Rapid optimization of cost-based tolerancing

Akira Yabe

doi:10.1364/AO.51.000855

Applied Optics
Vol. 51,
Issue 7,
pp. 855-860
(2012)
•https://doi.org/10.1364/AO.51.000855

Rapid optimization of cost-based tolerancing

Akira Yabe

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Akira Yabe, "Rapid optimization of cost-based tolerancing," Appl. Opt. 51, 855-860 (2012)

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Abstract

In this paper, a rapid optimization method of cost-based tolerancing is proposed. An example shows that only a few cases of the Monte Carlo simulation are necessary to find the best balance of the yield and the tolerance cost for the practical tolerancing problem.

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Criterion	Nominal	Requirement
Object to image distance	400 mm	$400 mm \pm 0.2 mm$
Distortion at 0.85 full field	0.256%	$\pm 0.3 %$
Tangential MTF at full field	64.5%	$> 55 %$

FNO	4.5
Object height	160 mm
Magnification	$- 0.1$
Object to image distance	400 mm
Lens length	$< 30 mm$
Distortion	$< 0.25 %$
Wavelength	546.1 486.1 587.6 nm
Spectral weight	1 1 1
MTF evaluation at	$50 lp / mm$

	RDY	THI	GLA	APE
OBJ	INFINITY	357.0082800
1	12.1760935	2.7188281	N-LAF21	5.8315813
2	35.6137262	0.4695552		5.0663202
3	$- 115.2954762$	3.5227863	SF15	5.0699115
4	12.4943648	0.9687071		3.4711074
STOP	INFINITY	0.0001701		3.2511716
6	15.9228565	12.2809315	N-LAF21	3.5246525
7	$- 23.6598978$	2.8120746		5.7953646
8	$- 9.3191630$	7.22219507	F5	6.0150377
9	$- 37.3344782$	12.5950279		9.2822689

	Standard	Tight	Additional Cost
Newtonian fringe	5	2	1
Surface separation	0.03 mm	0.01 mm	1
Refractive index (Nd)	$50 d - 5$	$20 d - 5$	1
Abbe number (Vd)	0.80%	0.30%	1

Criterion	Nominal	SD	Requirement	Yield
O/I dist.	400 mm	0.181 mm	$400 mm \pm 200 um$	0.70
Distortion
0.5ff	0.146%	0.009%	$\pm 0.3 %$	1.00
0.7ff	0.223%	0.018%	$\pm 0.3 %$	1.00
0.85ff	0.256%	0.029%	$\pm 0.3 %$	0.96
1.0ff	0.206%	0.039%	$\pm 0.3 %$	1.00
Criterion	Nominal	AL	Requirement	Yield
MTF $50 lp / mm$
On axis	72.8%	2.7%	$> 60 %$	0.98
0.5ff S	76.3%	1.3%	$> 60 %$	1.00
0.5ff T	75.9%	0.5%	$> 60 %$	1.00
0.7ff S	74.1%	0.7%	$> 60 %$	1.00
0.7ff T	77.1%	1.5%	$> 60 %$	1.00
0.85ff S	73.3%	0.8%	$> 60 %$	1.00
0.85ff T	73.3%	4.9%	$> 60 %$	0.91
1.0ff S	65.5%	0.8%	$> 55 %$	1.00
1.0ff T	64.5%	10.5%	$> 55 %$	0.59
DOF	0.072 mm	0.034 mm	$> 0.04 mm$	0.55

	O/I dist.		MTF ff-T		DOF		Total
	Yield	SD	Yield	AL	Yield	AL	Yield	Cost
T1	0.70	0.188 mm	0.59	15.1%	0.55	0.095 mm	0.38	0
T2	1.00	0.071 mm	0.98	1.9%	0.99	0.026 mm	0.98	23
T3 aiming	0.90	0.140 mm	0.90	4.5%	0.90	0.040 mm
result	0.89		0.86		0.83		0.72	5
T4 aiming	0.89	0.140 mm	0.90	3.7%	0.90	0.034 mm
result	0.93		0.92		0.93		0.83	6

O/I	MTF	DOF	T1	T3	T4
out	out	out	0.12	0.01	0.00
OK	out	out	0.27	0.12	0.06
out	OK	out	0.04	0.01	0.00
out	out	OK	0.00	0.01	0.00
out	OK	OK	0.14	0.08	0.07
OK	out	OK	0.02	0.01	0.02
OK	OK	out	0.02	0.03	0.01

Cost	Best Yield
0	0.38
1	0.49
2	0.55
3	0.6
4	0.69
5	0.73
6	0.83
7	0.9

Cost	Best Yield
0	0.38
1	0.49
2	0.55
3	0.6
4	0.69
5	0.73
6	0.83
7	0.9

Abstract

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Tables (9)

Equations (11)

Applied Optics