Abstract

This paper describes two superresolution coherent imaging techniques, which both use a diffraction grating to direct high spatial frequency information that would otherwise be lost through the imaging system pupil. The techniques employ digital holography to measure the optical field in the image plane and rely on capturing multiple holograms with the illumination condition altered between exposures. In one case, we used linear signal processing to separate aliased spectral regions, while in the second case we directly measured spectral regions without aliasing. In both cases, we stitched together higher-bandwidth synthetic aperture spectra and used them to reconstruct superresolution images. Our experimental results validated the approaches, demonstrating a resolution gain factor of approximately 2.5.

© 2016 Optical Society of America

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References

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2015 (1)

2013 (1)

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7, 739–745 (2013).
[Crossref]

2011 (1)

M. Mishali, Y. C. Eldar, O. Dounaevsky, and E. Shoshan, “Xampling: analog to digital at sub-Nyquist rates,” IET Circuits Dev. Syst. 5, 8–20 (2011).
[Crossref]

2010 (2)

A. Faridian, D. Hopp, G. Pedrini, U. Eigenthaler, M. Hirscher, and W. Osten, “Nanoscale imaging using deep ultraviolet digital holographic microscopy,” Opt. Express 18, 14159–14164 (2010).
[Crossref]

M. Mishali and Y. C. Eldar, “From theory to practice: Sub-Nyquist sampling of sparse wideband analog signals,” IEEE J. Sel. Top. Signal Process. 4, 375–391 (2010).
[Crossref]

2009 (3)

2008 (4)

2006 (1)

2005 (1)

M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy: Wide-field fluorescence imaging with theoretically unlimited esolution,” Proc. Natl. Acad. Sci. USA 102, 13081–13086 (2005).
[Crossref]

2003 (1)

2002 (2)

J. H. Massig, “Digital off-axis holography with a synthetic aperture,” Opt. Lett. 27, 2179–2181 (2002).
[Crossref]

C. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, “Super-resolution digital holographic imaging method,” Appl. Phys. Lett. 81, 3143–3145 (2002).
[Crossref]

2000 (1)

1997 (1)

1996 (1)

1967 (1)

1966 (1)

1964 (1)

Alexandrov, S. A.

Bo, F.

C. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, “Super-resolution digital holographic imaging method,” Appl. Phys. Lett. 81, 3143–3145 (2002).
[Crossref]

Brueck, S. R. J.

Cojoc, D.

Dorsch, R. G.

Dounaevsky, O.

M. Mishali, Y. C. Eldar, O. Dounaevsky, and E. Shoshan, “Xampling: analog to digital at sub-Nyquist rates,” IET Circuits Dev. Syst. 5, 8–20 (2011).
[Crossref]

Eigenthaler, U.

Eldar, Y. C.

M. Mishali, Y. C. Eldar, O. Dounaevsky, and E. Shoshan, “Xampling: analog to digital at sub-Nyquist rates,” IET Circuits Dev. Syst. 5, 8–20 (2011).
[Crossref]

M. Mishali and Y. C. Eldar, “From theory to practice: Sub-Nyquist sampling of sparse wideband analog signals,” IEEE J. Sel. Top. Signal Process. 4, 375–391 (2010).
[Crossref]

S. Gazit, A. Szameit, Y. C. Eldar, and M. Segev, “Super-resolution and reconstruction of sparse sub-wavelength images,” Opt. Express 17, 23920–23946 (2009).
[Crossref]

J. P. Wilde, J. W. Goodman, Y. C. Eldar, and Y. Takashima, “Grating-enhanced coherent imaging,” in 9th International Conference on Sampling Theory and Applications (SampTA) (2011), p. P0213.

J. P. Wilde, Y. C. Eldar, and J. W. Goodman, “Grating-enhanced optical imaging,” US Patent8,841,591 (23September2014).

J. P. Wilde, J. W. Goodman, Y. C. Eldar, and Y. Takashima, “Grating-enhanced coherent imaging,” in Optics in the Life Sciences (Optical Society of America, 2011).

Y. C. Eldar, Sampling Theory: Beyond Bandlimited Systems (Cambridge University, 2015).

Faridian, A.

