A direct-search method for the computer design of holograms

Clark, Matt; Smith, R. W.

doi:10.1016/0030-4018(95)00633-8

Cited by 26 publications

(6 citation statements)

References 12 publications

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“…Genetic algorithms [18] seek the global minimum of the cost function, and as such are computationally demanding but accurate. Direct search algorithms [19,20], in which SLM pixel values are sequentially altered with only changes reducing the cost function being retained, are limited to just a few phase levels due to computational intensity, and as such work well for simple targets but struggle to reproduce more intricate patterns.…”

Section: Introductionmentioning

confidence: 99%

Conjugate gradient minimisation approach to generating holographic traps for ultracold atoms

Harte¹,

Bruce²,

Keeling³

et al. 2014

Opt. Express

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Direct minimisation of a cost function can in principle provide a versatile and highly controllable route to computational hologram generation. However, to date iterative Fourier transform algorithms have been predominantly used. Here we show that the careful design of cost functions, combined with numerically efficient conjugate gradient minimisation, establishes a practical method for the generation of holograms for a wide range of target light distributions. This results in a guided optimisation process, with a crucial advantage illustrated by the ability to circumvent optical vortex formation during hologram calculation. We demonstrate the implementation of the conjugate gradient method for both discrete and continuous intensity distributions and discuss its applicability to optical trapping of ultracold atoms. References and links1. I. Bloch, J. Dalibard, and S. Nascimbene, "Quantum simulations with ultracold quantum gases," Nat Phys 8, 267-276 (2012). 2. A. D. Cronin, J. Schmiedmayer, and D. E. Pritchard, "Optics and interferometry with atoms and molecules," Rev.

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Section: Introductionmentioning

confidence: 99%

Conjugate gradient minimisation approach to generating holographic traps for ultracold atoms

Harte¹,

Bruce²,

Keeling³

et al. 2014

Opt. Express

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“…It is also possible to use a different algorithm altogether. The DS algorithm could, for example, be extended to become a simulated-annealing algorithm (see [18] for an explanation and comparison of different algorithms applied to traveling-wave intensity shaping), which is better at finding the global maximum of the quality function (DS often only finds a local maximum).…”

Section: Discussionmentioning

confidence: 99%

Simulated holographic three-dimensional intensity shaping of evanescent-wave fields

et al. 2008

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Thomson, L.C., Whyte, G., Mazilu, M., and Courtial, J. (2008 The size of bright structures in traveling-wave light fields is limited by diffraction. This in turn limits a number of technologies, for example, optical trapping. One way to beat the diffraction limit is to use evanescent waves instead of traveling waves. Here we apply a holographic algorithm, direct search, to the shaping of complex evanescent-wave fields. We simulate three-dimensional intensity shaping of evanescent-wave fields using this approach, and we investigate some of its limitations.

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“…A widely used family of algorithms for phase sensitive replay fields are the holographic search algorithms (HSAs), of which the most famous is perhaps direct search (DS). [14][15][16][17][18][19] Broadly speaking, these algorithms proceed by changing a pixel value and evaluating whether the error metric has improved. If the error metric has improved the pixel change is adopted, else the pixel change is rejected.…”

Section: Established Holographic Search Algorithmsmentioning

confidence: 99%

Linear time algorithm for phase sensitive holography

Christopher¹,

Mouthaan²,

Guendy³

et al. 2020

Preprint

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Holographic search algorithms such as direct search and simulated annealing allow high-quality holograms to be generated at the expense of long execution times. This is due to single iteration computational costs of O(N x N y ) and number of required iterations of order O(N x N y ), where N x and N y are the image dimensions. This gives a combined performance of order O(N 2x N 2 y ). In this paper we use a novel technique to reduce the iteration cost down to O(1) for phase-sensitive computer generated holograms giving a final algorithmic performance of O(N x N y ). We do this by reformulating the mean-squared error metric to allow it to be calculated from the diffraction field rather than requiring a forward transform step. For a 1024 × 1024 pixel test images this gave us a ≈ 50, 000× speed-up when compared with traditional direct search with little additional complexity.When applied to phase-modulating or amplitude-modulating devices the proposed algorithm converges on a global minimum mean squared error in O(N x N y ) time. By comparison, most extant algorithms do not guarantee a global minimum is obtained and those that do have a computational complexity of at least O(N 2x N 2 y ) with the naive algorithm being O((N x N y )!).

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A direct-search method for the computer design of holograms

Cited by 26 publications

References 12 publications

Conjugate gradient minimisation approach to generating holographic traps for ultracold atoms

Conjugate gradient minimisation approach to generating holographic traps for ultracold atoms

Simulated holographic three-dimensional intensity shaping of evanescent-wave fields

Linear time algorithm for phase sensitive holography

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