Linear astigmatism of confocal off-axis reflective imaging systems with N-conic mirrors and its elimination

Seunghyuk Chang

doi:10.1364/JOSAA.32.000852

Journal of the Optical Society of America A
Vol. 32,
Issue 5,
pp. 852-859
(2015)
•https://doi.org/10.1364/JOSAA.32.000852

Linear astigmatism of confocal off-axis reflective imaging systems with N-conic mirrors and its elimination

Seunghyuk Chang

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Seunghyuk Chang, "Linear astigmatism of confocal off-axis reflective imaging systems with N-conic mirrors and its elimination," J. Opt. Soc. Am. A 32, 852-859 (2015)

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Abstract

Linear astigmatism of plane-symmetric confocal off-axis reflective imaging systems with an arbitrary number of conic mirrors is derived. Linear astigmatism, a consequence of tilted astigmatic image planes, is the dominant aberration of this type of imaging system. In this work, the tilt angles of astigmatic image planes are obtained in closed form. An equation to eliminate the linear astigmatism is also derived. The presented theory is verified by examples.

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Parameters	Measurement
$D$ (aperture diameter)	1000 mm
$f$ (telescope focal length)	5050 mm
$f_{1}$ (M1 parent mirror focal length)	1500 mm
$K_{1}$ (M1 parent mirror conic constant)	−1
$ℓ_{1}$	Infinity
$ℓ_{1}^{'}$	1666.67 mm
$m_{1}$	0
$i_{1}$	−18.4349°
$2 c_{2}$ (M2 parent mirror interfocal distance)	17333.33 mm
$K_{2}$ (M2 parent mirror conic constant)	−3.44898
$ℓ_{2}$	−459.77 mm
$ℓ_{2}^{'}$	1393.10 mm
$m_{2}$	−3.03
$i_{2}$	24.1455°
$θ_{i m}^{t}$	−5.71059°
$θ_{i m}^{s}$	5.71059°

Parameters	Measurement
$D$ (aperture diameter)	1000 mm
$f$ (telescope focal length)	6565 mm
$2 c_{3}$ (M3 parent mirror interfocal distance)	326.43 mm
$K_{3}$ (M3 parent mirror conic constant)	−0.0201436
$ℓ_{3}$	1000 mm
$ℓ_{3}^{'}$	1300 mm
$m_{3}$	1.3
$i_{3}$	−3.23502°
$β$	15.2425°
$θ_{i m}^{t}$	0°
$θ_{i m}^{s}$	0°

Parameters	Measurement
$D$ (aperture diameter)	1000 mm
$f$ (telescope focal length)	5050 mm
$f_{1}$ (M1 parent mirror focal length)	1500 mm
$K_{1}$ (M1 parent mirror conic constant)	−1
$ℓ_{1}$	Infinity
$ℓ_{1}^{'}$	1666.67 mm
$m_{1}$	0
$i_{1}$	−18.4349°
$2 c_{2}$ (M2 parent mirror interfocal distance)	17333.33 mm
$K_{2}$ (M2 parent mirror conic constant)	−3.44898
$ℓ_{2}$	−459.77 mm
$ℓ_{2}^{'}$	1393.10 mm
$m_{2}$	−3.03
$i_{2}$	24.1455°
$θ_{i m}^{t}$	−5.71059°
$θ_{i m}^{s}$	5.71059°

Parameters	Measurement
$D$ (aperture diameter)	1000 mm
$f$ (telescope focal length)	6565 mm
$2 c_{3}$ (M3 parent mirror interfocal distance)	326.43 mm
$K_{3}$ (M3 parent mirror conic constant)	−0.0201436
$ℓ_{3}$	1000 mm
$ℓ_{3}^{'}$	1300 mm
$m_{3}$	1.3
$i_{3}$	−3.23502°
$β$	15.2425°
$θ_{i m}^{t}$	0°
$θ_{i m}^{s}$	0°

Abstract

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Figures (9)

Tables (2)

Equations (39)

Journal of the Optical Society of America A