Farkas, D.

Ferraro, P.

Ferreira, C.

Fienup, J. R.

S. A. Shroff, J. R. Fienup, and D. R. Williams, “Phase-shift estimation in sinusoidally illuminated images for lateral superresolution,” J. Opt. Soc. Am. A 26, 413–424 (2009).
[Crossref]

S. A. Shroff, J. R. Fienup, and D. R. Williams, “OTF compensation in structured illumination superresolution images,” Proc. SPIE 7094, 709402 (2008).
[Crossref]

Finizio, A.

García, J.

García-Martínez, P.

Gazit, S.

Goodman, J. W.

J. P. Wilde, Y. C. Eldar, and J. W. Goodman, “Grating-enhanced optical imaging,” US Patent8,841,591 (23September2014).

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005).

J. P. Wilde, J. W. Goodman, Y. C. Eldar, and Y. Takashima, “Grating-enhanced coherent imaging,” in Optics in the Life Sciences (Optical Society of America, 2011).

J. P. Wilde, J. W. Goodman, Y. C. Eldar, and Y. Takashima, “Grating-enhanced coherent imaging,” in 9th International Conference on Sampling Theory and Applications (SampTA) (2011), p. P0213.

Grilli, S.

Gustafsson, M. G. L.

M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy: Wide-field fluorescence imaging with theoretically unlimited esolution,” Proc. Natl. Acad. Sci. USA 102, 13081–13086 (2005).
[Crossref]

Gutzler, T.

Hillman, T. R.

Hirscher, M.

Hopp, D.

Horstmeyer, R.

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7, 739–745 (2013).
[Crossref]

Ilovitsh, A.

Kiryuschev, I.

Kuznetsova, Y.

Liu, C.

C. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, “Super-resolution digital holographic imaging method,” Appl. Phys. Lett. 81, 3143–3145 (2002).
[Crossref]

Liu, Z.

C. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, “Super-resolution digital holographic imaging method,” Appl. Phys. Lett. 81, 3143–3145 (2002).
[Crossref]

Lohmann, A. W.

Lukosz, W.

Massig, J. H.

Mendlovic, D.

Merola, F.

Mertz, J.

J. Mertz, Introduction to Optical Microscopy (Roberts & Company, 2009).

Mico, V.

Micó, V.

Mishali, M.

M. Mishali, Y. C. Eldar, O. Dounaevsky, and E. Shoshan, “Xampling: analog to digital at sub-Nyquist rates,” IET Circuits Dev. Syst. 5, 8–20 (2011).
[Crossref]

M. Mishali and Y. C. Eldar, “From theory to practice: Sub-Nyquist sampling of sparse wideband analog signals,” IEEE J. Sel. Top. Signal Process. 4, 375–391 (2010).
[Crossref]

Neumann, A.

Nicola, S. D.

Osten, W.

Paris, D. P.

Paturzo, M.

Pedrini, G.

Sampson, D. D.

Schwarz, C. J.

Segev, M.

Shoshan, E.

M. Mishali, Y. C. Eldar, O. Dounaevsky, and E. Shoshan, “Xampling: analog to digital at sub-Nyquist rates,” IET Circuits Dev. Syst. 5, 8–20 (2011).
[Crossref]

Shroff, S. A.

S. A. Shroff, J. R. Fienup, and D. R. Williams, “Phase-shift estimation in sinusoidally illuminated images for lateral superresolution,” J. Opt. Soc. Am. A 26, 413–424 (2009).
[Crossref]

S. A. Shroff, J. R. Fienup, and D. R. Williams, “OTF compensation in structured illumination superresolution images,” Proc. SPIE 7094, 709402 (2008).
[Crossref]

Szameit, A.

Takashima, Y.

J. P. Wilde, J. W. Goodman, Y. C. Eldar, and Y. Takashima, “Grating-enhanced coherent imaging,” in 9th International Conference on Sampling Theory and Applications (SampTA) (2011), p. P0213.

J. P. Wilde, J. W. Goodman, Y. C. Eldar, and Y. Takashima, “Grating-enhanced coherent imaging,” in Optics in the Life Sciences (Optical Society of America, 2011).

