Journal of the Korea Institute of Information and Communication Engineering (한국정보통신학회논문지)

The Korea Institute of Information and Commucation Engineering (한국정보통신학회)
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Design of Fresnelet Transform based on Wavelet function for Efficient Analysis of Digital Hologram

디지털 홀로그램의 효율적인 분해를 위한 웨이블릿 함수 기반 프레넬릿 변환의 설계

  • Seo, Young-Ho (Department of Electronic Material Engineering, Kwangwoon University) ;
  • Kim, Jin-Kyum (Department of Electronic Material Engineering, Kwangwoon University) ;
  • Kim, Dong-Wook (Department of Electronic Material Engineering, Kwangwoon University)
  • Received : 2018.12.30
  • Accepted : 2019.02.18
  • Published : 2019.03.31
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Abstract

In this paper, we propose a Fresnel transform method using various wavelet functions to efficiently decompose digital holograms. After implementing the proposed wavelet function-based Fresnelet transforms, we apply it to the digital hologram and analyze the energy characteristics of the coefficients. The implemented wavelet transform-based Fresnelet transform is well suited for reconstructing and processing holograms which are optically obtained or generated by computer-generated hologram technique. After analyzing the characteristics of the spline function, we discuss wavelet multiresolution analysis method based on it. Through this process, we proposed a transform tool that can effectively decompose fringe patterns generated by optical interference phenomena. We implement Fresnelet transform based on wavelet function with various decomposition properties and show the results of decomposing fringe pattern using it. The results show that the energy distribution of the coefficients is significantly different depending on whether the random phase is included or not.

본 논문에서는 디지털 홀로그램을 효율적으로 분해하기 위해서 다양한 웨이블릿 함수들을 이용한 프레넬릿 변환 방식을 제안하였다. 제안한 웨이블릿 함수 기반의 프레넬릿 변환들을 구현한 후에 디지털 홀로그램에 적용하고 계수들의 에너지에 대한 특성을 분석한다. 구현한 웨이블릿 함수 기반의 프레넬릿 변환은 광학적으로 획득되거나 혹은 컴퓨터 생성 홀로그램 기법으로 생성된 홀로그램의 복원과 처리에 매우 적합하다. 스플라인 함수의 특성을 분석한 이후에 이를 기반으로 하는 웨이블릿 다해상도 해석 방법에 대해서 살펴본다. 이러한 과정을 통해 광학적 간섭 현상을 통해 생성된 프린지 패턴을 효과적으로 분해할 수 있는 변환 도구를 제안하였다. 다양한 분해 특성을 갖는 웨이블릿 함수기반의 프레넬릿 변환을 구현하였고 이를 이용하여 프린지 패턴을 분해한 결과들을 보인다. 결과를 살펴보면 랜덤 위상의 포함여부에 따라 계수들의 에너지 분포가 크게 다르다는 것을 확인할 수 있다.

Keywords

HOJBC0_2019_v23n3_291_f0001.png 이미지

Fig. 1 Digital hologram (a) recoding (b) reconstruction

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Fig. 2 Test images (a) luminance, (b) depth, (c) fringe pattern, (d) S/W reconstruction, (e) optical reconstruction

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Fig. 3 Wavelet functions (a) (3/1), (b) (5/5), and (c) (6/8) filter

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Fig. 4 Hologram result by Frenelet transform in the case of using (a) (3/1), (b) (5/5), (c) (6/8) filters, (d) reconstruction result

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Fig. 5 Dataset of JPEG Pleno (a) 3D Multi, (b) 3D Dices

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Fig. 6 Fresnelet transform result (real and imaginary parts) in case of (a) 3D Multi decomposed by bi-orthogonal (1,1) filter, (b) 3D Dices decomposed by bi-orthogonal (1,1) filter, (c) 3D Multi decomposed by reverse bi-orthogonal (3,3) filter, (d) 3D Dices decomposed by reverse bi-orthogonal (3,3) filter

HOJBC0_2019_v23n3_291_f0007.png 이미지

Fig. 7 Average energy of subbands in the Fresnelet domain (average of real and imaginary parts) in case of (a) 3D Multi decomposed by bi-orthogonal (1,1) filter, (b) 3D Dices decomposed by bi-orthogonal (1,1) filter, (c) 3D Multi decomposed by reverse bi-orthogonal (3,3) filter, (d) 3D Dices decomposed by reverse bi-orthogonal (3,3) filter

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