Abstract

Rotational transformation based on coordinate rotation in Fourier space is a useful technique for simulating wave field propagation between nonparallel planes. This technique is characterized by fast computation because the transformation only requires executing a fast Fourier transform twice and a single interpolation. It is proved that the formula of the rotational transformation mathematically satisfies the Helmholtz equation. Moreover, to verify the formulation and its usefulness in wave optics, it is also demonstrated that the transformation makes it possible to reconstruct an image on arbitrarily tilted planes from a wave field captured experimentally by using digital holography.

© 2008 Optical Society of America

Free-viewpoint images captured using phase-shifting synthetic aperture digital holography

Tatsuya Nakatsuji and Kyoji Matsushima
Appl. Opt. 47(19) D136-D143 (2008)

General theoretical formulation of image formation in digital Fresnel holography

Pascal Picart and Julien Leval
J. Opt. Soc. Am. A 25(7) 1744-1761 (2008)

Pixel-size-maintained image reconstruction of digital holograms on arbitrarily tilted planes by the angular spectrum method

Seung Jun Jeong and Chung Ki Hong
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Angular spectrum method with correction of anamorphism for numerical reconstruction of digital holograms on tilted planes

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Fast calculation method for optical diffraction on tilted planes by use of the angular spectrum of plane waves

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