Cassegrainian/Gregorian-type null correctors for surface measurements of radio telescope reflectors

A. Greve

doi:10.1364/AO.36.005283

Applied Optics
Vol. 36,
Issue 22,
pp. 5283-5287
(1997)
•https://doi.org/10.1364/AO.36.005283

Cassegrainian/Gregorian-type null correctors for surface measurements of radio telescope reflectors

A. Greve

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A. Greve, "Cassegrainian/Gregorian-type null correctors for surface measurements of radio telescope reflectors," Appl. Opt. 36, 5283-5287 (1997)

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Abstract

The (sub)millimeter wavelength radio observatory of the next generation will probably be an interferometer array of some 50 telescopes with parabolic reflectors 10–15 m in diameter. At this scale of mass production it is convenient to have at hand for workshop assembly a reflector surface measurement technique that is precise and easy to operate. We discuss the possibility of reflector measurements based on 10.6-µm CO₂ laser interferometry using Cassegrainian/Gregorian-type null correctors.

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System	Path Length (C _i)	Distance between Vertexes (S _i)
C1, G1	C ₁ = (D/2) [F ₁(α, ψ) + F ₃(ψ*)]	S ₁ = (C ₁ - s - z ₀ - g)/2
C2, G2	C ₂ = (D/2) [F ₁(α, ψ) + F ₂(ψ*) + Z ₀]	S ₂ = (C ₂ - s - z ₀ - g)/2
C3, G3	C ₃ = (D/2) F ₁(α, ψ)	S ₃ = C ₃ - s - z ₀
C4	C ₄ = (D/2) [F ₂(α)/cos(α) + F ₃(α*)]	S ₄ = (C ₄ - g)/2
C5	C ₅ =(D/2) [F ₂(δ)/cos(δ) + F ₂(δ*) + Z ₀]	S ₅ = (C ₅ - g)/2

System	Auxiliary Relation A/Corrector Coordinate x′	Auxiliary Relation B/Corrector Coordinate z′	H(ψ, δ, γ)
C1, G1	A = C ₁ - f _R(α) - f _R(ψ)	B = B(ψ)	(ψ ∓ γ)/2
	x′ = (B ² - A ²) sin ψ/2(A + B cos ψ)	z′ = z′(ψ)
C2, G2	A = C ₂ - f _R (α) - f _R(ψ)[1 + cos ψ]		ψ/2
	x′ = (z _R - A)sin ψ/(1 + cos ψ)	z′ = z′(ψ)
C3, G3	x′ = x _R + f _R(α)sin ψ - C ₃ sin ψ	z′ = z′(ψ)	ψ
C4	A = C ₄ - f _R(α)	B = B(α)	(ψ ∓ γ)/2 = (δ ∓ γ)/2
	x′ = (B ² - A ²) sin α/2(A + B cos α)	z′ = z′(ψ)
C5	x′ = (z _R - C ₅)sin δ/(1 + cos δ) + x _R	z′ = z′(δ)	ψ/2 = δ/2

Corrector System	N _F	N _C	S _C/S _sub a
Cassegrainian
C1b	3.0	0.12	1.2
C2	3.0	0.12	1.2
C3	3.0	0.07	1.2
C4	0.33	0.23	2.1
C5	—	0.22	2.1
Gregorian
G1	3.0	0.20	1.7
G2	3.0	0.20	1.7
G3	3.0	0.22	1.7

System	Path Length (C _i)	Distance between Vertexes (S _i)
C1, G1	C ₁ = (D/2) [F ₁(α, ψ) + F ₃(ψ*)]	S ₁ = (C ₁ - s - z ₀ - g)/2
C2, G2	C ₂ = (D/2) [F ₁(α, ψ) + F ₂(ψ*) + Z ₀]	S ₂ = (C ₂ - s - z ₀ - g)/2
C3, G3	C ₃ = (D/2) F ₁(α, ψ)	S ₃ = C ₃ - s - z ₀
C4	C ₄ = (D/2) [F ₂(α)/cos(α) + F ₃(α*)]	S ₄ = (C ₄ - g)/2
C5	C ₅ =(D/2) [F ₂(δ)/cos(δ) + F ₂(δ*) + Z ₀]	S ₅ = (C ₅ - g)/2

System	Auxiliary Relation A/Corrector Coordinate x′	Auxiliary Relation B/Corrector Coordinate z′	H(ψ, δ, γ)
C1, G1	A = C ₁ - f _R(α) - f _R(ψ)	B = B(ψ)	(ψ ∓ γ)/2
	x′ = (B ² - A ²) sin ψ/2(A + B cos ψ)	z′ = z′(ψ)
C2, G2	A = C ₂ - f _R (α) - f _R(ψ)[1 + cos ψ]		ψ/2
	x′ = (z _R - A)sin ψ/(1 + cos ψ)	z′ = z′(ψ)
C3, G3	x′ = x _R + f _R(α)sin ψ - C ₃ sin ψ	z′ = z′(ψ)	ψ
C4	A = C ₄ - f _R(α)	B = B(α)	(ψ ∓ γ)/2 = (δ ∓ γ)/2
	x′ = (B ² - A ²) sin α/2(A + B cos α)	z′ = z′(ψ)
C5	x′ = (z _R - C ₅)sin δ/(1 + cos δ) + x _R	z′ = z′(δ)	ψ/2 = δ/2

Abstract

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Applied Optics