Abstract

Optical sparse aperture imaging shows great promise for the next generation of high resolution systems. In this paper, we propose and demonstrate an active sparse aperture imaging approach using independent transmitter modulation to digitally overcome phasing errors, correct aberrations, and further improve resolution. The reported imaging scheme consists of a general sparse aperture system and an active illumination unit, specifically an independent pattern projector. A series of raw images are captured with the projector scanned to illuminate the object. Based on the acquired data set, the improved incoherent Fourier ptychographic algorithm is utilized to reconstruct sparse aperture images with distortions removed and contrast enhanced. Furthermore, thanks to illumination pattern modulation, higher resolution beyond the diffraction limit of the synthetic aperture system is gained as a benefit. Good-quality and higher-resolution sparse aperture imagery obtained by employing our proposed technique in both simulation and experiment demonstrates the effectiveness. The reported approach may provide new insights to address the phasing and image restoration problems of sparse aperture systems in the transmitting path rather than only in the receiving path.

© 2017 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Synthetic aperture imaging by using spatial modulation diversity technology with stochastic parallel gradient descent algorithm

Haotong Ma, Zongliang Xie, Xuejun Long, Bo Qi, Ge Ren, Jianliang Shi, Zhangang Cui, Yang Jiang, and Xiaojun Xu
Opt. Express 23(11) 14836-14849 (2015)

Adaptive piston correction of sparse aperture systems with stochastic parallel gradient descent algorithm

Zongliang Xie, Haotong Ma, Xiaojun He, Bo Qi, Ge Ren, Li Dong, and Yufeng Tan
Opt. Express 26(8) 9541-9551 (2018)

Multi-transmitter aperture synthesis

David J. Rabb, Douglas F. Jameson, Jason W. Stafford, and Andrew J. Stokes
Opt. Express 18(24) 24937-24945 (2010)

References

  • View by:
  • |
  • |
  • |

  1. J. S. Fender, “Synthetic apertures: an overview,” Proc. SPIE 440, 2–7 (1984).
    [Crossref]
  2. M. Deprez, C. Bellanger, L. Lombard, B. Wattellier, and J. Primot, “Piston and tilt interferometry for segmented wavefront sensing,” Opt. Lett. 41(6), 1078–1081 (2016).
    [Crossref] [PubMed]
  3. D. Mourard, W. Dali Ali, A. Meilland, N. Tarmoul, F. Patru, J. M. Clausse, P. Girard, F. Henault, A. Marcotto, and N. Mauclert, “Group and phase delay sensing for cophasing large optical arrays,” Mon. Not. R. Astron. Soc. 445(2), 2082–2092 (2014).
    [Crossref]
  4. D. Yue, S. Xu, and H. Nie, “Co-phasing of the segmented mirror and image retrieval based on phase diversity using a modified algorithm,” Appl. Opt. 54(26), 7917–7924 (2015).
    [Crossref] [PubMed]
  5. M. R. Bolcar and J. R. Fienup, “Sub-aperture piston phase diversity for segmented and multi-aperture systems,” Appl. Opt. 48(1), A5–A12 (2009).
    [Crossref] [PubMed]
  6. H. Ma, Z. Xie, X. Long, B. Qi, G. Ren, J. Shi, Z. Cui, Y. Jiang, and X. Xu, “Synthetic aperture imaging by using spatial modulation diversity technology with stochastic parallel gradient descent algorithm,” Opt. Express 23(11), 14836–14849 (2015).
    [Crossref] [PubMed]
  7. I. Paykin, L. Yacobi, J. Adler, and E. N. Ribak, “Phasing a segmented telescope,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 91(2), 023302 (2015).
    [Crossref] [PubMed]
  8. D. J. Rabb, D. F. Jameson, J. W. Stafford, and A. J. Stokes, “Multi-transmitter aperture synthesis,” Opt. Express 18(24), 24937–24945 (2010).
    [Crossref] [PubMed]
  9. D. Rabb, D. Jameson, A. Stokes, and J. Stafford, “Distributed aperture synthesis,” Opt. Express 18(10), 10334–10342 (2010).
    [Crossref] [PubMed]
  10. D. J. Rabb, J. W. Stafford, and D. F. Jameson, “Non-iterative aberration correction of a multiple transmitter system,” Opt. Express 19(25), 25048–25056 (2011).
    [Crossref] [PubMed]
  11. B. K. Gunturk, D. J. Rabb, and D. F. Jameson, “Multi-transmitter aperture synthesis with Zernike based aberration correction,” Opt. Express 20(24), 26448–26457 (2012).
    [Crossref] [PubMed]
  12. S. Dong, P. Nanda, R. Shiradkar, K. Guo, and G. Zheng, “High-resolution fluorescence imaging via pattern-illuminated Fourier ptychography,” Opt. Express 22(17), 20856–20870 (2014).
    [Crossref] [PubMed]
  13. S. Dong, P. Nanda, K. Guo, J. Liao, and G. Zheng, “Incoherent Fourier ptychographic photography using structured light,” Photon. Res. 3(1), 19–23 (2015).
    [Crossref]
  14. J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts and Company, 2004).
  15. P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
    [Crossref] [PubMed]
  16. X. Ou, G. Zheng, and C. Yang, “Embedded pupil function recovery for Fourier ptychographic microscopy,” Opt. Express 22(5), 4960–4972 (2014).
    [Crossref] [PubMed]
  17. F. Hüe, J. M. Rodenburg, A. M. Maiden, and P. A. Midgley, “Extended ptychography in the transmission electron microscope: possibilities and limitations,” Ultramicroscopy 111(8), 1117–1123 (2011).
    [Crossref] [PubMed]
  18. Y. Shi, T. Li, Y. Wang, Q. Gao, S. Zhang, and H. Li, “Optical image encryption via ptychography,” Opt. Lett. 38(9), 1425–1427 (2013).
    [Crossref] [PubMed]
  19. R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66(3), 207–211 (1976).
    [Crossref]
  20. S. J. Chung, D. W. Miller, and O. L. Weck, “ARGOS testbed: study of multidisciplinary challenges of future spaceborne interferometric arrays,” Opt. Eng. 43(9), 2156 (2004).
    [Crossref]
  21. L. Bian, J. Suo, J. Chung, X. Ou, C. Yang, F. Chen, and Q. Dai, “Fourier ptychographic reconstruction using Poisson maximum likelihood and truncated Wirtinger gradient,” Sci. Rep. 6(1), 27384 (2016).
    [Crossref] [PubMed]

