Numerical optimization strategy for multi-lens imaging systems containing freeform surfaces

Chang Liu; Herbert Gross

doi:10.1364/AO.57.005758

Applied Optics
Vol. 57,
Issue 20,
pp. 5758-5768
(2018)
•https://doi.org/10.1364/AO.57.005758

Numerical optimization strategy for multi-lens imaging systems containing freeform surfaces

Chang Liu and Herbert Gross

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Chang Liu and Herbert Gross, "Numerical optimization strategy for multi-lens imaging systems containing freeform surfaces," Appl. Opt. 57, 5758-5768 (2018)

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Abstract

With progress in freeform technology, freeform components are entering real system designs. Although freeform surfaces increase the degrees of freedom of systems, optimization strategies for placing multiple freeforms are still underdeveloped. We therefore investigated strategies for placing freeforms to achieve significant improvement in system performance for optical imaging systems. For demonstrating our findings and supporting our observations, we have chosen a Scheimpflug system and a lithography system. Several aspects are investigated and implemented in optimization strategies. These strategies are used to optimize and demonstrate the performance on selected examples, i.e., multi-lens imaging systems containing one or two freeforms. Finally, we describe a workflow to guide the design process from start to the end for implementing freeforms in order to achieve improved system performance.

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$f$ Number	Object Tilt	Surface Number	Surface Type
1.08	70°	23	Spherical

$f$ Number	Surface Number	Surface Type
0.43	41	Spherical

	Original	1 Freeform	2 Freeform
Averaged rms radius, $Ø_{ave}$ (μm)	3.33	2.86	0.53
Non-uniformity, $Ø_{\max} / Ø_{\min}$	5.84	2.07	1.48

Surface	Type	Radius (mm)	Thickness (mm)	Glass	Conic
Object	Tilted		155.939
1	Freeform	95.263	1.126	SF3	0.345
2	Standard	13.136	7.000	K5
3	Standard	209.215	4.052
4	Standard	−20.491	4.911	BK7
5	Standard	−70.324	0.500
Stop	Standard	Infinity	2.219
7	Standard	53.802	6.000	SF3
8	Standard	−42.965	1.000
9	Standard	34.136	4.000	SF3
10	Standard	−339.021	1.244
11	Standard	17.521	4.463	SF5
12	Standard	12.130	9.000
13	Standard	−14.487	2.403	SF5
14	Standard	−42.392	2.267
15	Standard	16.476	5.413	SF6
16	Freeform	−27.384	1.000	BK7	−19.383
17	Standard	11.994	2.329
18	Standard	15.462	5.000	SF6
19	Standard	−51.482	0.897
20	Standard	−24.724	1.757	K5
21	Standard	8.117	1.000
22	Standard	8.715	5.057	N-LAF21
23	Standard	19.615	0.791
24	Coordinate break
Image	Standard	Infinity

Zernike Fringe Term	Surface 1	Surface 16
5	$1.775 E - 02$	$- 1.589 E - 02$
8	$- 3.851 E - 02$	$- 2.642 E - 02$
9	$- 4.102 E - 03$	$2.921 E - 01$
11	$- 3.806 E - 02$	$- 1.392 E - 01$
12	$- 2.314 E - 03$	$- 8.545 E - 02$
15	$- 4.488 E - 03$	$7.798 E - 02$
16	$- 2.826 E - 03$	$6.548 E - 02$
17	$1.442 E - 02$	$- 6.747 E - 03$
20	$- 8.216 E - 03$	$5.633 E - 03$
21	$- 4.947 E - 03$	$- 3.600 E - 02$
24	$2.664 E - 03$	$1.582 E - 02$
25	$- 1.571 e - 03$	$2.894 E - 02$
27	$- 4.385 E - 04$	$- 1.911 E - 02$
28	$9.675 E - 04$	$- 2.913 E - 02$
31	$- 8.614 E - 04$	$2.063 E - 03$
32	$- 1.175 E - 03$	$- 1.859 E - 03$
35	$9.064 E - 04$	$1.634 E - 03$
36	$- 4.320 E - 04$	$1.288 E - 02$

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Applied Optics