Lens design with reduced sensitivity to thermally induced stress birefringence

Andrew F. Kurtz; Joseph R. Bietry

doi:10.1364/AO.52.004311

Applied Optics
Vol. 52,
Issue 18,
pp. 4311-4322
(2013)
•https://doi.org/10.1364/AO.52.004311

Lens design with reduced sensitivity to thermally induced stress birefringence

Andrew F. Kurtz and Joseph R. Bietry

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Andrew F. Kurtz and Joseph R. Bietry, "Lens design with reduced sensitivity to thermally induced stress birefringence," Appl. Opt. 52, 4311-4322 (2013)

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Abstract

In optical systems required to maintain the polarization states of the transiting light, mechanically induced stress birefringence can degrade performance, at least locally altering polarization phase and ultimately reducing polarization contrast. Although thermally induced stress birefringence can cause similar problems in imaging systems bearing high optical flux, appropriate design approaches to resolve this problem have been lacking. This paper first develops criteria to select optical glasses with reduced sensitivity to thermally induced stress birefringence. The design of projection lenses using the resulting thermal stress desensitized reduced glass list is then discussed, as is the application of such lenses in laser projection systems.

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	Refractive Indices	ABBE	Thermal Conductivity K	Thermal Expansion; CTE or $ϑ$ ; ( $- 30 \sim + 70 ° C$ )	Poisson’s Ratio ( $μ$ )	Young’s Modulus–Elasticity (E)	Stress Optical Coefficient ( $ϑ$ )	Absorption Coefficient $ϑ τ$ Blue	Figures of Merit
Glass	$n_{d}$	$v_{d}$	( $W / m K$ )	( $10^{- 6} / K$ )	( $μ$ )	$10^{3} N / {mm}^{2}$	$10^{- 6} {mm}^{2} / N$	${mm}^{- 1}$	$M_{1}^{'}$ : with CTE, $ϑ$ , and K only	$M_{1}^{''}$ : with $ϑ$ , $ϑ$ , and E only	$M_{1}$ : Glass Only: with CTE, $ϑ$ , $ϑ$ , E, $ϑ$ and K
Schott
LITHOSIL-Q	1.45844	67.83	1.31	0.50	0.17	72.0	3.4	0.0000100	0.000017	66.219	0.00113
Schott SF57HHT	1.84666	23.83	0.62	8.3	0.248	54.0	0.02	0.0008898	0.000148	115.820	0.01711
Ohara S-FSL 5	1.487490	70.23	1.007	9.0	0.227	62.3	2.87	0.0000100	0.000258	80.035	0.02067
Schott SF57	1.84666	23.83	0.62	8.3	0.248	54.0	0.02	0.0013009	0.000216	115.820	0.02501
Ohara PBH56	1.841390	24.56	0.635	8.4	0.250	59.2	0.09	0.0005013	0.000379	124.304	0.04710
