Photocopy reduction arrays: design and analysis

Jill F. Goldenberg; Joseph J. Miceli; Duncan T. Moore

doi:10.1364/AO.24.004288

Applied Optics
Vol. 24,
Issue 24,
pp. 4288-4296
(1985)
•https://doi.org/10.1364/AO.24.004288

Photocopy reduction arrays: design and analysis

Jill F. Goldenberg, Joseph J. Miceli, and Duncan T. Moore

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Jill F. Goldenberg, Joseph J. Miceli, and Duncan T. Moore, "Photocopy reduction arrays: design and analysis," Appl. Opt. 24, 4288-4296 (1985)

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Abstract

Third-order aberration theory is extended to analyze gradient-index arrays. This theory is used to design a reduction array for photocopy applications. An array with untilted endfaces is designed and shown to have better image quality than previously designed arrays.

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Equations (42)

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h₀ and h₁	= Object and image heights, respectively
t₀ and t₁	= Object and image distances, respectively
t_ENP and t_EXP	= Entrance and exit pupil distances, respectively
t_AS	= Aperture stop distance.
L	= Length of rod.
R	= Radius of rod
θ	= Field angle
A₀	= Aperture angle
d_ENP and d_EXP	= Diameter of entrance and exit pupils, respectively

Total conjugates = 100.00 mm
Magnification = 0.707
N₀₀ = 1.537
N₁₀ = −0.005684/mm²
$\sqrt A$ = 0.08600
Radius of rods = 0.5 mm

Rod	X₀	l₀	L	l₁	ϕ₀′	ϕ₁′	α
(0,0)	0.0	33.908	42.723	23.368	0.0	0.0	0.0
(1,0)	145.686	40.017	41.856	27.210	0.2704	0.3145	0.0318
(2,0)	147.143	40.139	41.842	27.278	0.2727	0.3172	0.0321
(3,0)	148.600	40.261	41.828	27.346	0.2749	0.3198	0.0324
(4,0)	150.057	40.414	41.814	27.414	0.2770	0.3224	0.0327
(5,0)	151.513	27.483	41.800	27.482	0.2792	0.3201	0.0330

Rod	Object height (mm)	Image height (mm)	Magnification
(1,0)	2.617	1.724	0.659
(2,0)	1.306	0.881	0.675
(3,0)	0.0	0.0	0.692
(4,0)	−1.301	0.924	0.710
(5,0)	−2.598	−1.896	0.730

Rod	X (mm)	Z (mm)
(1,0)	104.802	100.278
(2,0)	104.954	100.141
(3,0)	105.063	99.994
(4,0)	105.126	99.838
(5,0)	105.139	99.670
(Ideal image point X = 105.06 mm, Z = 100 mm)

Total conjugates = 100.00 mm
Magnification = 0.707
N₀₀ = 1.537
N₁₀ = −0.005684/mm²
$\sqrt A$ = 0.086
Radius of rod = 0.5 mm

Rod	X₀	l₀	L	l₀	α
(0,0)	0.0	33.908	42.723	23.368	0.0
(1,0)	145.686	39.473	41.865	27.390	0.403
(2,0)	147.143	39.579	41.851	27.466	0.407
(3,0)	148.600	39.686	41.837	27.543	0.410
(4,0)	150.057	39.794	41.823	27.622	0.414
(5,0)	151.513	39.902	41.809	26.649	0.417

Rod	X (mm)	Z (mm)
(1.0)	104.308	100.136
(2.0)	104.392	100.034
(3.0)	104.433	99.923
(4.0)	104.428	99.805
(5,0)	Does not see object point

Rod	Spherical	Coma	Astigmatism	Petzval	Distortion
(0,0)	0.00312	0.00017	0.00105	0.00551	−0.00031
(1,0)	0.00349	0.00017	0.00099	0.00617	−0.00029
(2,0)	0.00353	0.00016	0.00101	0.00624	−0.00027
(3,0)	0.00357	0.00015	0.00102	0.00632	−0.00026
(4,0)	0.00362	0.00014	0.00103	0.00639	−0.000245
(5,0)	Does not see object point

Abstract

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Figures (12)

Tables (7)

Equations (42)

Applied Optics