Modulation-transfer-function-based optical sensitivity and tolerancing programs

John P. Starke; Charles M. Wise

doi:10.1364/AO.19.001768

Applied Optics
Vol. 19,
Issue 11,
pp. 1768-1772
(1980)
•https://doi.org/10.1364/AO.19.001768

Modulation-transfer-function-based optical sensitivity and tolerancing programs

John P. Starke and Charles M. Wise

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John P. Starke and Charles M. Wise, "Modulation-transfer-function-based optical sensitivity and tolerancing programs," Appl. Opt. 19, 1768-1772 (1980)

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Abstract

Two new computer programs are described. The first, zest, predicts the sensitivity of lens performance to perturbations of the constructional parameters of the lens. The second, zealot, predicts the statistical distribution of the performance expected from a sample of actual manufactured lenses. Both programs are based on the wave front and the modulation transfer function and permit a more general approach to lens specification, tolerancing, and testing.

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W(X,Y) = C₁ + C₂Y + C₃X +	Bias and tilts
C₄(2R² − 1) +	Defocus
2C₅XY + C₆(X² − Y²) +	Primary astigmatism
(3R² − 2)(C₇Y + C₈X) +	Primary coma
C₉(6R⁴ − 6R² + 1) +	Primary spherical
C₁₀(20R⁶ − 30R⁴ + 12R² − 1) +	Secondary spherical
(10R⁴ − 12R² + 3)(C₁₁X + C₁₂Y) +	Secondary coma
(4R² − 3)[C₁₃(X² − Y²) + 2C₁₄XY] +	Secondary astigmatism
C₁₅(X³ − 3XY²) + C₁₆(3X²Y − Y³) +	Primary trefoil
(5R² − 4)[C₁₇(X³ − 3XY²) + C₁₈(3X²Y − Y³)] +	Secondary trefoil
C₁₉(70R⁸ − 140R⁶ + 90R⁴ − 20R⁴ + 1) +	Tertiary spherical
(35R⁶ − 60R⁴ + 30R² − 4)(C₂₀X + C₂₁Y) +	Tertiary coma
C₂₂(X⁴ − 6X²Y² + Y⁴) + 4C₂₃XY(X² − Y²) +	Primary tetrafoil
(15R⁴ − 20R² + 6)[C₂₄(X² − Y²) + 2C₂₅XY] +	Tertiary astigmatism
C₂₆(252R¹⁰ − 630R⁸ + 560R⁶ − 210R⁴ + 30R² − 1)	Quaternary spherical

Description	Built-in perturbation value
Thickness/spacing	0.1 mm
Radius of curvature	5.0λ
Index of refraction	0.001
Primary Zernike spherical on surface^a	0.75λ P to V
Secondary Zernike spherical on surface^a	0.50λ P to V
Tertiary Zernike spherical on surface^a	0.286λ P to V
Quaternary Zernike spherical on surface^a	0.20λ P to V
Saddle—high at 0°	2.50λ P to V
Saddle—high at 45°	2.50λ P to V
Saddle—high at 90°	2.50λ P to V
Minus tilt about X axis	4.0 min
Plus Y displacement	0.01 mm
Plus tilt about X axis	4.0 min
Minus Y displacement	0.01 mm
Minus tilt about Y axis	4.0 min
Plus X displacement	0.01 mm

Lens	0.7 Field	Spatial frequency used in study (cycles/mm)	Comments
26 mm, f/1.9	18.0°	16	110 format camera lens (4 elements)
9 mm, f/4.8	25.0°	20	Reader lens (6 elements)
101 mm, f/12.5	20.0°	1	Instant camera lens (singlet)
22 mm, f/1.4	6.6°	20	8-mm movie projector lens(4 elements)
497 mm, f/14.6	157.4 mm	1	One-to-one copier lens (6 elements)

Lens	A	B	Linear correlation
On-axis coefficients
26 mm, f/1.9	1.183	−0.186	0.997
9 mm, f/4.8	1.243	−0.232	0.995
101 mm, f/12.5	1.305	−0.303	1.0
22 mm, f/1.4	1.115	−0.120	0.998
497 mm, f/14.6	1.301	−0.299	1.0
Off-axis coefficients
26 mm, f/1.9	1.106	−0.114	0.999
9 mm, f/4.8	1.219	−0.209	1.0
101 mm, f/12.5	1.288	−0.286	1.0
22 mm, f/l.4	1.127	−0.136	0.999
497 mm, f/14.6	1.298	−0.296	1.0

Lens	Axial perturbed MTF		0.7 Field perturbed MTF

	Actual	Synthesis	Actual	Synthesis
26 mm, f/1.9	0.837	0.836	0.790	0.793
9 mm, f/4.8	0.908	0.908	0.869	0.870
101 mm, f/12.5	0.982	0.981	0.961	0.963
22 mm, f/1.4	0.843	0.838	0.867	0.864
497 mm, f/14.6	0.977	0.977	0.971	0.971

	On-axis		Off-axis

	Exact method	zealot	Exact method	zealot
Nominal lens	0.890	0.890	0.809	0.809
Lens 1	0.749	0.752	0.784	0.779
Lens 2	0.833	0.830	0.560	0.563

Abstract

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Applied Optics