Measurement of group refractive index wavelength dependence using a low-coherence tandem interferometer

Akiko Hirai; Hirokazu Matsumoto

doi:10.1364/AO.45.005614

Measurement of group refractive index wavelength dependence using a low-coherence tandem interferometer

Akiko Hirai and Hirokazu Matsumoto

Applied Optics
Vol. 45,
Issue 22,
pp. 5614-5620
(2006)
•doi: 10.1364/AO.45.005614

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Akiko Hirai and Hirokazu Matsumoto, "Measurement of group refractive index wavelength dependence using a low-coherence tandem interferometer," Appl. Opt. 45, 5614-5620 (2006)

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Abstract

A technique for the measurement of the group refractive index wavelength dependence of optical materials using a low-coherence tandem interferometer and a spectrometer is proposed. Four channeled spectra resulting from interferences of light beams from different pairs of optical paths are used for the calculation of optical path differences. The group refractive index wavelength dependence is calculated from these optical path differences generated from the sample under measurement. No a priori information of the geometric thickness of a sample is required. The wavelength dependence of the group refractive index of the samples BK7 parallel plate of 5.200 and $10.025 mm$ from 675 to $850 nm$ is experimentally measured with an accuracy of the order of $10^{- 5}$ and a repeatability of the order of $10^{- 9}$ .

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Factor x _i	Standard Uncertainty u(x _i)	Coefficient \|c _i\|	u _i = \|c _i\|u(x _i)
n _ga	1 × 10⁻⁷	n _gS∕n _ga	1.5 × 10⁻⁷
d ₄″^a	4.3 × 10⁻¹ μm	(n _gS − n _ga)∕(2n _ga L _S)	2.2 × 10⁻⁵
d ₃″	4.3 × 10⁻¹ μm	n _gS∕(2n _ga L _S)	6.2 × 10⁻⁵
T	0.1 K	dn _gS∕dT	8.0 × 10⁻⁸
θ_i	2 × 10⁻⁴ rad	See text	1.8 × 10⁻⁹
α	2.4 × 10⁻⁶ rad	See text	1.7 × 10⁻¹⁰
	Combined standard uncertainty		6.6 × 10⁻⁵

Factor x _i	Standard Uncertainty u(x _i)	Coefficient \|c _i\|	u _i = \|c _i\|u(x _i) (μm)
n _ga	1 × 10⁻⁷	2(d ₄ − d ₁)	1.6 × 10⁻³
d ₄	1.0 × 10⁻² μm	2n _ga	2.0 × 10⁻²
d ₁	1.0 × 10⁻² μm	2n _ga	2.0 × 10⁻²
D ₄	3.0 × 10⁻¹ μm	1	3.0 × 10⁻¹
D ₁	3.0 × 10⁻¹ μm	1	3.0 × 10⁻¹
	Combined standard uncertainty		4.3 × 10⁻¹

Factor x _i	Standard Uncertainty u(x _i)	Coefficient \|c _i\|	u _i = \|c _i\|u(x _i) (μm)
n _ga	1 × 10⁻⁷	2(d ₃ − d ₂)	5.5 × 10⁻⁴
d ₃	1.0 × 10⁻² μm	2n _ga	2.0 × 10⁻²
d ₂	1.0 × 10⁻² μm	2n _ga	2.0 × 10⁻²
D ₃	3.0 × 10⁻¹ μm	1	3.0 × 10⁻¹
D ₂	3.0 × 10⁻¹ μm	1	3.0 × 10⁻¹
	Combined standard uncertainty		4.3 × 10⁻¹

Factor x _i	Standard Uncertainty u(x _i)	Coefficient \|c _i\|	u _i = \|c _i\|u(x _i)
n _ga	1 × 10⁻⁷	n _gS∕n _ga	1.5 × 10⁻⁷
d ₄″^a	4.3 × 10⁻¹ μm	(n _gS − n _ga)∕(2n _ga L _S)	2.2 × 10⁻⁵
d ₃″	4.3 × 10⁻¹ μm	n _gS∕(2n _ga L _S)	6.2 × 10⁻⁵
T	0.1 K	dn _gS∕dT	8.0 × 10⁻⁸
θ_i	2 × 10⁻⁴ rad	See text	1.8 × 10⁻⁹
α	2.4 × 10⁻⁶ rad	See text	1.7 × 10⁻¹⁰
	Combined standard uncertainty		6.6 × 10⁻⁵

Factor x _i	Standard Uncertainty u(x _i)	Coefficient \|c _i\|	u _i = \|c _i\|u(x _i) (μm)
n _ga	1 × 10⁻⁷	2(d ₄ − d ₁)	1.6 × 10⁻³
d ₄	1.0 × 10⁻² μm	2n _ga	2.0 × 10⁻²
d ₁	1.0 × 10⁻² μm	2n _ga	2.0 × 10⁻²
D ₄	3.0 × 10⁻¹ μm	1	3.0 × 10⁻¹
D ₁	3.0 × 10⁻¹ μm	1	3.0 × 10⁻¹
	Combined standard uncertainty		4.3 × 10⁻¹

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