef] [PubMed]

] and stochastic optical reconstruction microscopy (STORM) [11

11. M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006). [CrossRef] [PubMed]

] and typically construct a functional superresolution image from thousands or tens of thousands of raw images acquired over the course of several minutes or hours. These post-recovery techniques have achieved position resolution at the tens of nanometer scale.

One of the main drawbacks of the superresolution techniques described above is that they rely on fluorescence detection either from intrinsic or extrinsic fluorophores. While these techniques have advanced life science, a broader impact has not been realized in chemical and materials science. Key barriers that have limited the practical pursuit of superresolution chemical imaging include chemical selectivity, sensitivity, and fabrication of superresolvingoptical elements. Recent developments in four-wave mixing microscopy (namely, coherent Raman microscopy) and in programmable optics (spatial light modulators) provide practical solutions to these limitations. Coherent anti-Stokes Raman (CARS) microscopy is one of the more widely used four-wave mixing (FWM) techniques [12

12. E. O. Potma and X. Xie, “CARS microscopy for biology and medicine,” Opt. Photonics News 15(11), 40–45 (2004). [CrossRef]

]. CARS is a third order nonlinear optical process that involves multiwave, multicolor excitation comprised of a pump, Stokes, and probe beam. When the energy difference between the pump and Stokes beams matches a vibrational resonance in the sample, the detected signal is strongly enhanced, see Fig. 1(a)
Fig. 1 (A) Energy diagram for coherent anti-Stoke Raman scattering (CARS). P and S stand for pump and Stokes beams. Ω is the vibrational energy. g is the vibrational ground state; e, excitation state; g’, virtual ground state; e’, virtual excitation state, respectively. (B) P, the focal fields calculated for the flat wave front; S, focal fields for the π-stepped annular (≈0.42 of beam diameter) phase mask; CARS, the product of the squared P and S. Insets in P and S are the illustrations for each wavefront. (C) A cartoon shows how a spatial light modulator (SLM) controls the PSF of microscope. PC; personal computer, OL; objective lens, SiNW; silicon nanowire, BS; beam splitter.
. This sensitivity to vibrational resonances makes CARS highly chemically specific, and the amplification caused by the coherent nature of the signal provides for rapid image collection: the CARS process can be many orders-of-magnitude more efficient than conventional Raman. The chemical sensitivity of CARS along with the increased signal has enabled researchers to achieve video-rate, molecular imaging of lipid-rich cells [13

13. X. Nan, J. X. Cheng, and X. S. Xie, “Vibrational imaging of lipid droplets in live fibroblast cells with coherent anti-Stokes Raman scattering microscopy,” J. Lipid Res. 44(11), 2202–2208 (2003). [CrossRef] [PubMed]

] and in vivo imaging of live mouse tissue [14

14. 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(46), 16807–16812 (2005). [CrossRef] [PubMed]

].

Two electronically-synchronized, 2.2 picosecond pulsed lasers were used as pump and Stokes beams for the four-wave mixing generation (see Fig. 2
Fig. 2 A schematic diagram of the super-resolution, four-wave mixing microscope. SL; SychroLock, BE; beam expander, CL0 – CL4; convex lenses, TS; a manual xy directional translation stage, BS; beam splitter, SS; piezo-driven xy image scanning stages, NPBS; non-polarizing beam splitter, BF; bandpass filter, CCD; charge coupled device, APD; avalanche photodiode, SLM; spatial light modulator, WS; wavefront sensor.
for the optical setup). The details on optical elements for the control of polarization, intensity and beam manipulation have been outlined previously [23

23. H. Kim, C. A. Michaels, G. W. Bryant, and S. J. Stranick, “Comparison of the sensitivity and image contrast in spontaneous Raman and coherent Stokes Raman scattering microscopy of geometry-controlled samples,” J. Biomed. Opt. 16(2), 021107 (2011). [CrossRef] [PubMed]

]. The Stokes beam (785 nm) was telescopically expanded to fill the active area (2 cm x 2 cm) of the nematic liquid crystal SLM (X8267, Hamamatsu) [24

24. Certain commercial equipment, instruments, or materials are identified in this paper to specify adequately the experimental procedure. In no case does such identification imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the materials or equipment identified are necessarily the best available for the purpose.

