Abstract

In remote-sensing applications, digital holography data often includes both phase errors from atmospheric turbulence and fully developed laser speckle from rough objects. When processing single-shot data, i.e., data from a single hologram, the high speckle contrast makes it more difficult to correct for atmospheric phase errors compared to scenarios where multiple speckle realizations are available for processing. A Bayesian phase-error correction algorithm [J. Opt. Soc. Am. A 34, 1659 (2017) [CrossRef]  ] was recently developed for use with single-shot data. The features of this approach are discussed and used to implement an alternative algorithm based on image-sharpness maximization. Algorithm performance is tested using simulated data for a range of signal-to-noise ratios (SNRs) and turbulence conditions. Using a combination of appropriate parameterization of the phase-error estimates and spatial binning for speckle-contrast reduction, the image-sharpness algorithm achieves performance comparable (better in the high-SNR regime but worse in the low-SNR regime) to the Bayesian approach. Limited experimental results are also presented.

© 2019 Optical Society of America

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References

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2019 (2)

H. Wang, Z. Dong, X. Wang, Y. Lou, and S. Xi, “Phase compensation in digital holographic microscopy using a quantitative evaluation metric,” Opt. Commun. 430, 262–267 (2019).
[Crossref]

C. J. Pellizzari, M. F. Spencer, and C. A. Bouman, “Imaging through distributed-volume aberrations using single-shot digital holography,” J. Opt. Soc. Am. A 36, A20–A33 (2019).
[Crossref]

2018 (5)

2017 (2)

C. J. Pellizzari, M. F. Spencer, and C. A. Bouman, “Phase-error estimation and image reconstruction from digital-holography data using a Bayesian framework,” J. Opt. Soc. Am. A 34, 1659–1669 (2017).
[Crossref]

M. T. Banet and M. F. Spencer, “Spatial-heterodyne sampling requirements in the off-axis pupil plane recording geometry for deep-turbulence wavefront sensing,” Proc. SPIE 10410, 104100E (2017).
[Crossref]

2016 (1)

V. Bianco, P. Memmolo, M. Paturzo, A. Finizio, B. Javidi, and P. Ferraro, “Quasi noise-free digital holography,” Light Sci. Appl. 5, e16142 (2016).
[Crossref]

2015 (1)

2013 (2)

2011 (1)

2010 (3)

2009 (2)

2008 (1)

2007 (1)

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3-D transform-domain collaborative filtering,” IEEE Trans. Image Proc. 16, 2080–2095 (2007).
[Crossref]

2006 (3)

2005 (1)

2003 (1)

2002 (1)

S. M. Ebstein, “Pseudo-random phase plates,” Proc. SPIE 4493, 150–155 (2002).
[Crossref]

2001 (1)

W. Osten, S. Seebacher, and W. P. O. Jueptner, “Application of digital holography for the inspection of microcomponents,” Proc. SPIE 4400, 1–15 (2001).
[Crossref]

1999 (2)

1997 (2)

M. Adams, T. M. Kreis, and W. P. O. Jueptner, “Particle size and position measurement with digital holography,” Proc. SPIE 3098, 234–240 (1997).
[Crossref]

J. R. Fienup, “Invariant error metrics for image reconstruction,” Appl. Opt. 36, 8352–8357 (1997).
[Crossref]

1994 (1)

1993 (1)

M. Unser, A. Aldroubi, and M. Eden, “B-spline signal processing: part I–theory,” IEEE Trans. Signal Process. 41, 821–833 (1993).
[Crossref]

1992 (1)

R. G. Lane, A. Glindemann, and J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2, 209–224 (1992).
[Crossref]

1988 (1)

R. G. Paxman and J. C. Marron, “Aberration correction of speckled imagery with an image-sharpness criterion,” Proc. SPIE 976, 37–47 (1988).
[Crossref]

1976 (1)

1974 (1)

1967 (1)

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

1966 (1)

1947 (1)

A. Maréchal, “Étude des effets combinés de la diffraction et des aberrations géométriques sur l’image d’un point lumineux,” Rev. Opt. Theor. Instrum. 26, 257 (1947).

Adams, M.

M. Adams, T. M. Kreis, and W. P. O. Jueptner, “Particle size and position measurement with digital holography,” Proc. SPIE 3098, 234–240 (1997).
[Crossref]

Aldroubi, A.