Schott N-PK52A	1.49700	81.61	0.73	13.01	0.298	71.0	0.67	0.0003005	0.002619	138.547	0.36285
Schott N-FK51A	1.48656	84.47	0.76	12.74	0.302	73.0	0.7	0.0003005	0.002679	137.649	0.36882
Schott LLF1	1.54814	45.75	0.80	8.1	0.208	60.0	3.05	0.0001603	0.003961	94.697	0.37507
Ohara S-FPL53	1.438750	94.93	0.857	14.5	0.303	69.1	0.57	0.0004008	0.003313	115.682	0.38321
Schott F2	1.62004	36.37	0.78	8.2	0.22	57.0	2.81	0.0002002	0.004613	93.688	0.43219
Schott LF5	1.58144	40.85	0.866	9.1	0.223	59.0	2.83	0.0002005	0.005164	87.683	0.45275
Ohara S-NSL36	1.517417	52.43	1.089	8.0	0.139	64.0	2.82	0.0003005	0.006778	68.257	0.46266
Schott N-BK7	1.51680	64.17	1.114	7.1	0.206	82.0	2.77	0.0002810	0.005526	92.706	0.51231
Schott SF6	1.80518	25.43	0.673	8.1	0.244	55.0	0.65	0.0009041	0.004760	108.100	0.51455
Ohara S-BAL11	1.572501	57.74	0.974	6.6	0.237	81.9	2.42	0.0003005	0.004799	110.205	0.52885
Ohara S-BAL35	1.589130	61.14	0.915	5.7	0.250	83.2	2.15	0.0004008	0.004912	121.239	0.59550
Ohara S-NSL 3	1.518229	58.90	1.026	9.0	0.217	70.0	2.60	0.0003005	0.007031	87.134	0.61260
Ohara S-BSM10	1.622799	57.05	0.822	6.5	0.266	83.5	1.88	0.0004008	0.004898	138.394	0.67783
Ohara S-LAL18	1.729157	54.68	0.871	5.9	0.289	120.4	1.58	0.0004008	0.003736	194.419	0.72640
Schott SF1	1.71736	29.51	0.702	8.1	0.232	56.0	1.8	0.0006452	0.009407	103.870	0.97707
Schott SF4	1.75520	27.58	0.65	8.0	0.241	56.0	1.36	0.0008081	0.008792	113.510	0.99800
Schott SF2	1.64769	33.85	0.735	8.4	0.227	55.0	2.62	0.0004829	0.010628	96.805	1.02881
Ohara S-LAH66	1.772499	49.60	0.845	6.2	0.291	121.9	1.43	0.0006018	0.005336	203.470	1.08564
Ohara S-LAL54	1.650996	56.16	0.761	7.1	0.277	87.7	1.66	0.0007025	0.008279	159.396	1.31967
Ohara S-LAM60	1.743198	49.34	0.845	5.4	0.294	113.2	1.90	0.0007025	0.007207	189.751	1.36759
Ohara S-LAL61	1.740999	52.64	0.861	5.7	0.291	119.0	1.55	0.0009041	0.007987	194.938	1.55707
Ohara S-LAM54	1.756998	47.82	0.891	5.7	0.292	117.2	1.70	0.0010050	0.009739	185.788	1.80934
Schott N-SSK8	1.61773	49.83	0.84	7.21	0.251	84.0	2.36	0.0012596	0.021433	133.511	2.86159
Schott N-SF2	1.64769	33.82	1.14	6.68	0.231	86.0	3.06	0.0016129	0.032970	98.100	3.23432
Schott N-KZFS4	1.61336	44.49	0.84	7.3	0.241	78.0	3.9	0.0010050	0.028613	122.341	3.50059
Schott N-SF4	1.75513	27.38	0.95	9.45	0.256	90.0	2.76	0.0041864	0.109190	127.334	13.90368
Ohara S-NPH 2	1.922860	18.90	0.969	6.7	0.249	99.1	3.31	0.0094311	0.209153	136.179	28.48221

