Optimal realizable filters and the minimum Euclidean distance principle

Juday, Richard D.

doi:10.1364/ao.32.005100

Cited by 116 publications

(67 citation statements)

References 20 publications

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“…The display produces in general a complex modulation m(ϕ)=a(ϕ)exp(ip(ϕ)) which is a function of the addressed phase ϕ. The minimum Euclidean projection states that the most efficient way of projecting a complex diffractive mask onto a restricted modulation domain is to assign the available complex value closest in the complex plane [17,18]. In Refs.…”

Section: Minimum Euclidean Projectionmentioning

confidence: 99%

“…[16] that the application of a projection of the complex values based on the minimum Euclidean distance principle [17,18] leads to important improvement of the efficiency of a diffractive phase element, even if the phase modulation depth provided by the display is seriously reduced. The technique is valid for phase-only functions with values distributed over a 2π range with a constant probability density function.…”

Section: Introductionmentioning

confidence: 99%

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Anamorphic and spatial frequency dependent phase modulation on liquid crystal displays. Optimization of the modulation diffraction efficiency

Márquez¹,

Iemmi²,

Moreno³

et al. 2005

Opt. Express

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Abstract:In this work we present experimental evidence of an anamorphic and spatial frequency dependent phase modulation in commercially available twisted nematic liquid crystal spatial light modulators. We have found that the phase modulation depth depends on the magnitude of the local spatial frequency component along the horizontal direction. Along the vertical direction the phase modulation depth does not depend on the spatial frequency. This phenomenon is related with the electronics driving the device and in no way related to liquid crystal physics. It causes a reduction of the optical efficiency of a diffractive optical element displayed onto this type of modulator. We present an algorithm to correct this effect and more efficiently display a diffractive optical element. We apply it to the particular case of a Fresnel lens. Experimental results that confirm the improvements in the efficiency of the displayed diffractive lens are presented.

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Section: Minimum Euclidean Projectionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Anamorphic and spatial frequency dependent phase modulation on liquid crystal displays. Optimization of the modulation diffraction efficiency

Márquez¹,

Iemmi²,

Moreno³

et al. 2005

Opt. Express

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show abstract

“…The first is to map the values to be represented on to the values that a SLM can represent using a minimum Euclidean distance method. 21 The second approach referred to as pseudorandom encoding, 22 statistically approximates the desired complex values with those values that are achievable with a given SLM. Originally developed for phase-only modulators, pseudorandom encoding has been extended to modulators for which amplitude is a function of phase by transforming the phase statistics to compensate for the amplitude coupling.…”

Section: 17mentioning

confidence: 99%

<title>Capture, encryption, compression, and display of digital holograms of three-dimensional objects</title>

et al. 2006

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Digital holography can be used to capture the whole Fresnel field from a reflective or transmissive object. Applications include imaging and display of three-dimensional (3D) objects, and encryption and pattern recognition of two-dimensional (2D) and 3D objects. Often, these optical systems employ discrete spatial light modulators (SLMs) such as liquid-crystal displays. In the 2D case, SLMs can encode the inputs and keys during encryption and decryption. For 3D processing, the SLM can be used as part of an optical reconstruction technique for 3D objects, and can also represent the key during encryption and decryption. However, discrete SLMs can represent only discrete levels of data necessitating a quantisation of continuous valued analog information. To date, many such optical systems have been proposed in the literature, yet there has been relatively little experimental evaluation of the practical performance of discrete SLMs in these systems. In this paper, we characterise conventional phase-modulating liquid-crystal devices and examine their limitations (in terms of phase quantisation, alignment tolerances, and nonlinear response) for the encryption of 2D and 3D data. Finally, we highlight the practical importance of a highly controlled discretisation (optimal quantisation) for compression of digital holograms.

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“…A few of these include encoding for amplitude-phase coupled, 3,5,12 binary quantized, 16 and m-ary quantized characteristics. 6,8,12,17,21 Although specifying and evaluating such a variety of algorithms is beyond the scope of this paper, this section would also help in the development of blended algorithms for modulation characteristics other than phase-only. We first present the three individual algorithms MDE, ED, and PRE, followed by blended MD-PRE and the new ED-PRE.…”

Section: Description Of the Encoding Algorithmsmentioning

confidence: 99%

Improved-fidelity error diffusion through blending with pseudorandom encoding

Duelli

Cohn

2000

J. Opt. Soc. Am. A

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Error diffusion (ED) and pseudorandom encoding (PRE) methods of designing Fourier transform holograms are compared in terms of their properties and the optical performance of the resulting far-field diffraction patterns. Although both methods produce a diffuse noise pattern due to the error between the desired fully complex pattern and the encoded modulation, the PRE errors reconstruct uniformly over the nonredundant bandwidth of the discrete-pixel spatial light modulator, while the ED errors reconstruct outside the window of the designed diffraction pattern. Combining the two encoding methods produces higher-fidelity diffraction patterns than either method produces individually. For some designs the fidelity of the ED-PRE algorithm is even higher over the entire nonredundant bandwidth than for the previously reported [J. Opt. Soc. Am. A 16, 2425 (1999)] minimum-distance-PRE algorithm.

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Optimal realizable filters and the minimum Euclidean distance principle

Cited by 116 publications

References 20 publications

Anamorphic and spatial frequency dependent phase modulation on liquid crystal displays. Optimization of the modulation diffraction efficiency

Anamorphic and spatial frequency dependent phase modulation on liquid crystal displays. Optimization of the modulation diffraction efficiency

<title>Capture, encryption, compression, and display of digital holograms of three-dimensional objects</title>

Improved-fidelity error diffusion through blending with pseudorandom encoding

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