Simultaneous measurement of phase transmission and birefringence of an object under test

Sergej Rothau; Klaus Mantel; Norbert Lindlein

doi:10.1364/AO.57.004849

Applied Optics
Vol. 57,
Issue 17,
pp. 4849-4856
(2018)
•https://doi.org/10.1364/AO.57.004849

Simultaneous measurement of phase transmission and birefringence of an object under test

Sergej Rothau, Klaus Mantel, and Norbert Lindlein

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Sergej Rothau, Klaus Mantel, and Norbert Lindlein, "Simultaneous measurement of phase transmission and birefringence of an object under test," Appl. Opt. 57, 4849-4856 (2018)

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Abstract

This paper presents a novel interferometric method for the simultaneous spatially resolved analysis of an object under test regarding the phase transmission function and the magnitude and orientation of the (uniaxial) birefringence. The measurement strategy is based on variations of the phase and polarization and processing the interference patterns so obtained. With this method, which is very similar to the classical phase-shifting interferometry, a complete analysis of birefringent properties of the object and its impact on the phase of the incoming light can be done in one measurement cycle. The theoretical description of the investigated methods and their experimental implementation are presented.

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7a		$\det (\hat{A}) = 3.8 e + 03$ ; $κ (\hat{A}) = 10$ ;
	$ϕ_{i}$	${0, \frac{π}{3}, \frac{2 π}{3}, π, \frac{4 π}{3}, \frac{5 π}{3}, 2 π}$
	$α_{i}$	${0, 0, \frac{π}{3}, \frac{2 π}{3}, \frac{π}{3}, \frac{2 π}{3}, \frac{π}{3}}$
		${\to, \to, ↗, ↖, ↗, ↖, ↗}$
	$α_{i}^{'}$	${0, 0, \frac{π}{3}, \frac{2 π}{3}, 0, \frac{2 π}{3}, \frac{π}{3}}$
		${\to, \to, ↗, ↖, \to, ↖, ↗}$
7b		$\det (\hat{A}) = 2.9 e + 03$ ; $κ (\hat{A}) = 9$ ;
	$ϕ_{i}$	${0, 0, \frac{π}{2}, \frac{π}{2}, π, \frac{3 π}{2}, 2 π}$
	$α_{i}$	${0, \frac{π}{3}, \frac{π}{3}, \frac{2 π}{3}, \frac{π}{3}, 0, \frac{2 π}{3}}$
		${\to, ↗, ↗, ↖, ↗, \to, ↖}$
	$α_{i}^{'}$	${\frac{2 π}{3}, 0, \frac{π}{3}, \frac{2 π}{3}, \frac{π}{3}, 0, \frac{2 π}{3}}$
		${↖, \to, ↗, ↖, ↗, \to, ↖}$
7c		$\det (\hat{A}) = 1.4 e + 3$ ; $κ (\hat{A}) = 11$ ;
	$ϕ_{i}$	${0, \frac{2 π}{3}, \frac{2 π}{3}, \frac{2 π}{3}, \frac{4 π}{3}, \frac{4 π}{3}, \frac{4 π}{3}}$
	$α_{i}$	${\frac{π}{3}, 0, \frac{2 π}{3}, \frac{2 π}{3}, 0, \frac{2 π}{3}, \frac{2 π}{3}}$
		${↗, \to, ↖ ↖, \to, ↖, ↖}$
	$α_{i}^{'}$	${\frac{π}{2}, 0, 0, \frac{π}{2}, 0, 0, \frac{π}{2}}$
		${↑, \to, \to, ↑ \to, \to, ↑}$

Name	$N_{total}$	$ϕ_{i}$	$α_{i}$	$α_{i}^{'}$
$5^{*} / 2 / 2$	20	${0, \frac{π}{2}, π, \frac{3 π}{2}, 2 π}$	${0, \frac{π}{2}}$	${0, \frac{π}{2}}$
			${\to, ↑}$	${\to, ↑}$
	$\det (\hat{A}) = 4.1 e + 06$ ; $κ (\hat{A}) = 6.5$ ;
$3 / 3 / 2$	18	${0, \frac{2 π}{3}, \frac{4 π}{3}}$	${0, \frac{π}{3}, \frac{2 π}{3}}$	${0, \frac{π}{2}}$
			${\to, ↗, ↖}$	${\to, ↑}$
	$\det (\hat{A}) = 2.4 e + 06$ ; $κ (\hat{A}) = 4$ ;