Wang, Y.

C. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, “Super-resolution digital holographic imaging method,” Appl. Phys. Lett. 81, 3143–3145 (2002).
[Crossref]

Wilde, J. P.

J. P. Wilde, J. W. Goodman, Y. C. Eldar, and Y. Takashima, “Grating-enhanced coherent imaging,” in 9th International Conference on Sampling Theory and Applications (SampTA) (2011), p. P0213.

J. P. Wilde, J. W. Goodman, Y. C. Eldar, and Y. Takashima, “Grating-enhanced coherent imaging,” in Optics in the Life Sciences (Optical Society of America, 2011).

J. P. Wilde, Y. C. Eldar, and J. W. Goodman, “Grating-enhanced optical imaging,” US Patent8,841,591 (23September2014).

Williams, D. R.

S. A. Shroff, J. R. Fienup, and D. R. Williams, “Phase-shift estimation in sinusoidally illuminated images for lateral superresolution,” J. Opt. Soc. Am. A 26, 413–424 (2009).
[Crossref]

S. A. Shroff, J. R. Fienup, and D. R. Williams, “OTF compensation in structured illumination superresolution images,” Proc. SPIE 7094, 709402 (2008).
[Crossref]

Yang, C.

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7, 739–745 (2013).
[Crossref]

Zalevsky, Z.

Zheng, G.

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7, 739–745 (2013).
[Crossref]

Zhu, J.

C. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, “Super-resolution digital holographic imaging method,” Appl. Phys. Lett. 81, 3143–3145 (2002).
[Crossref]

Appl. Opt. (4)

Appl. Phys. Lett. (1)

C. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, “Super-resolution digital holographic imaging method,” Appl. Phys. Lett. 81, 3143–3145 (2002).
[Crossref]

IEEE J. Sel. Top. Signal Process. (1)

M. Mishali and Y. C. Eldar, “From theory to practice: Sub-Nyquist sampling of sparse wideband analog signals,” IEEE J. Sel. Top. Signal Process. 4, 375–391 (2010).
[Crossref]

IET Circuits Dev. Syst. (1)

M. Mishali, Y. C. Eldar, O. Dounaevsky, and E. Shoshan, “Xampling: analog to digital at sub-Nyquist rates,” IET Circuits Dev. Syst. 5, 8–20 (2011).
[Crossref]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (3)

Nat. Photonics (1)

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7, 739–745 (2013).
[Crossref]

Opt. Express (6)

Opt. Lett. (2)

Proc. Natl. Acad. Sci. USA (1)

M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy: Wide-field fluorescence imaging with theoretically unlimited esolution,” Proc. Natl. Acad. Sci. USA 102, 13081–13086 (2005).
[Crossref]

Proc. SPIE (1)

S. A. Shroff, J. R. Fienup, and D. R. Williams, “OTF compensation in structured illumination superresolution images,” Proc. SPIE 7094, 709402 (2008).
[Crossref]

Other (6)

J. P. Wilde, Y. C. Eldar, and J. W. Goodman, “Grating-enhanced optical imaging,” US Patent8,841,591 (23September2014).

J. P. Wilde, J. W. Goodman, Y. C. Eldar, and Y. Takashima, “Grating-enhanced coherent imaging,” in Optics in the Life Sciences (Optical Society of America, 2011).

J. P. Wilde, J. W. Goodman, Y. C. Eldar, and Y. Takashima, “Grating-enhanced coherent imaging,” in 9th International Conference on Sampling Theory and Applications (SampTA) (2011), p. P0213.

Y. C. Eldar, Sampling Theory: Beyond Bandlimited Systems (Cambridge University, 2015).

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005).

