A phase-retrieval system with a Gaussian filter of known width is proposed. Using this system, one can retrieve the Fourier phase of a complex-valued object function from intensity measurements of two Fourier transforms of the object modulated by the Gaussian filter and the object modulated by the laterally shifted Gaussian filter with known displacement. The shift of the Gaussian filter has the same effect as the modulation of the object with an exponential filter, which is used in the previous phase-retrieval method based on the properties of analytic functions. In addition, the same situation as for the exponential filtering with variable inclination can be easily produced by changing the displacement quantity of the Gaussian filter.
© 1998 Optical Society of America
Original Manuscript: April 21, 1997
Revised Manuscript: October 3, 1997
Manuscript Accepted: September 22, 1997
Published: February 1, 1998
Nobuharu Nakajima, "Phase-retrieval system using a shifted Gaussian filter," J. Opt. Soc. Am. A 15, 402-406 (1998)