Name	$N_{total}$	$ϕ_{i}$	$α_{i}, α_{i}^{'}$
3/3a	9	${0; \frac{2 π}{3}; \frac{4 π}{3}}$	${0, 0}$ , ${\frac{π}{2}, \frac{π}{4}}$ , ${\frac{π}{2}, \frac{3 π}{4}}$
			${\to, \to}$ , ${↑, ↗}$ , ${↑, ↖}$
	$\det (\hat{A}) = 2.6 e + 04$ ; $κ (\hat{A}) = 3$ ;
3/3b	9	${0; \frac{2 π}{3}; \frac{4 π}{3}}$	${0, 0}$ , ${\frac{π}{4}, \frac{π}{4}}$ , ${\frac{3 π}{4}, \frac{3 π}{4}}$
3/3b			${\to, \to}$ , ${↗, ↗}$ , ${↖, ↖}$
	$\det (\hat{A}) = 2.6 e + 04$ ; $κ (\hat{A}) = 6$ ;

7a		$\det (\hat{A}) = 3.8 e + 03$ ; $κ (\hat{A}) = 10$ ;
	$ϕ_{i}$	${0, \frac{π}{3}, \frac{2 π}{3}, π, \frac{4 π}{3}, \frac{5 π}{3}, 2 π}$
	$α_{i}$	${0, 0, \frac{π}{3}, \frac{2 π}{3}, \frac{π}{3}, \frac{2 π}{3}, \frac{π}{3}}$
		${\to, \to, ↗, ↖, ↗, ↖, ↗}$
	$α_{i}^{'}$	${0, 0, \frac{π}{3}, \frac{2 π}{3}, 0, \frac{2 π}{3}, \frac{π}{3}}$
		${\to, \to, ↗, ↖, \to, ↖, ↗}$
7b		$\det (\hat{A}) = 2.9 e + 03$ ; $κ (\hat{A}) = 9$ ;
	$ϕ_{i}$	${0, 0, \frac{π}{2}, \frac{π}{2}, π, \frac{3 π}{2}, 2 π}$
	$α_{i}$	${0, \frac{π}{3}, \frac{π}{3}, \frac{2 π}{3}, \frac{π}{3}, 0, \frac{2 π}{3}}$
		${\to, ↗, ↗, ↖, ↗, \to, ↖}$
	$α_{i}^{'}$	${\frac{2 π}{3}, 0, \frac{π}{3}, \frac{2 π}{3}, \frac{π}{3}, 0, \frac{2 π}{3}}$
		${↖, \to, ↗, ↖, ↗, \to, ↖}$
7c		$\det (\hat{A}) = 1.4 e + 3$ ; $κ (\hat{A}) = 11$ ;
	$ϕ_{i}$	${0, \frac{2 π}{3}, \frac{2 π}{3}, \frac{2 π}{3}, \frac{4 π}{3}, \frac{4 π}{3}, \frac{4 π}{3}}$
	$α_{i}$	${\frac{π}{3}, 0, \frac{2 π}{3}, \frac{2 π}{3}, 0, \frac{2 π}{3}, \frac{2 π}{3}}$
		${↗, \to, ↖ ↖, \to, ↖, ↖}$
	$α_{i}^{'}$	${\frac{π}{2}, 0, 0, \frac{π}{2}, 0, 0, \frac{π}{2}}$
		${↑, \to, \to, ↑ \to, \to, ↑}$

Name	$N_{total}$	$ϕ_{i}$	$α_{i}$	$α_{i}^{'}$
$5^{*} / 2 / 2$	20	${0, \frac{π}{2}, π, \frac{3 π}{2}, 2 π}$	${0, \frac{π}{2}}$	${0, \frac{π}{2}}$
			${\to, ↑}$	${\to, ↑}$
	$\det (\hat{A}) = 4.1 e + 06$ ; $κ (\hat{A}) = 6.5$ ;
$3 / 3 / 2$	18	${0, \frac{2 π}{3}, \frac{4 π}{3}}$	${0, \frac{π}{3}, \frac{2 π}{3}}$	${0, \frac{π}{2}}$
			${\to, ↗, ↖}$	${\to, ↑}$
	$\det (\hat{A}) = 2.4 e + 06$ ; $κ (\hat{A}) = 4$ ;

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Applied Optics