J. Mertz, Introduction to Optical Microscopy (Roberts & Company, 2009).

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Figures (9)

Fig. 1.
Fig. 1. Grating-based pupil multiplexing.
Fig. 2.
Fig. 2. Grating-based oblique illumination method.
Fig. 3.
Fig. 3. Plots of the n = ± 1 matrix-element phases for the ideal pupil multiplexing case of Eq. (10), along with a more realistic simulated case based on Eq. (11) after subtracting out the interferometer phase drift terms θ k . Values for φ 1 and φ + 1 are identified as vertical shifts from the ideal case.
Fig. 4.
Fig. 4. Pupil multiplexing experimental demonstration setup.
Fig. 5.
Fig. 5. (a) High-resolution coherent image of the USAF test target object used in the pupil multiplexing setup, obtained by opening the pupil in Fig. 4 to an NA of 0.18. The region-of-interest for subsequent testing (with the pupil stopped down to an NA of 0.063) is shown by the inset box (Group 7, Elements 3-6), corresponding to the smallest set of features available on the target. (b) Spectral magnitude of a typical pupil-multiplexed image hologram plotted on a log scale spanning four orders of magnitude.
Fig. 6.
Fig. 6. Experimental results for the pupil multiplexing setup shown in Fig. 4 that demonstrate resolution enhancement in the horizontal direction. The images displayed in the right-hand column correspond to the inset box area of the test target as shown above in Fig. 5(a). (a) Image spectrum for the conventional system (no enhancement) with NA 0 = 0.063 , and (b) the corresponding conventional image with none of the bar patterns being resolved. (c) Enhanced image spectrum found using three diffracted beams (0 and ± 1 orders) yielding NA 1 = 0.114 , and (d) the corresponding image with the two upper sets of vertical bars now resolved. (e) Enhanced image spectrum found using five diffracted beams (0, ± 1 and ± 2 orders) yielding NA 2 = 0.164 , and (f) the corresponding image with all four sets of vertical bars now resolved. The spectra are displayed on a log-magnitude scale spanning six orders of magnitude. The images, plotted on a linear scale, are found by inverse Fourier transforming the spectra after zero padding.
Fig. 7.
Fig. 7. Sequential oblique illumination experimental demonstration setup.
Fig. 8.
Fig. 8. Off-axis illumination using the 1 diffraction order of the grating. Shifting the aperture allows the other diffraction orders to provide illumination.
Fig. 9.
Fig. 9. (a) Test target object having a 1000 lp/mm square pattern, used to assess coherent superresolution imaging via the sequential oblique illumination method. (b) Experimental image of the target formed by conventional coherent imaging with NA 0 = 0.42 , corresponding to a cutoff frequency of 664 cycles/mm (at 633 nm). The test pattern is clearly not resolved. (c) Experimentally reconstructed image spectrum magnitude (log scale) using nine exposures corresponding to the 0-order beam combined with the ± 1 and ± 2 orders along the x- and y-axis. The grating was first oriented along the x-axis, then rotated by ninety degrees to align with the y-axis. (d) Experimental superresolution image of the target formed by an inverse Fourier transform of the spectrum shown in (c) after zero padding to obtain spatial sampling equivalent to the camera pixel dimensions. The new cutoff frequency (along the x and y directions) is approximately 1640 cycles/mm, and the test pattern with a frequency of 1000 lp/mm is now resolved.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

P ( x ) = n = p n exp ( j 2 π n f g x ) .
t o ( x ) P ( x ) = t o ( x ) n = p n exp ( j 2 π n f g x ) .
U ( ν x ) = T o ( ν x ) * n = p n δ ( ν x n f g ) ,
A k ( ν x ) = n = N N p k , n T o ( ν x n f g ) rect ( ν x / 2 f p ) , k = K , K ,
A ( ν x ) = P T ( ν x ) ,
A ( ν x ) = [ A K ( ν x ) A K ( ν x ) ] ,
T ( ν x ) = [ T o ( ν x + N f g ) rect ( ν x / 2 f p ) T o ( ν x N f g ) rect ( ν x / 2 f p ) ] ,
P = [ p K , N p K , N p K , N p K , N ] .
T ( ν x ) = P 1 A ( ν x ) .
p k , n = exp [ j 2 π k n / ( 2 N + 1 ) ] , k , n = N , N .
p ˜ k , n = A n A 0 exp { j [ 2 π k n 2 K + 1 + θ k + δ k , n + φ n ] } , k = K , K ; n = N , N .

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