Abstract

When the optical Hartley transform of a real, 2-D input object is constructed by the addition of two Fourier transforms with the correct relative amplitude, phase, and orientation the resulting field then encodes, in the form of amplitude only, all the information normally associated with Fourier amplitude and phase. If the transformer fails to correctly realize the desired relationship between the two Fourier transforms, the field at the transform plane no longer represents a true Hartley transform. Nevertheless knowledge of the nature of the error along with measurements in the transform plane enables the Hartley transform to be precisely recovered.

© 1989 Optical Society of America

Comparison of algorithms for computing the two-dimensional discrete Hartley transform

Stephen E. Reichenbach, John C. Burton, and Keith W. Miller
J. Opt. Soc. Am. A 6(6) 818-822 (1989)

Separable two-dimensional discrete Hartley transform

Andrew B. Watson and Allen Poirson
J. Opt. Soc. Am. A 3(12) 2001-2004 (1986)

Optical correlator performance of binary phase-only filters using Fourier and Hartley transforms

Don M. Cottrell, Roger A. Lilly, Jeffrey A. Davis, and Timothy Day
Appl. Opt. 26(18) 3755-3761 (1987)

Algorithm for the recovery of a real signal from its Hartley-transform modulus only

Bizhen Dong, Benyuan Gu, and Guozhen Yang
J. Opt. Soc. Am. A 8(7) 1048-1054 (1991)

Reconstruction of a real function from its Hartley-transform intensity

N. Nakajima
J. Opt. Soc. Am. A 5(6) 858-863 (1988)