]. The Stokes beam, once reflected from the SLM, was imprinted with a computer controlled phase profile. This profile was comprised of controllable circular phase steps and a calibrated background field that cancels out systematic phase distortions. The background correction was measured using a Shack-Hartmann wavefront sensor followed by reformatting and phase response calibration to obtain a flat phase field or wavefront. The phase-modulated Stokes beam was then relayed by four convex lenses to the back pupil plane of the microscopic objective (1.3 NA, oil immersion). The output diameter of the Stokes beam from the SLM was matched to the diameter of the pupil plane of the objective. The pump beam was also matched to this diameter using a beam expander. The pump and Stokes beams were collinearly combined by a 50:50 beam splitter. The reflected FWM signal generated by the specimen was separated from excitation beams by use of a non-polarizing beam splitter and bandpass filters.

In the microscopy measurements, the samples were scanned using a closed-loop, piezoelectric scan stage with 10 nm resolution in x,y and z. The cross-sectional mapping of the focal field distributions were carried out by scanning an isolated nanoparticle through the focus. This was done to verify the intended effects of the SLM generated phase filters. A complete mathematical representation of the converging fields in the focus was adapted from the literature [25

25. E. Wolf, “Electromagnetic diffraction in optical systems: I An integral representation of the image field,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 349–357 (1959). [CrossRef]

]. These calculated focal field distributions for an optical system comprised of an annular phased-step wavefront (phase masked beam) focused by a 1.3 NA oil immersion objective were used for predictive and diagnostic purposes.

The geometry of the annular phase masks used in programming the SLM are shown in Fig. 3(a)
Fig. 3 Geometry of the annular phase masks used in programming the SLM. () A background mask which corrects the wavefront distortion in the optical system along with the series of annular masks used to generate the Toraldo phase filters. (B) A series of focal distributions (xy) resulting from application of the associated phase masks in (A) recorded by epi-two photon luminescence imaging of an isolated gold nanoparticle with 785 nm excitation. (C) shows a series of focal field calculations for the each of the annular phase masks in (A). The dimension is indicated by the λ: the wavelength of the incident beam. (D) xz focal field distributions resulting from application of the associated phase masks and recorded in a similar manner as the xy fields. (E) A series of xz focal field calculations.
. The field variations in the grayscale are the background correction values used to obtain a flat phase field as measured by the wavefront sensor. The annular features (disks) in the grayscale are set to give a π phase step relative to background over the region of interest. The diameter of the annular phase step (d) is denoted relative to the dimension of the backstop of the microscope objective (d0), i.e., it is normalized to d0. The range of diameters (d) used in the measurements that follow are shown in Fig. 3(a). Measurements of the resulting xy field distributions were recorded for each value of d by monitoring the two-photon emission, excited at 785 nm, from an isolated gold nanoparticle while scanning the sample, Fig. 3(b), along with the associated calculated xy field distributions, Fig. 3(c) [26

26. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems: II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959). [CrossRef]

]. The prominent features, which include a narrowed center lobe as well as the satellite lobes, in both the experimental and calculated profiles are in good agreement. The xz field distributions were measured and calculated in the same fashion and are shown in Figs. 3(d) and 3(e) respectively. As with the xy field distributions, the calculated and measured values are in excellent agreement. This can be seen both in terms of the feature evolution with increasing values of d as well as the emergence of the side lobe intensity that is coupled with the narrowing of the centroid. Relative to the conventional PSF in the first column in Fig. 3(b), the centroid of the PSF becomes smaller (with a gradual increase in the side lobe intensity) up to a diameter of d = 0.42. As the diameter is increased further, the centroid elongates in xz until splitting in two (at d = 0.56) and then the trend is reversed with a re-emergence of a conventional PSF at d = 0.84. Also of note is the relative drop of intensity in the focal plane, both measured Fig. 3(d) and calculated Fig. 3 (e), from a maximum when d = conventional to a minimum at d = 0.42 and then restored again at d = 0.84: the centroid intensities relative to the conventional PSF (1) were 0.85 at d = 0.14, 0.72 at d = 0.28, 0.51 at d = 0.35, 0.25 at d = 0.42, 0.09 at d = 0.56, 0.31 at d = 0.70, and 0.83 at d = 0.84.

