Conditions for correction of linear and quadratic field-dependent aberrations in plane-symmetric optical systems

Chunyu Zhao; James H. Burge

doi:10.1364/JOSAA.19.002467

Conditions for correction of linear and quadratic field-dependent aberrations in plane-symmetric optical systems

Chunyu Zhao and James H. Burge

Journal of the Optical Society of America A
Vol. 19,
Issue 12,
pp. 2467-2472
(2002)
•https://doi.org/10.1364/JOSAA.19.002467

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Chunyu Zhao and James H. Burge, "Conditions for correction of linear and quadratic field-dependent aberrations in plane-symmetric optical systems," J. Opt. Soc. Am. A 19, 2467-2472 (2002)

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Previously assigned OCIS codes
- Aberrations (global) (220.1010)
- Lens system design (220.3620)
- Systems design (220.4830)

About this Article
History
- Original Manuscript: January 10, 2002
- Revised Manuscript: June 20, 2002
- Manuscript Accepted: June 20, 2002
- Published: December 1, 2002

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Abstract

The Abbe sine condition and the recently developed pupil astigmatism conditions provide a powerful set of relationships for describing imaging systems that are free from aberrations that have linear and quadratic dependence on field, to all orders in the pupil. We have proved both of these conditions and applied them to axisymmetric imaging systems. We now extend our approach to plane-symmetric systems. Still using Hamilton’s characteristic functions, we derive the general sine conditions and the pupil astigmatism conditions that describe plane-symmetric systems that are free of all aberrations with linear and quadratic field dependence.

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Vector Form	Name
$W_{12010} (i \cdot h_{0}) (ρ_{1} \cdot ρ_{1})$	Field tilt
$W_{12101} (h_{0} \cdot ρ_{1}) (i \cdot ρ_{1})$	Linear astigmatism
$W_{13100} (h_{0} \cdot ρ_{1}) (ρ_{1} \cdot ρ_{1})$	Linear coma

Vector Form	Name
$W_{21001} (h_{0} \cdot h_{0}) (i \cdot ρ_{1})$	Quadratic distortion I
$W_{22000} (h_{0} \cdot h_{0}) (ρ_{1} \cdot ρ_{1})$	Field curvature
$W_{21110} (h_{0} \cdot ρ_{1}) (h_{0} \cdot i)$	Quadratic distortion II
$W_{22200} (h_{0} \cdot ρ_{1})^{2}$	Quadratic astigmatism
$W_{21021} (h_{0} \cdot i)^{2} (i \cdot ρ_{1})$	N/A

Vector Form	Name
$W_{12010} (i \cdot h_{0}) (ρ_{1} \cdot ρ_{1})$	Field tilt
$W_{12101} (h_{0} \cdot ρ_{1}) (i \cdot ρ_{1})$	Linear astigmatism
$W_{13100} (h_{0} \cdot ρ_{1}) (ρ_{1} \cdot ρ_{1})$	Linear coma

Vector Form	Name
$W_{21001} (h_{0} \cdot h_{0}) (i \cdot ρ_{1})$	Quadratic distortion I
$W_{22000} (h_{0} \cdot h_{0}) (ρ_{1} \cdot ρ_{1})$	Field curvature
$W_{21110} (h_{0} \cdot ρ_{1}) (h_{0} \cdot i)$	Quadratic distortion II
$W_{22200} (h_{0} \cdot ρ_{1})^{2}$	Quadratic astigmatism
$W_{21021} (h_{0} \cdot i)^{2} (i \cdot ρ_{1})$	N/A

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Equations (34)

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