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
Original Manuscript: September 17, 2007
Revised Manuscript: February 11, 2008
Manuscript Accepted: February 11, 2008
Published: April 2, 2008
Kyoji Matsushima, "Formulation of the rotational transformation of wave fields and their application to digital holography," Appl. Opt. 47, D110-D116 (2008)