Abstract

A high-resolution Shack-Hartmann wavefront sensor has been used for coherent holographic imaging, by computer reconstruction and propagation of the complex field in a lensless imaging setup. The resolution of the images obtained with the experimental data is in a good agreement with the diffraction theory. Although a proper calibration with a reference beam improves the image quality, the method has a potential for reference-less holographic imaging with spatially coherent monochromatic and narrowband polychromatic sources in microscopy and imaging through turbulence.

© 2016 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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2016 (1)

R. Horstmeyer, R. Heintzmann, G. Popescu, L. Waller, and C. Yang, “Standardizing the resolution claims for coherent microscopy,” Nat. Photon. 10, 71 (2016).
[Crossref]

2015 (1)

G. Vdovin, H. Gong, O. Soloviev, P. Pozzi, and M. Verhaegen, “Lensless coherent imaging by sampling of the optical field with digital micromirror device,” J. Opt. 17, 122001 (2015).
[Crossref]

2014 (1)

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging,” IEEE Signal Process Mag. 32(3), 1–25 (2014).

2011 (1)

2009 (1)

F. Meng, D. Zhang, X. Wu, and H. Liu, “A comparison of iterative algorithms and a mixed approach for in-line x-ray phase retrieval,” Opt. Commun. 282, 3392–3396 (2009).
[Crossref]

2007 (1)

2006 (2)

A. Talmi and E. N. Ribak, “Wavefront reconstruction from its gradients,” J. Opt. Soc. Am. A 23, 288–297 (2006).
[Crossref]

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture fourier holographic optical microscopy,” Phys. Rev. Lett. 97, 168102 (2006).
[Crossref] [PubMed]

2004 (2)

A. Talmi and E. N. Ribak, “Direct demodulation of Hartmann-Shack patterns,” J. Opt. Soc. Am. A 21, 632–639 (2004).
[Crossref]

D. de Lima Monteiro, G. Vdovin, and P. Sarro, “High-speed wavefront sensor compatible with standard CMOS technology,” Sens. Actuat. A 109, 220–230 (2004).
[Crossref]

2003 (2)

2001 (1)

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17, 573–577 (2001).

1991 (1)

1988 (1)

R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
[Crossref]

1986 (1)

1982 (2)

J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982).
[Crossref] [PubMed]

R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng. 21, 829 (1982).
[Crossref]

1980 (1)

1972 (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237 (1972).

1967 (1)

J. W. Goodman and R. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[Crossref]

1948 (1)

D. Gabor, “A new microscopic principle,” Nature 161, 777–778 (1948).
[Crossref] [PubMed]

Alexandrov, S. A.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture fourier holographic optical microscopy,” Phys. Rev. Lett. 97, 168102 (2006).
[Crossref] [PubMed]

Canovas, C.

Carmon, Y.

Y. Carmon and E. N. Ribak, “Phase retrieval by demodulation of a Hartmann-Shack sensor,” Opt. Commun. 215, 285–288 (2003).
[Crossref]

Chapman, H. N.

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging,” IEEE Signal Process Mag. 32(3), 1–25 (2014).

Cohen, O.

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging,” IEEE Signal Process Mag. 32(3), 1–25 (2014).

Coppola, G.

Dai, G.

G. Dai, Wavefront optics for vision correction, Vol. 179 (SPIE Press, 2008).
[Crossref]

de Lima Monteiro, D.

D. de Lima Monteiro, G. Vdovin, and P. Sarro, “High-speed wavefront sensor compatible with standard CMOS technology,” Sens. Actuat. A 109, 220–230 (2004).
[Crossref]

De Nicola, S.

Eldar, Y. C.

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging,” IEEE Signal Process Mag. 32(3), 1–25 (2014).

Falldorf, C.

U. Schnars, C. Falldorf, J. Watson, and W. Jüptner, Digital Holography and Wavefront Sensing (Springer, 2015).

Ferraro, P.

Fienup, J. R.

Finizio, A.

Freischlad, K. R.

Gabor, D.

D. Gabor, “A new microscopic principle,” Nature 161, 777–778 (1948).
[Crossref] [PubMed]

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237 (1972).

