A three-dimensional point spread function for phase retrieval and deconvolution

doi:10.1364/OE.20.015392

A three-dimensional point spread function for phase retrieval and deconvolution

Xinyue Liu, Liang Wang, Jianli Wang, and Haoran Meng »View Author Affiliations

Optics Express, Vol. 20, Issue 14, pp. 15392-15405 (2012)
http://dx.doi.org/10.1364/OE.20.015392

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Abstract
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References (23)
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Abstract

We present a formulation of optical point spread function based on a scaled three-dimensional Fourier transform expression of focal field distribution and the expansion of generalized aperture function. It provides an equivalent but more flexible representation compared with the analytic expression of the extended Nijboer-Zernike approach. A phase diversity algorithm combined with an appropriate regularization strategy is derived and analyzed to demonstrate the effectiveness of the presented formulation for phase retrieval and deconvolution. Experimental results validate the performance of presented algorithm.

OCIS Codes
(010.7350) Atmospheric and oceanic optics : Wave-front sensing
(100.1830) Image processing : Deconvolution
(100.5070) Image processing : Phase retrieval
(100.6890) Image processing : Three-dimensional image processing

ToC Category:
Image Processing

History
Original Manuscript: May 9, 2012
Revised Manuscript: June 16, 2012
Manuscript Accepted: June 18, 2012
Published: June 25, 2012

Citation
Xinyue Liu, Liang Wang, Jianli Wang, and Haoran Meng, "A three-dimensional point spread function for phase retrieval and deconvolution," Opt. Express 20, 15392-15405 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-14-15392

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References

J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt.21(15), 2758–2769 (1982). [CrossRef] [PubMed]
R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng.21, 829–832 (1982).
R. G. Paxman, T. J. Schulz, and J. R. Fienup, “Joint estimation of object and aberrations using phase diversity,” J. Opt. Soc. Am. A9(7), 1072–1085 (1992). [CrossRef]
J. R. Fienup, “Phase-retrieval algorithms for a complicated optical system,” Appl. Opt.32(10), 1737–1746 (1993). [CrossRef] [PubMed]
J. B. Sibarita, “Deconvolution Microscopy,” Adv. Biochem. Eng. Biotechnol.95, 201–243 (2005). [PubMed]
G. Chenegros, L. M. Mugnier, F. Lacombe, and M. Glanc, “3D phase diversity: a myopic deconvolution method for short-exposure images: application to retinal imaging,” J. Opt. Soc. Am. A24(5), 1349–1357 (2007). [CrossRef] [PubMed]
B. M. Hanser, M. G. L. Gustafsson, D. A. Agard, and J. W. Sedat, “Phase-retrieved pupil functions in wide-field fluorescence microscopy,” J. Microsc.216(1), 32–48 (2004). [CrossRef] [PubMed]
A. J. E. M. Janssen, “Extended Nijboer-Zernike approach for the computation of optical point-spread functions,” J. Opt. Soc. Am. A19(5), 849–857 (2002). [CrossRef] [PubMed]
J. J. M. Braat, P. Dirksen, and A. J. E. M. Janssen, “Assessment of an extended Nijboer-Zernike approach for the computation of optical point-spread functions,” J. Opt. Soc. Am. A19(5), 858–870 (2002). [CrossRef] [PubMed]
J. J. M. Braat, S. van Haver, A. J. E. M. Janssen, and P. Dirksen, “Assessment of optical systems by means of point-spread functions,” in Progress in Optics, E. Wolf, ed., (Elsevier, 2008), 51, 349–468.
A. A. Ramos and A. L. Ariste, “Image reconstruction with analytical point spread functions,” Astron. Astrophys. 518, paper A6 (2010).
C. W. McCutchen, “Generalized Aperture and the Three-Dimensional Diffraction Image,” J. Opt. Soc. Am.54(2), 240–242 (1964). [CrossRef]
E. Wolf and Y. Li, “Conditions for the validity of the Debye integral representation of focused fields,” Opt. Commun.39(4), 205–210 (1981). [CrossRef]
J. Lin, X.-C. Yuan, S. S. Kou, C. J. R. Sheppard, O. G. Rodríguez-Herrera, and J. C. Dainty, “Direct calculation of a three-dimensional diffracted field,” Opt. Lett.36(8), 1341–1343 (2011). [CrossRef] [PubMed]
M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University Press, 1999).
S. van Haver, “The Extended Nijboer-Zernike diffraction theory and its applications,” PhD Dissertation, Delft University of Technology (2010).
J. J. M. Braat, S. van Haver, and S. F. Pereira, “Microlens quality assessment using the Extended Nijboer-Zernike (ENZ) diffraction theory,” presented at EOS Optical Microsystems, Capri, Italy, 27–30 Sept. 2009.
C. J. R. Sheppard and P. Török, “Focal shift and the axial optical coordinate for high-aperture systems of finite Fresnel number,” J. Opt. Soc. Am. A20(11), 2156–2162 (2003). [CrossRef] [PubMed]
S. M. Jefferies, M. Lloyd-Hart, E. K. Hege, and J. Georges, “Sensing wave-front amplitude and phase with phase diversity,” Appl. Opt.41(11), 2095–2102 (2002). [CrossRef] [PubMed]
C. R. Vogel, T. Chan, and R. Plemmons, “Fast algorithms for phase diversity-based blind deconvolution,” Proc. SPIE3353, 994–1005 (1998). [CrossRef]
J. Nocedal and S. J. Wright, Numerical Optimization 2nd ed. (Springer, 2006).
D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley-Interscience, 1998).
M. Leutenegger, R. Rao, R. A. Leitgeb, and T. Lasser, “Fast focus field calculations,” Opt. Express14(23), 11277–11291 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-23-11277 . [CrossRef] [PubMed]