2016 (2)

M. Deprez, C. Bellanger, L. Lombard, B. Wattellier, and J. Primot, “Piston and tilt interferometry for segmented wavefront sensing,” Opt. Lett. 41(6), 1078–1081 (2016).
[Crossref] [PubMed]

L. Bian, J. Suo, J. Chung, X. Ou, C. Yang, F. Chen, and Q. Dai, “Fourier ptychographic reconstruction using Poisson maximum likelihood and truncated Wirtinger gradient,” Sci. Rep. 6(1), 27384 (2016).
[Crossref] [PubMed]

2015 (4)

2014 (3)

X. Ou, G. Zheng, and C. Yang, “Embedded pupil function recovery for Fourier ptychographic microscopy,” Opt. Express 22(5), 4960–4972 (2014).
[Crossref] [PubMed]

S. Dong, P. Nanda, R. Shiradkar, K. Guo, and G. Zheng, “High-resolution fluorescence imaging via pattern-illuminated Fourier ptychography,” Opt. Express 22(17), 20856–20870 (2014).
[Crossref] [PubMed]

D. Mourard, W. Dali Ali, A. Meilland, N. Tarmoul, F. Patru, J. M. Clausse, P. Girard, F. Henault, A. Marcotto, and N. Mauclert, “Group and phase delay sensing for cophasing large optical arrays,” Mon. Not. R. Astron. Soc. 445(2), 2082–2092 (2014).
[Crossref]

2013 (1)

2012 (1)

2011 (2)

D. J. Rabb, J. W. Stafford, and D. F. Jameson, “Non-iterative aberration correction of a multiple transmitter system,” Opt. Express 19(25), 25048–25056 (2011).
[Crossref] [PubMed]

F. Hüe, J. M. Rodenburg, A. M. Maiden, and P. A. Midgley, “Extended ptychography in the transmission electron microscope: possibilities and limitations,” Ultramicroscopy 111(8), 1117–1123 (2011).
[Crossref] [PubMed]

2010 (2)

2009 (2)

M. R. Bolcar and J. R. Fienup, “Sub-aperture piston phase diversity for segmented and multi-aperture systems,” Appl. Opt. 48(1), A5–A12 (2009).
[Crossref] [PubMed]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
[Crossref] [PubMed]

2004 (1)

S. J. Chung, D. W. Miller, and O. L. Weck, “ARGOS testbed: study of multidisciplinary challenges of future spaceborne interferometric arrays,” Opt. Eng. 43(9), 2156 (2004).
[Crossref]

1984 (1)

J. S. Fender, “Synthetic apertures: an overview,” Proc. SPIE 440, 2–7 (1984).
[Crossref]

1976 (1)

Adler, J.

