Experimental comparison of a Shack–Hartmann sensor and a phase-shifting interferometer for large-optics metrology applications

Jeffrey A. Koch; Robert W. Presta; Richard A. Sacks; Richard A. Zacharias; Erlan S. Bliss; Michael J. Dailey; Mark Feldman; Andrew A. Grey; Fred R. Holdener; Joseph T. Salmon; Lynn G. Seppala; John S. Toeppen; Lewis Van Atta; Bruno M. Van Wonterghem; Wayne T. Whistler; Scott E. Winters; Bruce W. Woods

doi:10.1364/AO.39.004540

Applied Optics
Vol. 39,
Issue 25,
pp. 4540-4546
(2000)
•https://doi.org/10.1364/AO.39.004540

Experimental comparison of a Shack–Hartmann sensor and a phase-shifting interferometer for large-optics metrology applications

Jeffrey A. Koch, Robert W. Presta, Richard A. Sacks, Richard A. Zacharias, Erlan S. Bliss, Michael J. Dailey, Mark Feldman, Andrew A. Grey, Fred R. Holdener, Joseph T. Salmon, Lynn G. Seppala, John S. Toeppen, Lewis Van Atta, Bruno M. Van Wonterghem, Wayne T. Whistler, Scott E. Winters, and Bruce W. Woods

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Jeffrey A. Koch, Robert W. Presta, Richard A. Sacks, Richard A. Zacharias, Erlan S. Bliss, Michael J. Dailey, Mark Feldman, Andrew A. Grey, Fred R. Holdener, Joseph T. Salmon, Lynn G. Seppala, John S. Toeppen, Lewis Van Atta, Bruno M. Van Wonterghem, Wayne T. Whistler, Scott E. Winters, and Bruce W. Woods, "Experimental comparison of a Shack–Hartmann sensor and a phase-shifting interferometer for large-optics metrology applications," Appl. Opt. 39, 4540-4546 (2000)

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Abstract

We performed a direct side-by-side comparison of a Shack–Hartmann wave-front sensor and a phase-shifting interferometer for the purpose of characterizing large optics. An expansion telescope of our own design allowed us to measure the surface figure of a 400-mm-square mirror with both instruments simultaneously. The Shack–Hartmann sensor produced data that closely matched the interferometer data over spatial scales appropriate for the lenslet spacing, and much of the <20-nm rms systematic difference between the two measurements was due to diffraction artifacts that were present in the interferometer data but not in the Shack–Hartmann sensor data. The results suggest that Shack–Hartmann sensors could replace phase-shifting interferometers for many applications, with particular advantages for large-optic metrology.

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Parameters	TF	BS	L2	M2	M1	L1	RF	DM
Axial position	0.0	305	(a) 617.4 (b) 637.4	1405.47	2767.47	4780.47	5322	5880.47
Clear aperture	101.6	152.4	102	76.2	394	610	622	400 × 400
Angle	Normal	45°	Normal	11°	11°	Normal	Normal	Normal
First surface radius, coating	N/A	∞, 1.06 µm anti- reflection	(a) 344.3 convex, 1.06 µm anti- reflection	∞, Al	∞, Al	∞, 1.06-µm antireflection	∞, Al	Variable, 1.06-µm high reflection
			(b) 586.7 concave, 1.06-µm anti- reflection
Second surface radius, coating	∞, Coated for high-reflection mirror testing	∞, bare	(a) 1986.0 convex, 1.06-µm anti- reflection	N/A	N/A	1854.32 convex asphere/ 1.06-µm antireflection	N/A	N/A
			(b) 988.0 convex, 1.06-µm anti- reflection
Thickness	N/A	20, 0.5° wedge	(a) 16.0 (b) 13.0	N/A	N/A	74.2	N/A	N/A
Material	N/A	Fused Silica	SF64A	BK7	Corning 7971	BK7	Corning 7971	Varies
Mount	θ/ϕ	θ/ϕ	x/y/z/θ/ϕ	θ/ϕ	Rough θ/ϕ	Fixed	θ/ϕ	θ/ϕ

Parameters	Notes	Measurements
Precision	Mean P–V or rms of the difference between two consecutive surface measurements during a sequence	30-nm P–V 5.3-nm rms

Stability	Mean P–V or rms of the difference between any surface measurement relative to the first during a sequence	36-nm P–V 6.4-nm rms (during 1-h measurement period)

Accuracy	P–V or rms of the average of many sequential surface measurements	213-nm P–V 36-nm rms

Repeatability	Root-mean-square deviation of the values of the P–V or rms during a sequence of surface measurements	4.3-nm P–V 0.64-nm rms

Reference flat surface figure	Measured on another, calibrated, large-aperture interferometer; the figure errors are primarily focus and astigmatism	415-nm P–V 27-nm rms (over 440-mm-square aperture)

Parameters	TF	BS	L2	M2	M1	L1	RF	DM
Axial position	0.0	305	(a) 617.4 (b) 637.4	1405.47	2767.47	4780.47	5322	5880.47
Clear aperture	101.6	152.4	102	76.2	394	610	622	400 × 400
Angle	Normal	45°	Normal	11°	11°	Normal	Normal	Normal
First surface radius, coating	N/A	∞, 1.06 µm anti- reflection	(a) 344.3 convex, 1.06 µm anti- reflection	∞, Al	∞, Al	∞, 1.06-µm antireflection	∞, Al	Variable, 1.06-µm high reflection
			(b) 586.7 concave, 1.06-µm anti- reflection
Second surface radius, coating	∞, Coated for high-reflection mirror testing	∞, bare	(a) 1986.0 convex, 1.06-µm anti- reflection	N/A	N/A	1854.32 convex asphere/ 1.06-µm antireflection	N/A	N/A
			(b) 988.0 convex, 1.06-µm anti- reflection
Thickness	N/A	20, 0.5° wedge	(a) 16.0 (b) 13.0	N/A	N/A	74.2	N/A	N/A
Material	N/A	Fused Silica	SF64A	BK7	Corning 7971	BK7	Corning 7971	Varies
Mount	θ/ϕ	θ/ϕ	x/y/z/θ/ϕ	θ/ϕ	Rough θ/ϕ	Fixed	θ/ϕ	θ/ϕ

Parameters	Notes	Measurements
Precision	Mean P–V or rms of the difference between two consecutive surface measurements during a sequence	30-nm P–V 5.3-nm rms

Stability	Mean P–V or rms of the difference between any surface measurement relative to the first during a sequence	36-nm P–V 6.4-nm rms (during 1-h measurement period)

Accuracy	P–V or rms of the average of many sequential surface measurements	213-nm P–V 36-nm rms

Repeatability	Root-mean-square deviation of the values of the P–V or rms during a sequence of surface measurements	4.3-nm P–V 0.64-nm rms

Reference flat surface figure	Measured on another, calibrated, large-aperture interferometer; the figure errors are primarily focus and astigmatism	415-nm P–V 27-nm rms (over 440-mm-square aperture)

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Applied Optics