Resolution enhancement of optical scanning holography with a spiral modulated point spread function

Ni Chen; Zhenbo Ren; Haiyan Ou; Edmund Y. Lam

doi:10.1364/prj.4.000001

Journals >Photonics Research >Volume 4 >Issue 1 >Page 0001 > Article

Photonics Research
Vol. 4, Issue 1, 0001 (2016)

Resolution enhancement of optical scanning holography with a spiral modulated point spread function

Ni Chen¹, Zhenbo Ren¹, Haiyan Ou², and Edmund Y. Lam^1,*

Author Affiliations

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

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

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DOI: 10.1364/prj.4.000001 Cite this Article Set citation alerts

Ni Chen, Zhenbo Ren, Haiyan Ou, Edmund Y. Lam, "Resolution enhancement of optical scanning holography with a spiral modulated point spread function," Photonics Res. 4, 0001 (2016) Copy Citation Text

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Abstract

In optical scanning holography, one pupil produces a spherical wave and another produces a plane wave. They interfere with each other and result in a fringe pattern for scanning a three-dimensional object. The resolution of the hologram reconstruction is affected by the point spread function (PSF) of the optical system. In this paper, we modulate the PSF by a spiral phase plate, which significantly enhances the lateral and depth resolution. We explain the theory for such resolution enhancement and show simulation results to verify the efficacy of the approach.

Keywords

Computational imaging Digital holography Optical transfer functions

t (r, θ) = circ (\frac{r}{R}) \exp (- j θ),

(1)

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p_{2} (ρ, φ) = \frac{k π R}{2 f ρ} \exp [j (φ + \frac{π}{2})] [H_{0} (ξ) J_{1} (ξ) - H_{1} (ξ) J_{0} (ξ)],

(2)

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H (ρ, φ; z) = \exp [j \frac{z}{2 k} ρ^{2}] \int_{0}^{2 π} \int_{0}^{\infty} p_{1}^{*} (r^{'}) p_{2} (r^{'} + r) \times \exp [j \frac{z}{f} r^{'} ρ \cos (θ - φ)] d r^{'} d θ .

(3)

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H (ρ, φ; z) = \exp [j \frac{z}{2 k} ρ^{2}] \int_{0}^{2 π} \int_{0}^{\infty} p_{2} (\frac{r^{'} + r}{R}) \times \exp [j \frac{z}{f} r^{'} ρ \cos (θ - φ)] d r^{'} d θ = \exp [- j \frac{z}{2 k} ρ^{2}] I {p_{2}^{*} (r, θ)},

(4)

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h (r, θ; z) = I^{- 1} {\exp [- j \frac{z}{2 k} ρ^{2}] I {p_{2}^{*} (r, θ)}} = {- \frac{k}{2 π z} \exp [j \frac{k}{2 z} r^{2}]} {π^{2} r {(\frac{k}{2 π z})}^{\frac{1}{2}} \exp [j (θ - \frac{π}{4})] [J_{0} (\frac{k r^{2}}{2 z}) - j J_{1} (\frac{k r^{2}}{2 z})]} circ (\frac{r f}{z R}),

(5)

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\begin{matrix} g (x, y; z) = \int_{- \infty}^{\infty} O (x, y; z) * h (x, y; z) d z, \end{matrix}

(6)

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O (x, y; z) = \sum_{n = 1}^{N} O (x, y; z_{n}),

(7)

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g (x, y; z) = \sum_{n = 1}^{N} O (x, y; z_{n}) * h (x, y; z_{n}) .

(8)

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Ni Chen, Zhenbo Ren, Haiyan Ou, Edmund Y. Lam, "Resolution enhancement of optical scanning holography with a spiral modulated point spread function," Photonics Res. 4, 0001 (2016)

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