Original Projection Lens Design with Common Glasses, Per Fig. 6a
Element No.	Material	Thickness (t) (mm)	Glass Only Figure of Merit	F.O.M. w/Thickness $M^{'} = M_{1} * t$	(With Disruptor) ( $W / {mm}^{2}$ )	Normalized	(Using Normalized Peak Power)
1	SBSM10_OHARA	8.28	0.6778	5.6124	0.06	0.126	0.707
2	SLAM60_OHARA	5.35	1.3676	7.3166	0.117	0.246	1.798
3	SF1_SCHOTT	2.7	0.97707	2.6381	0.182	0.382	1.009
4	SF2_SCHOTT	2.7	1.0288	2.7778	0.476	1.000	2.778
5	SLAM60_OHARA	5.7	1.3676	7.7952	0.25	0.525	4.094
6	SLAM60_OHARA	7.21	1.3676	9.8603	0.142	0.298	2.942
	$M_{1}$ Glass only FOM for lens		6.7865		$M_{2}$ : Glass & applied power FOM		13.328
Alternate Design—Using Only Fused Silica and PBH56, Per Fig. 8a
Element No.	Material	Thickness (t) (mm)	Glass Only Figure of Merit	F.O.M. w/Thickness $M^{'} = M_{1} * t$	(With Disruptor) ( $W / {mm}^{2}$ )	Normalized	(Using Normalized Peak Power)
1	SIO2_SCHOTT	5.778	0.00113	0.0065	0.06	0.126	0.001
2	SIO2_SCHOTT	6.0238	0.00113	0.0068	0.117	0.246	0.002
3	PBH56_OHARA	8.1486	0.04710	0.3838	0.182	0.382	0.147
4	PBH56_OHARA	2.7	0.04710	0.1272	0.476	1.000	0.127
5	PBH56_OHARA	2.7	0.04710	0.1272	0.4	0.840	0.107
6	PBH56_OHARA	8.4576	0.04710	0.3984	0.25	0.525	0.209
7	SIO2_SCHOTT	7.1162	0.00113	0.0080	0.18	0.378	0.003
8	SIO2_SCHOTT	6.3744	0.00113	0.0072	0.142	0.298	0.002
	$M_{1}$ Glass only FOM for lens		0.1929		$M_{2}$ : Glass and applied power FOM		0.598
	Improvement Ratio—lens only		35.17		Improv. Ratio—w/thickness & power		22.30
Alternate Design—Using Low Figure of Merit Glasses and Common Glasses, Per Figure 9a
Element No.	Material	Thickness (t) (mm)	Glass Only Figure of Merit	F.O.M. w/Thickness $M^{'} = M_{1} * t$	Peak Power (With Disruptor)	Peak Power Normalized	F.O.M. for Glass and Power (Using Normalized Peak Power)
1	SLAL18_OHARA	8.52	0.7264	6.1890	1.0968	0.124	0.765
2	SLAL18_OHARA	5.5	0.7264	3.9952	5.6881	0.641	2.561
3	PBH56_OHARA	2.5	0.04710	0.1178	8.8721	1.000	0.118
4	SIO2_SCHOTT	2.7	0.00113	0.0031	1.9927	0.225	0.001
5	SLAL18_OHARA	5.07	0.7264	3.6829	1.5989	0.180	0.664
6	SLAL18_OHARA	6.98	0.7264	5.0703	1.1521	0.130	0.658
	$M_{1}$ Glass only FOM for lens		2.9538		$M_{2}$ : Glass & applied power FOM		4.767
	Improvement Ratio—lens only		2.297		Improv. Ratio—w/thickness & power		2.80

