Simultaneous measurement of phase transmission and linear or circular dichroism of an object under test

Sergej Rothau; Xiao Rao; Norbert Lindlein

doi:10.1364/AO.58.001739

Applied Optics
Vol. 58,
Issue 7,
pp. 1739-1746
(2019)
•https://doi.org/10.1364/AO.58.001739

Simultaneous measurement of phase transmission and linear or circular dichroism of an object under test

Sergej Rothau, Xiao Rao, and Norbert Lindlein

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Sergej Rothau, Xiao Rao, and Norbert Lindlein, "Simultaneous measurement of phase transmission and linear or circular dichroism of an object under test," Appl. Opt. 58, 1739-1746 (2019)

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Abstract

This publication 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 dichroism. Analogous to the classical phase-shifting interferometry, the measurement strategy is based on the variation of phase and polarization in an interferometer. This procedure allows one to analyze simultaneously and spatially resolved the dichroic properties of the object and its impact on the phase of the incoming light in one measurement cycle. The theoretical description of the investigated methods and their experimental implementation are presented.

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Name	$N_{total}$ ^a	$ϕ_{i}$	$δ_{i}$	$α_{i}^{'}$
$5^{*} / 2 / 1$	10	${0, \frac{π}{2}, π, \frac{3 π}{2}, 2 π}$	${\frac{π}{2}, \frac{3 π}{2}}$	${0}$
			${↻, ↺}$	${\to}$
	$\det (\hat{A}) = 8.0 e + 05; κ (\hat{A}) = 2.29;$
Each 5 phase steps $ϕ_{i}$ for the two pol. values $δ_{i}$
$3 / 2 / 1$	6	${0, \frac{2 π}{3}, \frac{4 π}{3}}$	${\frac{π}{2}, \frac{3 π}{2}}$	${0}$
			${↻, ↺}$	${\to}$
	$\det (\hat{A}) = 4.7 e + 04; κ (\hat{A}) = 1;$
Each 3 phase steps $ϕ_{i}$ for the two pol. values $δ_{i}$
$3 / 2 A$	6	${0, \frac{2 π}{3}, \frac{4 π}{3}}$	${\frac{π}{2}, \frac{3 π}{2}}$	${0, \frac{π}{2}}$
			${↻, ↺}$	${\to, ↑}$
	$\det (\hat{A}) = 2.4 e + 06; κ (\hat{A}) = 1;$
Pol. variation in both arms simultaneously: ( $δ_{1} / α_{1}^{'}$ ), ( $δ_{2} / α_{2}^{'}$ )

Name	$N_{total}$ ^a	$ϕ_{i}$	$α_{i}$	$α_{i}^{'}$
$3 / 3 / 2$	18	${0, \frac{2 π}{3}, \frac{4 π}{3}}$	${0, \frac{π}{3}, \frac{2 π}{3}}$	${0, \frac{π}{2}}$
			${\to, ↗, ↖}$	${\to, ↑}$
	$\det (\hat{A}) = 1.2 e + 07; κ (\hat{A}) = 4;$
Polarization variation in each arm successively
$3 / 3 B$	9	${0, \frac{2 π}{3}, \frac{4 π}{3}}$	${0, \frac{π}{3}, \frac{2 π}{3}}$	$α = α^{'}$
			${\to, ↗, ↖}$	${\to, ↗, ↖}$
	$\det (\hat{A}) = 9.5 e + 04; κ (\hat{A}) = 4;$
Pol. var. in both arms simultaneously: $(α_{1} / α_{1}^{'}), \dots, (α_{3} / α_{3}^{'})$
$3 / 3 C$	9	${0, \frac{2 π}{3}, \frac{4 π}{3}}$	${0, \frac{π}{3}, \frac{2 π}{3}}$	${0, \frac{π}{4}, \frac{π}{2}}$
			${\to, ↗, ↖}$	${\to, ↗, ↑}$
	$\det (\hat{A}) = 9.5 e + 04; κ (\hat{A}) = 7.21;$
Pol. var. in both arms simultaneously: $(α_{1} / α_{1}^{'}), \dots, (α_{3} / α_{3}^{'})$

Name	$N_{total}$ ^a	$ϕ_{i}$	$δ_{i}$	$α_{i}^{'}$
$5^{*} / 2 / 1$	10	${0, \frac{π}{2}, π, \frac{3 π}{2}, 2 π}$	${\frac{π}{2}, \frac{3 π}{2}}$	${0}$
			${↻, ↺}$	${\to}$
	$\det (\hat{A}) = 8.0 e + 05; κ (\hat{A}) = 2.29;$
Each 5 phase steps $ϕ_{i}$ for the two pol. values $δ_{i}$
$3 / 2 / 1$	6	${0, \frac{2 π}{3}, \frac{4 π}{3}}$	${\frac{π}{2}, \frac{3 π}{2}}$	${0}$
			${↻, ↺}$	${\to}$
	$\det (\hat{A}) = 4.7 e + 04; κ (\hat{A}) = 1;$
Each 3 phase steps $ϕ_{i}$ for the two pol. values $δ_{i}$
$3 / 2 A$	6	${0, \frac{2 π}{3}, \frac{4 π}{3}}$	${\frac{π}{2}, \frac{3 π}{2}}$	${0, \frac{π}{2}}$
			${↻, ↺}$	${\to, ↑}$
	$\det (\hat{A}) = 2.4 e + 06; κ (\hat{A}) = 1;$
Pol. variation in both arms simultaneously: ( $δ_{1} / α_{1}^{'}$ ), ( $δ_{2} / α_{2}^{'}$ )

Name	$N_{total}$ ^a	$ϕ_{i}$	$α_{i}$	$α_{i}^{'}$
$3 / 3 / 2$	18	${0, \frac{2 π}{3}, \frac{4 π}{3}}$	${0, \frac{π}{3}, \frac{2 π}{3}}$	${0, \frac{π}{2}}$
			${\to, ↗, ↖}$	${\to, ↑}$
	$\det (\hat{A}) = 1.2 e + 07; κ (\hat{A}) = 4;$
Polarization variation in each arm successively
$3 / 3 B$	9	${0, \frac{2 π}{3}, \frac{4 π}{3}}$	${0, \frac{π}{3}, \frac{2 π}{3}}$	$α = α^{'}$
			${\to, ↗, ↖}$	${\to, ↗, ↖}$
	$\det (\hat{A}) = 9.5 e + 04; κ (\hat{A}) = 4;$
Pol. var. in both arms simultaneously: $(α_{1} / α_{1}^{'}), \dots, (α_{3} / α_{3}^{'})$
$3 / 3 C$	9	${0, \frac{2 π}{3}, \frac{4 π}{3}}$	${0, \frac{π}{3}, \frac{2 π}{3}}$	${0, \frac{π}{4}, \frac{π}{2}}$
			${\to, ↗, ↖}$	${\to, ↗, ↑}$
	$\det (\hat{A}) = 9.5 e + 04; κ (\hat{A}) = 7.21;$
Pol. var. in both arms simultaneously: $(α_{1} / α_{1}^{'}), \dots, (α_{3} / α_{3}^{'})$

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Applied Optics