M. Unser, A. Aldroubi, and M. Eden, “B-spline signal processing: part I–theory,” IEEE Trans. Signal Process. 41, 821–833 (1993).
[Crossref]

Alfieri, D.

Aspert, N.

Asundi, A.

Banet, M. T.

C. J. Pellizzari, M. T. Banet, M. F. Spencer, and C. A. Bouman, “Demonstration of single-shot digital holography using a Bayesian framework,” J. Opt. Soc. Am. A 35, 103–107 (2018).
[Crossref]

M. T. Banet and M. F. Spencer, “Spatial-heterodyne sampling requirements in the off-axis pupil plane recording geometry for deep-turbulence wavefront sensing,” Proc. SPIE 10410, 104100E (2017).
[Crossref]

Bevilacqua, F.

Bianco, V.

Bouman, C. A.

Bratcher, A.

J. Marron, R. Kendrick, S. Thurman, N. Seldomridge, T. Grow, C. Embry, and A. Bratcher, “Extended-range digital holographic imaging,” Proc. SPIE 7684, 76841J (2010).
[Crossref]

Buffington, A.

Charrière, F.

Chen, Q.

Colomb, T.

Coppola, G.

Cuche, E.

Dabov, K.

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3-D transform-domain collaborative filtering,” IEEE Trans. Image Proc. 16, 2080–2095 (2007).
[Crossref]

Dainty, J. C.

R. G. Lane, A. Glindemann, and J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2, 209–224 (1992).
[Crossref]

J. C. Dainty, Laser Speckle and Related Phenomena (Springer-Verlag, 1984).

De Nicola, S.

Depeursinge, C.

Dong, Z.

H. Wang, Z. Dong, X. Wang, Y. Lou, and S. Xi, “Phase compensation in digital holographic microscopy using a quantitative evaluation metric,” Opt. Commun. 430, 262–267 (2019).
[Crossref]

Ebstein, S. M.

S. M. Ebstein, “Pseudo-random phase plates,” Proc. SPIE 4493, 150–155 (2002).
[Crossref]

Eden, M.

M. Unser, A. Aldroubi, and M. Eden, “B-spline signal processing: part I–theory,” IEEE Trans. Signal Process. 41, 821–833 (1993).
[Crossref]

Egiazarian, K.

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3-D transform-domain collaborative filtering,” IEEE Trans. Image Proc. 16, 2080–2095 (2007).
[Crossref]

Embry, C.

J. Marron, R. Kendrick, S. Thurman, N. Seldomridge, T. Grow, C. Embry, and A. Bratcher, “Extended-range digital holographic imaging,” Proc. SPIE 7684, 76841J (2010).
[Crossref]

Farriss, W. E.

W. E. Farriss, J. R. Fienup, J. W. Stafford, and N. J. Miller, “Sharpness-based correction methods in holographic aperture ladar (HAL),” Proc. SPIE 10772, 107720K (2018).
[Crossref]

Ferraro, P.

Fienup, J. R.

Finizio, A.

Foi, A.

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3-D transform-domain collaborative filtering,” IEEE Trans. Image Proc. 16, 2080–2095 (2007).
[Crossref]

Fried, D. L.

Gibson, S.

Glindemann, A.

R. G. Lane, A. Glindemann, and J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2, 209–224 (1992).
[Crossref]

Goodman, J. W.

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

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts and Company Publishers, 2007).

J. W. Goodman, Statistical Optics (Wiley, 1985).

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

Grilli, S.

Grow, T.

J. Marron, R. Kendrick, S. Thurman, N. Seldomridge, T. Grow, C. Embry, and A. Bratcher, “Extended-range digital holographic imaging,” Proc. SPIE 7684, 76841J (2010).
[Crossref]

Grow, T. D.

Hardy, J. W.

J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford University, 1998).

Höft, T. A.

Hossain, M. M.

M. M. Hossain, D. S. Mehta, and C. Shakher, “Refractive index determination: an application of lensless Fourier digital holography,” Opt. Eng. 45, 106203 (2006).
[Crossref]

Hunt, B. R.

