Study on High Precision Magnification Measurement of Imaging Systems

Guanji Dong; Feng Tang; Xiangzhao Wang; Peng Feng; Fudong Guo; Changzhe Peng

doi:10.3788/AOS201838.0712007

Acta Optica Sinica, Volume. 38, Issue 7, 0712007(2018)

Study on High Precision Magnification Measurement of Imaging Systems

Guanji Dong^1,2、*, Feng Tang^1,3, Xiangzhao Wang^1,2, Peng Feng¹, Fudong Guo¹, and Changzhe Peng^1,2

¹ Laboratory of Information Optics and Opto-Electronic Technology, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China

² University of Chinese Academy of Sciences, Beijing 100049, China

³ State Key Laboratory of Applied Optics, Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun, Jilin 130033, China

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Figures & Tables(17)

Fig. 1. Schematic of magnification measurement

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Fig. 2. Schematic diagram of object plane fibers spacing measurement system

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Fig. 3. Mathematical model of fiber spacing measurement

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Fig. 4. Wavefront and its Zernike coefficient obtained from ideal and non-ideal conditions. (a) Ideal wavefront; (b) ideal wavefront (without tilt); (c) Zernike coefficient of ideal wavefront; (d) non-ideal wavefront; (e) non-ideal wavefront (without tilt); (f) Zernike coefficient of non-ideal wavefront

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Fig. 5. Quantitative relationship among point source separation distance, spatial location parameter of the CCD camera, and the Zernike polynomial coefficient. (a) Quantitative relationship between point source spacing and Z2 term coefficient; (b) quantitative relationship between vertical distance and Z7 term coefficient; (c) quantitative relationship between CCD rotation angle and Z2 term coefficient; (d) quantitative relationship between CCD rotation angle and Z3 term coefficient; (e) quantitative re

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Fig. 6. Flow chart of fiber spacing measurement algorithm

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Fig. 7. Schematic diagram of image plane fibers’ imaging points separation distance measurement system

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Fig. 8. Spot center recognition results. (a),(b) Object location results; (c),(d) image location results

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Fig. 9. Experimental wavefront and its Zernike coefficient values. (a) Object plane wavefront; (b) object plane wavefront (without tilt term); (c) Zernike coefficient of object plane wavefront; (d) image plane wavefront; (e) image plane wavefront (without tilt term); (f) Zernike coefficient of image plane wavefront

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Fig. 10. Measurement repeatability of Zernike polynomial coefficient. (a) Object plane measurement result; (b) image plane measurement result

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Table 1. Error requirement of fiber spacing measurement
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Table 1. Error requirement of fiber spacing measurement
Magnification measurement error /10^-6 Fiber separation distance measurement error /nm
1 0.0620
5 1.5509
10 6.2035

Table 2. Settings of simulation conditions

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Table 2. Settings of simulation conditions

Simulation parameter	Ideal condition	Non-ideal condition
Light source wavelength λ /nm	532	532
Interference region produced by fiber /(pixel×pixel)	400×400	400×400
Pixel size /μm	9.9×9.9	9.9×9.9
d /μm	254	254
z /mm	32.941	32.941
θ /(°)	0	3
γ_x /(°)	0	2
γ_y /(°)	0	1

Table 3. Initial parameter setting of iterative calculation

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Table 3. Initial parameter setting of iterative calculation

Initial parameter setting of iterative calculation	Setting value
d	Estimating rough value d₀ according to the position of fiber end
z	Using the tool to measure the rough value z₀
θ	Calculation according to the formula:θ=tan^-1(-Z₀₃/Z₀₂)
γ_x	Setting to 0°
γ_y	Setting to 0°

Table 4. Quantitative relationship among two fibers separation distance, spatial position parameters of the CCD camera, and the Zernike polynomial coefficient, and its calculation formula

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Table 4. Quantitative relationship among two fibers separation distance, spatial position parameters of the CCD camera, and the Zernike polynomial coefficient, and its calculation formula