Original Relay Lens with Only Common Glasses
Element No.	Material Type	Thickness (mm)	$M_{1}$ Glass Only Figure of Merit	F.O.M w/Thickness $M^{'} = M_{1} * t$	Peak Power ( $W / {mm}^{2}$ )	Peak Power Normalized	F.O.M ( $M_{2}$ )
1	S-BAL35 Ohara	10.00	0.5955	5.955	0.02	0.080	0.4764
2	S-BAL35 Ohara	5.58	0.5955	3.323	0.045	0.180	0.5981
3	SF4_SCHOTT	4.00	0.998	3.992	0.122	0.488	1.9481
4	SF4_SCHOTT	4.00	0.998	3.992	0.25	1.000	3.9920
5	SLAM54_OHARA	8.00	1.8093	14.475	0.097	0.388	5.6162
6	SNSL3_OHARA	14.00	0.6126	8.576	0.084	0.336	2.8817
7	SLAM54_OHARA	8.00	1.8093	14.475	0.063	0.252	3.6476
	Glass only FOM value for lens		7.4183			Aggregate M2:	19.1601
Alternate Design—Using Only Fused Silica and Schott SF-57
Element No.	Material Type	Thickness (mm)	$M_{1}$ Glass Only Figure of Merit	F.O.M w/Thickness $M^{'} = M_{1} * t$	Peak Power ( $W / {mm}^{2}$ )	Peak Power Normalized	F.O.M ( $M_{2}$ )
1	SIO2_SCHOTT	9.998	0.00113	0.011	0.02	0.080	0.0009
2	SIO2_SCHOTT	15.000	0.00113	0.017	0.045	0.180	0.0031
3	Schott SF 57	5.000	0.025012	0.125	0.122	0.488	0.0610
4	Schott SF 57	4.000	0.025012	0.100	0.25	1.000	0.1000
5	SIO2_SCHOTT	15.000	0.00113	0.017	0.097	0.388	0.0066
6	SIO2_SCHOTT	9.926	0.00113	0.011	0.084	0.336	0.0038
7	Schott SF 57	7.000	0.025012	0.175	0.063	0.252	0.0441
	Glass only FOM value for lens		0.0796		Aggregate M2:		0.2195
	Improvement ratio—glass only		93.25		Improvement: with thickness & power		87.291
Alternate Design—Using Both Low Figure of Merit Glass and Common Glasses, Per Fig. 9c
Element No. Re-Design	Material Type	Thickness (mm)	$M_{1}$ Glass only Figure of Merit	F.O.M w/Thickness $M^{'} = M_{1} * t$	Peak Power lux	Peak Power Normalized	F.O.M ( $M_{2}$ )
1	SLAL18 Ohara	7.73	0.72640	5.615	6.5314	0.2752	1.5453
2	SIO2_SCHOTT	8.97	0.00113	0.010	12.127	0.5110	0.0052
3	PBH56_OHARA	5.0	0.04710	0.236	13.719	0.5781	0.1361
4	PBH56_OHARA	4.13	0.04710	0.195	23.733	1.0000	0.1945
5	SLAL18 Ohara	11.88	0.72640	8.630	13.865	0.5842	5.0415
6	SLAL18 Ohara	11.43	0.72640	8.303	4.7171	0.1988	1.6502
7	PBH56_OHARA	9.53	0.04710	0.449	3.5212	0.1484	0.0666
	Glass only FOM value for lens		2.3217		Aggregate M2:		8.6395
	Improvement ratio—lens only		3.195		Improvement: with thickness & power		2.218

