A Multi-Image Optical System

Dmetro Andrychuk

doi:10.1364/AO.3.000933

Applied Optics
Vol. 3,
Issue 8,
pp. 933-938
(1964)
•https://doi.org/10.1364/AO.3.000933

A Multi-Image Optical System

Dmetro Andrychuk

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Dmetro Andrychuk, "A Multi-Image Optical System," Appl. Opt. 3, 933-938 (1964)

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Abstract

An optical system, consisting of cylindrical, spherical, and conical optics, capable of producing multiple images of a point source is described. The relative energy content of each image is calculated and compared to measured values. It was tested in a system for simultaneously monitoring CO₂, CH₄, and CO in a gas mixture by infrared radiation absorption. Other possible applications in radiometry and laser communications are suggested.

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Cone	S_i: Solid angle of cone K_i
K₀	2π{1 − 1/[1 + (r/L)²]^1/2}
K₁	2π{1/[1 + (r/L)²]^1/2 − 1/[1 + (3r/L)²]^1/2}
K₂	2π{1/[1 + (3r/L)²]^1/2 − 1/[1 + (5r/L)²]^1/2}
K₃	2π{1/[1 + (5r/L)²]^1/2 − 1/[1 + (7r/L)²]^1/2}

Cone_i	α_i	${\bar{α}}_{i}$	r_pi	r_si	R_mi	S_i 2π· 10⁻³×	A_αi (2 dl/π)×
K₀	3°58^′	1°59^′	—	—	(1.00)	(2.41)	1.57
K₁	11°47^′	7°52^′	0.94	0.996	0.968	(18.67)	1.56
K₂	19°10^′	15°29^′	0.94	0.994	0.936	(34.40)	1.54
K₃	25°58^′	22°34^′	0.95	0.991	0.909	(45.42)	1.51

Image order	Ring		Detector output (V)	Vignett.	I_i: ring Energy (V-cm)	I_i/I₀
Image order	Diam (cm)	Circum (cm)	Detector output (V)	Vignett.	I_i: ring Energy (V-cm)	I_i/I₀
0 (direct)	—	—	0.057	1.00	0.057	1.00
1	4.45	14.00	0.037	1.00	0.517	9.05
2	7.65	24.00	0.031	0.94	0.791	13.90
3	8.80	27.70	0.031	0.88	0.978	17.10

Image order	A_α_i (2 dl/π)×	S_i 2π· 10⁻³×	R_mi	E_iC^a×	E_i/E₀
0	1.57	2.41	1.00	3.78	1.00
1	1.56	18.67	0.968	28.10	7.45
2	1.54	34.40	0.936	49.60	13.10
3	1.51	45.42	0.909	62.30	16.50

Cone	S_i: Solid angle of cone K_i
K₀	2π{1 − 1/[1 + (r/L)²]^1/2}
K₁	2π{1/[1 + (r/L)²]^1/2 − 1/[1 + (3r/L)²]^1/2}
K₂	2π{1/[1 + (3r/L)²]^1/2 − 1/[1 + (5r/L)²]^1/2}
K₃	2π{1/[1 + (5r/L)²]^1/2 − 1/[1 + (7r/L)²]^1/2}

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Equations (10)

Applied Optics