Parameter	Term of Zernike polynomial	Quantitative relationship type	Calculation formula
d	Z₂	Linear relationship	d_cal=d_cur+(Z₀₂-Z_2cur)/ $\begin{matrix} \frac{\partial Z_{2}}{\partial d} \end{matrix}$
z	Z₇	Linear relationship	z_cal=z_cur+(Z₀₇-Z_7cur)/ $\begin{matrix} \frac{\partial Z_{7}}{\partial z} \end{matrix}$
θ	Z₂	Cosine relationship	θ_cal=θ_cur+(Z₀₃-Z_3cur)/ $\begin{matrix} \frac{\partial Z_{3}}{\partial θ} \end{matrix}$
	Z₃	Sine relationship
γ_x	Z₄	Linear relationship
	Z₆	Linear relationship	$\begin{matrix} \{\begin{matrix} γ_{xcal} = γ_{xcur} + (Z_{04} - Z_{4 cur}) / \frac{\partial Z_{4}}{\partial γ_{x}} \\ γ_{ycal} = γ_{ycur} + (Z_{06} - γ_{xcal} \times \frac{\partial Z_{6}}{\partial γ_{x}} - Z_{6 cur}) / \frac{\partial Z_{6}}{\partial γ_{y}} \end{matrix} \end{matrix}$
γ_y	Z₄	Uncorrelated
	Z₆	Linear relationship

Table 5. Simulation results of the effectiveness of the method for measuring the separation distance between two fibers
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Table 5. Simulation results of the effectiveness of the method for measuring the separation distance between two fibers
Average value Standard deviation Maximum value Minimum value
Number of iterations 14.6000 0.4900 15.0000 14.0000
Measurement error of fiber separation distance /nm 0.5500 0.9337 5.0000 0

Table 6. Iterative calculation results of object plane separation distance between fibers

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Table 6. Iterative calculation results of object plane separation distance between fibers

Parameter	Initial value	1	2	3	…	10	11
d /μm	297.000	315.307	272.399	267.318	…	264.818	264.817
z /μm	30000.000	25877.260	25380.070	25219.260	…	25140.380	25140.350
θ /(°)	2.231	1.925	2.188	2.217	…	2.231	2.231
γ_x /(°)	0	-3.050	-3.411	-3.433	…	-3.444	-3.444
γ_y /(°)	0	0.015	-0.015	-0.018	…	-0.020	-0.020

Table 7. Iterative calculation results of image plane separation distance between fiber image points

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Table 7. Iterative calculation results of image plane separation distance between fiber image points

Parameter	Initial value	1	2	3	…	6	7
d /μm	49.500	51.011	50.911	50.843	…	50.810	50.809
z /μm	6600.000	6584.231	6575.157	6572.180	…	6570.711	6570.667
θ /(°)	2.357	2.352	2.354	2.356	…	2.357	2.357
γ_x /(°)	0	1.633	1.633	1.634	…	1.635	1.635
γ_y /(°)	0	0.249	0.249	0.249	…	0.250	0.250

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Guanji Dong, Feng Tang, Xiangzhao Wang, Peng Feng, Fudong Guo, Changzhe Peng. Study on High Precision Magnification Measurement of Imaging Systems[J]. Acta Optica Sinica, 2018, 38(7): 0712007

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Paper Information

Category: Instrumentation, Measurement and Metrology

Received: Jan. 10, 2018

Accepted: --

Published Online: Sep. 5, 2018

The Author Email: Guanji Dong (dongguanji@siom.ac.cn)

DOI:10.3788/AOS201838.0712007

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Error requirement of fiber spacing measurement

Table 1. Error requirement of fiber spacing measurement

Table 2. Settings of simulation conditions

Table 2. Settings of simulation conditions

Table 3. Initial parameter setting of iterative calculation

Table 3. Initial parameter setting of iterative calculation

Table 4. Quantitative relationship among two fibers separation distance, spatial position parameters of the CCD camera, and the Zernike polynomial coefficient, and its calculation formula

Table 4. Quantitative relationship among two fibers separation distance, spatial position parameters of the CCD camera, and the Zernike polynomial coefficient, and its calculation formula

Table 5. Simulation results of the effectiveness of the method for measuring the separation distance between two fibers

Table 5. Simulation results of the effectiveness of the method for measuring the separation distance between two fibers

Table 6. Iterative calculation results of object plane separation distance between fibers

Table 6. Iterative calculation results of object plane separation distance between fibers

Table 7. Iterative calculation results of image plane separation distance between fiber image points

Table 7. Iterative calculation results of image plane separation distance between fiber image points