Fully complex diffractive optics by means of patterned diffuser arrays: encoding concept and implications for fabrication

Abstract

Arbitrary complex-valued functions can be implemented as arrays of individually specified diffusers. For any diffuser, only average step height and vertical roughness are needed to control phase and amplitude. This modulation concept suggests potentially low-cost fabrication methods in which desired topographies are patterned by exposing photoresist with partially developed speckle patterns. Analyses and experimental demonstrations that illustrate the modulation concept and aspects of the fabrication method are presented, with particular emphasis on limitations of complex recording set by various photoresist and exposure properties. Applications of diffuser array concepts to spatial light modulators and to gray-scale lithographic printing of micro-optics are also mentioned. © 1997 Optical Society of America [S0740-3232(97)

Ternary pseudorandom encoding of Fourier transform holograms

“…Ϫl 23 cos 23 ͬͩ p q ͪ , (15) where l 13 , l 23 , and l c3 represent the respective lengths from a 1 , a 2 , a c to a 3 and where 13 and 23 are the angles from a c -a 3 to a 1 -a 3 and a 2 -a 3 , respectively. The solution for Eq.…”

Nonlinear effects of phase blurring on Fourier transform holograms

“…The metrics of signal-to-noise ratio (SNR), signal-to-peak-noise ratio (SPR), nonuniformity (NU), and diffraction efficiency () are reviewed from earlier work. 5,[8][9][10] Additional metrics that are useful for describing the nonlinear effects of blurring are the intensities I k and the energies E k of the kth diffraction order that result from blurring of the desired modulation.…”

“…[1][2][3][4] For instance, we recently studied a LCLV that was quoted as having 40 line pairs/mm resolution for low illumination levels and 4 line pairs/mm for high illumination levels. 5 Thus a simple convolution model of resolution loss is not appropriate for LCLV's used as intensity displays. However, a convolution relationship appears to exist between input intensity images and output phase images.…”

“…Various encoding techniques have been developed for which the Fourier transform of exp( j) approximates the Fourier transform of a desired fully complex modulation a c ϵ a c exp( j). 6,7 One such encoding method, pseudorandom encoding, 5,[8][9][10][11] (PRE), approximates the desired modulation in an average sense (which is reviewed in Subsection 4.A). Here we note that this approximate mapping from the desired signal a c to the encoded phaseonly signal exp( j) can be viewed as a linear (or more precisely, a quasi-linear) space-invariant system.…”

“…9 and earlier studies, while we were aware of a spatial-frequency-dependent loss of phase range, we did not model this as phase blurring, nor did we consider the related nonlinear effects on the diffraction pattern. 5,8,9 Instead, we attempted to minimize phase blurring by making the pixel spacing of the discretely sampled CGH's large with respect to the maximum phase slope anticipated. At the time, the major source of errors between the experimentally measured and the simulated results was assumed to be various point nonlinearitiese.g., the inaccurate setting of the mapping between input intensity and phase, variations in response across the SLM, and quantized phase levels.…”