一种改进的空间相机在轨调制传递函数检测方法 
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Improved Method for On-Orbit Modulation Transfer Function Detection of Space Cameras
1 中国科学院西安光学精密机械研究所, 陕西 西安 710119
2 中国科学院大学, 北京 100049
3 陕西师范大学物理学与信息技术学院, 陕西 西安 710119
图 & 表
图 1. 月球边缘刃边法的算法步骤
Fig. 1. Algorithmic process of lunar-edge method
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图 2. 月球刃边法的流程图
Fig. 2. Flow chart of lunar-edge method
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图 3. ESF加密配准示意图
Fig. 3. Encryption matching schematic of ESF
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图 4. 生成的圆形刃边仿真图像。(a)高分辨率仿真图像;(b)低分辨率仿真图像;(c)仿真图像理论MTF曲线
Fig. 4. Generated round-edge simulation images. (a) High-resolution simulation image; (b) low-resolution simulation image; (c) theoretical MTF curve of simulation image
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图 5. 边缘区域图像
Fig. 5. Edge-area image
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图 6. 双高斯曲线拟合方法
Fig. 6. Double Gaussian curve fitting method
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图 7. 测试系统示意图
Fig. 7. Schematic of test system
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图 8. 两种测试靶标采集图像。(a)三线靶标;(b)三线靶标(局部放大);(c)圆形边缘靶标1;(d)圆形边缘靶标2;(e)圆形靶标3
Fig. 8. Acquisition images of two test targets. (a) Three-bar target; (b) three-bar target (local amplification); (c) round-edge target 1; (d) round-edge target 2; (e) round-edge target 3
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图 9. 三线靶标测试的MTF过焦曲线
Fig. 9. MTF over-focus curve of three-bar target test
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图 10. 实验图像月球边缘刃边法计算结果。(a)三个不同半径的圆形靶标图像;(b)亚像素边缘检测位置;(c) ESF曲线;(d) LSF曲线;(e) MTF曲线
Fig. 10. Results of lunar-edge method from laboratory images. (a) Images of three round-edge targets with different radii; (b) positions of subpixel-edge detection; (c) ESF curves; (d) LSF curves; (e) MTF curves
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图 11. 月球边缘刃边法MTF过焦曲线
Fig. 11. MTF over-focus curves of lunar-edge method
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表 1在各空间频率处的理论MTF数值
Table1. Theoretical MTF values at various spatial frequencies
| Spatial frequency | MTF | Spatial frequency | MTF | Spatial frequency | MTF |
|---|
| 0 | 1.000000 | 14 | 0.800863 | 28 | 0.409192 | | 1 | 0.998751 | 15 | 0.774989 | 29 | 0.383224 | | 2 | 0.995458 | 16 | 0.748124 | 30 | 0.358026 | | 3 | 0.989765 | 17 | 0.720620 | 31 | 0.333701 | | 4 | 0.982020 | 18 | 0.692468 | 32 | 0.310255 | | 5 | 0.972031 | 19 | 0.663928 | 33 | 0.287773 | | 6 | 0.960040 | 20 | 0.635065 | 34 | 0.266251 | | 7 | 0.946013 | 21 | 0.606066 | 35 | 0.245743 | | 8 | 0.930090 | 22 | 0.577041 | 36 | 0.226245 | | 9 | 0.912383 | 23 | 0.548127 | 37 | 0.207774 | | 10 | 0.892939 | 24 | 0.519447 | 38 | 0.190336 | | 11 | 0.871990 | 25 | 0.491109 | 39 | 0.173907 | | 12 | 0.849512 | 26 | 0.463225 | 40 | 0.158507 | | 13 | 0.825830 | 27 | 0.435892 | 41 | 0.144072 |