We achieve a superresolving PSF free of secondary features/artifacts by multiplicatively combining a conventional pump PSF with a Toraldo filtered Stokes PSF. This schema was critically assessed in terms of our ability to reproduce the calculated FWM field distribution as well as the degree to which the centroid of the PSF could be defined while abating the artifactual, side lobes. Figure 4
Fig. 4 (A) FWM microscopy images of Si nanowires on glass taken with 754 nm and 785 nm excitation beams. The arrow indicates the direction of the polarization and the dotted line indicates the region where the xz scans were recorded. (B) Shows the FWM PSF (xz) that results from two conventional beams. FWM PSF images that result from phase filtering with annular masks are shown in (C) for d = 0.14, (D) for d = 0.28, (E) for d = 0.42, (F) for d = 0.56, (G) for d = 0.70 and (H) for d = 0.83.
shows the results of the calculated (inset) and measured FWM PSF. The calculated values are the products of two conventional, and one phase filtered point spread function from the calculated values shown in Fig. 3(c): PSFFWM = PSFconventional * PSFconventional * PSFphase filtered [27

27. Recall that in FWM three incident fields combine to generate a fourth field, thus two conventional and one phase filtered. Also of note, we do not account for the relative phase of the fields (intensity only) which will become increasingly important as the sample systems become microscopically complex/extended.

]. The measurements of the FWM PSF were carried out by scanning an isolated region of a normally 100 nm diameter Si nanowire sample. The region is shown in Fig. 4(a) and it is denoted by the dashed line over the bright feature associated with the nanowire. The excitation wavelengths for this FWM measurement were 754 nm for the conventional and 785 nm for the phase filtered beams with each being nominally 1 mW as measured at the objective back stop. The xz FWM field distribution maps are shown in Figs. 4(b) through 4(h). In each image, the resulting PSF is mapped for a range of phase filtered PSFs combined with a conventional PSF. The associated d values for each image are 4(b) = conventional, 4(c) = 0.14, 4(d) = 0.28, 4(e) = 0.42, 4(f) = 0.56, 4(g) = 0.70, 4(h) = 0.83. As can be seen from the results in Fig. 4, the experimental and calculated values are in excellent agreement. The xz maps of the FWM PSFs exhibit the trend seen for the phase filtered PSF in Fig. 3 with a narrowing of the centroid from the conventional PSF in Fig. 4(b) from 300 nm down to nominally 150 nm in Fig. 4(e). More importantly, the side lobe intensity has been reduced dramatically. Additionally, the elongation of the focal volume in the z direction is now less severe than that in Fig. 3. This is also a result of the multiplicative FWM response where the regions of non-overlap of the PSFs do not contribute to the FWM field. Thus the FWM PSF’s side lobes are removed as well as its elongation in z, and the PSF’s centroid is spatially confined to well below the diffraction limit.

To evaluate the resolution enhancement of the SR-FWM PSF, images of an individual, nominally 100 nm Si nanowire were recorded. Figure 5(a)
Fig. 5 The FWM images of an isolated nanowire using conventional (A) and engineered PSFs corresponding to phase filters with annular diameters of (B) d = 0.14, (C) d = 0.28, (D) d = 0.35, (E) d = 0.42 and (F) d = 0.56. Insets in the lower-left corners correspond to simulated images using the calculated PSF for each phase filter. (G) The line profiles for the white dotted lines noted as (1, 2) in (A) and (D) are the average of three adjacent line scans: there was a mean variation of ~5% from line to line. (H) Simulated cross sections from the calculated images (inset) of a 100 nm feature using a conventional FWM PSF (black) and a SR-PSF (red). Note: The color scales are normalized, and the total signal strength relative to the conventional PSF case (maximum) is down a factor of 3.2 (minimum) for the d = 0.35 case.
through 5(f) show the results for a range of phase filter geometries: 5(a) = conventional/ d = 0, 5(b) d = 0.14, 5(c) d = 0.28, 5(d) d = 0.35, 5(e) d = 0.46, and 5(f) d = 0.56. As can be seen from this image series, the feature associated with the nanowire is initially broadened by the conventional PSF, 5(a), and then becomes increasingly narrower, 5(b) −5(e), before becoming broadened again, 5(f). As is shown in Fig. 5(g), cross-sectional analysis of the features from the conventional PSF, 5(a), and the SR-PSF, 5(d), shown an improvement of the resolution from nominally 300 nm full-width at half-maximum (FWHM) to nominally 150 nm FWHM. The actual spatial extent of the PSFs will be less than that derived from this analysis due to convolution with the 100 nm diameter nanowires. To further evaluate the true spatial extent of the PSF, simulated cross sections were performed by convolving a feature of width 100 nm with the calculated conventional PSF (inset of Fig. 5(a)) and phase filtered PSFs with associated values for d: inset of Figs. 5(b) for d = 0.14, 5(c) for d = 0.28, 5(d) for d = 0.35, 5(e) for d = 0.46, and 5(f) for d = 0.56 [28