I. Paykin, L. Yacobi, J. Adler, and E. N. Ribak, “Phasing a segmented telescope,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 91(2), 023302 (2015).
[Crossref] [PubMed]

Bellanger, C.

Bian, L.

L. Bian, J. Suo, J. Chung, X. Ou, C. Yang, F. Chen, and Q. Dai, “Fourier ptychographic reconstruction using Poisson maximum likelihood and truncated Wirtinger gradient,” Sci. Rep. 6(1), 27384 (2016).
[Crossref] [PubMed]

Bolcar, M. R.

Bunk, O.

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
[Crossref] [PubMed]

Chen, F.

L. Bian, J. Suo, J. Chung, X. Ou, C. Yang, F. Chen, and Q. Dai, “Fourier ptychographic reconstruction using Poisson maximum likelihood and truncated Wirtinger gradient,” Sci. Rep. 6(1), 27384 (2016).
[Crossref] [PubMed]

Chung, J.

L. Bian, J. Suo, J. Chung, X. Ou, C. Yang, F. Chen, and Q. Dai, “Fourier ptychographic reconstruction using Poisson maximum likelihood and truncated Wirtinger gradient,” Sci. Rep. 6(1), 27384 (2016).
[Crossref] [PubMed]

Chung, S. J.

S. J. Chung, D. W. Miller, and O. L. Weck, “ARGOS testbed: study of multidisciplinary challenges of future spaceborne interferometric arrays,” Opt. Eng. 43(9), 2156 (2004).
[Crossref]

Clausse, J. M.

D. Mourard, W. Dali Ali, A. Meilland, N. Tarmoul, F. Patru, J. M. Clausse, P. Girard, F. Henault, A. Marcotto, and N. Mauclert, “Group and phase delay sensing for cophasing large optical arrays,” Mon. Not. R. Astron. Soc. 445(2), 2082–2092 (2014).
[Crossref]

Cui, Z.

Dai, Q.

L. Bian, J. Suo, J. Chung, X. Ou, C. Yang, F. Chen, and Q. Dai, “Fourier ptychographic reconstruction using Poisson maximum likelihood and truncated Wirtinger gradient,” Sci. Rep. 6(1), 27384 (2016).
[Crossref] [PubMed]

Dali Ali, W.

D. Mourard, W. Dali Ali, A. Meilland, N. Tarmoul, F. Patru, J. M. Clausse, P. Girard, F. Henault, A. Marcotto, and N. Mauclert, “Group and phase delay sensing for cophasing large optical arrays,” Mon. Not. R. Astron. Soc. 445(2), 2082–2092 (2014).
[Crossref]

Deprez, M.

Dierolf, M.

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
[Crossref] [PubMed]

Dong, S.

Fender, J. S.

J. S. Fender, “Synthetic apertures: an overview,” Proc. SPIE 440, 2–7 (1984).
[Crossref]

Fienup, J. R.

Gao, Q.

Girard, P.

D. Mourard, W. Dali Ali, A. Meilland, N. Tarmoul, F. Patru, J. M. Clausse, P. Girard, F. Henault, A. Marcotto, and N. Mauclert, “Group and phase delay sensing for cophasing large optical arrays,” Mon. Not. R. Astron. Soc. 445(2), 2082–2092 (2014).
[Crossref]

Gunturk, B. K.

Guo, K.

Henault, F.

D. Mourard, W. Dali Ali, A. Meilland, N. Tarmoul, F. Patru, J. M. Clausse, P. Girard, F. Henault, A. Marcotto, and N. Mauclert, “Group and phase delay sensing for cophasing large optical arrays,” Mon. Not. R. Astron. Soc. 445(2), 2082–2092 (2014).
[Crossref]

Hüe, F.

F. Hüe, J. M. Rodenburg, A. M. Maiden, and P. A. Midgley, “Extended ptychography in the transmission electron microscope: possibilities and limitations,” Ultramicroscopy 111(8), 1117–1123 (2011).
[Crossref] [PubMed]

Jameson, D.

Jameson, D. F.

Jiang, Y.

Li, H.

Li, T.

Liao, J.

Lombard, L.

Long, X.

Ma, H.

Maiden, A. M.

