Detour phase Talbot array illuminator

Zhigang Li; Rui Yang; Meiyu Sun; Jing Han; Dengying Zhang; Jiannong Chen; Dawei Zhang; Linwei Zhu

doi:10.3788/COL201917.070501

Journals >Chinese Optics Letters >Volume 17 >Issue 7 >Page 070501 > Article

Chinese Optics Letters
Vol. 17, Issue 7, 070501 (2019)

Detour phase Talbot array illuminator

Zhigang Li¹, Rui Yang¹, Meiyu Sun¹, Jing Han¹, Dengying Zhang¹, Jiannong Chen¹, Dawei Zhang², and Linwei Zhu^1、*

Author Affiliations

¹School of Physics and Optoelectronic Engineering, Ludong University, Yantai 264025, China

²Engineering Research Center of Optical Instrument and System, Ministry of Education, Shanghai Key Laboratory of Modern Optical System, School of Optical-Electrical and Computer Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China

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DOI: 10.3788/COL201917.070501 Cite this Article Set citation alerts

Zhigang Li, Rui Yang, Meiyu Sun, Jing Han, Dengying Zhang, Jiannong Chen, Dawei Zhang, Linwei Zhu. Detour phase Talbot array illuminator[J]. Chinese Optics Letters, 2019, 17(7): 070501 Copy Citation Text

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Abstract

In this Letter, we propose a simple and effective approach for transforming a conventional Talbot array illuminator (TAI) with multilevel phase steps into a binary-phase TAI (BP-TAI) through detour phase encoding. The BP-TAI is a binary (0

π

) phase-only diffractive optical element, which can be utilized to generate a large-scale focal spots array with a high compression ratio. As an example, we design a square BP-TAI with the fraction parameter

β

= 15 for achieving a square multifocal lattice with a high compression ratio

β

². Theoretical analysis and experimental results demonstrate that the detour phase encoding is efficient for designing the BP-TAI, especially with the high compression ratio. Such results may be exploited in practical large-scale optical trapping and X-ray imaging.

φ (m, n, β) = {\begin{cases} (1 - 1 / β) (m^{2} + n^{2}) π, & β = 4 L - 2 \\ (- 1 / β) (m^{2} + n^{2}) π, & β = 4 L \\ (- 1 - 1 / β) (m^{2} + n^{2}) π / 2, & β = 4 L - 1 \\ (1 - 1 / β) (m^{2} + n^{2}) π / 2, & β = 4 L + 1 \end{cases},

(1)

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u (x, y) = rect (\frac{x}{w}, \frac{y}{w}) \times {u_{0} (x, y) \otimes \sum_{m = 0}^{β - 1} \sum_{n = 0}^{β - 1} δ (x - m Δ, y - n Δ) \exp [i φ (m, n, β)]},

(2)

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U (x, y) = u (x, y) \otimes \sum_{M_{0} = 1}^{M} \sum_{N_{0} = 1}^{N} δ (x - M_{0} w, y - N_{0} w),

(3)

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δ_{m n} = \frac{φ (m, n, β)}{2 π} Δ,

(4)

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u_{m n} (x, y) = u_{0} (x, y) - 2 \times rect (\frac{x - δ_{m n}}{Δ / 2}, \frac{y}{Δ}),

(5)

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u (x, y) = rect (\frac{x}{w}, \frac{y}{w}) \times [\sum_{m = 0}^{β - 1} \sum_{n = 0}^{β - 1} u_{m n} (x, y) \otimes δ (x - m Δ, y - n Δ)] .

(6)

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Zhigang Li, Rui Yang, Meiyu Sun, Jing Han, Dengying Zhang, Jiannong Chen, Dawei Zhang, Linwei Zhu. Detour phase Talbot array illuminator[J]. Chinese Optics Letters, 2019, 17(7): 070501

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