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[1] J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt.21(15), 2758–2769 (1982). [CrossRef] [PubMed]

[2] R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng.21, 829–832 (1982).

[3] R. G. Paxman, T. J. Schulz, and J. R. Fienup, “Joint estimation of object and aberrations using phase diversity,” J. Opt. Soc. Am. A9(7), 1072–1085 (1992). [CrossRef]

[4] J. R. Fienup, “Phase-retrieval algorithms for a complicated optical system,” Appl. Opt.32(10), 1737–1746 (1993). [CrossRef] [PubMed]

[5] J. B. Sibarita, “Deconvolution Microscopy,” Adv. Biochem. Eng. Biotechnol.95, 201–243 (2005). [PubMed]

[6] G. Chenegros, L. M. Mugnier, F. Lacombe, and M. Glanc, “3D phase diversity: a myopic deconvolution method for short-exposure images: application to retinal imaging,” J. Opt. Soc. Am. A24(5), 1349–1357 (2007). [CrossRef] [PubMed]

[7] B. M. Hanser, M. G. L. Gustafsson, D. A. Agard, and J. W. Sedat, “Phase-retrieved pupil functions in wide-field fluorescence microscopy,” J. Microsc.216(1), 32–48 (2004). [CrossRef] [PubMed]

[8] A. J. E. M. Janssen, “Extended Nijboer-Zernike approach for the computation of optical point-spread functions,” J. Opt. Soc. Am. A19(5), 849–857 (2002). [CrossRef] [PubMed]

[9] J. J. M. Braat, P. Dirksen, and A. J. E. M. Janssen, “Assessment of an extended Nijboer-Zernike approach for the computation of optical point-spread functions,” J. Opt. Soc. Am. A19(5), 858–870 (2002). [CrossRef] [PubMed]

[10] J. J. M. Braat, S. van Haver, A. J. E. M. Janssen, and P. Dirksen, “Assessment of optical systems by means of point-spread functions,” in Progress in Optics, E. Wolf, ed., (Elsevier, 2008), 51, 349–468.

[11] A. A. Ramos and A. L. Ariste, “Image reconstruction with analytical point spread functions,” Astron. Astrophys. 518, paper A6 (2010).

[12] C. W. McCutchen, “Generalized Aperture and the Three-Dimensional Diffraction Image,” J. Opt. Soc. Am.54(2), 240–242 (1964). [CrossRef]

[13] E. Wolf and Y. Li, “Conditions for the validity of the Debye integral representation of focused fields,” Opt. Commun.39(4), 205–210 (1981). [CrossRef]

[14] J. Lin, X.-C. Yuan, S. S. Kou, C. J. R. Sheppard, O. G. Rodríguez-Herrera, and J. C. Dainty, “Direct calculation of a three-dimensional diffracted field,” Opt. Lett.36(8), 1341–1343 (2011). [CrossRef] [PubMed]

[15] M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University Press, 1999).

[16] S. van Haver, “The Extended Nijboer-Zernike diffraction theory and its applications,” PhD Dissertation, Delft University of Technology (2010).

[17] J. J. M. Braat, S. van Haver, and S. F. Pereira, “Microlens quality assessment using the Extended Nijboer-Zernike (ENZ) diffraction theory,” presented at EOS Optical Microsystems, Capri, Italy, 27–30 Sept. 2009.

[18] C. J. R. Sheppard and P. Török, “Focal shift and the axial optical coordinate for high-aperture systems of finite Fresnel number,” J. Opt. Soc. Am. A20(11), 2156–2162 (2003). [CrossRef] [PubMed]

[19] S. M. Jefferies, M. Lloyd-Hart, E. K. Hege, and J. Georges, “Sensing wave-front amplitude and phase with phase diversity,” Appl. Opt.41(11), 2095–2102 (2002). [CrossRef] [PubMed]

[20] C. R. Vogel, T. Chan, and R. Plemmons, “Fast algorithms for phase diversity-based blind deconvolution,” Proc. SPIE3353, 994–1005 (1998). [CrossRef]

[21] J. Nocedal and S. J. Wright, Numerical Optimization 2nd ed. (Springer, 2006).

[22] D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley-Interscience, 1998).

[23] M. Leutenegger, R. Rao, R. A. Leitgeb, and T. Lasser, “Fast focus field calculations,” Opt. Express14(23), 11277–11291 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-23-11277 . [CrossRef] [PubMed]

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A three-dimensional point spread function for phase retrieval and deconvolution