	Refractive Indices	ABBE	Thermal Conductivity K	Thermal Expansion; CTE or $ϑ$ ; ( $- 30 \sim + 70 ° C$ )	Poisson’s Ratio ( $μ$ )	Young’s Modulus–Elasticity (E)	Stress Optical Coefficient ( $ϑ$ )	Absorption Coefficient $ϑ τ$ Blue	Figures of Merit
Glass	$n_{d}$	$v_{d}$	( $W / m K$ )	( $10^{- 6} / K$ )	( $μ$ )	$10^{3} N / {mm}^{2}$	$10^{- 6} {mm}^{2} / N$	${mm}^{- 1}$	$M_{1}^{'}$ : with CTE, $ϑ$ , and K only	$M_{1}^{''}$ : with $ϑ$ , $ϑ$ , and E only	$M_{1}$ : Glass Only: with CTE, $ϑ$ , $ϑ$ , E, $ϑ$ and K
Schott
LITHOSIL-Q	1.45844	67.83	1.31	0.50	0.17	72.0	3.4	0.0000100	0.000017	66.219	0.00113
Schott SF57HHT	1.84666	23.83	0.62	8.3	0.248	54.0	0.02	0.0008898	0.000148	115.820	0.01711
Ohara S-FSL 5	1.487490	70.23	1.007	9.0	0.227	62.3	2.87	0.0000100	0.000258	80.035	0.02067
Schott SF57	1.84666	23.83	0.62	8.3	0.248	54.0	0.02	0.0013009	0.000216	115.820	0.02501
Ohara PBH56	1.841390	24.56	0.635	8.4	0.250	59.2	0.09	0.0005013	0.000379	124.304	0.04710
Schott N-PK52A	1.49700	81.61	0.73	13.01	0.298	71.0	0.67	0.0003005	0.002619	138.547	0.36285
Schott N-FK51A	1.48656	84.47	0.76	12.74	0.302	73.0	0.7	0.0003005	0.002679	137.649	0.36882
Schott LLF1	1.54814	45.75	0.80	8.1	0.208	60.0	3.05	0.0001603	0.003961	94.697	0.37507
Ohara S-FPL53	1.438750	94.93	0.857	14.5	0.303	69.1	0.57	0.0004008	0.003313	115.682	0.38321
Schott F2	1.62004	36.37	0.78	8.2	0.22	57.0	2.81	0.0002002	0.004613	93.688	0.43219
Schott LF5	1.58144	40.85	0.866	9.1	0.223	59.0	2.83	0.0002005	0.005164	87.683	0.45275
Ohara S-NSL36	1.517417	52.43	1.089	8.0	0.139	64.0	2.82	0.0003005	0.006778	68.257	0.46266
Schott N-BK7	1.51680	64.17	1.114	7.1	0.206	82.0	2.77	0.0002810	0.005526	92.706	0.51231
Schott SF6	1.80518	25.43	0.673	8.1	0.244	55.0	0.65	0.0009041	0.004760	108.100	0.51455
Ohara S-BAL11	1.572501	57.74	0.974	6.6	0.237	81.9	2.42	0.0003005	0.004799	110.205	0.52885
Ohara S-BAL35	1.589130	61.14	0.915	5.7	0.250	83.2	2.15	0.0004008	0.004912	121.239	0.59550
Ohara S-NSL 3	1.518229	58.90	1.026	9.0	0.217	70.0	2.60	0.0003005	0.007031	87.134	0.61260
Ohara S-BSM10	1.622799	57.05	0.822	6.5	0.266	83.5	1.88	0.0004008	0.004898	138.394	0.67783
Ohara S-LAL18	1.729157	54.68	0.871	5.9	0.289	120.4	1.58	0.0004008	0.003736	194.419	0.72640
Schott SF1	1.71736	29.51	0.702	8.1	0.232	56.0	1.8	0.0006452	0.009407	103.870	0.97707
Schott SF4	1.75520	27.58	0.65	8.0	0.241	56.0	1.36	0.0008081	0.008792	113.510	0.99800
Schott SF2	1.64769	33.85	0.735	8.4	0.227	55.0	2.62	0.0004829	0.010628	96.805	1.02881
Ohara S-LAH66	1.772499	49.60	0.845	6.2	0.291	121.9	1.43	0.0006018	0.005336	203.470	1.08564
Ohara S-LAL54	1.650996	56.16	0.761	7.1	0.277	87.7	1.66	0.0007025	0.008279	159.396	1.31967
Ohara S-LAM60	1.743198	49.34	0.845	5.4	0.294	113.2	1.90	0.0007025	0.007207	189.751	1.36759
Ohara S-LAL61	1.740999	52.64	0.861	5.7	0.291	119.0	1.55	0.0009041	0.007987	194.938	1.55707
Ohara S-LAM54	1.756998	47.82	0.891	5.7	0.292	117.2	1.70	0.0010050	0.009739	185.788	1.80934
Schott N-SSK8	1.61773	49.83	0.84	7.21	0.251	84.0	2.36	0.0012596	0.021433	133.511	2.86159
Schott N-SF2	1.64769	33.82	1.14	6.68	0.231	86.0	3.06	0.0016129	0.032970	98.100	3.23432
Schott N-KZFS4	1.61336	44.49	0.84	7.3	0.241	78.0	3.9	0.0010050	0.028613	122.341	3.50059
Schott N-SF4	1.75513	27.38	0.95	9.45	0.256	90.0	2.76	0.0041864	0.109190	127.334	13.90368
Ohara S-NPH 2	1.922860	18.90	0.969	6.7	0.249	99.1	3.31	0.0094311	0.209153	136.179	28.48221