M. C. Roggemann, B. M. Welsh, and B. R. Hunt, Imaging Through Turbulence (CRC Press, 2018).

Jameson, D.

Javidi, B.

Jueptner, W. P. O.

W. Osten, S. Seebacher, and W. P. O. Jueptner, “Application of digital holography for the inspection of microcomponents,” Proc. SPIE 4400, 1–15 (2001).
[Crossref]

M. Adams, T. M. Kreis, and W. P. O. Jueptner, “Particle size and position measurement with digital holography,” Proc. SPIE 3098, 234–240 (1997).
[Crossref]

Jüptner, W.

Katkovnik, V.

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3-D transform-domain collaborative filtering,” IEEE Trans. Image Proc. 16, 2080–2095 (2007).
[Crossref]

Katz, J.

Kendrick, R.

J. Marron, R. Kendrick, S. Thurman, N. Seldomridge, T. Grow, C. Embry, and A. Bratcher, “Extended-range digital holographic imaging,” Proc. SPIE 7684, 76841J (2010).
[Crossref]

Kendrick, R. L.

Kreis, T. M.

M. Adams, T. M. Kreis, and W. P. O. Jueptner, “Particle size and position measurement with digital holography,” Proc. SPIE 3098, 234–240 (1997).
[Crossref]

Kühn, J.

Kumar, A.

Lane, R. G.

R. G. Lane, A. Glindemann, and J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2, 209–224 (1992).
[Crossref]

Lawrence, R. W.

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

Lian, Q.

Liu, S.

Lou, Y.

H. Wang, Z. Dong, X. Wang, Y. Lou, and S. Xi, “Phase compensation in digital holographic microscopy using a quantitative evaluation metric,” Opt. Commun. 430, 262–267 (2019).
[Crossref]

Malkiel, E.

Maréchal, A.

A. Maréchal, “Étude des effets combinés de la diffraction et des aberrations géométriques sur l’image d’un point lumineux,” Rev. Opt. Theor. Instrum. 26, 257 (1947).

Marquet, P.

Marron, J.

J. Marron, R. Kendrick, S. Thurman, N. Seldomridge, T. Grow, C. Embry, and A. Bratcher, “Extended-range digital holographic imaging,” Proc. SPIE 7684, 76841J (2010).
[Crossref]

Marron, J. C.

Mehta, D. S.

M. M. Hossain, D. S. Mehta, and C. Shakher, “Refractive index determination: an application of lensless Fourier digital holography,” Opt. Eng. 45, 106203 (2006).
[Crossref]

Memmolo, P.

Miller, J. J.

Miller, N. J.

W. E. Farriss, J. R. Fienup, J. W. Stafford, and N. J. Miller, “Sharpness-based correction methods in holographic aperture ladar (HAL),” Proc. SPIE 10772, 107720K (2018).
[Crossref]

Montfort, F.

Muller, R. A.

Noll, R. J.

Osten, W.

W. Osten, S. Seebacher, and W. P. O. Jueptner, “Application of digital holography for the inspection of microcomponents,” Proc. SPIE 4400, 1–15 (2001).
[Crossref]

Pan, W.

Paturzo, M.

Paxman, R. G.

R. G. Paxman and J. C. Marron, “Aberration correction of speckled imagery with an image-sharpness criterion,” Proc. SPIE 976, 37–47 (1988).
[Crossref]

Pedrini, G.

Pellizzari, C. J.

Pierattini, G.

Qing, Y.

Qu, W.

Rabb, D.

Roggemann, M. C.

M. C. Roggemann, B. M. Welsh, and B. R. Hunt, Imaging Through Turbulence (CRC Press, 2018).

Santoyo, F. M.

Schedin, S.

Schnars, U.

Seebacher, S.

W. Osten, S. Seebacher, and W. P. O. Jueptner, “Application of digital holography for the inspection of microcomponents,” Proc. SPIE 4400, 1–15 (2001).
[Crossref]

Seldomridge, N.

J. Marron, R. Kendrick, S. Thurman, N. Seldomridge, T. Grow, C. Embry, and A. Bratcher, “Extended-range digital holographic imaging,” Proc. SPIE 7684, 76841J (2010).
[Crossref]

J. C. Marron, R. L. Kendrick, N. Seldomridge, T. D. Grow, and T. A. Höft, “Atmospheric turbulence correction using digital holographic detection: experimental results,” Opt. Express 17, 11638–11651 (2009).
[Crossref]

Shakher, C.