Ghiglia, D. C.

D. C. Ghiglia and M. D. Pritt, Two-dimensional phase unwrapping: theory, algorithms, and software, vol. 4 (WileyNew York, 1998).

Goldstein, R. M.

R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
[Crossref]

Gong, H.

G. Vdovin, H. Gong, O. Soloviev, P. Pozzi, and M. Verhaegen, “Lensless coherent imaging by sampling of the optical field with digital micromirror device,” J. Opt. 17, 122001 (2015).
[Crossref]

Gonsalves, R. A.

R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng. 21, 829 (1982).
[Crossref]

Goodman, J. W.

J. W. Goodman and R. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[Crossref]

J. W. Goodman, Introduction to Fourier Optics (Roberts and Company Publishers, 2005).

Grilli, S.

Gutzler, T.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture fourier holographic optical microscopy,” Phys. Rev. Lett. 97, 168102 (2006).
[Crossref] [PubMed]

Heintzmann, R.

R. Horstmeyer, R. Heintzmann, G. Popescu, L. Waller, and C. Yang, “Standardizing the resolution claims for coherent microscopy,” Nat. Photon. 10, 71 (2016).
[Crossref]

Hillman, T. R.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture fourier holographic optical microscopy,” Phys. Rev. Lett. 97, 168102 (2006).
[Crossref] [PubMed]

Horstmeyer, R.

R. Horstmeyer, R. Heintzmann, G. Popescu, L. Waller, and C. Yang, “Standardizing the resolution claims for coherent microscopy,” Nat. Photon. 10, 71 (2016).
[Crossref]

Jüptner, W.

U. Schnars, C. Falldorf, J. Watson, and W. Jüptner, Digital Holography and Wavefront Sensing (Springer, 2015).

Kim, M. K.

M. K. Kim, Digital Holographic Microscopy (Springer, 2011).
[Crossref]

Koliopoulos, C. L.

Lawrence, R.

J. W. Goodman and R. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[Crossref]

Liu, H.

F. Meng, D. Zhang, X. Wu, and H. Liu, “A comparison of iterative algorithms and a mixed approach for in-line x-ray phase retrieval,” Opt. Commun. 282, 3392–3396 (2009).
[Crossref]

Loktev, M.

Magro, C.

Meng, F.

F. Meng, D. Zhang, X. Wu, and H. Liu, “A comparison of iterative algorithms and a mixed approach for in-line x-ray phase retrieval,” Opt. Commun. 282, 3392–3396 (2009).
[Crossref]

Miao, J.

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging,” IEEE Signal Process Mag. 32(3), 1–25 (2014).

Pierattini, G.

Platt, B. C.

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17, 573–577 (2001).

Popescu, G.

R. Horstmeyer, R. Heintzmann, G. Popescu, L. Waller, and C. Yang, “Standardizing the resolution claims for coherent microscopy,” Nat. Photon. 10, 71 (2016).
[Crossref]

Pozzi, P.

G. Vdovin, H. Gong, O. Soloviev, P. Pozzi, and M. Verhaegen, “Lensless coherent imaging by sampling of the optical field with digital micromirror device,” J. Opt. 17, 122001 (2015).
[Crossref]

Pritt, M. D.

D. C. Ghiglia and M. D. Pritt, Two-dimensional phase unwrapping: theory, algorithms, and software, vol. 4 (WileyNew York, 1998).

Ribak, E. N.

Roddier, C.

Roddier, F.

Sampson, D. D.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture fourier holographic optical microscopy,” Phys. Rev. Lett. 97, 168102 (2006).
[Crossref] [PubMed]

Sarro, P.

D. de Lima Monteiro, G. Vdovin, and P. Sarro, “High-speed wavefront sensor compatible with standard CMOS technology,” Sens. Actuat. A 109, 220–230 (2004).
[Crossref]

Savenko, S.

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237 (1972).

Schnars, U.

U. Schnars, C. Falldorf, J. Watson, and W. Jüptner, Digital Holography and Wavefront Sensing (Springer, 2015).

Segev, M.

