Direct Detection Method for Spatial Resolution of Optical Imaging Loads Based on Spherical Target

Song Ji; Yongsheng Zhang; Kai Li; Dazhao Fan; Weiming Yang

doi:10.3788/AOS221698

Acta Optica Sinica, Volume. 43, Issue 18, 1812001(2023)

Direct Detection Method for Spatial Resolution of Optical Imaging Loads Based on Spherical Target

Song Ji¹, Yongsheng Zhang^1、*, Kai Li², Dazhao Fan¹, and Weiming Yang²

Author Affiliations

¹Institute of Geospatial Information, Information Engineering University, Zhengzhou 450001, Henan, China

²Institute of System Engineering, Academy of Military Sciences, Beijing 100044, China

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Figures & Tables(19)

Fig. 1. Deployment type of spherical target. (a) Three-dimensional fan-shape deployment; (b) three-dimensional grid deployment; (c) three-dimensional fan-shape and grid mixture deployment

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Fig. 2. Spatial resolution detection range of spherical target. (a) Three-dimensional fan-shaped target resolution detection; (b) three-dimensional fan-grid-shaped target resolution detection; (c) three-dimensional grid-shaped target resolution detection

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Fig. 3. Schematic diagram of spherical target center projection. (a) 3D target center projection; (b) center projection of target Z axis; (c) center projection of fan-shaped arc along target Z axis

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Fig. 4. Spherical target image of China (Songshan) satellite remote sensing calibration field

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Fig. 5. Imaging and fitting of central circle ellipse of spherical fan-shaped target strip. (a)-(d) Simulation imaging of target circle from mode 1 to mode 4; (e)-(h) ellipse fitting of the outmost target imaging circle from mode 1 to mode 4; (i)-(l) ellipse center line fitting of target imaging circle

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Fig. 6. Target oblique photographic image and its edge extraction results. (a) Oblique photographic image; (b) local image;(c) edge extraction results

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Fig. 7. Ellipse fitting result of imaging target. (a) Axis fitting of ellipse;(b) direction line of target center; (c) positional relationship between ellipse axis and target center direction line

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Fig. 8. Multi-scale ellipse construction and sampling point acquisition. (a) Sampling interval is 5°; (b) sampling interval is 10°; (c) sampling interval is 30°

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Fig. 9. Spatial resolution detection at the centroid of fan-shaped target strip. (a) Multi-scale ellipse construction; (b) partial enlarged view of multi-scale ellipse; (c) local maximum points and connecting lines of elliptical gray value; (d) gray curve of target strip image intercepted by multi-scale ellipse

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Fig. 10. Moving ellipse fitting on fixed direction and gray curve of target strip image. (a)-(d) Sampling ellipse of 0.5, 1.0, 1.5, and 2.5 pixel movement; (e)-(h) gray curve of target strip image of 0.5, 1.0, 1.5, and 2.5 pixel movement

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Fig. 11. Moving ellipse fitting on fixed direction and gray curve of target strip image (wide threshold)

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Table 1. Parameter value and features of spherical target equal dividing mode

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Table 1. Parameter value and features of spherical target equal dividing mode

Equal dividing mode	Vertical arc	X axis	Z axis
Variation parameter	θ，τ	Positive half of X axis，τ	Positive half of Z axis，τ
Value range	0≤θ≤π，0≤τ≤2π	0≤X≤r，0≤τ≤2π	-r≤Z≤r，0≤τ≤2π
Feature	Grid arc length is equal in the vertical direction	Projection length of grid arc to XOY plane is equal	Projection length of grid arc to ZOX or ZOY plane is equal

Table 2. Deployment parameters and resolution detection range of spherical target (target radius r=3.26 m)

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Table 2. Deployment parameters and resolution detection range of spherical target (target radius r=3.26 m)

Spherical target

deployment mode

Horizontal arc division［number/angle /（°）］

Value range of

θ /（°）

Value range of R₁/m

Value range of R_max /m

Target 1，Fig. 2（a）

20/18

［0，90］

（0，1.0242）

Target 2，Fig. 2（b）

20/18

［0，65］

（0，0.9282）

（0，1.0242）

Target 3，Fig. 2（c）

20/18

［0，6］

（0，0.1071）

（0，1.0242）

Table 3. Eccentricity of circular ellipse of spherical fan-shaped target strip (spherical target radius r=3.26 m)

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Table 3. Eccentricity of circular ellipse of spherical fan-shaped target strip (spherical target radius r=3.26 m)

θ angle of spherical target （r=3.26 m）（f=0.004 m）	Ellipse eccentricity e
	Mode 1	Mode 2	Mode 3	Mode 4
	X₀=200 m φ=15° Y₀=100 m ω=20° Z₀=300 m κ=10°	X₀=400 m φ=25° Y₀=300 m ω=25° Z₀=400 m κ=20°	X₀=600 m φ=35° Y₀=500 m ω=30° Z₀=500 m κ=30°	X₀=10 km φ=35° Y₀=5 km ω=30° Z₀=400 km κ=10°
Max resolution detection error /m	0.0024	0.0043	0.0043	0.0035
45°	0.7961	0.9943	0.9206	0.8572
40°	0.7963	0.9943	0.9205	0.8575
30°	0.7965	0.9944	0.9202	0.8578
20°	0.7967	0.9944	0.9199	0.8581
10°	0.7968	0.9944	0.9198	0.8581
5°	0.7969	0.9944	0.9198	0.8581
2°	0.7969	0.9945	0.9198	0.8581
Max eccentricity error	0.0008	0.0002	0.0008	0.0009

