Deformation-free form error measurement of thin, plane-parallel optics floated on a heavy liquid

Jiyoung Chu; Ulf Griesmann; Quandou Wang; Johannes A. Soons; Eric C. Benck

doi:10.1364/AO.49.001849

Applied Optics
Vol. 49,
Issue 10,
pp. 1849-1858
(2010)
•https://doi.org/10.1364/AO.49.001849

Deformation-free form error measurement of thin, plane-parallel optics floated on a heavy liquid

Jiyoung Chu, Ulf Griesmann, Quandou Wang, Johannes A. Soons, and Eric C. Benck

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Jiyoung Chu, Ulf Griesmann, Quandou Wang, Johannes A. Soons, and Eric C. Benck, "Deformation-free form error measurement of thin, plane-parallel optics floated on a heavy liquid," Appl. Opt. 49, 1849-1858 (2010)

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Table of Contents Category
- Instrumentation, Measurement, and Metrology
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About this Article
History
- Original Manuscript: January 15, 2010
- Revised Manuscript: March 1, 2010
- Manuscript Accepted: March 4, 2010
- Published: March 29, 2010

Abstract

We describe a novel method for measuring the unconstrained flatness error of thin, plane-parallel precision optics. Test parts are floated on high-density aqueous metatungstate solutions while measuring the flatness error with an interferometer. The support of the flat optics by the uniform hydrostatic pressure at the submerged face of the flat optic eliminates flatness errors caused by mounting forces. A small, well characterized flatness error results from the bending of the floating flat by the hydrostatic pressure gradient at the edges. An equation describing the bending of thin, flat plates floating on a liquid is derived, which can be used to correct the flatness measurements of arbitrarily shaped plates. The method can be used to measure flatness errors of both nontransparent and transparent parts, and it is illustrated with flatness measurements of photomask blanks and substrates for extreme ultraviolet lithography. The refractive index of a saturated aqueous lithium metatungstate solution was measured at $632.8 nm$ and was found to be close to the refractive indices of several low thermal expansion optical materials.

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Name Abbreviation	Sodium Metatungstate (SMT)	Lithium Metatungstate (LMT)	Lithium Polytungstate (LST)
Formula	${Na}_{6} [H_{2} W_{12} O_{40}] \cdot 3 H_{2} O$	${Li}_{6} [H_{2} W_{12} O_{40}] \cdot 3 H_{2} O$	proprietary
Density $ρ [g / {cm}^{3}]$		2.95	2.85
pH	$\approx 3$	$\approx 4$	$\approx 4$
Viscosity $μ [mPa \cdot s]$	$20 \pm 1$	$36 \pm 1$	$12 \pm 1$
n at $632.8 nm$ and $16.6 ° C$		$1.5888 \pm 0.0002$

Name	Density $[g / {cm}^{3}]$	Refractive Index
Fused silica (generic)	2.201	1.45701 (see [21])
Corning ULE 7972^a	2.21	1.4840
Schott ZERODUR^a	2.55	1.5404
Ohara CLEARCERAM-Z ^a	2.53	1.5477

Samples	Sampling coefficients	η (see Ref. [17])
13	$\frac{[- 1, - 8, - 11, 10, 43, 46, 0, - 46, - 43, - 10, 11, 8, 1]}{\sqrt{3} [1, 0, - 9, - 18, - 9, 18, 34, 18, - 9, - 18, - 9, 0, 1]}$	$\frac{108}{\sqrt{18239}} ≃ 0.8$
7	$\frac{[- 1, - 3, 3, 0, - 3, 3, 1]}{\sqrt{3} [1, - 1, - 1, 2, - 1, - 1, 1]}$	$\frac{6 \sqrt{3}}{\sqrt{119}} ≃ 0.95$

Name Abbreviation	Sodium Metatungstate (SMT)	Lithium Metatungstate (LMT)	Lithium Polytungstate (LST)
Formula	${Na}_{6} [H_{2} W_{12} O_{40}] \cdot 3 H_{2} O$	${Li}_{6} [H_{2} W_{12} O_{40}] \cdot 3 H_{2} O$	proprietary
Density $ρ [g / {cm}^{3}]$		2.95	2.85
pH	$\approx 3$	$\approx 4$	$\approx 4$
Viscosity $μ [mPa \cdot s]$	$20 \pm 1$	$36 \pm 1$	$12 \pm 1$
n at $632.8 nm$ and $16.6 ° C$		$1.5888 \pm 0.0002$

Name	Density $[g / {cm}^{3}]$	Refractive Index
Fused silica (generic)	2.201	1.45701 (see [21])
Corning ULE 7972^a	2.21	1.4840
Schott ZERODUR^a	2.55	1.5404
Ohara CLEARCERAM-Z ^a	2.53	1.5477

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Applied Optics