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging,” IEEE Signal Process Mag. 32(3), 1–25 (2014).

Shack, R.

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17, 573–577 (2001).

Shechtman, Y.

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging,” IEEE Signal Process Mag. 32(3), 1–25 (2014).

Soloviev, O.

G. Vdovin, H. Gong, O. Soloviev, P. Pozzi, and M. Verhaegen, “Lensless coherent imaging by sampling of the optical field with digital micromirror device,” J. Opt. 17, 122001 (2015).
[Crossref]

M. Loktev, O. Soloviev, S. Savenko, and G. Vdovin, “Speckle imaging through turbulent atmosphere based on adaptable pupil segmentation,” Opt. Lett. 36, 2656–2658 (2011).
[Crossref] [PubMed]

Southwell, W.

Talmi, A.

Vdovin, G.

G. Vdovin, H. Gong, O. Soloviev, P. Pozzi, and M. Verhaegen, “Lensless coherent imaging by sampling of the optical field with digital micromirror device,” J. Opt. 17, 122001 (2015).
[Crossref]

M. Loktev, O. Soloviev, S. Savenko, and G. Vdovin, “Speckle imaging through turbulent atmosphere based on adaptable pupil segmentation,” Opt. Lett. 36, 2656–2658 (2011).
[Crossref] [PubMed]

D. de Lima Monteiro, G. Vdovin, and P. Sarro, “High-speed wavefront sensor compatible with standard CMOS technology,” Sens. Actuat. A 109, 220–230 (2004).
[Crossref]

Verhaegen, M.

G. Vdovin, H. Gong, O. Soloviev, P. Pozzi, and M. Verhaegen, “Lensless coherent imaging by sampling of the optical field with digital micromirror device,” J. Opt. 17, 122001 (2015).
[Crossref]

Waller, L.

R. Horstmeyer, R. Heintzmann, G. Popescu, L. Waller, and C. Yang, “Standardizing the resolution claims for coherent microscopy,” Nat. Photon. 10, 71 (2016).
[Crossref]

Watson, J.

U. Schnars, C. Falldorf, J. Watson, and W. Jüptner, Digital Holography and Wavefront Sensing (Springer, 2015).

Werner, C. L.

R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
[Crossref]

Wu, X.

F. Meng, D. Zhang, X. Wu, and H. Liu, “A comparison of iterative algorithms and a mixed approach for in-line x-ray phase retrieval,” Opt. Commun. 282, 3392–3396 (2009).
[Crossref]

Yang, C.

R. Horstmeyer, R. Heintzmann, G. Popescu, L. Waller, and C. Yang, “Standardizing the resolution claims for coherent microscopy,” Nat. Photon. 10, 71 (2016).
[Crossref]

Zebker, H. A.

R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
[Crossref]

Zhang, D.

F. Meng, D. Zhang, X. Wu, and H. Liu, “A comparison of iterative algorithms and a mixed approach for in-line x-ray phase retrieval,” Opt. Commun. 282, 3392–3396 (2009).
[Crossref]

Appl. Opt. (4)

Appl. Phys. Lett. (1)

J. W. Goodman and R. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[Crossref]

IEEE Signal Process Mag. (1)

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging,” IEEE Signal Process Mag. 32(3), 1–25 (2014).

J. Opt. (1)

G. Vdovin, H. Gong, O. Soloviev, P. Pozzi, and M. Verhaegen, “Lensless coherent imaging by sampling of the optical field with digital micromirror device,” J. Opt. 17, 122001 (2015).
[Crossref]

J. Opt. Soc. Am. (1)

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

J. Refract. Surg. (1)

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17, 573–577 (2001).

Nat. Photon. (1)

R. Horstmeyer, R. Heintzmann, G. Popescu, L. Waller, and C. Yang, “Standardizing the resolution claims for coherent microscopy,” Nat. Photon. 10, 71 (2016).
[Crossref]

Nature (1)

D. Gabor, “A new microscopic principle,” Nature 161, 777–778 (1948).
[Crossref] [PubMed]

Opt. Commun. (2)

Y. Carmon and E. N. Ribak, “Phase retrieval by demodulation of a Hartmann-Shack sensor,” Opt. Commun. 215, 285–288 (2003).
[Crossref]

F. Meng, D. Zhang, X. Wu, and H. Liu, “A comparison of iterative algorithms and a mixed approach for in-line x-ray phase retrieval,” Opt. Commun. 282, 3392–3396 (2009).
[Crossref]

Opt. Eng. (1)

R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng. 21, 829 (1982).
[Crossref]

Opt. Lett. (1)

Optik (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237 (1972).

