ANALYTICAL DESIGN OF HOLOGRAPHIC OPTICAL-ELEMENTS FOR FOURIER-TRANSFORM

A new method for designing holographic optical elements for Fourier transform is described. A phase function is assumed as a power series of coordinates of the optical element, and an analytical expression of wave-front aberration is derived. The coefficients in the phase function are explicitly determined such that the wave-front aberration may be kept small during variation of inputs. The location of the circle of least confusion and the balancing of the aberration over an entire spatial-frequency range are taken into consideration. By the simulation of spot diagrams it is confirmed that our designed phase function is optimum for a sufficiently wide spatial- frequency range. © 1990 Optical Society of America.