Point-diffraction interferometer wavefront sensor with birefringent crystal

Ryo Tsukui; Masaru Kino; Kodai Yamamoto; Mikio Kurita

doi:10.1364/AO.397735

Applied Optics
Vol. 59,
Issue 27,
pp. 8370-8379
(2020)
•https://doi.org/10.1364/AO.397735

Point-diffraction interferometer wavefront sensor with birefringent crystal

Ryo Tsukui, Masaru Kino, Kodai Yamamoto, and Mikio Kurita

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Ryo Tsukui, Masaru Kino, Kodai Yamamoto, and Mikio Kurita, "Point-diffraction interferometer wavefront sensor with birefringent crystal," Appl. Opt. 59, 8370-8379 (2020)

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Abstract

A key technique in direct imaging of extrasolar planets with ground-based telescopes is extreme adaptive optics. It requires a wavefront sensor capable of achieving high accuracy with a small number of photons. Imada et al. [Appl. Opt. 54, 7870 (2015) [CrossRef] ] proposed a type of wavefront sensor that employs a point-diffraction interferometer (PDI). This type of sensor has problems concerning a low photon-usage efficiency and manufacturing feasibility. In addition, they did not give sufficient study on the optimum pinhole size. Here, we propose a novel PDI, with which these problems are overcome, and study the optimum pinhole size for it. The sensor is incorporated with birefringent crystal as the key component to achieve high efficiency and is feasible to manufacture realistically. We run numerical simulations to optimize the pinhole size, where the photon noise is evaluated.

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Equations (37)

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	(A)	(B)
Birefringent crystal	${{\rm TiO}_2}$ (rutile)	${{\rm YVO}_4}$
${n_o}$	2.52 [5]	1.97 [6]
${n_e}$	2.79 [5]	2.19 [6]
Non-birefringent material	${{\rm Nb}_{2}}{{\rm O}_{5}}$	${{\rm Ta}_{2}}{{\rm O}_{5}}$
$n$	2.28 [7]	2.10 [7]
$d$	$1.32{\lambda _C}$	$2.90{\lambda _C}$
${\theta _o}$	${-}0.634\pi\,\,{\rm rad}$	$0.754\pi\,\,{\rm rad}$
${\theta _e}$	${-}1.34\pi\,\,{\rm rad}$	${-}0.522\pi\,\,{\rm rad}$

	Parallel to the $x$ Axis ( $o$ )	Parallel to the $y$ Axis ( $e$ )
Transmission
Inside ^a	$T_{{\rm in}}^o\exp (i{\theta _o}) = 0.922\exp (i{\theta _o})$	$T_{{\rm in}}^e\;\exp (i{\theta _e}) = 0.913\exp (i{\theta _e})$
Outside ^b	$T_{{\rm out}}^o = 0.904$	$T_{{\rm out}}^e = 0.879$
Reflection
Inside	$R_{{\rm in}}^o = 0.385$	$R_{{\rm in}}^e = - 0.395$
Outside	$R_{{\rm out}}^o = 0.427$	$R_{{\rm out}}^e = - 0.477$

Telescope Diameter	3.8 m
Loop gain	0.3
Wavefront sensor model
Sensing wavelength ${\lambda _C}$	800 nm
Number of sub-apertures	$24 \times 24$
Frame rate	6.5 kHz
Magnitude of the guide star	4.8 mag (Ic-band)
Number of photons per sub-aperture	100 (50 for each polarization component)
Quantum efficiency of the detectors	0.5
Readout noise	$1.6{{\rm e}^ -}$ (RMS)
Photon noise	(random numbers following a Poisson distribution)
Deformable mirror model
Number of actuators	$24 \times 24$
Maximum stroke	1200 nm

Wavefront Error	1200 nm (P-V), 150 nm (RMS)
Woofer AO
Number of sub-apertures/actuators	$8 \times 8$
Wavefront sensor type	Shack–Hartmann
Frame rate	1 kHz
Fried parameter	0.15 m
Wind speed	10 m/s

	(A)	(B)
Birefringent crystal	${{\rm TiO}_2}$ (rutile)	${{\rm YVO}_4}$
${n_o}$	2.52 [5]	1.97 [6]
${n_e}$	2.79 [5]	2.19 [6]
Non-birefringent material	${{\rm Nb}_{2}}{{\rm O}_{5}}$	${{\rm Ta}_{2}}{{\rm O}_{5}}$
$n$	2.28 [7]	2.10 [7]
$d$	$1.32{\lambda _C}$	$2.90{\lambda _C}$
${\theta _o}$	${-}0.634\pi\,\,{\rm rad}$	$0.754\pi\,\,{\rm rad}$
${\theta _e}$	${-}1.34\pi\,\,{\rm rad}$	${-}0.522\pi\,\,{\rm rad}$

Abstract

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Equations (37)

Applied Optics