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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 42, Iss. 29 — Oct. 10, 2003
  • pp: 5816–5824

Imaging phase objects with square-root, Foucault, and Hoffman real filters: a comparison

Arkadiusz Sagan, Slawomir Nowicki, Ryszard Buczynski, Marek Kowalczyk, and Tomasz Szoplik  »View Author Affiliations


Applied Optics, Vol. 42, Issue 29, pp. 5816-5824 (2003)
http://dx.doi.org/10.1364/AO.42.005816


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Abstract

Methods of imaging phase objects are considered. First the square-root filter is inferred from a definition of fractional-order derivatives given in terms of the integration of a fractional order called the Riemann-Liouville integral. Then we present a comparison of the performance of three frequency-domain real filters: square root, Foucault, and Hoffman. The phase-object imaging method is useful as a phase-shift measurement technique under the condition that the output image intensity is a known function of object phase. For the square-root filter it is the first derivative of the object phase function. The Foucault filter, in spite of its position, gives output image intensities expressed by Hilbert transforms. The output image intensity obtained with the Hoffman filter is not expressed by an analytical formula. The performance of the filters in a 4f imaging system with coherent illumination is simulated by use of VirtualLab 1.0 software.

© 2003 Optical Society of America

OCIS Codes
(070.0070) Fourier optics and signal processing : Fourier optics and signal processing
(070.1170) Fourier optics and signal processing : Analog optical signal processing
(070.6110) Fourier optics and signal processing : Spatial filtering
(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology
(120.5050) Instrumentation, measurement, and metrology : Phase measurement

History
Original Manuscript: December 13, 2002
Revised Manuscript: July 16, 2003
Published: October 10, 2003

Citation
Arkadiusz Sagan, Slawomir Nowicki, Ryszard Buczynski, Marek Kowalczyk, and Tomasz Szoplik, "Imaging phase objects with square-root, Foucault, and Hoffman real filters: a comparison," Appl. Opt. 42, 5816-5824 (2003)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-42-29-5816


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