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表 2仿真图像对应行数的理论边缘位置
Table2. Theoretical edge position of each line in simulation image
| Row No. | Edge position | Row No. | Edge position | Row No. | Edge position |
|---|
| 1 | 33.7188 | 11 | 35.4844 | 21 | 36.5000 | | 2 | 33.9375 | 12 | 35.6094 | 22 | 36.5156 | | 3 | 34.1406 | 13 | 35.7500 | 23 | 36.6250 | | 4 | 34.3281 | 14 | 35.8750 | 24 | 36.6250 | | 5 | 34.5313 | 15 | 35.9844 | 25 | 36.6406 | | 6 | 34.7031 | 16 | 36.0781 | 26 | 36.7500 | | 7 | 34.8750 | 17 | 36.1719 | 27 | 36.7500 | | 8 | 35.0469 | 18 | 36.2500 | 28 | 36.7500 | | 9 | 35.1875 | 19 | 36.3594 | 29 | 36.7500 | | 10 | 35.3438 | 20 | 36.4063 | 30 | 36.7500 |
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表 3三种方法的边缘检测误差
Table3. Edge detection error of three methods
| SNR /dB | Edge detection error /pixel |
|---|
| Interpolationmethod | Gray momentmethod | Fittingmethod |
|---|
| 50 | 0.2205 | 0.0156 | 0.0133 | | 40 | 0.2570 | 0.0222 | 0.0215 | | 30 | 0.5167 | 0.0871 | 0.0422 |
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表 4不同长度圆弧的边缘拟合误差
Table4. Edge fitting errorof arcs with different lengths
| SNR /dB | Arc degree /(°) | Fitting error /pixel |
|---|
| Straight line fitting | Polynomial fitting | Circle fitting |
|---|
| 4(6 rows) | 0.0052 | 0.0068 | 0.0084 | | 8(12 rows) | 0.0575 | 0.0254 | 0.0255 | | 12(18 rows) | 0.0970 | 0.0290 | 0.0288 | | 50 | 16(24 rows) | 0.1653 | 0.0259 | 0.0257 | | 20(30 rows) | 0.2523 | 0.0235 | 0.0234 | | 40(60 rows) | 1.0042 | 0.0171 | 0.0169 | | 60(90 rows) | 2.2933 | 0.0220 | 0.0144 | | 4(6 rows) | 0.0098 | 0.0100 | 0.1247 | | 8(12 rows) | 0.0581 | 0.0273 | 0.0267 | | 12(18 rows) | 0.0976 | 0.0308 | 0.0306 | | 40 | 16(24 rows) | 0.1653 | 0.0269 | 0.0262 | | 20(30 rows) | 0.2524 | 0.0239 | 0.0238 | | 40(60 rows) | 1.0042 | 0.0181 | 0.0181 | | 60(90 rows) | 2.2933 | 0.0235 | 0.0166 | | 4(6 rows) | 0.0788 | 0.0803 | 0.2666 | | 8(12 rows) | 0.0936 | 0.0784 | 0.0796 | | 12(18 rows) | 0.1024 | 0.0467 | 0.0722 | | 30 | 16(24 rows) | 0.1666 | 0.0347 | 0.0381 | | 20(30 rows) | 0.2532 | 0.0351 | 0.0442 | | 40(60 rows) | 1.0050 | 0.0432 | 0.0424 | | 60(90 rows) | 2.2936 | 0.0499 | 0.0461 |
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表 5不同方法的精度结果
Table5. Accuracy results of different methods
| SNR /dB | Fermi | MSG+singleGaussian fitting | MSG+doubleGaussian fitting |
|---|
| 50.0 | 0.0106 | 0.0273 | 0.0084 | | 47.5 | 0.0107 | 0.0290 | 0.0090 | | 45.0 | 0.0108 | 0.0308 | 0.0095 | | 42.5 | 0.0112 | 0.0373 | 0.0103 | | 40.0 | 0.0112 | 0.0393 | 0.0107 | | 37.5 | 0.0131 | 0.0404 | 0.0129 | | 35.0 | 0.0133 | 0.0573 | 0.0136 | | 32.5 | 0.0144 | 0.0665 | 0.0140 | | 30.0 | 0.0139 | 0.1049 | 0.0142 |
