Method of determining effects of heat-induced irregular refractive index on an optical system

Xifa Song; Lin Li; Yifan Huang

doi:10.1364/AO.54.007701

Applied Optics
Vol. 54,
Issue 25,
pp. 7701-7707
(2015)
•https://doi.org/10.1364/AO.54.007701

Method of determining effects of heat-induced irregular refractive index on an optical system

Xifa Song, Lin Li, and Yifan Huang

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Xifa Song, Lin Li, and Yifan Huang, "Method of determining effects of heat-induced irregular refractive index on an optical system," Appl. Opt. 54, 7701-7707 (2015)

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Abstract

The effects of an irregular refractive index on optical performance are examined. A method was developed to express a lens’s irregular refractive index distribution. An optical system and its mountings were modeled by a thermomechanical finite element (FE) program in the predicted operating temperature range, $- 45 ° C - 50 ° C$ . FE outputs were elaborated using a MATLAB optimization routine; a nonlinear least squares algorithm was adopted to determine which gradient equation best fit each lens’s refractive index distribution. The obtained gradient data were imported into Zemax for sequential ray-tracing analysis. The root mean square spot diameter, modulation transfer function, and diffraction ensquared energy were computed for an optical system under an irregular refractive index and under thermoelastic deformation. These properties are greatly reduced by the irregular refractive index effect, which is one-third to five-sevenths the size of the thermoelastic deformation effect. Thus, thermal analyses of optical systems should consider not only thermoelastic deformation but also refractive index irregularities caused by inhomogeneous temperature.

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Material	Conductivity (W/mK)	Expansion (m/K)	Young’s Modulus (MPa)	Density ( $t / {mm}^{3}$ )	Specific Heat (MJ/tK)	Poisson’s Ratio
Aluminum	217.7	$2.4 e - 5$	69,000	$2.7 e - 9$	88,800,000	0.330
Polyimide	0.16	$1.0 e - 6$	2000	$1.4 e - 9$	10,046,000	0.323
JGS1	1.40	$5.5 e - 7$	72,000	$2.2 e - 9$	670,000,000	0.170
LaK3	0.925	$6.0 e - 6$	119,240	$4.2 e - 9$	7.9e8	0.283
ZF4	0.721	$9.7 e - 6$	52,880	$4.5 e - 9$	7.9e8	0.235
BK7	1.114	$7.7 e - 6$	82,000	$2.5 e - 9$	8.58e8	0.206

Label No.	Size ( ${mm}^{3}$ )	Heat flux (W)
U1	$29 \times 29 \times 1.78$	0.35
U2	$28 \times 28 \times 2$	0.3
U3	$21 \times 12 \times 5$	0.1
U4	$7.6 \times 10 \times 2$	0.15
U5	$7.6 \times 10 \times 2$	0.15
U6	$7.6 \times 10 \times 2$	0.1
U7	$7.6 \times 10 \times 2$	0.15
U8	$6 \times 10 \times 3.5$	0.1

Mesh Point No.	Temperature (°C)	Refractive Index Variation ( $* 1.0 e - 006$ )
40	50.0738	0.1023
39	50.0736	0.102
38	50.0734	0.1017
37	50.0731	0.1013
36	50.0727	0.1008
35	50.0723	0.1002
34	50.0717	0.0994
33	50.0711	0.0986
32	50.0703	0.0975
31	50.0693	0.0961

Surface	Type	Radius	Thickness	Glass	Semi-Diameter	Delta T	$N_{0}$	$N_{x 1}$	$N_{x 2}$	$N_{y 1}$	$N_{y 2}$	$N_{z 1}$	$N_{z 2}$
OBJ	Standard	infinity	infinity		infinity	1
1	Gradient4	48.79	6	F_SILICA	23.716	1	1.458	$7.70 e - 9$	$- 5.24 e - 9$	$1.31 e - 11$	$- 3.9 e - 10$	$- 4.8 e - 11$	$- 3.16 e - 11$
2	Standard	151.794	6.301		23.158	1
3	Gradient4	41.074	7.38	LAK3	19.105	1	1.747	$7.60 e - 9$	$- 4.245 e - 9$	$9.999 e - 12$	$- 2.27 e - 10$	$- 3.95 e - 11$	$- 3.963 e - 11$
4	Standard	156.538	5.49		17.378	1
5	Gradient4	−80.424	4	ZF4	14.597	1	1.728	$- 1.67 e - 8$	$- 9.97 e - 9$	$2.928 e - 11$	$5.00 e - 10$	$- 9.27 e - 11$	$- 9.050 e - 11$
6	Standard	89.289	2.563		12.746	1
7	Gradient4	109.696	2	ZF4	11.793	1	1.728	$- 6.17 e - 9$	$- 9.20 e - 9$	$2.484 e - 11$	$1.38 e - 10$	$- 8.55 e - 11$	$- 8.524 e - 11$
8	Standard	30.026	1		12.117	1
9	Gradient4	30.903	8.243	LAK3	12.906	1	1.747	$- 7.26 e - 9$	$- 1.02 e - 8$	$1.597 e - 11$	$1.43 e - 10$	$- 9.58 e - 11$	$- 9.901 e - 11$
10	Standard	−88.823	6.511		13.203	1
11	Gradient4	27.269	9.6	LAK3	13.259	1	1.747	$- 1.88 e - 8$	$- 2.47 e - 8$	$- 3.69 e - 10$	$2.25 e - 10$	$- 2.3 e - 10$	$- 2.595 e - 10$
12	Standard	21.155	1.497		11.142	1
13	Gradient4	28.329	7.5	LAK3	11.174	1	1.747	$- 1.18 e - 7$	$- 1.33 e - 7$	$- 1.91 e - 10$	$1.082 e - 9$	$- 1.24 e - 9$	$- 1.330 e - 9$
14	Standard	365.078	3.758		10.361	1
15	Gradient4	−20.802	2.00	ZF4	10.116	1	1.728	$- 1.59 e - 7$	$- 1.41 e - 7$	$3.10 e - 10$	$1.642 e - 9$	$- 1.31 e - 9$	$- 1.16 e - 9$
16	Standard	−119.91	1.326		10.542	1
17	Standard	infinity	1	BK7	10.774	1
18	Standard	infinity	0.5		10.847	1
IMA	Standard	Infinity	—		10.952	—

	RMS (μm)
Field Angle	Uniform Refractive Index	Irregular Refractive Index
Zero-field	2.747	5.176
Half-field	4.590	8.725
Full-field	20.370	25.438

	RMS (μm)
Field Angle	Irregular Refractive Index	Thermoelastic Deformation
Zero-field	5.176	16.030
Half-field	8.725	16.800
Full-field	25.438	34.865

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Tables (6)

Equations (11)

Applied Optics