Quantifying the 2.5D imaging performance of digital holographic systems

D. P. Kelly; J. J. Healy; B. M. Hennelly; J. T. Sheridan

doi:10.2971/jeos.2011.11034

Journal of the European Optical Society - Rapid publications, Vol 6 (2011)

Quantifying the 2.5D imaging performance of digital holographic systems

D. P. Kelly, J. J. Healy, B. M. Hennelly, J. T. Sheridan

Abstract

Digital holographic systems are a class of two step, opto-numerical, three-dimensional imaging techniques. The role of the digital camera in limiting the resolution and ﬁeld of view of the reconstructed image, and the interaction of these limits with a general optical system is poorly understood. The linear canonical transform describes any optical system consisting of lenses and/or free space in a uniﬁed manner. Expressions derived using it are parametrised in terms of the parameters of the optical system, as well as those of the digital camera: aperture size, pixel size and pixel pitch. We develop rules of thumb for selecting an optical system to minimise mean squared error for given input and digital camera parameters. In the limit, our results constitute a point spread function analysis. The results presented in this paper will allow digital holography practitioners to select an optical system to maximise the quality of their reconstructed image using a priori knowledge of the camera and object.

Full Text: PDF

Citation Details

Cite this article

References

D. Gabor, "A new microscope principle" Nature 161, 777-778 (1948).

D. Gabor, "Microscopy by reconstructed wave-fronts" Royal Society of London Proceedings Series A 197, 454-487 (1949).

D. Gabor, "Microscopy by reconstructed wave fronts: II", Proc. Phys. Soc. B 64, 449-469 (1951).

D. Gabor, and W. P. Goss, "Interference microscope with total wavefront reconstruction" J. Opt. Soc. Am. 56, 849-856 (1966).

J. Goodman, Introduction to Fourier Optics (Second Edition, McGraw-Hill, New York, 1966).

J. W. Goodman, and R. W. Lawrence, "Digital image formation from electronically detected holograms" Appl. Phy. Lett. 11, 77-79 (1967).

U. Schnars, and W. Jüptner, "Direct recording of holograms by a CCD target and numerical reconstruction" Appl. Opt. 33, 179-181 (1994).

U. Schnars, and W. P. O. Juptner, "Digital recording and numerical reconstruction of holograms" Meas. Sci. Technol. 13, R85-R101 (2002).

C.-S. Guo, L. Zhang, Z.-Y. Rong, and H.-T. Wang, "Effect of the fill factor of CCD pixels on digital holograms: comment on the papers "Frequency analysis of digital holography" and "Frequency analysis of digital holography with reconstruction by convolution" Opt. Eng. 42, 2768-2771 (2003).

D. P. Kelly, B. M. Hennelly, N. Pandey, T. J. Naughton, and W. T. Rhodes, "Resolution limits in practical digital holographic systems" Opt. Eng. 48, 095801 (2009).

J. W. Goodman, Statistical Optics (John Wiley and Sons, 1985).

R. Bracewell, The Fourier Transform and its Applications (McGraw- Hill, New York, 1965).

A. Stern, "Sampling of linear canonical transformed signals" Signal Process. 86, 1421-1425 (2006).

T. M. Kreis, "Frequency analysis of digital holography" Opt. Eng. 41, 771-778 (2002).

T. M. Kreis, "Frequency analysis of digital holography with reconstruction by convolution" Opt. Eng. 41, 1829-1839 (2002).

T. M. Kreis, "Response to "Effect of the fill factor of CCD pixels on digital holograms: comment on the papers 'Frequency analysis of digital holography' and 'Frequency analysis of digital holography with reconstruction by convolution' "" Opt. Eng. 42, 2772-2772 (2003).

E. N. Leith, and J. Upatnieks, "Reconstructed wavefronts and communication theory" J. Opt. Soc. Am. 52, 1123-1128 (1962).

T. Latychevskaia, and H.-W. Fink, "Solution to the Twin Image Problem in Holography" Phys. Rev. Lett. 98, 233901 (2007).

D. S. Monaghan, D. P. Kelly, N. Pandey, and B. M. Hennelly, "Twin removal in digital holography using diffuse illumination" Opt. Lett. 34, 3610-3612 (2009).