28. A two-dimensional (2D) spatial filtering of a 100 nm feature was carried out with the 2D filter function or kernel consisting of a spatially calibrated PSF.

]. The resulting cross sections for the conventional and for d = 0.35 PSFs are shown in Fig. 5(h). The broadened feature widths are in excellent agreement with the experimentally obtained values for FWHM. From this analysis we can estimate that the resulting SR-PSF (d = 0.35) has a true spatial extent that approaches 130 nm FWHM (deconvolved) as compared to the measured value of 150 nm FWHM (convolved).

As stated above, a key variant of FWM microscopy is coherent Raman microscopy, namely CARS microscopy. This is due in large part to the outstanding sensitivity and chemical selectivity of the CARS process. To illustrate the use of a SR-PSF in a CARS microscope, we carried out measurements of dispersed polystyrene beads on glass. Chemically sensitive CARS contrast is achieved by probing the 1000 cm−1 C-C ring vibrational mode of polystyrene. To do this, a 727.8 nm pump (≈2 mW at the objective) and 785 nm (≈4 mW at the objective) Stokes beams were used with the resulting CARS signal collected in an epi geometry. Figure 6(a)
Fig. 6 (A) A Raman spectrum of polystyrene beads. CARS images tuned to (B) 1000 cm−1 and (C) 900 cm−1. The contrast gap in (B) corresponds to a region when the phases of the laser pulses are temporally mismatched. (D) Identical 20 µm x 20 µm regions of dispersed 0.30 µm diameter polystyrene beads imaged with CARS and (E) SR-CARS. CARS Images were taken using 728 nm pump (≈2 mW) and 785 nm Stokes (≈4 mW) beams; 0.35 d0 sized annular mask was used to record the image in (E). The dotted rectangle denotes the subportion of the images (D) and (E) shown in 3D rendering in (F) and (G) respectively.
shows a Raman spectrum from a cluster of polystyrene beads. The positions for the vibration modes used in Fig. 6(b) (1000 cm−1 = on resonance) and 6(c) (900 cm−1 = off resonance) are indicated in the Raman spectrum, and the resulting contrast is shown in Figs. 6(b) and 6(c). Additionally, a contrast gap is indicated by two parallel lines in Fig. 6(b). This contrast gap was created by momentarily removing the temporal overlap between pump and Stokes pulses by ≈800 ps and further illustrates that the image contrast is from FWM. The polystyrene beads imaged in this study were nominally 0.50 µm for Figs. 6(b) and 6(c) and 0.30 µm in diameter for Figs. 6(d) through 6(g). Figure 6(d) shows a 20 µm x 20 µm CARS image recorded on the 1000 cm−1 resonance and with a conventional PSF. A signal-to-noise level > 100 was obtained with morphological features such as rafts of beads and isolated beads similar to those observed in other microscopy studies of these particles [29

29. E. O. Potma, D. J. Jones, J.-X. Cheng, X. S. Xie, and J. Ye, “High-sensitivity coherent anti-Stokes Raman scattering microscopy with two tightly synchronized picosecond lasers,” Opt. Lett. 27(13), 1168–1170 (2002). [CrossRef] [PubMed]