M. M. Hossain, D. S. Mehta, and C. Shakher, “Refractive index determination: an application of lensless Fourier digital holography,” Opt. Eng. 45, 106203 (2006).
[Crossref]

Sheng, J.

Spencer, M.

Spencer, M. F.

Stafford, J.

Stafford, J. W.

W. E. Farriss, J. R. Fienup, J. W. Stafford, and N. J. Miller, “Sharpness-based correction methods in holographic aperture ladar (HAL),” Proc. SPIE 10772, 107720K (2018).
[Crossref]

Stokes, A.

Striano, V.

Sulaiman, S.

Thurman, S.

J. Marron, R. Kendrick, S. Thurman, N. Seldomridge, T. Grow, C. Embry, and A. Bratcher, “Extended-range digital holographic imaging,” Proc. SPIE 7684, 76841J (2010).
[Crossref]

Thurman, S. T.

Tian, K.

Tippie, A. E.

Tiziani, H. J.

Unser, M.

M. Unser, A. Aldroubi, and M. Eden, “B-spline signal processing: part I–theory,” IEEE Trans. Signal Process. 41, 821–833 (1993).
[Crossref]

Wang, H.

H. Wang, Z. Dong, X. Wang, Y. Lou, and S. Xi, “Phase compensation in digital holographic microscopy using a quantitative evaluation metric,” Opt. Commun. 430, 262–267 (2019).
[Crossref]

Wang, X.

H. Wang, Z. Dong, X. Wang, Y. Lou, and S. Xi, “Phase compensation in digital holographic microscopy using a quantitative evaluation metric,” Opt. Commun. 430, 262–267 (2019).
[Crossref]

Welsh, B. M.

M. C. Roggemann, B. M. Welsh, and B. R. Hunt, Imaging Through Turbulence (CRC Press, 2018).

Xi, S.

H. Wang, Z. Dong, X. Wang, Y. Lou, and S. Xi, “Phase compensation in digital holographic microscopy using a quantitative evaluation metric,” Opt. Commun. 430, 262–267 (2019).
[Crossref]

Xu, Z.

Zhang, C.

Zuo, C.

Appl. Opt. (6)

Appl. Phys. Lett. (1)

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

IEEE Trans. Image Proc. (1)

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3-D transform-domain collaborative filtering,” IEEE Trans. Image Proc. 16, 2080–2095 (2007).
[Crossref]

IEEE Trans. Signal Process. (1)

M. Unser, A. Aldroubi, and M. Eden, “B-spline signal processing: part I–theory,” IEEE Trans. Signal Process. 41, 821–833 (1993).
[Crossref]

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (6)

Light Sci. Appl. (1)

V. Bianco, P. Memmolo, M. Paturzo, A. Finizio, B. Javidi, and P. Ferraro, “Quasi noise-free digital holography,” Light Sci. Appl. 5, e16142 (2016).
[Crossref]

Opt. Commun. (1)

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Figures (10)

