Complete analysis of a two-mirror unit magnification system. Part 2

Akiyoshi Suzuki

doi:10.1364/AO.22.003950

Applied Optics
Vol. 22,
Issue 24,
pp. 3950-3956
(1983)
•https://doi.org/10.1364/AO.22.003950

Complete analysis of a two-mirror unit magnification system. Part 2

Akiyoshi Suzuki

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Akiyoshi Suzuki, "Complete analysis of a two-mirror unit magnification system. Part 2," Appl. Opt. 22, 3950-3956 (1983)

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Abstract

In a concentric two-mirror unit magnification system, only meridional imagery suffers from higher-order field curvature and residual aberration. Here a new parameter is introduced to optimize these two problems. It is demonstrated that they are simultaneously optimized when the convex-mirror radius is exactly half of that of the concave mirror. Then the inclination of sagittal and meridional fields is balanced, and residual aberration is minimized at several times less than that of the concentric system.

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NO.	R	D	N
1	−R	$- R (1 - \frac{1}{2 cos Θ})$	−1
2	$- \frac{R}{2 cos Θ (1 - k)}$	$R (1 - \frac{1}{2 cos Θ})$	1
3	−R		−1

Fe	imaginary limit		practical limit
Fe	sin Θ	$\frac{1}{2 cos Θ (1 - k_{1})}$	sin Θ	$\frac{1}{2 cos Θ (1 - k_{1})}$
2	1/4	0.499811	1.05/4	0.499779
2.5	1/5	0.499135	1.05/5	0.499897
3	1/6	0.499956	1.05/6	0.499947
3.5	1/7	0.499976	1.05/7	0.499971
4	1/8	0.499984	1.05/8	0.499982

NO.	R	D	N
1	$- \frac{R}{cos Θ} \frac{2 {cos}^{2} Θ - k cos 2 Θ}{2 - k}$	$- \frac{cos 2 Θ}{2 cos Θ} R$	−1
2	$- \frac{R}{2 cos Θ (1 - k)}$	$\frac{cos 2 Θ}{2 cos Θ} R$	1
3	$- \frac{R}{cos Θ} \frac{2 {cos}^{2} Θ - k cos 2 Θ}{2 - k}$		−1

NO.	R	D	N	E.A.
1	−590.747	−291.0484	−1	420.0
2	−299.6986	-291.7484	1	99.0
3	−590.747		−1	420.0
No.	R	D	N	E.A.
1	−590.747	−291.0484	−1	420.0
2	−295.3735	−291.0484	1	99.0
3	−590.747		−1	420.0

NO.	R	d	N^--
1	−R	$- R (1 - \frac{1}{2 cos Θ})$	−1
2	$- \frac{R}{2}$	$R (1 - \frac{1}{2 cos Θ})$	1
3	−R		−1

object distance (from concave mirror)					$- R {1 + \frac{cos 2 Θ}{2 {cos}^{4} Θ} (1 - cos Θ) (2 cos Θ - 1)}$
image distance (from concave mirror)					$- R {1 + \frac{cos 2 Θ}{2 {cos}^{4} Θ} (1 - cos Θ) (2 cos Θ - 1)}$
image point where AS-0					$h {1 + \frac{{(1 - cos Θ)}^{2}}{{tan}^{2} 2 Θ {cos}^{2} Θ}}$
best image point					$h {1 + \frac{{(1 - cos Θ)}^{2}}{{tan}^{2} 2 Θ {cos}^{2} Θ}}$
inclination of sagittal image field at h					$\frac{2 {sin}^{3} Θ}{cos Θ cos 2 Θ}$
inclination of meridional image field at h					$- \frac{2 {sin}^{3} Θ}{cos Θ cos 2 Θ}$
wave aberration of sagittal imagery at h					$W_{s} = - \frac{h}{4} \frac{{(1 - cos Θ)}^{2}}{sin 2 Θ} {sin}^{4} ϕ$
wave aberration of meridional imagery at h					=W_s
telecentricity at best image point					$\frac{sin Θ cos 2 Θ}{2 {cos}^{5} Θ} {(1 - cos Θ)}^{2}$
range of good imagery					$2 λ {Fe}^{2} \frac{cos Θ cos 2 Θ}{{sin}^{3} Θ}$

Abstract

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Equations (78)

Applied Optics