Phys. Rev. Lett. (1)

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture fourier holographic optical microscopy,” Phys. Rev. Lett. 97, 168102 (2006).
[Crossref] [PubMed]

Radio Sci. (1)

R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
[Crossref]

Sens. Actuat. A (1)

D. de Lima Monteiro, G. Vdovin, and P. Sarro, “High-speed wavefront sensor compatible with standard CMOS technology,” Sens. Actuat. A 109, 220–230 (2004).
[Crossref]

Other (7)

D. C. Ghiglia and M. D. Pritt, Two-dimensional phase unwrapping: theory, algorithms, and software, vol. 4 (WileyNew York, 1998).

G. Dai, Wavefront optics for vision correction, Vol. 179 (SPIE Press, 2008).
[Crossref]

J. Holloway, M. S. Asif, M. K. Sharma, N. Matsuda, R. Horstmeyer, O. Cossairt, and A. Veeraraghavan, “Toward long distance, sub-diffraction imaging using coherent camera arrays,” http://arxiv.org/abs/1510.08470 (2015).

C. Guo, C. Wei, J. Tan, K. Chen, S. Liu, Q. Wu, and Z. Liu, “A review of iterative phase retrieval for measurement and encryption,” Opt. Lasers Eng., http://www.sciencedirect.com/science/article/pii/S0143816616300197 (2016).
[Crossref]

M. K. Kim, Digital Holographic Microscopy (Springer, 2011).
[Crossref]

U. Schnars, C. Falldorf, J. Watson, and W. Jüptner, Digital Holography and Wavefront Sensing (Springer, 2015).

J. W. Goodman, Introduction to Fourier Optics (Roberts and Company Publishers, 2005).

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Figures (7)

Fig. 1
Fig. 1 Imaging holographic setup based on the SH sensor.
Fig. 2
Fig. 2 Numerical model: resolution test chart (left). Intensity pattern retrieved from the SH sensor at a distance of 0.5 m from the chart (middle). The central part of the Fourier transform of the intensity pattern with sidelobes (inset) used to reconstruct the x and y components of local WF tilts (right).
Fig. 3
Fig. 3 Gradients ϕx, ϕy, corresponding to the diffraction on USAF test chart, reconstructed from the inverse Fourier transform (left, middle), and the wavefront reconstruction (right).
Fig. 4
Fig. 4 Sensor intensity obtained in simulation, by filtering the SH pattern (left), and the reconstruction of the resolution test chart by back propagation of the reconstructed complex field to the object plane (right).
Fig. 5
Fig. 5 Simulated image reconstruction obtained with spatially coherent 633 nm monochromatic source (left) and polychromatic sources with bandwidth of 20, 50 and 200 nm, centered at 633 nm (images 2 to 4, counted from left to right).
Fig. 6
Fig. 6 Positive 1951 USAF test target (R1DS1P, Thorlabs, U.S) (left), and the image registered by the SH sensor (right).
Fig. 7
Fig. 7 Filtered experimentally registered intensity (left), and object reconstruction, obtained by back propagation of the reconstructed wave to −0.5 m (right).

Equations (8)

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

δ = λ L B .
B min = λ L A ,
B max = λ L 2 p .
B max B min = A / 2 p .
W x = p ϕ x / ( 2 π F ) , W y = p ϕ y / ( 2 π F ) ,
W ^ ( f x , f y ) = i ( f x W ^ x + f y W ^ y ) 2 π ( f x 2 + f y 2 ) .
B min = λ L A = 35 μ m
U ( x , y , 0 ) = 1 { e i L k 2 f x 2 f y 2 ( U ( x , y , L ) ) } .

Metrics