]. In Fig. 6(d), the individual, 0.30 µm particles that comprise the raft features are not clearly resolved. In Fig. 6(e), the same area was imaged with a SR-PSF (d = 0.35). The individual 0.30 µm beads are now more clearly defined in this SR-CARS image. Three dimensional (3D) renderings of subportions, denoted by dashed rectangles, of these images provide for a closer comparison and show the degree to which the particles are resolved from each other in the SR-CARS image (Fig. 6(f)) relative to the conventional CARS image (Fig. 6(g)). Features of note in these 3D images include that of the two particles on the left and the degree to which they are resolved in the two cases (conventional vs. superresolution) as well as the appearance of the three particles in the feature on the right in the SR-CARS image, Fig. 6(g), that appears as only a single peaked feature in the conventional image, Fig. 6(f).

In summary, we demonstrate that the resolving power of FWM microscopy can be improved below the diffraction limit while retaining the microscope's ability to acquire materials- and chemical- specific contrast. The functional superresolution effect was achieved by narrowing the microscope’s excitation volume in the focal plane through the combined use of a Toraldo-style pupil phase filter with the multiplicative nature of four-wave mixing. The SR-FWM microscopy images of isolated nanoparticles demonstrated that resolution approaching 130 nm was obtainable with adequate signal-to-noise. Work is on-going to address the questions of the practical limits of this approach in terms of ultimate resolving power, detection limits, and the utility of this scheme for imaging microscopically complex/extended sample systems where the effects of coherency will become prominent.

Acknowledgments

The authors would like to thank Prof. Eric Potma for valuable discussions and Dr. Lee Richter for critical review of the manuscript.

References and links

1.

W. Lukosz, “Optical systems with resolving powers exceeding the classical limit,” J. Opt. Soc. Am. A 56(11), 1463–1472 (1966). [CrossRef]

2.

M. A. Neil, R. Juskaitis, and T. Wilson, “Method of obtaining optical sectioning by using structured light in a conventional microscope,” Opt. Lett. 22(24), 1905–1907 (1997). [CrossRef] [PubMed]

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M. A. Neil, A. Squire, R. Juškaitis, P. I. Bastiaens, and T. Wilson, “Wide-field optically sectioning fluorescence microscopy with laser illumination,” J. Microsc. 197(1), 1–4 (2000). [CrossRef] [PubMed]

4.

M. G. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198(2), 82–87 (2000). [CrossRef] [PubMed]

5.

G. T. Francia, “Super-gain antennas and optical resolving power,” Nuovo Cim. 9(S3), 426–438 (1952). [CrossRef]

6.

M. Dyba and S. W. Hell, “Focal spots of size λ/23 open up far-field fluorescence microscopy at 33 nm axial resolution,” Phys. Rev. Lett. 88(16), 163901 (2002). [CrossRef] [PubMed]

7.

R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, “Spherical nanosized focal spot unravels the interior of cells,” Nat. Methods 5(6), 539–544 (2008). [CrossRef] [PubMed]

8.

W. Richardson, “Bayesian-based iterative method of image restoration,” J. Opt. Soc. Am. A 62(1), 55–59 (1972). [CrossRef]

9.

I. Cox and C. Sheppard, “Information capacity and resolution in an optical system,” J. Opt. Soc. Am. A 3(8), 1152–1158 (1986). [CrossRef]

10.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006). [CrossRef] [PubMed]

11.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006). [CrossRef] [PubMed]

12.

E. O. Potma and X. Xie, “CARS microscopy for biology and medicine,” Opt. Photonics News 15(11), 40–45 (2004). [CrossRef]

13.

X. Nan, J. X. Cheng, and X. S. Xie, “Vibrational imaging of lipid droplets in live fibroblast cells with coherent anti-Stokes Raman scattering microscopy,” J. Lipid Res. 44(11), 2202–2208 (2003). [CrossRef] [PubMed]

14.

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(46), 16807–16812 (2005). [CrossRef] [PubMed]

15.

