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Development of the point-diffraction interferometer wavefront sensor for extreme adaptive optics

Tsukui, Ryo 京都大学 DOI:10.14989/doctor.k24416

2023.03.23

概要

Direct observation of exoplanets is crucial for solving the following two problems: clarifying the mechanisms of planet formation and searching for extraterrestrial biological activities. Potential targets have small angular separations (∼ 0.01 − 0.1 arcsec) from their host stars and small planet-to-star
contrasts (∼ 10−7 ). Thus, direct observation requires a high angular resolution and high contrast. Such observation with ground-based telescopes
is affected by the Earth’s atmospheric turbulence. This is because the turbulence causes wavefront aberrations, which scatter the host star’s light to
degrade the angular resolution and contrast. Therefore, wavefront correction
with adaptive optics (AO) is necessary. AO measures the incident wavefront
aberration with a wavefront sensor (WFS) and corrects the aberration with
a deformable mirror (DM), controlled by a real-time controller (RTC).
A highly accurate wavefront correction is required to obtain a 10−7 level final contrast. Such correction can be achieved with extreme adaptive
optics (ExAO), which has ∼ 40000 measurement/correction points in a 30-m
telescope aperture and runs at ∼ 5 kHz. ExAO requires a high-performance
WFS with the following properties:
• high efficiency: a small measurement error with a limited number of
photons,
• high-speed capabilities: low calculation cost and a small readout region
for wavefront sensing,
• a large dynamic range.
As for high efficiency, ExAO favors phase sensors, such as a fixed pyramid
WFS and a Zernike WFS. However, These current phase sensors have room
to improve high-speed capabilities and dynamic ranges.
This thesis describes the development of a new phase sensor named bPDI (birefringent point-diffraction interferometer). The b-PDI utilizes birefringent crystal as its key optical element. ...

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参考文献

[61] Benjamin L Gerard, Javier Perez-Soto, Vincent Chambouleyron,

Maaike AM van Kooten, Daren Dillon, Sylvain Cetre, Rebecca JensenClem, Qiang Fu, Hadi Amata, and Wolfgang Heidrich. Various wavefront sensing and control developments on the Santa Cruz extreme AO

laboratory (SEAL) testbed. In Adaptive Optics Systems VIII, volume

12185, pages 778–790. SPIE, 2022.

[62] 国立天文台 TMT 科学諮問委員会. TMT 次期装置実現に向けたロードマ

ップ, 2022. https://tmt.nao.ac.jp/researchers/jsac/TMT_inst_

roadmap_FY2022.pdf. Accessed on 2022-12-15.

[63] 田村元秀. 新天文学ライブラリー 1 太陽系外惑星, 2015.

108

Appendix A

Simulation: linearity in

practical cases

The linearity of the b-PDI, which was tested in Section 8.1.6, was also simulated. The simulation assumed a single wavelength of 800 nm and used

the numerical model (Section 6.1.1), which reflected the actual Pinhole A

(#03-40) geometry shown in Table 7.1. Assuming the input phase aberration expressed by the Zernike polynomial Z20 , the simulation generated the

interferograms without any noise and reconstructed the phase δrec . Then,

the RMS values RM Sinput of the input phase and RM Soutput of the reconstructed phase were compared in the same way as Section 8.1.6.

Figure A.1 shows the simulated result; the iterative algorithm enabled

the linear response within RM Sinput ≲ 0.7 rad (P-V ≤ 1λC ).

RMSoutput

0.8

y=x

Normal algorithm

Iterative algorithm

0.6

0.4

0.2

00

0.2

0.4

0.6

RMSinput

0.8

Figure A.1: Simulated response of RM Soutput against RM Sinput with a single

wavelength of 800 nm.

109

Appendix B

Estimation of the number of

photons

This chapter estimates the number of photons collected by a subaperture of

a Tweeter WFS, assuming the parameters in Table B.1. The flux density

f (m) [erg sec−1 cm−2 µm−1 ] from a m-th magnitude guide star is given by:

f (m) = 10a−0.4m .

(B.1)

Here, a is a correction term; a = −4.947 at Ic-band (calculated with the

values in Tamura [63]). At the loop speed FAO , the Tweeter WFS’s integration time is 1/FAO . In the integration time, the number of photons Nph (m)

collected by a subaperture is expressed as:

Nph (m) =

f (m) L2 ∆λ λC P

FAO h c

(B.2)

Here, h is Plack’s constant and c is light speed. Figure B.1 shows the values

of Nph (m) at various values of FAO .

110

Table B.1: Parameters used in the estimation.

Parameter

Central wavelength

Band width

Size of the subaperture

Throughput of the optics before Tweeter WFS

Notation

Value

λC

∆λ

0.8 µm

0.2 µm

14.6 cm (= 380/26)

0.24

Figure B.1: The number of photons per subaperture Nph (m) plotted against the

Ic-band magnitude m of a guide star. The assumed loop speed FAO

is 1.0 kHz (purple), 3.0 kHz (green), and 6.5 kHz (blue).

111

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