Two-dimensional optical Hartley transforms in the presence of errors

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to correctly realize the desired relationship between the two Fourier transforms, the field at the transform plane no longer represents a true Hartley transform.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.