Full-color holographic 3D display using slice-based fractional Fourier transform combined with free-space Fresnel diffraction: erratum

Zhen Zhang; Siqing Chen; Huadong Zheng; Zhenxiang Zeng; Hongyue Gao; Yingjie Yu; Anand K. Asundi

doi:10.1364/AO.56.007656

Abstract

We have addressed some errors in our recent work [Appl. Opt. 56, 5668 (2017) [CrossRef] ]. Especially, we note that the formulae for reconstruction of phase-only holograms are different from the formulae for amplitude holograms. So Eqs. (9) and (12) must be modified.

We would draw attentions to some errors in our recent paper [1].

1. The symbol “j” should be added to Eq. (9), and the modified equation is $G_{t} (x, y) = \frac{\exp (j k z)}{j λ z} \iint \exp [j H_{t} (u, v)] \exp [\frac{j k}{2 z} (x^{2} + y^{2} + u^{2} + v^{2}) - \frac{j 2 π}{λ z} (x u + y v)] d u d v .$
2. Eq. (12) is not correct, and it should be modified as $G_{t, i} (x^{'}, y^{'}) = \iint \exp [j H_{t} (u, v)] \exp {j π \frac{u^{2} + v^{2} + {[x^{'} / \cos (p_{i}^{'} π / 2)]}^{2} + {[y^{'} / \cos (p_{i}^{'} π / 2)]}^{2}}{λ f_{e} \tan (p_{i}^{'} π / 2)} - j 2 π \frac{(x^{'} u + y^{'} v)}{λ f_{e} \sin (p_{i}^{'} π / 2)}} d u d v .$
3. Reference citation “[10,-12]” in the first paragraph of introduction should be “[10–12]”.
4. The font type of symbols “j” and “ $π$ ” in Eq. (6) should be non-italic.

REFERENCE

1. Z. Zhang, S. Chen, H. Zheng, Z. Zeng, H. Gao, Y. Yu, and A. K. Asundi, “Full-color holographic 3D display using slice-based fractional Fourier transform combined with free-space Fresnel diffraction,” Appl. Opt. 56, 5668–5675 (2017). [CrossRef]

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G_{t} (x, y) = \frac{\exp (j k z)}{j λ z} \iint \exp [j H_{t} (u, v)] \exp [\frac{j k}{2 z} (x^{2} + y^{2} + u^{2} + v^{2}) - \frac{j 2 π}{λ z} (x u + y v)] d u d v .

G_{t, i} (x^{'}, y^{'}) = \iint \exp [j H_{t} (u, v)] \exp {j π \frac{u^{2} + v^{2} + {[x^{'} / \cos (p_{i}^{'} π / 2)]}^{2} + {[y^{'} / \cos (p_{i}^{'} π / 2)]}^{2}}{λ f_{e} \tan (p_{i}^{'} π / 2)} - j 2 π \frac{(x^{'} u + y^{'} v)}{λ f_{e} \sin (p_{i}^{'} π / 2)}} d u d v .

Abstract

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Applied Optics