Design of freeform surface off-axis reflective optical systems based on quantum genetic algorithm

Lin Miao; Boyu Tian; Nianchun Sun; Bin Zhang

doi:10.3788/IRLA20210365

Journals >Infrared and Laser Engineering >Volume 50 >Issue 12 >Page 20210365 > Article

Infrared and Laser Engineering
Vol. 50, Issue 12, 20210365 (2021)

Design of freeform surface off-axis reflective optical systems based on quantum genetic algorithm

Lin Miao, Boyu Tian, Nianchun Sun, and Bin Zhang

Author Affiliations

College of Electronics and Information Engineering, Sichuan University, Chengdu 610064, China

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DOI: 10.3788/IRLA20210365 Cite this Article

Lin Miao, Boyu Tian, Nianchun Sun, Bin Zhang. Design of freeform surface off-axis reflective optical systems based on quantum genetic algorithm[J]. Infrared and Laser Engineering, 2021, 50(12): 20210365 Copy Citation Text

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Fig. 1. Schematic diagram of the initial structure of the on-axis three-mirror system

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Fig. 2. Flowchart of the design process

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Fig. 3. Convergence curve of error function

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Fig. 4. (a) Layout and (b) MTF of the initial structure of the on-axis three-mirror system

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Fig. 5. Schematic diagram of (a) layout constraint and (b) expansion the field of view

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Fig. 6. Optical system: (a) Structure layout；(b) Integrated simulation of M₁-M₃ components

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Fig. 7. Performance evaluation of off-axis three-mirror system with freeform surface. (a) Encircle energy in the field of view; (b) RMS wavefront error; (c) MTF

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Parameter	Specification
Field of view/(°)	10×4
F-number	2
Wavelength/nm	400-760
Effective focal length/mm	120
MTF/lp·mm⁻¹	>0.9@50
Pixel size/μm	10

Table 1. Optical system parameters

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Parameter	α₁	α₂	$ - e_1^2$	$ - e_2^2$	$ - e_3^2$
Range	[0.1,0.5]	[1.5,2.1]	[−5,5]	[−5,5]	[−5,5]

Table 2. Ranges of parameters

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x_i	best_i	f(x)>f(best_i)	Δθ_i	s(A_i,B_i)
x_i	best_i	f(x)>f(best_i)	Δθ_i	A_iB_i>0	A_iB_i<0	A_i=0	B_i=0
0	0	False	0	0	0	0	0
0	0	True	0	0	0	0	0
0	1	False	0.01π	1	−1	0	±1
0	1	True	0.01π	−1	1	±1	0
1	0	False	0.005π	−1	1	±1	0
1	1	True	0.005π	1	−1	0	±1
1	1	False	0	0	0	0	0
1	1	True	0	0	0	0	0

Table 3. Quantum gate rotation update strategy

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Mirror	Radius/mm	Thickness/mm	Conic
M₁	−467.19	−141.68	0.117
M₂	−109.60	141.68	2.052
M₃	−143.19	−96.51	−0.044

Table 4. Initial configuration parameters of the on-axis three-mirror system

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Item	M₁	M₂	M₃
y	−5.825E-003	−1.148E-003	−5.519E-004
x²	−1.352E-003	2.242E-004	−1.851E-004
y²	−1.336E-003	2.196E-004	−1.895E-004
x²y	1.374E-008	−4.828E-008	−5.616E-009
y³	−2.060E-008	−1.371E-007	−6.372E-009
x⁴	7.533E-010	1.052E-010	−3.402E-010
x²y²	1.136E-009	−2.277E-010	−7.071E-010
y⁴	6.287E-010	−1.3E-010	−3.559E-010
x⁴y	−2.124E-012		3.946E-014
x²y³	1.941E-013		6.297E-014
y⁵	−7.222E-015		8.015E-014
x⁶	−3.345E-015		−1.147E-015
x⁴y²	8.395E-015		−4.474E-015
x²y⁴	−2.407E-015		−5.253E-015
y⁶	−7.531E-016		−1.681E-015

Table 5. Polynomial coefficients of freeform surface for three-mirror system

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Mirror	Radius/mm	Thickness/mm	Conic
M₁	−436.92	−218.86	−1.611
M₂	−243.10	218.86	3.461
M₃	−329.40	−240.47	0.548

Table 6. Final configuration parameters of the off-axis three-mirror system

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