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表 6实验器件参数
Table6. Parameters of experimental devices
| Experimental device | Parameter |
|---|
| Light source | Center wavelength:650 nm | | Parallel light pipe | Focallength:1000 mm | | Lens | Relative aperture:1∶12 | | CCD detector | Cell size:0.012 mm |
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表 7三线靶标测试的MTF值
Table7. MTF values of three-bar target test
| Defocus position /mm | MTF | Defocus position /mm | MTF | Defocus position /mm | MTF |
|---|
| -0.75 | 0.00920 | -0.25 | 0.16764 | 0.25 | 0.19157 | | -0.70 | 0.01141 | -0.20 | 0.18051 | 0.30 | 0.14862 | | -0.65 | 0.02217 | -0.15 | 0.19376 | 0.35 | 0.13900 | | -0.60 | 0.03439 | -0.10 | 0.22116 | 0.40 | 0.11761 | | -0.55 | 0.04168 | -0.05 | 0.2333 | 0.45 | 0.09270 | | -0.50 | 0.05688 | 0.00 | 0.22568 | 0.50 | 0.05384 | | -0.45 | 0.08602 | 0.05 | 0.22186 | 0.55 | 0.04535 | | -0.40 | 0.10215 | 0.10 | 0.21710 | 0.60 | 0.01680 | | -0.35 | 0.12632 | 0.15 | 0.21792 | 0.65 | 0.00032 | | -0.30 | 0.13891 | 0.20 | 0.19957 | 0.70 | 0.00012 |
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表 8圆形刃边靶标测试的MTF值
Table8. MTF values of round-edge target test
| Defocusposition /mm | Round-edgetarget 1 | Round-edgetarget 2 | Round-edgetarget 3 |
|---|
| -0.75 | 0.00109 | 0.05828 | 0.06555 | | -0.70 | 0.03612 | 0.06823 | 0.07635 | | -0.65 | 0.06608 | 0.08410 | 0.08156 | | -0.60 | 0.03407 | 0.08210 | 0.09555 | | -0.55 | 0.07076 | 0.08805 | 0.09635 | | -0.50 | 0.08372 | 0.11530 | 0.13225 | | -0.45 | 0.08201 | 0.14231 | 0.12667 | | -0.40 | 0.10369 | 0.15450 | 0.15703 | | -0.35 | 0.11279 | 0.15477 | 0.16997 | | -0.30 | 0.14080 | 0.17789 | 0.19099 | | -0.25 | 0.16225 | 0.17268 | 0.19216 | | -0.20 | 0.18424 | 0.18441 | 0.21711 | | -0.15 | 0.19507 | 0.20169 | 0.22634 | | -0.10 | 0.19621 | 0.20218 | 0.23121 | | -0.05 | 0.21491 | 0.19751 | 0.21939 | | 0.00 | 0.22924 | 0.20478 | 0.23830 | | 0.05 | 0.22083 | 0.20034 | 0.21507 | | 0.10 | 0.22078 | 0.21254 | 0.20748 | | 0.15 | 0.21589 | 0.18054 | 0.19756 | | 0.20 | 0.20750 | 0.18907 | 0.18829 | | 0.25 | 0.18407 | 0.17510 | 0.17659 | | 0.30 | 0.14150 | 0.14235 | 0.15959 | | 0.35 | 0.13955 | 0.12649 | 0.10052 | | 0.40 | 0.10618 | 0.10087 | 0.08592 | | 0.45 | 0.09021 | 0.06674 | 0.08080 | | 0.50 | 0.07664 | 0.06061 | 0.06878 | | 0.55 | 0.06089 | 0.02211 | 0.00700 | | 0.60 | 0.05772 | 0.00595 | 0.03814 | | 0.65 | 0.00038 | 0.00249 | 0.03138 | | 0.70 | 0.00081 | 0.00034 | 0.03958 |
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程莹, 易红伟, 刘鑫龙. 一种改进的空间相机在轨调制传递函数检测方法[J]. 中国激光, 2019, 46(7): 0704010. Ying Cheng, Hongwei Yi, Xinlong Liu. Improved Method for On-Orbit Modulation Transfer Function Detection of Space Cameras[J]. Chinese Journal of Lasers, 2019, 46(7): 0704010.
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