X-ray Spot Localization Method Based on Dual Gratings

$Schematic diagram of dual-grating positioning system. (a) Optical layout of the system; (b) simulated diffraction pattern; (c) front view of dual-grating structure$

Fig. 1. Schematic diagram of dual-grating positioning system. (a) Optical layout of the system; (b) simulated diffraction pattern; (c) front view of dual-grating structure

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$Diffraction patterns with different photon counts. (a) 104; (b) 105; (c) 106; (d) 107$

Fig. 2. Diffraction patterns with different photon counts. (a) 10⁴; (b) 10⁵; (c) 10⁶; (d) 10⁷

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Fig. 3. Relationship curves between spot position and relative light intensity in different areas. (a) $I_{Σ_{1}}$ ; (b) $I_{Σ_{2}}$ ; (c) $I_{Σ_{3}}$ ; (d) $I_{Σ_{i}}$ in the plane with $Δ y = 0$

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Fig. 4. Probability density histograms of positioning accuracy. (a) $x$ direction; (b) $y$ direction

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Fig. 5. Logarithmic curves of positioning accuracy versus photon counts

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$Diffraction patterns on the detector at different spot positions. (a) (50 μm, 50 μm); (b) (-50 μm, -50 μm); (c) (50 μm, -50 μm); (d) (-50 μm, 50 μm); (e) (50 μm, 0 μm); (f) (0 μm, 50 μm)$

Fig. 6. Diffraction patterns on the detector at different spot positions. (a) (50 μm, 50 μm); (b) (-50 μm, -50 μm); (c) (50 μm, -50 μm); (d) (-50 μm, 50 μm); (e) (50 μm, 0 μm); (f) (0 μm, 50 μm)

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Fig. 7. Positioning accuracy when the spot moves to different positions. (a) $3 σ_{x}$ ; (b) $3 σ_{y}$ ; (c) $3 σ$ in the plane of $Δ x = Δ y$

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Fig. 8. Error analysis of grating machining defects. (a) Periodic error; (b) sidewall roughness

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Table 1. Positioning accuracy with multi-point sampling methods when the number of photons is 10⁵

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Table 1. Positioning accuracy with multi-point sampling methods when the number of photons is 10⁵

Initial coordinate	Number of sampled points	Sampling interval /μm	3σ_x /μm	3σ_y /μm
(0 μm, 0 μm)	1		1.60	1.53
(0 μm, 0 μm)	2	10	0.90	1.03
(0 μm, 0 μm)	3	10	0.83	0.72
(0 μm, 0 μm)	4	10	0.58	0.54
(0 μm, 0 μm)	5	10	0.50	0.49

Table 2. Comparison of different spot positioning methods

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Table 2. Comparison of different spot positioning methods

Method	Advantage	Disadvantage
Knife edge^[14]	High precision	Multiple blade scans required
BPM^[17-18]	High precision	Complex equipment
High-precision imaging^[12]	Easy to implement	Additional detectors required
Shelter coverage^[19]	Simple step	Low precision
Proposed method: dual-grating	Single exposure, easy to integrate, high localization efficiency	Grating fabrication required

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Guopeng Zhou, Zhijie Tan, Hong Yu. X-ray Spot Localization Method Based on Dual Gratings[J]. Acta Optica Sinica, 2025, 45(11): 1134001

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Paper Information

Category: X-Ray Optics

Received: Mar. 5, 2025

Accepted: Apr. 13, 2025

Published Online: Jun. 24, 2025

The Author Email: Zhijie Tan (tanzj@siom.ac.cn)

DOI:10.3788/AOS250694

CSTR:32393.14.AOS250694

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Positioning accuracy with multi-point sampling methods when the number of photons is 105

Table 1. Positioning accuracy with multi-point sampling methods when the number of photons is 105

Table 2. Comparison of different spot positioning methods

Table 2. Comparison of different spot positioning methods

Table 1. Positioning accuracy with multi-point sampling methods when the number of photons is 10⁵

Table 1. Positioning accuracy with multi-point sampling methods when the number of photons is 10⁵