F. Hüe, J. M. Rodenburg, A. M. Maiden, and P. A. Midgley, “Extended ptychography in the transmission electron microscope: possibilities and limitations,” Ultramicroscopy 111(8), 1117–1123 (2011).
[Crossref] [PubMed]

Marcotto, A.

D. Mourard, W. Dali Ali, A. Meilland, N. Tarmoul, F. Patru, J. M. Clausse, P. Girard, F. Henault, A. Marcotto, and N. Mauclert, “Group and phase delay sensing for cophasing large optical arrays,” Mon. Not. R. Astron. Soc. 445(2), 2082–2092 (2014).
[Crossref]

Mauclert, N.

D. Mourard, W. Dali Ali, A. Meilland, N. Tarmoul, F. Patru, J. M. Clausse, P. Girard, F. Henault, A. Marcotto, and N. Mauclert, “Group and phase delay sensing for cophasing large optical arrays,” Mon. Not. R. Astron. Soc. 445(2), 2082–2092 (2014).
[Crossref]

Meilland, A.

D. Mourard, W. Dali Ali, A. Meilland, N. Tarmoul, F. Patru, J. M. Clausse, P. Girard, F. Henault, A. Marcotto, and N. Mauclert, “Group and phase delay sensing for cophasing large optical arrays,” Mon. Not. R. Astron. Soc. 445(2), 2082–2092 (2014).
[Crossref]

Menzel, A.

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
[Crossref] [PubMed]

Midgley, P. A.

F. Hüe, J. M. Rodenburg, A. M. Maiden, and P. A. Midgley, “Extended ptychography in the transmission electron microscope: possibilities and limitations,” Ultramicroscopy 111(8), 1117–1123 (2011).
[Crossref] [PubMed]

Miller, D. W.

S. J. Chung, D. W. Miller, and O. L. Weck, “ARGOS testbed: study of multidisciplinary challenges of future spaceborne interferometric arrays,” Opt. Eng. 43(9), 2156 (2004).
[Crossref]

Mourard, D.

D. Mourard, W. Dali Ali, A. Meilland, N. Tarmoul, F. Patru, J. M. Clausse, P. Girard, F. Henault, A. Marcotto, and N. Mauclert, “Group and phase delay sensing for cophasing large optical arrays,” Mon. Not. R. Astron. Soc. 445(2), 2082–2092 (2014).
[Crossref]

Nanda, P.

Nie, H.

Noll, R. J.

Ou, X.

L. Bian, J. Suo, J. Chung, X. Ou, C. Yang, F. Chen, and Q. Dai, “Fourier ptychographic reconstruction using Poisson maximum likelihood and truncated Wirtinger gradient,” Sci. Rep. 6(1), 27384 (2016).
[Crossref] [PubMed]

X. Ou, G. Zheng, and C. Yang, “Embedded pupil function recovery for Fourier ptychographic microscopy,” Opt. Express 22(5), 4960–4972 (2014).
[Crossref] [PubMed]

Patru, F.

D. Mourard, W. Dali Ali, A. Meilland, N. Tarmoul, F. Patru, J. M. Clausse, P. Girard, F. Henault, A. Marcotto, and N. Mauclert, “Group and phase delay sensing for cophasing large optical arrays,” Mon. Not. R. Astron. Soc. 445(2), 2082–2092 (2014).
[Crossref]

Paykin, I.

I. Paykin, L. Yacobi, J. Adler, and E. N. Ribak, “Phasing a segmented telescope,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 91(2), 023302 (2015).
[Crossref] [PubMed]

Pfeiffer, F.

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
[Crossref] [PubMed]

Primot, J.

Qi, B.

Rabb, D.

Rabb, D. J.

Ren, G.

Ribak, E. N.

I. Paykin, L. Yacobi, J. Adler, and E. N. Ribak, “Phasing a segmented telescope,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 91(2), 023302 (2015).
[Crossref] [PubMed]

Rodenburg, J. M.

F. Hüe, J. M. Rodenburg, A. M. Maiden, and P. A. Midgley, “Extended ptychography in the transmission electron microscope: possibilities and limitations,” Ultramicroscopy 111(8), 1117–1123 (2011).
[Crossref] [PubMed]

Shi, J.

Shi, Y.

Shiradkar, R.

Stafford, J.

Stafford, J. W.

Stokes, A.

Stokes, A. J.

Suo, J.