G.-S. Han, and S.-W. Kim, "Numerical correction of reference phases in phase-shifting interferometry by iterative least-squares fitting" Appl. Opt. 33, 7321-7325 (1994).

Z. Wang, and B. Han, "Advanced iterative algorithm for phase extraction of randomly phase-shifted interferograms" Opt. Lett. 29, 1671-1673 (2004).

I. Yamaguchi, and T. Zhang, "Phase-shifting digital holography" Opt. Lett. 22, 1268-1270 (1997).

M. North Morris, J. Millerd, N. Brock, J. Hayes, and B. Saif, "Dynamic phase-shifting electronic speckle pattern interferometer", in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, H. P. Stahl, ed. (2005), Presented at the Society of Photo-Optical Instrumentation Engineers (SPIE) Conference, vol. 5869, 337-345.

P. K. Rastogi, Digital Speckle Pattern Interferometry and Related Techniques (Wiley, New York, 2000).

S. A. Collins-Jnr, "Lens-system diffraction integral written in terms of matrix optics" J. Opt. Soc. Am. 60, 1168-1177 (1970).

D. P. Kelly, J. E. Ward, U. Gopinathan, and J. T. Sheridan, "Controlling speckle using lenses and free space" Opt. Lett. 32, 3394-3396 (2007).

J. J. Healy, B. M. Hennelly, and J. T. Sheridan, "Additional sampling criterion for the linear canonical transform" Opt. Lett. 33, 2599-2601 (2008).

D. P. Kelly, B. M. Hennelly, W. T. Rhodes, and J. T. Sheridan, "Analytical and numerical analysis of linear optical systems" Opt. Eng. 45, 088201 (2006).

F. Oktem, and H. M. Ozaktas, "Exact relation between continuous and discrete linear canonical transforms" IEEE Signal Proc. Let. 16, 727-730 (2009).

J. J. Healy, and J. T. Sheridan, "Fast linear canonical transforms" J. Opt. Soc. Am. A 27, 21-30 (2010).

J. J. Healy, and J. T. Sheridan, "Reevaluation of the direct method of calculating Fresnel and other linear canonical transforms" Opt. Lett. 35, 947-949 (2010).

F. Gori, "Fresnel transform and sampling theorem" Opt. Commun. 39, 293-297 (1981).

L. Onural, "Sampling of the diffraction field" Appl. Opt. 39, 5929-5935 (2000).

A. Stern, and B. Javidi, "Sampling in the light of Wigner distribution" J. Opt. Soc. Am. A 21, 360-366 (2004).

A. Stern, and B. Javidi, "Sampling in the light of Wigner distribution: errata" J. Opt. Soc. Am. A 21, 2038-2038 (2004).

A. Stern, and B. Javidi, "Analysis of practical sampling and reconstruction from Fresnel fields" Opt. Eng. 43, 239-250 (2004).

L. Onural, "Exact analysis of the effects of sampling of the scalar diffraction field" J. Opt. Soc. Am. A 24, 359-367 (2007).

H. Jin, H. Wan, Y. Zhang, Y. Li, and P. Qiu, "The influence of structural parameters of CCD on the reconstruction image of digital holograms" J. Mod. Optic. 55, 2989-3000 (2008).

G. T. D. Francia, "Degrees of freedom of an image" J. Opt. Soc. Am. 59, 799-803 (1969).

D. Mendlovic, and A. W. Lohmann, "Space-bandwidth product adaptation and its application to superresolution: fundamentals" J. Opt. Soc. Am. A 14, 558-562 (1997).

D. Mendlovic, A. W. Lohmann, and Z. Zalevsky, "Space-bandwidth product adaptation and its application to superresolution: examples" J. Opt. Soc. Am. A 14, 563-567 (1997).

R. Piestun, and D. A. B. Miller, "Electromagnetic degrees of freedom of an optical system" J. Opt. Soc. Am. A 17, 892-902 (2000).

