Design of the freeform imaging system with large field of view and large relative aperture

Fig. 2. Change trend of RMS diameter of spot diagram

Fig. 3. Interval constraint range

Fig. 4. In-progress and final results for design of the initial configuration. (a) Initial system; (b) Results for system construction using Φ(X1, Y1); (c) Final result

Fig. 5. Field map of RMS wavefront error for final system

Fig. 6. MTF for the final system

Fig. 7. Encircled energy distribution of all field

Fig. 8. (a) PM 3D free-form surface; (b) SM 3D free-form surface; (c) TM 3D free-form surface

Fig. 9. Tolerance probability curve

Table 1.
Zernike polynomials and XYpolynomials correspond to aberration relations
Zernike多项式与XY多项式对应像差关系

Table 1.
Zernike polynomials and XYpolynomials correspond to aberration relations
Zernike多项式与XY多项式对应像差关系

Term	Zernike polynomial	XY polynomial	Corresponding aberration type
1			Piston(constant)
1			0th order in wavefront
2			Distortion-tilt(x-axis)
2			2nd order in wavefront
3			Distortion-tilt(y-axis)
3			2nd order in wavefront
4			Defocus
4			2nd order in wavefront
5			Astigmatism, primary (axis at 0°or 90°)
5			4th order in wavefront
6			Astigmatism, primary (axis at ±45°)
6			4th order in wavefront
7			Coma,Primary(x-axis)
7			4th order in wavefront
8			Coma,Primary(y-axis)
8			4th order in wavefront
9			Spherical aberration,Primary
9			4th order in wavefront

Table 2.
Optical system specification
光学系统参数
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Table 2.
Optical system specification
光学系统参数
Parameter Specification
Wavelength range/μm 8-12
Focal length/mm 400
F-number 2
Field of view
Pixel size/μm 30

Table 3.
Ranges of configuration parameters and optimization result
解空间结构参数范围和求解结果

Table 3.
Ranges of configuration parameters and optimization result
解空间结构参数范围和求解结果

Parameter	Range	Result
d₁/mm	[−250,−100]	−201.4271
d₂/mm	[100,250]	210.6225
r₁/mm	[−800,−50]	−780.0523
r₂/mm	[−800,−50]	−115.2459
r₃/mm	[−800,−50]	−279.4206
k₁	[−10,10]	9.0266
k₂	[−10,10]	2.5360
k₃	[−10,10]	0.1883
α₁/(°)	[10,30]	15
α₂/(°)	[10,30]	25.0181
α₃/(°)	[10,30]	10.0006

Table 4.
Tolerances distribution of the system
系统公差分配表

Table 4.
Tolerances distribution of the system
系统公差分配表

Surface	△R/mm	△K	RMS surface error(λ=9 μm)	Displacement			Tilt
Surface	△R/mm	△K	RMS surface error(λ=9 μm)	X/μm	Y/μm	Z/μm	X/(″)	Y/(″)	Z/(″)
PM	0.02	0.10%	1/50λ	20	20	25	30	30	20
SM	0.05	0.05%	1/40λ	40	40	20	20	20	20
TM	0.05	0.10%	1/50λ	20	20	20	20	20	30

Table 5.
Tolerances performance of all field
全视场公差变动表现