High-accuracy interferometer with a prism pair for measurement of the absolute refractive index of glass

Yasuaki Hori; Akiko Hirai; Kaoru Minoshima; Hirokazu Matsumoto

doi:10.1364/AO.48.002045

Applied Optics
Vol. 48,
Issue 11,
pp. 2045-2050
(2009)
•https://doi.org/10.1364/AO.48.002045

High-accuracy interferometer with a prism pair for measurement of the absolute refractive index of glass

Yasuaki Hori, Akiko Hirai, Kaoru Minoshima, and Hirokazu Matsumoto

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Yasuaki Hori, Akiko Hirai, Kaoru Minoshima, and Hirokazu Matsumoto, "High-accuracy interferometer with a prism pair for measurement of the absolute refractive index of glass," Appl. Opt. 48, 2045-2050 (2009)

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Abstract

We propose a variable-path interferometric technique for the measurement of the absolute refractive index of optical glasses. We use two interferometers to decide the ratio between changes in the optical path in a prism-shaped sample glass and in air resulting from displacement of the sample. The method allows precise measurements to be made without prior knowledge of the properties of the sample. The combined standard uncertainty of the proposed method is $1.6 \times 10^{- 6}$ .

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Category	Factor $x_{i}$	$u (x_{i})$	$\partial f / \partial x_{i}$	Uncertainty $u_{i}$
Interferometer	Wavelength ( $633 nm$ )	$3.8 \times 10^{- 9} μm$	$n_{s} / λ_{2}$	$9.1 \times 10^{- 9}$
	Wavelength ( $543 nm$ )	$3.1 \times 10^{- 7} μm$	$n_{s} λ_{1} / {λ_{2}}^{2}$	$8.6 \times 10^{- 7}$
	Phase measurement of interferometer 1	$0.16 rad$	$λ_{1} / 4 π Δ x_{2}$	$(9.5 \times 10^{- 7})$ ^b
	Alignment of interferometer 1	$2.3 \times 10^{- 4} rad$	$(n_{s} / 6) \times u (θ_{1})$ ^c	$1.3 \times 10^{- 8}$
	Phase measurement of interferometer 2	$0.16 rad$	$n_{s} λ_{2} / 4 π Δ x_{2}$	$(1.2 \times 10^{- 6})$ ^b
	Alignment of interferometer 2	$4.3 \times 10^{- 4} rad$	$(n_{s} / 6) \times u (θ_{2})$ ^c	$4.7 \times 10^{- 8}$
	Alignment between prism and stage	$0.038 μm$	$(n_{s} - n_{L}) / Δ x_{2} \cos θ_{a}$	$2.5 \times 10^{- 7}$
	Abbe’s error (yawing, pitching)	$1.0 \times 10^{- 5} rad$	$n_{s} Δ d / Δ x_{2}$	$8.7 \times 10^{- 7}$
Measurement	Repeatability	$1.91 \times 10^{- 6} / \sqrt{10}$	1	$6.0 \times 10^{- 7}$
	Drift	$4.3 \times 10^{- 7}$	1	$4.3 \times 10^{- 7}$
	Sample setting	negligible	1	negligible
	Movement of incident prism	$1.9 \times 10^{- 3} μm$	$1 / Δ x_{2}$	$2.2 \times 10^{- 7}$
Refractive index of air	Temperature measurement of air	$20 mK$	$n_{s} (d n_{a} / d T)$	$2.8 \times 10^{- 8}$
Refractive index of air	Pressure measurement of air	$0.05 hPa$	$n_{s} (d n_{a} / d P)$	$2.0 \times 10^{- 8}$
Sample under measurement	Temperature measurement of sample	$20 mK$	$d n / d T$	$5.8 \times 10^{- 8}$
	Flatness of sample	$λ / 10 μm$	$(n_{s} - n_{L}) / Δ x_{2} \cos θ_{a}$	$4.0 \times 10^{- 7}$
	Homogeneity of sample	$5.8 \times 10^{- 7}$	1	$5.8 \times 10^{- 7}$
		Combined standard uncertainty		$1.6 \times 10^{- 6}$
		Expanded uncertainty ( $k = 2$ )		$3.3 \times 10^{- 6}$

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Applied Optics