Integrating multiple images in a sampled phase-only hologram

P. W. M. Tsang; T.-C. Poon; W. Wang; X. Zhu; K. Chan

doi:10.3788/COL201917.050901

Journals >Chinese Optics Letters >Volume 17 >Issue 5 >Page 050901 > Article

Chinese Optics Letters
Vol. 17, Issue 5, 050901 (2019)

Integrating multiple images in a sampled phase-only hologram

P. W. M. Tsang^1、*, T.-C. Poon², W. Wang³, X. Zhu³, and K. Chan³

Author Affiliations

¹Department of Electronic Engineering, City University of Hong Kong, Hong Kong SAR, China

²Bradley Department of Electrical and Computer Engineering, Virginia Tech, Blacksburg, Virginia 24061, USA

³Hong Kong Applied Science and Technology Research Institute Company Limited, Hong Kong SAR, China

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DOI: 10.3788/COL201917.050901 Cite this Article Set citation alerts

P. W. M. Tsang, T.-C. Poon, W. Wang, X. Zhu, K. Chan. Integrating multiple images in a sampled phase-only hologram[J]. Chinese Optics Letters, 2019, 17(5): 050901 Copy Citation Text

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Abstract

Past research has demonstrated that a sampled phase-only hologram (SPOH) is capable of representing an image without the magnitude component of the hologram. At present, an SPOH can only record and reconstruct a single source image. In this Letter, we propose, for the first time, to the best of our knowledge, a method for representing multiple images with a single integrated SPOH (ISPOH). Subsequently, each image can be retrieved from the ISPOH with a unique key parameter and displayed as a visible image on a phase-only spatial light modulator.

{I_{j} (m, n) |}_{0 \leq j < P} = S_{j} (m, n) \times L (m, n) .

(1)

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L (m, n) = {\begin{cases} 1 & (p = 0) \lor (q = 0) \lor (p = q) \lor [p = (τ - 1) - q] \\ 0 & otherwise \end{cases},

(2)

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H_{j} (m, n) = I_{j} (m, n) * f (m, n; z_{0}),

(3)

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[\begin{matrix} m_{k + 1} \\ n_{k + 1} \end{matrix}] = [\begin{matrix} 1 & a \\ b & a b + 1 \end{matrix}] [\begin{matrix} m_{k} \\ n_{k} \end{matrix}] % N = A [\begin{matrix} m_{k} \\ n_{k} \end{matrix}] % N,

(4)

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[\begin{matrix} m_{k} \\ n_{k} \end{matrix}] = [\begin{matrix} a b + 1 & - a \\ - b & 1 \end{matrix}] [\begin{matrix} m_{k + 1} \\ n_{k + 1} \end{matrix}] % N .

(5)

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H_{ph} (m, n) = \arg [\sum_{j = 0}^{P - 1} H_{j}^{e_{j}} (m_{e_{j}}, n_{e_{j}})],

(6)

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G_{e_{j}}^{a} (m, n) = G_{e_{j}} (m, n) \times \exp (i 2 π n λ^{- 1} \sin θ_{r}) .

(7)

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{\tilde{I}}_{j} (m, n) = G_{e_{j}}^{a} (m, n) * conj [f (m, n; z_{0})],

(8)

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P. W. M. Tsang, T.-C. Poon, W. Wang, X. Zhu, K. Chan. Integrating multiple images in a sampled phase-only hologram[J]. Chinese Optics Letters, 2019, 17(5): 050901

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