Stellar Interferometer for Figure Sensing of Orbiting Astronomical Telescopes

W. N. Peters; R. A. Arnold; S. Gowrinathan

doi:10.1364/AO.13.001785

Applied Optics
Vol. 13,
Issue 8,
pp. 1785-1795
(1974)
•https://doi.org/10.1364/AO.13.001785

Stellar Interferometer for Figure Sensing of Orbiting Astronomical Telescopes

W. N. Peters, R. A. Arnold, and S. Gowrinathan

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W. N. Peters, R. A. Arnold, and S. Gowrinathan, "Stellar Interferometer for Figure Sensing of Orbiting Astronomical Telescopes," Appl. Opt. 13, 1785-1795 (1974)

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Abstract

An interferometric device designed to be located in the focal plane of a large astronomical telescope is presented. The prime application is for the forthcoming large space telescope. The device is to perform interferometry on the optical wavefront arising from a single star after it has propagated through the telescope. The concept of a focal plane figure sensor has been experimentally verified by fabricating and testing an operating laboratory breadboard figure sensor. A set of linear independent control equations are derived that define the operations for utilizing a focal plane figure sensor in the control loops for the positioning of the secondary mirror and for the active control of the primary mirror optical figure. A number of scientific experiments that could be performed with the interferometer are also briefly discussed.

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${SNR}_{I F} = \frac{{(G η q λ / h c)}^{2} H^{2} A^{2} (d^{2} / D^{2}) T R Γ^{2}}{\frac{G^{2} q B_{I F} η q H A λ}{h c} (R + \frac{d^{2}}{D^{2}} T) + G^{2} q B_{I F} (\frac{4 A}{π D^{2}} \frac{η q P_{B} λ}{h c} + I_{D}) + 2 K T_{R} B_{I F} / R_{L}}$
H	= irradiance (watts/m²),	A	= area of stop preceding photodetector as viewed in object space,
d	= diameter of reference beam reflective dot viewed in object space (m),	η	= photodetector quantum efficiency,
D	= telescope pupil diameter (m),	G	= internal gain of photomultiplier,
P_S	= power in interferometer signal beam (watts),	I_D	= cathode dark current,
P_R	= power in interferometer reference beam (watts),	B_IF	= intermediate frequency zonal low pass filter bandwidth,
R	= reflectance of beam splitter,	B_IF	= intermediate frequency zonal low pass filter bandwidth,
T	= transmission of beam splitter,	R_L	= load resistor,
K	= Boltzman’s constant,	q	= charge of electron (1.6 × 10⁻¹⁹)
T_R	= temperature of load resistor in (°K),	h	= Planck’s constant (6.625 × 10⁻³⁴),
		c	= speed of light (3 × 10⁸),
		λ	= optical wavelength (m),
		Γ	= coherence function.

31034 Photodetector quantum efficiency η = 0.25
B_IF	= IF bandwidth
A	= 7 × 10⁻² m² (assuming 100 sample points in pupil of 3-m telescope)
d/D	= 0.2 (ratio of reference spot diameter to pupil diameter)
Γ	= 0.8 coherence function
τ_OPT	= 0.7 transmission of optics
Δλ	= 400 Å
λ	= 5000 Å

Input aberration	n	m	SFS detection coefficient of input aberration	Additional aberrations
X coma	3	1	A₃₁(1 + M⁻³) cosΞ	−A₃₁(1 − M⁻³) ρ³ sinθ sinΞ (y coma)
Defocus	2	0	A₂₀(1 + M⁻²)
Spherical	4	0	A₄₀(1 + M⁻⁴)
X astigmatism	2	2	A₂₂(1 + M⁻²) cos² (θ + Ξ)	(ρ²/M²) sin2θ sin2Ξ
Tilt	1	1	A₁₁(1 + M⁻¹) cosΞ	−A₁₁(1 − M⁻¹) sinθ sinΞ (y tilt)

${SNR}_{I F} = \frac{{(G η q λ / h c)}^{2} H^{2} A^{2} (d^{2} / D^{2}) T R Γ^{2}}{\frac{G^{2} q B_{I F} η q H A λ}{h c} (R + \frac{d^{2}}{D^{2}} T) + G^{2} q B_{I F} (\frac{4 A}{π D^{2}} \frac{η q P_{B} λ}{h c} + I_{D}) + 2 K T_{R} B_{I F} / R_{L}}$
H	= irradiance (watts/m²),	A	= area of stop preceding photodetector as viewed in object space,
d	= diameter of reference beam reflective dot viewed in object space (m),	η	= photodetector quantum efficiency,
D	= telescope pupil diameter (m),	G	= internal gain of photomultiplier,
P_S	= power in interferometer signal beam (watts),	I_D	= cathode dark current,
P_R	= power in interferometer reference beam (watts),	B_IF	= intermediate frequency zonal low pass filter bandwidth,
R	= reflectance of beam splitter,	B_IF	= intermediate frequency zonal low pass filter bandwidth,
T	= transmission of beam splitter,	R_L	= load resistor,
K	= Boltzman’s constant,	q	= charge of electron (1.6 × 10⁻¹⁹)
T_R	= temperature of load resistor in (°K),	h	= Planck’s constant (6.625 × 10⁻³⁴),
		c	= speed of light (3 × 10⁸),
		λ	= optical wavelength (m),
		Γ	= coherence function.

31034 Photodetector quantum efficiency η = 0.25
B_IF	= IF bandwidth
A	= 7 × 10⁻² m² (assuming 100 sample points in pupil of 3-m telescope)
d/D	= 0.2 (ratio of reference spot diameter to pupil diameter)
Γ	= 0.8 coherence function
τ_OPT	= 0.7 transmission of optics
Δλ	= 400 Å
λ	= 5000 Å

Abstract

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Tables (3)

Equations (35)

Applied Optics