Optimized design of a gravitational wave telescope system based on pupil aberration

Jie Song; Wentong Fan; Sijun Fang; Hongwen Hai; Kai Zhao; Jian Luo; Rui Zhang; Bohong Li; Qicheng Sun; Lei Fan; Zizheng Li; Yong Yan

doi:10.1364/AO.515579

Applied Optics
Vol. 63,
Issue 7,
pp. 1815-1821
(2024)
•https://doi.org/10.1364/AO.515579

Optimized design of a gravitational wave telescope system based on pupil aberration

Jie Song, Wentong Fan, Sijun Fang, Hongwen Hai, Kai Zhao, Jian Luo, Rui Zhang, Bohong Li, Qicheng Sun, Lei Fan, Zizheng Li, and Yong Yan

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Jie Song, Wentong Fan, Sijun Fang, Hongwen Hai, Kai Zhao, Jian Luo, Rui Zhang, Bohong Li, Qicheng Sun, Lei Fan, Zizheng Li, and Yong Yan, "Optimized design of a gravitational wave telescope system based on pupil aberration," Appl. Opt. 63, 1815-1821 (2024)

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Abstract

The telescope is vital for accurate gravitational wave detection in the TianQin project. It must meet criteria like a geometric tilt-to-length (TTL) coupling noise ${\rm coefficient} \;{\le} {0.02}\surd {2}\;{\rm nm/\unicode{x00B5}rad}$ and wavefront ${\rm RMS} \le \lambda /{30}$. Analyzing the pupil aberration’s impact on geometric TTL noise, we devised an optimization method using the chief ray spot diagram’s standard deviation. Implementing this in Zemax with a ZPL macro, we designed an optical system meeting TianQin’s requirements. The system has a maximum geometric TTL noise coefficient of 0.0250 nm/µrad over the science FOV and a wavefront RMS of ${0.0111}\lambda$, confirming the method’s feasibility.

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Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Parameter Term	Parameter Value
Wavelength	1064 nm
Entrance pupil diameter	300 mm
Exit pupil diameter	4 mm
Entrance pupil position	230 mm behind $M_{1}$
Exit pupil position	300 mm behind $M_{1}$
Optical efficiency	$> 0.85$
Acquisition FOR	$\pm 200 µ r a d$
Science FOV	$\pm 30 µ r a d$
Wavefront RMS	$λ / 30$
TTL Noise	$0.4 p m / \sqrt H z a t 0.1 m H z t o 1 H z$

Term	Name
${\bar{W}}_{20020} (\vec{i} \cdot \vec{ρ})^{2}$	Quadratic piston
${\bar{W}}_{11011} (\vec{i} \cdot \vec{H}) (\vec{i} \cdot \vec{ρ})$	Anamorphism
${\bar{W}}_{02002} (\vec{i} \cdot \vec{H})^{2}$	Constant astigmatism
${\bar{W}}_{30010} (\vec{i} \cdot \vec{ρ}) (\vec{ρ} \cdot \vec{ρ})$	Cubic piston
${\bar{W}}_{21110} (\vec{i} \cdot \vec{ρ}) (\vec{H} \cdot \vec{ρ})$	Quadratic distortion II
${\bar{W}}_{21001} (\vec{i} \cdot \vec{H}) (\vec{ρ} \cdot \vec{ρ})$	Quadratic distortion I
${\bar{W}}_{12010} (\vec{i} \cdot \vec{ρ}) (\vec{H} \cdot \vec{H})$	Field tilt
${\bar{W}}_{12101} (\vec{i} \cdot \vec{H}) (\vec{H} \cdot \vec{ρ})$	Linear astigmatism
${\bar{W}}_{03001} (\vec{i} \cdot \vec{H}) (\vec{H} \cdot \vec{H})$	Constant coma
${\bar{W}}_{40000} (\vec{ρ} \cdot \vec{ρ})^{2}$	Quartic piston
${\bar{W}}_{31100} (\vec{H} \cdot \vec{ρ}) (\vec{ρ} \cdot \vec{ρ})$	Cubic distortion
${\bar{W}}_{22200} (\vec{H} \cdot \vec{ρ})^{2}$	Quadratic astigmatism
${\bar{W}}_{22000} (\vec{H} \cdot \vec{H}) (\vec{ρ} \cdot \vec{ρ})$	Field curvature
${\bar{W}}_{13100} (\vec{H} \cdot \vec{H}) (\vec{H} \cdot \vec{ρ})$	Linear coma
${\bar{W}}_{04000} (\vec{H} \cdot \vec{H})^{2}$	Spherical aberration

	Radius of Curvature/mm	Thickness/mm	Conic	Off-Axis Distance/mm	Tilt/°
$M_{1}$	−1483.417	−716.037	−1	210	/
$M_{2}$	−53.570	820.728	−1.185	−0.017	/
$M_{3}$	−787.868	−88.389	/	3.975	−5
$M_{4}$	1006.651	283.408	/	8.966	−5.360

	Radius of Curvature/mm	Thickness/mm	Conic	Off-Axis Distance/mm	Tilt/°
$M_{1}$	−1483.417	−716.037	−1	210	/
$M_{2}$	−53.570	859.583	−1.185	−0.017	/
$M_{3}$	−223.957	−83.860	−0.868	15.773	−8
$M_{4}$	/	244.005	/	3.020	−4.840

Parameter Term	Parameter Value
Wavelength	1064 nm
Entrance pupil diameter	300 mm
Exit pupil diameter	4 mm
Entrance pupil position	230 mm behind $M_{1}$
Exit pupil position	300 mm behind $M_{1}$
Optical efficiency	$> 0.85$
Acquisition FOR	$\pm 200 µ r a d$
Science FOV	$\pm 30 µ r a d$
Wavefront RMS	$λ / 30$
TTL Noise	$0.4 p m / \sqrt H z a t 0.1 m H z t o 1 H z$

Abstract

Data availability

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Figures (9)

Tables (5)

Equations (4)

Applied Optics