L. Bian, J. Suo, J. Chung, X. Ou, C. Yang, F. Chen, and Q. Dai, “Fourier ptychographic reconstruction using Poisson maximum likelihood and truncated Wirtinger gradient,” Sci. Rep. 6(1), 27384 (2016).
[Crossref] [PubMed]

Tarmoul, N.

D. Mourard, W. Dali Ali, A. Meilland, N. Tarmoul, F. Patru, J. M. Clausse, P. Girard, F. Henault, A. Marcotto, and N. Mauclert, “Group and phase delay sensing for cophasing large optical arrays,” Mon. Not. R. Astron. Soc. 445(2), 2082–2092 (2014).
[Crossref]

Thibault, P.

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
[Crossref] [PubMed]

Wang, Y.

Wattellier, B.

Weck, O. L.

S. J. Chung, D. W. Miller, and O. L. Weck, “ARGOS testbed: study of multidisciplinary challenges of future spaceborne interferometric arrays,” Opt. Eng. 43(9), 2156 (2004).
[Crossref]

Xie, Z.

Xu, S.

Xu, X.

Yacobi, L.

I. Paykin, L. Yacobi, J. Adler, and E. N. Ribak, “Phasing a segmented telescope,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 91(2), 023302 (2015).
[Crossref] [PubMed]

Yang, C.

L. Bian, J. Suo, J. Chung, X. Ou, C. Yang, F. Chen, and Q. Dai, “Fourier ptychographic reconstruction using Poisson maximum likelihood and truncated Wirtinger gradient,” Sci. Rep. 6(1), 27384 (2016).
[Crossref] [PubMed]

X. Ou, G. Zheng, and C. Yang, “Embedded pupil function recovery for Fourier ptychographic microscopy,” Opt. Express 22(5), 4960–4972 (2014).
[Crossref] [PubMed]

Yue, D.

Zhang, S.

Zheng, G.

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

Mon. Not. R. Astron. Soc. (1)

D. Mourard, W. Dali Ali, A. Meilland, N. Tarmoul, F. Patru, J. M. Clausse, P. Girard, F. Henault, A. Marcotto, and N. Mauclert, “Group and phase delay sensing for cophasing large optical arrays,” Mon. Not. R. Astron. Soc. 445(2), 2082–2092 (2014).
[Crossref]

Opt. Eng. (1)

S. J. Chung, D. W. Miller, and O. L. Weck, “ARGOS testbed: study of multidisciplinary challenges of future spaceborne interferometric arrays,” Opt. Eng. 43(9), 2156 (2004).
[Crossref]

Opt. Express (7)

Opt. Lett. (2)

Photon. Res. (1)

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

I. Paykin, L. Yacobi, J. Adler, and E. N. Ribak, “Phasing a segmented telescope,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 91(2), 023302 (2015).
[Crossref] [PubMed]

Proc. SPIE (1)

J. S. Fender, “Synthetic apertures: an overview,” Proc. SPIE 440, 2–7 (1984).
[Crossref]

Sci. Rep. (1)

L. Bian, J. Suo, J. Chung, X. Ou, C. Yang, F. Chen, and Q. Dai, “Fourier ptychographic reconstruction using Poisson maximum likelihood and truncated Wirtinger gradient,” Sci. Rep. 6(1), 27384 (2016).
[Crossref] [PubMed]

Ultramicroscopy (2)

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
[Crossref] [PubMed]

F. Hüe, J. M. Rodenburg, A. M. Maiden, and P. A. Midgley, “Extended ptychography in the transmission electron microscope: possibilities and limitations,” Ultramicroscopy 111(8), 1117–1123 (2011).
[Crossref] [PubMed]

Other (1)

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts and Company, 2004).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (14)