Fig. 1.
Fig. 1. Diagram of a simplified digital holography system with a pupil-plane recording geometry.
Fig. 2.
Fig. 2. Example steps in the simulation of digital hologram recording and replay: (a) object reflectance distribution $r(x{,}y)$, (b) object speckle realization $f(x{,}y)$, (c) object beam $O(u{,}v)$, (d) atmospheric phase screen $\phi (u{,}v)$, (e) recorded hologram $H(u{,}v)$, (f) Fast Fourier Transform (FFT) of $H(u{,}v)$, (g) replayed hologram image $g(x{,}y)$, and (h) replayed pupil data $G(u{,}v)$.
Fig. 3.
Fig. 3. Steps for computing sharpness metric $M$ for a candidate phase-error estimate ${\psi _{\rm bin}}(u{,}v)$.
Fig. 4.
Fig. 4. Simulation results for tuning the algorithm binning factors with different levels of atmospheric turbulence. Each plot shows the average Strehl ratio ($S$) versus the pupil (${B_p}$) and image (${B_i}$) binning factors. The $ \times $’s mark the binning factors that maximize performance with average values of $S = {0.902}$, 0.795, 0.565, and 0.278 for turbulence levels of $D/{r_0} = {10}$, 20, 30, and 40, respectively.
Fig. 5.
Fig. 5. Phase-error correction algorithm performance versus SNR for different turbulence levels. The top row of plots show performance in terms of the post-correction Strehl ratio $S$, while the bottom row shows performance in terms of the normalized root mean-squared error metric ($\varepsilon $) for the image, both with (black) and without (gray) binning. The horizontal dashed lines in the top row of plots represents the upper limit on performance given by ${S_{{\rm fit}}}$ in Eq. (9).
Fig. 6.
Fig. 6. Detailed simulation results for five individual Monte Carlo trials with $D/{r_0} = {30}$. From top to bottom, the various rows show atmospheric phase error realization $\phi (u{,}v)$, initial replayed hologram image $g(x{,}y)$, residual phase error $\phi (u{,}v) - \psi (u{,}v)$ after processing, sharpened image $I(x{,}y)$ without binning, and image ${I_{{\rm bin}}}(x{,}y)$ with binning. Each column contains data from a different trial. The SNR for each trial is listed along the bottom of the figure. The phase and image plots contain associated Strehl and image error metric values. The images are displayed on a normalized decibel scale.
Fig. 7.
Fig. 7. Algorithm performance data analogous to those shown in Fig. 5, except that this figure represents results for the multi-resolution version of the sharpness-maximization algorithm.
Fig. 8.
Fig. 8. Timing information for the algorithms used in Sections 4.B and 4.C for different turbulence levels. The plots show Strehl ratio ($S$) versus time for different turbulence levels for individual trials (thin gray lines) and the average of 20 trials (thick black lines). The dashed horizontal lines indicate the Strehl ratio limit ${S_{{\rm fit}}}$ for each case.
Fig. 9.
Fig. 9. Histograms of the number of algorithm iterations used in the various Monte Carlo trials in the algorithm timing study. In all cases, the maximum number of iterations was limited to 200, but fewer iterations were used for cases in which numerical convergence criteria for termination were met.
Fig. 10.
Fig. 10. Experimental results: (a) speckle-averaged (32 shots) image of a USAF bar chart viewed through an atmospheric phase screen, (b) multi-shot sharpened image, (c) single-shot sharpened image, (d) multi-shot phase correction corresponding to the image shown in (b), (e) single-shot phase correction corresponding to the image shown in (c), and (f) the difference between the phase corrections shown in (d) and (e). The intensity images on the top row are displayed using a normalized decibel scale, while the phase results shown on the bottom row are displayed in radians with $ 2\pi $ wrapping.

Tables (1)

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Table 1. Comparison of Phase-Error Correction Algorithms

Equations (11)

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O ( u , v ) = P ( u , v ) exp [ i ϕ ( u , v ) ] F ( u , v ) = P ( u , v ) exp [ i ϕ ( u , v ) ] IFFT { f ( x , y ) } ,
H ( u , v ) = | R ( u , v ) + O ( u , v ) | 2 + n ( u , v ) ,
G ( u , v ) = FFT { g ( x , y ) } O ( u , v ) = P ( u , v ) exp [ i ϕ ( u , v ) ] F ( u , v ) ,
S N R = | O ( u , v ) | 2 / n 2 ( u , v ) ,
S = max ( x , y ) [ | I F F T { P ( u , v ) exp [ i ϕ ( u , v ) ] } | 2 ] / max ( x , y ) [ | I F F T { P ( u , v ) } | 2 ] .
ε 2 = min ( α , x , y ) { ( x , y ) [ r ( x , y ) α I ( x + x , y + y ) ] 2 } / [ ( x , y ) r 2 ( x , y ) ] ,
Δ J 0.2944 J 3 / 2 ( D / r 0 ) 5 / 3 [ r a d 2 ] ,
J min [ 3.3967 ( 2 π / 14 ) 2 ( D / r 0 ) 5 / 3 ] 2 / 3 .
S f i t = exp [ 1.26 ( B p / r 0 ) 5 / 3 ] .
I ( x , y ) = | FFT { G ( u , v ) exp [ i ψ ( u , v ) ] } | 2 .
M = ( x , y ) I b i n β ( x , y ) ,

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