• Korean Journal of Optics and Photonics
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• v.9 no.6
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• pp.390-395
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• 1998

Iterative Fourier transform algorithm (IFTA) was utilized for the phase retrieval problem or the optimal of the IFTA depends strongly on the selection of initial phase value. In this paper, we proposed the modified interactive Fourier transform algorithm in order to improve the convergence speed of error and the stability of convergence. The modified IFTA was reduced number of iteration about 30% than existing IFTA with the image size of 128$\times$128 pixel.

• Korean Journal of Optics and Photonics
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• v.11 no.1
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• pp.47-57
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• 2000

A two-stage iterative Fourier transform algorithm, based on hybrid input-output algorithm and new Pnoise algorithm, is used to design continuous and quantized phase-only diffractive pattern elements which produce arbitrary given intensity patterns via Fraunhofer diffraction. Numerical results for two $128\times128$ binary patterns and two grayscale patterns are compared with those of other algorithms. It is found that the algorithm yields better signal-to-noise ratio and even better uniformity with slightly lower diffraction efficiency than other algorithms. We investigated the dependence of performance on parameters used in the algorithm, size of noise region, and the number of phase levels for quantized elements. In the case of quantized phase elements, the size of noise region plays a greater role in determining the performance of the algorithm than given intensity pattern itself. tself.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.46 no.3
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• pp.60-67
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• 2009

The phase retrieval problem is a problem of reconstructing a signal or the phase of Fourier transform of the signal from the magnitude of its Fourier transform. In this paper we address the problem of reconstructing an unknown signal from the magnitude of its Fourier transform and the magnitude of Fourier transform of another signal that is given by the addition of the desired signal. After we briefly mention the uniqueness conditions under which a signal can be uniquely specified from the given information and key equations of the iterative algorithm, we present mathematical background that the iterative algorithm converges to the desired signal, present an example that illustrates the performance of the reconstruction algorithm, and show its convergence property.

• Proceedings of the Optical Society of Korea Conference
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• 2001.08a
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• pp.80-81
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• 2001

• Proceedings of the Optical Society of Korea Conference
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• 2000.02a
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• pp.296-297
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• 2000

프라운호퍼 회절에 의하여 주어진 세기 무늬를 발생시키는 회절광학소자(Diffractive Optical Element, DOE)는 회절무늬소자, 키노폼(kinoform), 컴퓨터 푸리에 홀로그램 (computer-generated Fourier hologram) 등으로 불리우며, 광정보처리, 광연결, 레이저가공에서 중요한 역할을 한다. 이 소자를 설계하는 매우 다양한 방법들이 제안되었는데, iterative Fourier transform 알고리즘(IFTA)과 이를 변형한 알고리즘들이 가장 널리 사용된다. IFTA는 fast Fourier transform(FFT)를 활용하므로 계산시간이 절감되지만 국소 최소점에 고착되는 stagnation문제가 있어 이를 해결하기 위한 많은 변형된 알고리즘들이 제안되었다. 본 연구에서는 최근에 제안한 new Pnoise algorithm with hybrid input-output algorithm(NPA-HIOA)$^{(1)}$ 의 설계 성능을 IFTA, hybrid input-output 알고리즘(HIOA), new Pnoise 알고리즘(NPA)$^{(2)}$ , Nonlinear Least-Square (NLS)$^{(3)}$ 등의 기존의 알고리즘들과 비교하고자 한다. (중략)

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.40 no.5
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• pp.298-311
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• 2003

Iterative Fourier transform algorithm, (IFTA) is tile iterative numerical algorithm for the design of the diffractive optical elements (DOE), by which the phase distribution of a DOE converges on a local optimal solution. The convergence of IFTA depends on several factors 3s initial phase distribution, the structure of the degree of freedom on the observation plane, and the values of internal parameters. In this paper, we analyze tile dependence of the convergence of IFTA on an internal parameter of IFTA, the relaxation parameter, and propose a new hybrid scheme of genetic algorithm and IFTA to obtain more accurate solution.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.31B no.5
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• pp.26-33
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• 1994

Phase retrieval is concerned with the reconstruction of a signal from its Fourier transform magnitude (or intensity), which arises in many areas such as X-ray crystallography, optics, astronomy, or digital signal processing. In such areas, the Fourier transform phase of the desired signal is lost while measuring Fourier transform magnitude (F.T.M.). However, if a reference 'signal is added to the desired signal, then, in the Fourier trans form magnitude of the added signal, the Fourier transform phase of the desired signal is encoded. This paper addresses uniqueness and retrieval of the encoded Fourier phase of a multidimensional signal from the Fourier transform magnitude of the added signal along with the Fourier transform magnitude of the desired signal and the information of the additive reference signal. In Part I, several conditions under which the desired signal can be uniquely specified from the two Fourier transform magnitudes and the additive reference signal are presented. In Part II, the development of non-iterative algorithms and an iterative algorithm that may be used to reconstruct the desired signal(s) is considered.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.31B no.5
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• pp.34-41
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• 1994

Phase retrieval is concerned with the reconstruction of a signal from its Fourier transform magnitude (or intensity), which arises in many areas such as X-ray crystallography, optics, astronomy, or digital signal processing In such areas, the Fourier transform phase of the desired signal is lost while measuring Fourier transform magnitude (F.T.M.). However, if a reference 'signal is added to the desired signal, then, in the Fourier trans form magnitude of the added signal, the Fourier transform phase of the desired signal is encoded This paper addresses uniqueness and retrieval of the encoded Fourier phase of a multidimensional signal from the Fourier transform magnitude of the added signal along with Fourier transform magnitude of the desired signal and the information of the additive reference signal In Part I, several conditions under which the desired signal can be uniquely specified from the two Fourier transform magnitudes and the additive reference signal are presented In Part II, the development of non-iterative algorithms and an iterative algorithm that may be used to reconstruct the desired signal (s) is considered

• Journal of the Optical Society of Korea
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• v.19 no.2
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• pp.149-153
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• 2015

A digital micro-mirror device (DMD) has the potential to modulate an incident wave with high speed, and the application for holographic display has been studied by many researchers. However, the quality of reconstructed image isn't good in comparison with that from a gray-scale amplitude-only hologram since it is a binary amplitude-only spatial light modulator (SLM). In this paper, we suggest a method generating a set of binary holograms to improve the quality of the reconstructed image. Here, we are concerned with the case for which the object plane is positioned at the Fourier domain of the plane of the SLM. In this case, any point in the Fourier plane is related to all points in the hologram. So there is a chance to generate a set of binary holograms illuminated by incident wave with constant optical power. Moreover, we find an interesting fact that the quality of reconstructed image is improved when the spatial frequency bandwidth of the binary hologram is limited. Therefore, we propose an iterative segmentation algorithm generating a set of binary holograms that are designed to be illuminated by the wave with constant optical power. The feasibility of our method is experimentally confirmed with a DMD.

• Journal of the Optical Society of Korea
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• v.5 no.3
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• pp.93-98
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• 2001

In order to verify the performance of the two-stage iterative Fourier transform algorithm[Hankook Kwanghak Hoeji 11, 47 (2000)], a number of phase-only diffractive pattern elements which produce simple 16x16-pixel intensity patterns useful in the field of optical information processing have been designed and their performance has been compared with that from the nonlinear least-squares algorithm[Appl. Opt. 36, 7297(1977)] which is computationally intensive. for all intensity patterns, elements designed by the former algorithm show better overall signal-to noise ratio and uniformity, although they show essentially the same diffraction efficiency. In the case of continuous phase elements, they show far superior uniformity. Computationally,. the former algorithm is far more efficient than the latter.