Laser-guide-star systems for astronomical applications

Ronald R. Parenti; Richard J. Sasiela

doi:10.1364/JOSAA.11.000288

Journal of the Optical Society of America A
Vol. 11,
Issue 1,
pp. 288-309
(1994)
•https://doi.org/10.1364/JOSAA.11.000288

Laser-guide-star systems for astronomical applications

Ronald R. Parenti and Richard J. Sasiela

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Ronald R. Parenti and Richard J. Sasiela, "Laser-guide-star systems for astronomical applications," J. Opt. Soc. Am. A 11, 288-309 (1994)

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Abstract

With computational techniques developed in the investigation of high-energy laser-beam-control systems, a set of concise analytic models describing the essential properties of a laser-guide-star phase-conjugation system has been assembled. With the aid of these models an optimization strategy for mating adaptive optics to a 4-m-class optical telescope is evolved, and it is shown that such a system might be expected to improve the effective atmospheric seeing conditions by nearly a factor of 10 within the isoplanatic patch of the turbulence probe. For operation at visible wavelengths, a compensation system having ~300 actuators and a closed-loop bandwidth of 20 Hz is recommended. All the key hardware components have already been built and tested, with the exception of a suitable laser source for high-repetition-rate illumination of the Earth’s sodium layer.

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Model	Zenith	r₀ (cm)	θ_seeing (arcsec)	θ₀ (μrad)	τ₀ (ms)
SLC-Day
	0°	5.7	2.4	13.8	2.7
	45°	4.6	3.0	8.0	2.2
HV-21
	0°	5.6	2.5	7.8	2.1
	45°	4.5	3.1	4.5	1.7
Modified HV
	0°	20.0	0.69	20.0	6.3
	45°	16.2	0.85	11.5	5.1

Aperture diameter	D = 4 m
Wavelength	λ_p = λ_t = λ_c = 0.55 μm
Zenith angle	ζ = 45°
Total system throughput	γ_p = γ_t = 0.2
Detector quantum efficiency	η = 0.8
Detector noise level	N_rms = 20
	r₀ = 16.2 cm
	θ₀ = 11.5 μrad
Turbulence parameters	τ₀ = 5.1 ms
	(θ₀)_tilt = 40.3 μrad
	(τ₀)_tilt = 12.3 ms
	μ₀ = 2.65 × 10⁻¹³ m^1/3
Turbulence moments	μ_5/3 = 1.78 × 10⁻⁷ m²
	μ₂ = 3.96 × 10⁻⁶ m^7/3
	v_−1/3 = 1.40 × 10⁻¹³ s^1/3
Wind-velocity moments	v_5/3 = 1.23 × 10⁻¹³ m² − s^−5/3
	v_14/3 = 2.28 × 10⁻⁷ m⁵ − s^14/3

	Natural-Star System			Laser Guide-Star System

Specification	V Band (0.55 μm)	J Band (1.25 μm)	K Band (2.2 μm)	V Band (0.55 μm)	J Band (1.25 μm)	K Band (2.2 μm)
σ_fig² (rad² of phase)	4.2	2.4	1.3	2.9	1.2	0.49
σ_tilt² (rad² of tilt)	0	0	0	1.2 × 10⁻¹⁴	5.9 × 10⁻¹⁴	1.8 × 10⁻¹³
Number of actuators	290	85	45	250	90	65
Servo bandwidth, 1/10_τd (Hz)	23	12	9	21	12	11
Sodium-beacon laser power (W)	–	–	–	47	9	6
Beacon/tracking-star magnitude^a	8	10	11	13	16	18
Uncorrected Strehl	0.0016	0.012	0.044	0.0016	0.012	0.044
Corrected Strehl	0.016	0.11	0.32	0.015	0.082	0.17
Uncorrected resolution (×1.22λ/D)	25	9.2	4.8	25	9.2	4.8
Corrected resolution (×1.22λ/D)	2.6	1.3	1.0	3.1	2.0	2.0
Fractional sky coverage	3 × 10⁻⁶	7 × 10⁻⁵	3 × 10⁻⁴	0.003	0.2	1

Model	Zenith	r₀ (cm)	θ_seeing (arcsec)	θ₀ (μrad)	τ₀ (ms)
SLC-Day
	0°	5.7	2.4	13.8	2.7
	45°	4.6	3.0	8.0	2.2
HV-21
	0°	5.6	2.5	7.8	2.1
	45°	4.5	3.1	4.5	1.7
Modified HV
	0°	20.0	0.69	20.0	6.3
	45°	16.2	0.85	11.5	5.1

Aperture diameter	D = 4 m
Wavelength	λ_p = λ_t = λ_c = 0.55 μm
Zenith angle	ζ = 45°
Total system throughput	γ_p = γ_t = 0.2
Detector quantum efficiency	η = 0.8
Detector noise level	N_rms = 20
	r₀ = 16.2 cm
	θ₀ = 11.5 μrad
Turbulence parameters	τ₀ = 5.1 ms
	(θ₀)_tilt = 40.3 μrad
	(τ₀)_tilt = 12.3 ms
	μ₀ = 2.65 × 10⁻¹³ m^1/3
Turbulence moments	μ_5/3 = 1.78 × 10⁻⁷ m²
	μ₂ = 3.96 × 10⁻⁶ m^7/3
	v_−1/3 = 1.40 × 10⁻¹³ s^1/3
Wind-velocity moments	v_5/3 = 1.23 × 10⁻¹³ m² − s^−5/3
	v_14/3 = 2.28 × 10⁻⁷ m⁵ − s^14/3

Abstract

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Journal of the Optical Society of America A