Y. Jung, L. Tong, A. Tanaudommongkon, J.-X. Cheng, and C. Yang, “In vitro and in vivo nonlinear optical imaging of silicon nanowires,” Nano Lett. 9(6), 2440–2444 (2009). [CrossRef] [PubMed]

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T. Ichimura, N. Hayazawa, M. Hashimoto, Y. Inouye, and S. Kawata, “Tip-enhanced coherent anti-stokes Raman scattering for vibrational nanoimaging,” Phys. Rev. Lett. 92(22), 220801 (2004). [CrossRef] [PubMed]

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L. Cheng and D. Y. Kim, “Differential imaging in coherent anti-Stokes Raman scattering microscopy with Laguerre- Gaussian excitation beams,” Opt. Express 15(16), 10123–10134 (2007). [CrossRef] [PubMed]

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V. Raghunathan and E. O. Potma, “Multiplicative and subtractive focal volume engineering in coherent Raman microscopy,” J. Opt. Soc. Am. A 27(11), 2365–2374 (2010). [CrossRef] [PubMed]

20.

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]

21.

W. P. Beeker, P. Groß, C. J. Lee, C. Cleff, H. L. Offerhaus, C. Fallnich, J. L. Herek, and K.-J. Boller, “A route to sub-diffraction-limited CARS Microscopy,” Opt. Express 17(25), 22632–22638 (2009). [CrossRef] [PubMed]

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M. R. Beversluis and S. J. Stranick, “Enhanced contrast coherent anti-Stokes Raman scattering microscopy using annular phase masks,” Appl. Phys. Lett. 93(23), 231115 (2008). [CrossRef]

23.

H. Kim, C. A. Michaels, G. W. Bryant, and S. J. Stranick, “Comparison of the sensitivity and image contrast in spontaneous Raman and coherent Stokes Raman scattering microscopy of geometry-controlled samples,” J. Biomed. Opt. 16(2), 021107 (2011). [CrossRef] [PubMed]

24.

Certain commercial equipment, instruments, or materials are identified in this paper to specify adequately the experimental procedure. In no case does such identification imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the materials or equipment identified are necessarily the best available for the purpose.

25.

E. Wolf, “Electromagnetic diffraction in optical systems: I An integral representation of the image field,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 349–357 (1959). [CrossRef]

26.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems: II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959). [CrossRef]

27.

Recall that in FWM three incident fields combine to generate a fourth field, thus two conventional and one phase filtered. Also of note, we do not account for the relative phase of the fields (intensity only) which will become increasingly important as the sample systems become microscopically complex/extended.

28.

A two-dimensional (2D) spatial filtering of a 100 nm feature was carried out with the 2D filter function or kernel consisting of a spatially calibrated PSF.

29.

E. O. Potma, D. J. Jones, J.-X. Cheng, X. S. Xie, and J. Ye, “High-sensitivity coherent anti-Stokes Raman scattering microscopy with two tightly synchronized picosecond lasers,” Opt. Lett. 27(13), 1168–1170 (2002). [CrossRef] [PubMed]

OCIS Codes
(100.6640) Image processing : Superresolution
(180.0180) Microscopy : Microscopy
(300.6290) Spectroscopy : Spectroscopy, four-wave mixing
(070.6120) Fourier optics and signal processing : Spatial light modulators

ToC Category:
Microscopy

History
Original Manuscript: January 12, 2012
Revised Manuscript: February 22, 2012
Manuscript Accepted: February 23, 2012
Published: February 28, 2012

Virtual Issues
Vol. 7, Iss. 5 Virtual Journal for Biomedical Optics

Citation
Hyunmin Kim, Garnett W. Bryant, and Stephan J. Stranick, "Superresolution four-wave mixing microscopy," Opt. Express 20, 6042-6051 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-6-6042


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  24. Certain commercial equipment, instruments, or materials are identified in this paper to specify adequately the experimental procedure. In no case does such identification imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the materials or equipment identified are necessarily the best available for the purpose.
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  27. Recall that in FWM three incident fields combine to generate a fourth field, thus two conventional and one phase filtered. Also of note, we do not account for the relative phase of the fields (intensity only) which will become increasingly important as the sample systems become microscopically complex/extended.
  28. A two-dimensional (2D) spatial filtering of a 100 nm feature was carried out with the 2D filter function or kernel consisting of a spatially calibrated PSF.
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