Modulation light efficiency of diffractive lenses displayed in a restricted phase-mostly modulation display

Abstract

We present an analysis of the diffraction efficiency of diffractive lenses displayed on spatial light modulators that depends on the modulation response of the display. An ideal display would produce continuous phase-only modulation, reaching a maximum phase-modulation depth of 2pi. We introduce the concept of modulation diffraction efficiency that accounts for the effect of nonlinearities only in the phase modulation of the display. We review a diffractive model with which to evaluate this modulation efficiency, including modulation defects such as nonlinear phase modulation, coupled amplitude modulation, phase quantization, and a limited modulation depth. We apply this diffractive model to Fresnel lenses and show that these modulation defects produce a lens multiplex effect. Finally we demonstrate that the application of a minimum Euclidean projection principle leads to high modulation diffraction efficiency even if the phase-modulation depth is much less than 2pi. We demonstrate that the modulation efficiency can exceed 90% for a modulation depth of 1.4pi and can exceed 40% (the equivalent for a binary phase element) for a modulation depth of only 0.7pi. Experimental results from use of a twisted nematic liquid-crystal display are presented to confirm these conclusions.

Time fluctuations of the phase modulation in a liquid crystal on silicon display: characterization and effects in diffractive optics

“…This modulation regime maximizes the modulation diffraction efficiency [10]. Many works have demonstrated in the past the usefulness of liquid crystal displays to act as phase-only spatial light modulators [11][12][13][14].…”

Study of Liquid Crystal on Silicon Displays for Their Application in Digital Holography

“…In digital holography applications, the diffraction efficiency is maximized when operating in the phase-only modulation regime (Moreno et al, 2004). Therefore, in such applications is very desirable to operate with an LCoS display response achieving a linear phase modulation up to 360 degrees, without coupled depolarization or coupled amplitude modulation.…”

Experimental Minimum-Error Quantum-State Discrimination in High Dimensions

“…The aforementioned procedures were complemented with a convenient choice of the grating period and orientation [42] and an appropriate configuration of the SLM-i.e. phase modulation response to the addressed gray levels [43] and digital electric addressing sequences [44]-in order to improve the efficiency and temporal stability of the modulated phase. Figure 5 shows an example of |t(x, y)|, Arg(t(x, y)) and the corresponding phase masks addressed at the SLM (via PA or GD method) used to prepare a given spatial qudit state with D = 7.…”