Fig. 1
Fig. 1 Two implementations of a sparse aperture imaging system: (a) segmented mirror and (b) sub-aperture array.
Fig. 2
Fig. 2 Schematic of operation principle of our proposed technique. A sparse aperture system, with a transmitter of pattern projection, creates a set of pattern-modulated raw images by scanning the transmitter to different positions. Then, the timely collected images are input to the improved IFP iteration algorithm and ultimately a high quality image is obtained with distortions computationally corrected, and resolution further improved.
Fig. 3
Fig. 3 The simulation structure and the generated images. (a) The Golay-3 configuration with each sub-pupil close to each other, (b1) the ideal Golay-3 image without aberrations, and (b2) its spectrum. (c) The loaded phasing errors, (d1) the corresponding blurred Golay-3 image, and (d2) its spectrum.
Fig. 4
Fig. 4 Simulated raw images modulated by the scanning pattern. (a) The used unknown illumination pattern, which is translated to 64 different locations. (b1)-(b4) Four frames of the captured raw images.
Fig. 5
Fig. 5 Reconstruction results. (a) The reconstructed image and (b) its spectrum. (c) The loaded and (d) estimated MTFs
Fig. 6
Fig. 6 Results of simulations using different speckle sizes. (a1)-(a6) The illumination patterns with different speckle sizes corresponding to f-numbers of 60, 50, 40, 30, 20 and 10, respectively. (b) The Co value convergence curves with different speckle sizes.
Fig. 7
Fig. 7 Results of simulations against different levels of noises. (a1)-(c1) The phased Goaly-3 images with 0.1%, 0.5%, and 1% additive Gaussian noises, respectively. (a2)-(c2) The non-phased images blurred by the loaded phasing errors with the corresponding noises. (a3)-(c3) The corresponding reconstructed images using our proposed approach.
Fig. 8
Fig. 8 Results of simulations with different realizations of phasing errors. (a1)-(d1) the non-phased images blurred by loaded different phasing errors with RMSs of 0.26 λ, 0.29 λ, 0.34 λ, and 0.39 λ, respectively. (a2)-(d2) The corresponding reconstructed images.
Fig. 9
Fig. 9 Loaded distortions combing sub-aperture aberrations and phasing errors. (a) The global wavefront generated by the first 11 Zernike polynomials (piston, x and y tilt excluded). (b) The loaded phasing errors. (c) The final overall distortions combining both (a) and (b).
Fig. 10
Fig. 10 Results of simulations considering both the sub-aperture aberrations and phasing errors with a star resolution target. (a1) The blurred image aberrated by the loaded distortions, (b1) the ideal Golay-3 image without phase distortions, and (c1) the reconstructed image using our proposed technology. (a2)-(c2) The spectrums of (a1)-(c1), respectively. (d1) The loaded and (d2) estimated MTFs.
Fig. 11
Fig. 11 The configuration of the concept-demonstration experiment. A transmitter consists of a 2D translation stage, a 630 nm LED, a diffuser and a projection lens. A Golay-3 telescope is experimentally simulated by using a pupil-mask against an imaging lens, whose phasing errors and sub-aperture aberrations are characterized with a phase screen.
Fig. 12
Fig. 12 Experimental results of distortion correction. (a1)-(a4) Four frames of 64 raw images. (b) The low-quality Golay-3 image blurred by the phase screen. (c) The reconstructed image using our reported technique with 64 raw images. (d) The reconstructed image using previous IFP with 64 raw images.
Fig. 13
Fig. 13 Experimental results of resolution improvement. (a1) The Golay-3 image under uniform illumination without blurring (removing the phase screen). (b1) The recovered image. (c1) The higher-resolution image formed by a full-filled aperture of 25 mm diameter. (a2)-(c2) The trace lines of the same two-line features of (a1)-(c1) marked with dotted lines, respectively.
Fig. 14
Fig. 14 Recoveries using our proposed technology with (a) 16, (b) 25, (c) 36 and (d) 49 frames of raw images.

Tables (1)

Tables Icon

Table 1 Different realizations of phasing errors

Equations (12)

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

d(x,y)=o(x,y)h(x,y)+n(x,y)
h(x,y)= | F(P(u,v)) | 2
P(u,v)= n=1 N p(u u n ,v v n )
P(u,v)=P(u u 1 ,v v 1 )+ n=2 N P(u u n ,v v n ) exp[ 2πi λ ( p n + α n (u u n )+ β n (v v n ) ) ]
P(u,v)=P(u u 1 ,v v 1 )exp( i φ 1 (u,v) )+ n=2 N P(u u n ,v v n ) exp[ 2πi λ ( p n + α n (u u n )+ β n (v v n ) ) ]exp( i φ n (u,v) )
OTF( f u , f v )= F( h(x,y) ) h(x,y)dxdy
I tn = o n1 T n1 (x x n )
F( I tn update )=F( I tn )+OT F n1 [ F( d n )OT F n1 F( I tn ) ]
o n update = o n1 + T n1 ( max( T n1 ) ) 2 ( I tn update o n1 T n1 )
T n = T n1 + o n update ( max( o n update ) ) 2 ( I tn update I tn )
OT F n =OT F n1 +α conj( F( I tn ) ) ( max( F( I tn ) ) ) 2 ( F( d n )OT F n1 F( I tn ) )
Co(A,B)=cov(A,B) ( σ A σ B ) 1

Metrics