S. S. Kou, and C. J. Sheppard, "Imaging in digital holographic microscopy" Opt. Express 15, 13640-13648 (2007).

H. T. Yura, and S. G. Hanson, "Optical beam wave propagation through complex optical systems" J. Opt. Soc. Am. A 4, 1931-1948 (1987).

H. T. Yura, S. G. Hanson, and T. P. Grum, "Speckle: statistics and interferometric decorrelation effects in complex ABCD optical systems" J. Opt. Soc. Am. A 10, 316-323 (1993).

D. P. Kelly, J. E. Ward, B. M. Hennelly, U. Gopinathan, F. T. O'Neill, and J. T. Sheridan, "Paraxial speckle-based metrology systems with an aperture" J. Opt. Soc. Am. A 23, 2861-2870 (2006).

D. P. Kelly, N. Pandey, B. M. Hennelly, and T. J. Naughton, "Quantization noise: An additional constraint for the extended sampling theorem", in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2009), paper DWB12.

B. R. Frieden, "Restoring with maximum likelihood and maximum entropy" J. Opt. Soc. Am. 62, 511-518 (1972).

B. R. Frieden, and J. J. Burke, "Restoring with maximum entropy, II: Superresolution of photographs of diffraction-blurred impulses" J. Opt. Soc. Am. 62, 1202-1210 (1972).

F. Soulez, L. Denis, Éric Thiébaut, C. Fournier, and C. Goepfert, "Inverse problem approach in particle digital holography: outof-field particle detection made possible" J. Opt. Soc. Am. A 24, 3708-3716 (2007).

C. Fournier, L. Denis, and T. Fournel, "On the single point resolution of on-axis digital holography" J. Opt. Soc. Am. A 27, 1856-1862 (2010).

S. A. Alexandrov, T. R. Hillman, and D. D. Sampson, "Spatially resolved Fourier holographic light scattering angular spectroscopy" Opt. Lett. 30, 3305-3307 (2005).

T. Meinecke, N. Sabitov, and S. Sinzinger, "Information extraction from digital holograms for particle flow analysis" Appl. Opt. 49, 2446-2455 (2010).

A. W. Lohmann, Optical Information Processing (Universitätsverlag Ilmenau, 2006).

D. P. Kelly, J. T. Sheridan, and W. T. Rhodes, "Fundamental diffraction limitations in a paraxial 4-f imaging system with coherent and incoherent illumination" J. Opt. Soc. Am. A 24, 1911-1919 (2007).

L. Xu, X. Peng, Z. Guo, J. Miao, and A. Asundi, "Imaging analysis of digital holography" Opt. Express 13, 2444-2452 (2005).

T. Colomb, F. Montfort, J. Kühn, N. Aspert, E. Cuche, A. Marian, F. Charrière, S. Bourquin, P. Marquet, and C. Depeursinge, "Numerical parametric lens for shifting, magnification, and complete aberration compensation in digital holographic microscopy" J. Opt. Soc. Am. A 23, 3177-3190 (2006).

A. Stern, and B. Javidi, "Space-bandwidth conditions for efficient phase-shifting digital holographic microscopy" J. Opt. Soc. Am. A 25, 736-741 (2008).

D. S. M. N. P. Bryan, M. Hennelly, and D. P. Kelly, Information Optics and Photonics: Algorithms, Systems, and Applications (Springer, 2010).

J. J. Healy, and J. T. Sheridan, "Space-bandwidth ratio as a means of choosing between Fresnel and other linear canonical transform algorithms" J. Opt. Soc. Am. A 28, 786-790 (2011).

L. P. Yaroslavskii, and N. S. Merzlyakov Methods of Digital Holography (Consultants Bureau, Los Angeles, 1980).

L. P. Yaroslavskii, and J. Astola (eds.) Advances in Signal Transforms: Theory and Applications (Hindawi Publishing Corporation, Cairo, 2007).

Y. Hao, and A. Asundi, "Resolution analysis of a digital holography system" Appl. Opt. 50, 183-193 (2011).