Table 4. Imaging ellipse distance ratio of spherical fan-shaped target strip

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Table 4. Imaging ellipse distance ratio of spherical fan-shaped target strip

Parameter		θ=45°	θ=40°	θ=30°	θ=20°	θ=10°	θ=5°	θ=2°	Maximum deviation /%
Parameter		θ=45°	θ=40°	θ=30°	θ=20°	θ=10°	θ=5°	θ=2°	Semi-major axis	Center distance
Actual space distance ratio		1	0.9090	0.7071	0.4837	0.2456	0.1233	0.0494	-	-
Mode 1 ellipse	Semi-major axis ratio	1	0.9099	0.7089	0.4855	0.2467	0.1238	0.0496	0.18	27.92
Mode 1 ellipse	Center distance ratio	1	0.7986	0.4567	0.2045	0.0500	0.0110	-	0.18	27.92
Mode 2 ellipse	Semi-major axis ratio	1	0.9123	0.7141	0.4907	0.2498	0.1255	0.0503	0.70	27.86
Mode 2 ellipse	Center distance ratio	1	0.7993	0.4576	0.2051	0.0501	0.0110	-	0.70	27.86
Mode 3 ellipse	Semi-major axis ratio	1	0.9084	0.7058	0.4823	0.2448	0.1228	0.0492	0.13	27.97
Mode 3 ellipse	Center distance ratio	1	0.7981	0.4559	0.2040	0.0498	0.0109	-	0.13	27.97
Mode 4 ellipse	Semi-major axis ratio	1	0.9089	0.7069	0.4835	0.2455	0.1232	0.0493	0.02	29.25
Mode 4 ellipse	Center distance ratio	1	0.7924	0.4434	0.1912	0.0430	0.0090	-	0.02	29.25

Table 5. Fitting parameters of imaging target

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Table 5. Fitting parameters of imaging target

Imaging target

Eccentricity

Long half axis /pixel

Center coordinates /pixel

Eccentricity error（percentage /%）

Ellipse of fan-shaped target strip

Ellipse of square-shaped edge target

0.4438

24.8099

（43.0941，27.2098）

0.0148（3.33）

0.4586

33.1413

（42.8845，31.2837）

Table 6. Reference parameters for imaging target resolution detection
View table
Table 6. Reference parameters for imaging target resolution detection
Spherical target Reference eccentricity Reference direction line Reference long half axis size of maximum resolution /pixel
Imaging target 0.4512 y=-4.6849x+306.8001 24.8099

Table 7. Number of detected white fan-shaped target strip
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Table 7. Number of detected white fan-shaped target strip
Intercept ellipse scale Scale 1 Scale 2 Scale 3 Scale 4 Scale 5 Scale 6 Scale 7 Scale 8
Number of detected white target strips 0 0 2 5 8 9 9 9

Table 8. Moving ellipse fitting on fixed direction and spatial resolution detection

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Table 8. Moving ellipse fitting on fixed direction and spatial resolution detection

Intercept ellipse of imaging target		Size of long half axis /pixel
Intercept ellipse of imaging target		2.4	3.2	4.0	4.8	5.6
Number of detected white target strips	Sampling ellipse 0.5 pixel movement	0	2	4	7	-
	Sampling ellipse 1.0 pixel movement	-	2	4	7	9
	Sampling ellipse 1.5 pixel movement	-	2	4	6	9
	Sampling ellipse 2.5 pixel movement	-	2	3	6	7

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Song Ji, Yongsheng Zhang, Kai Li, Dazhao Fan, Weiming Yang. Direct Detection Method for Spatial Resolution of Optical Imaging Loads Based on Spherical Target[J]. Acta Optica Sinica, 2023, 43(18): 1812001

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Paper Information

Category: Instrumentation, Measurement and Metrology

Received: Sep. 13, 2022

Accepted: Dec. 12, 2022

Published Online: Sep. 4, 2023

The Author Email: Zhang Yongsheng (yszhang2001@vip.163.com)

DOI:10.3788/AOS221698

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Parameter value and features of spherical target equal dividing mode

Table 1. Parameter value and features of spherical target equal dividing mode

Table 2. Deployment parameters and resolution detection range of spherical target (target radius r=3.26 m)

Table 2. Deployment parameters and resolution detection range of spherical target (target radius r=3.26 m)

Table 3. Eccentricity of circular ellipse of spherical fan-shaped target strip (spherical target radius r=3.26 m)

Table 3. Eccentricity of circular ellipse of spherical fan-shaped target strip (spherical target radius r=3.26 m)

Table 4. Imaging ellipse distance ratio of spherical fan-shaped target strip

Table 4. Imaging ellipse distance ratio of spherical fan-shaped target strip

Table 5. Fitting parameters of imaging target

Table 5. Fitting parameters of imaging target

Table 6. Reference parameters for imaging target resolution detection

Table 6. Reference parameters for imaging target resolution detection

Table 7. Number of detected white fan-shaped target strip

Table 7. Number of detected white fan-shaped target strip

Table 8. Moving ellipse fitting on fixed direction and spatial resolution detection

Table 8. Moving ellipse fitting on fixed direction and spatial resolution detection