Original Projection Lens Design with Common Glasses, Per Fig. 6a
Element No.	Material	Thickness (t) (mm)	Glass Only Figure of Merit	F.O.M. w/Thickness $M^{'} = M_{1} * t$	(With Disruptor) ( $W / {mm}^{2}$ )	Normalized	(Using Normalized Peak Power)
1	SBSM10_OHARA	8.28	0.6778	5.6124	0.06	0.126	0.707
2	SLAM60_OHARA	5.35	1.3676	7.3166	0.117	0.246	1.798
3	SF1_SCHOTT	2.7	0.97707	2.6381	0.182	0.382	1.009
4	SF2_SCHOTT	2.7	1.0288	2.7778	0.476	1.000	2.778
5	SLAM60_OHARA	5.7	1.3676	7.7952	0.25	0.525	4.094
6	SLAM60_OHARA	7.21	1.3676	9.8603	0.142	0.298	2.942
	$M_{1}$ Glass only FOM for lens		6.7865		$M_{2}$ : Glass & applied power FOM		13.328
Alternate Design—Using Only Fused Silica and PBH56, Per Fig. 8a
Element No.	Material	Thickness (t) (mm)	Glass Only Figure of Merit	F.O.M. w/Thickness $M^{'} = M_{1} * t$	(With Disruptor) ( $W / {mm}^{2}$ )	Normalized	(Using Normalized Peak Power)
1	SIO2_SCHOTT	5.778	0.00113	0.0065	0.06	0.126	0.001
2	SIO2_SCHOTT	6.0238	0.00113	0.0068	0.117	0.246	0.002
3	PBH56_OHARA	8.1486	0.04710	0.3838	0.182	0.382	0.147
4	PBH56_OHARA	2.7	0.04710	0.1272	0.476	1.000	0.127
5	PBH56_OHARA	2.7	0.04710	0.1272	0.4	0.840	0.107
6	PBH56_OHARA	8.4576	0.04710	0.3984	0.25	0.525	0.209
7	SIO2_SCHOTT	7.1162	0.00113	0.0080	0.18	0.378	0.003
8	SIO2_SCHOTT	6.3744	0.00113	0.0072	0.142	0.298	0.002
	$M_{1}$ Glass only FOM for lens		0.1929		$M_{2}$ : Glass and applied power FOM		0.598
	Improvement Ratio—lens only		35.17		Improv. Ratio—w/thickness & power		22.30
Alternate Design—Using Low Figure of Merit Glasses and Common Glasses, Per Figure 9a
Element No.	Material	Thickness (t) (mm)	Glass Only Figure of Merit	F.O.M. w/Thickness $M^{'} = M_{1} * t$	Peak Power (With Disruptor)	Peak Power Normalized	F.O.M. for Glass and Power (Using Normalized Peak Power)
1	SLAL18_OHARA	8.52	0.7264	6.1890	1.0968	0.124	0.765
2	SLAL18_OHARA	5.5	0.7264	3.9952	5.6881	0.641	2.561
3	PBH56_OHARA	2.5	0.04710	0.1178	8.8721	1.000	0.118
4	SIO2_SCHOTT	2.7	0.00113	0.0031	1.9927	0.225	0.001
5	SLAL18_OHARA	5.07	0.7264	3.6829	1.5989	0.180	0.664
6	SLAL18_OHARA	6.98	0.7264	5.0703	1.1521	0.130	0.658
	$M_{1}$ Glass only FOM for lens		2.9538		$M_{2}$ : Glass & applied power FOM		4.767
	Improvement Ratio—lens only		2.297		Improv. Ratio—w/thickness & power		2.80

Abstract

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Figures (12)

Tables (3)

Equations (7)

Applied Optics