Enhanced depth resolution in optical scanning holography using a configurable pupil

Haiyan Ou; Ting-Chung Poon; Kenneth K. Y. Wong; and Edmund Y. Lam

doi:10.1364/PRJ.2.000064

Journals >Photonics Research >Volume 2 >Issue 2 >Page 64 > Article

Photonics Research
Vol. 2, Issue 2, 64 (2014)

Enhanced depth resolution in optical scanning holography using a configurable pupil

Haiyan Ou^1、2, Ting-Chung Poon³, Kenneth K. Y. Wong¹, and and Edmund Y. Lam^1、*

Author Affiliations

¹Department of Electrical and Electronic Engineering, University of Hong Kong, Pokfulam, Hong Kong, China

²Institute of Applied Physics, University of Electronic Science and Technology of China, 610054, Chengdu, China

³Bradley Department of Electrical and Computer Engineering, Virginia Tech, Blacksburg, Virginia 24061, USA

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DOI: 10.1364/PRJ.2.000064 Cite this Article Set citation alerts

Haiyan Ou, Ting-Chung Poon, Kenneth K. Y. Wong, and Edmund Y. Lam. Enhanced depth resolution in optical scanning holography using a configurable pupil[J]. Photonics Research, 2014, 2(2): 64 Copy Citation Text

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Abstract

The optical scanning holography (OSH) technique can capture all the three-dimensional volume information of an object in a hologram via a single raster scan. The digital hologram can then be processed to reconstruct individual sectional images of the object. In this paper, we present a scheme to reconstruct sectional images in OSH with enhanced depth resolution, where a spatial light modulator (SLM) is adopted as a configurable point pupil. By switching the SLM between two states, different Fresnel zone plates (FZPs) are generated based on the same optical system. With extra information provided by different FZPs, a depth resolution at 0.7 μm can be achieved.

Keywords

Computational imaging Digital holography Image reconstructionrestoration Inverse problems

H (k_{x}, k_{y}; z) = \exp [j \frac{z}{2 k_{0}} (k_{x}^{2} + k_{y}^{2})] \times \iint_{- \infty}^{\infty} p_{1}^{*} (x^{'}, y^{'}) p_{2} (x^{'} + \frac{f}{k_{0}} k_{x}, y^{'} + \frac{f}{k_{0}} k_{y}) \times \exp [j \frac{z}{f} (x^{'} k_{x} + y^{'} k_{y})] d x^{'} d y^{'},

(1)

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h_{1} (x, y; z) = j \frac{1}{λ z} \exp {j \frac{π}{λ z} (x^{2} + y^{2})},

(2)

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g_{1} (x, y) = \sum_{i = 1}^{n} φ (x, y; z_{i}) * h_{1} (x, y; z_{i}),

(3)

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H_{2} (k_{x}, k_{y}; z) = \exp [j \frac{z}{2 k_{0}} (k_{x}^{2} + k_{y}^{2})] \times \iint_{- \infty}^{\infty} δ [(x^{'} - x_{0}) + \frac{f}{k_{0}} k_{x}, (y^{'} - y_{0}) + \frac{f}{k_{0}} k_{y}] \times \exp [j \frac{z}{f} (x^{'} k_{x} + y^{'} k_{y})] d x^{'} d y^{'},

(4)

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h_{2} (x, y; z) = j \frac{1}{λ z} \exp {j \frac{π}{λ z} [{(x - x_{0})}^{2} + {(y - y_{0})}^{2}]},

(5)

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g_{2} (x, y) = \sum_{i = 1}^{n} φ (x, y; z_{i}) * h_{2} (x, y; z_{i}) .

(6)

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g = [\begin{matrix} g_{1} \\ g_{2} \end{matrix}] = [\begin{matrix} H_{1} (z_{1}) & H_{1} (z_{2}) & \dots & H_{1} (z_{n}) \\ H_{2} (z_{1}) & H_{2} (z_{2}) & \dots & H_{2} (z_{n}) \end{matrix}] [\begin{matrix} φ_{1} \\ φ_{2} \\ ⋮ \\ φ_{n} \end{matrix}] + [\begin{matrix} ϵ_{1} \\ ϵ_{2} \\ ⋮ \\ ϵ_{n} \end{matrix}] = [\begin{matrix} H_{1} \\ H_{2} \end{matrix}] φ + ϵ = H φ + ϵ,

(7)

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φ_{est} = \arg \min_{φ} {‖ H φ - g ‖}_{2}^{2} + λ {‖ C φ ‖}_{2}^{2},

(8)

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(H^{+} H + λ C^{+} C) φ_{est} = H^{+} g,

(9)

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N = \sum_{x = 1}^{N} \sum_{y = 1}^{M} \frac{\sum_{i = 1}^{N} \sum_{j = 1}^{M} H_{1} (x + i, y + j) \cdot H_{2} (i, j)}{\sqrt{\sum_{i = 1}^{N} \sum_{j = 1}^{M} H_{1} {(x + i, y + j)}^{2}} \cdot \sqrt{\sum_{i = 1}^{N} \sum_{j = 1}^{M} H_{2} {(i, j)}^{2}}} .

(10)

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Haiyan Ou, Ting-Chung Poon, Kenneth K. Y. Wong, and Edmund Y. Lam. Enhanced depth resolution in optical scanning holography using a configurable pupil[J]. Photonics Research, 2014, 2(2): 64

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