Aberrations of anamorphic optical systems III: the primary aberration theory for toroidal anamorphic systems

Sheng Yuan; Jose Sasian

doi:10.1364/AO.49.006802

Applied Optics
Vol. 49,
Issue 35,
pp. 6802-6807
(2010)
•https://doi.org/10.1364/AO.49.006802

Aberrations of anamorphic optical systems III: the primary aberration theory for toroidal anamorphic systems

Sheng Yuan and Jose Sasian

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Sheng Yuan and Jose Sasian, "Aberrations of anamorphic optical systems III: the primary aberration theory for toroidal anamorphic systems," Appl. Opt. 49, 6802-6807 (2010)

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Abstract

We apply a new method for optical aberration derivation to anamorphic systems made from toroidal surfaces and obtain a complete set of primary aberration coefficients. This set is written in a form similar to the well-known Seidel aberrations for rotationally symmetrical optical systems and includes first- order quantities only, thus it can be easily applied to anamorphic lens design practice. By tracing four nonskew paraxial marginal and chief rays, the 16 anamorphic primary aberration coefficients can be easily calculated.

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Equations (34)

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Aberration Types for Rays Contained in the $x - z$ Symmetry Plane
$D_{1} = - \frac{1}{8} S_{I x}$	$D_{4} = - \frac{1}{2} S_{I I x}$	$D_{8} = - \frac{1}{4} (3 S_{I I I x} + S_{I V x})$	$D_{13} = - \frac{1}{2} S_{V x}$
Aberration Types for Rays Contained in the $y - z$ Symmetry Plane
$D_{2} = - \frac{1}{8} S_{I y}$	$D_{7} = - \frac{1}{2} S_{I I y}$	$D_{9} = - \frac{1}{4} (3 S_{I I I y} + S_{I V y})$	$D_{14} = - \frac{1}{2} S_{V y}$
Additional Primary Aberration Types Associated with Skew Rays
$D_{3} = - \frac{1}{4} \sum_{j = 1}^{k} A_{x, j} (h_{x, j} Δ u_{y, j}^{2} + h_{y, j}^{2} c_{y, j} Δ u_{x, j})$		$D_{5} = - \frac{1}{2} \sum_{j = 1}^{k} A_{x, j} (h_{x, j} Δ u_{y, j} {\bar{u}}_{y, j} + h_{y, j} {\bar{h}}_{y, j} c_{y, j} Δ u_{x, j})$
$D_{6} = - \frac{1}{2} \sum_{j = 1}^{k} ({\bar{A}}_{x, j} h_{x, j} Δ u_{y, j}^{2} + A_{x, j} h_{y, j}^{2} c_{y, j} Δ {\bar{u}}_{x, j})$		$D_{10} = - \frac{1}{4} \sum_{j = 1}^{k} A_{x, j} (h_{x, j} Δ {\bar{u}}_{y, j}^{2} + {\bar{h}}_{y, j}^{2} c_{y, j} Δ u_{x, j})$
$D_{11} = - \frac{1}{4} \sum_{j = 1}^{k} A_{y, j} (h_{y, j} Δ {\bar{u}}_{x, j}^{2} + {\bar{h}}_{x, j}^{2} c_{x, j} Δ u_{y, j}) - \frac{1}{4} \sum_{j = 1}^{k} (c_{x, j} c_{y, j}^{2} - c_{x, j}^{2} c_{y, j}) {\bar{h}}_{x, j}^{2} h_{y, j}^{2} Δ n_{j}$
$D_{12} = - \sum_{j = 1}^{k} ({\bar{A}}_{x, j} h_{x, j} Δ u_{y, j} {\bar{u}}_{y, j} + A_{x, j} h_{y, j} {\bar{h}}_{y, j} c_{y, j} Δ {\bar{u}}_{x, j})$		$D_{15} = - \frac{1}{2} \sum_{j = 1}^{k} ({\bar{A}}_{x, j} h_{x, j} Δ {\bar{u}}_{y, j}^{2} + A_{x, j} {\bar{h}}_{y, j}^{2} c_{y, j} Δ {\bar{u}}_{x, j})$
$D_{16} = - \frac{1}{2} \sum_{j = 1}^{k} ({\bar{A}}_{y, j} h_{y, j} Δ {\bar{u}}_{x, j}^{2} + A_{y, j} {\bar{h}}_{x, j}^{2} c_{x, j} Δ {\bar{u}}_{y, j}) - \frac{1}{2} \sum_{j = 1}^{k} (c_{x, j} c_{y, j}^{2} - c_{x, j}^{2} c_{y, j}) {\bar{h}}_{x, j}^{2} h_{y, j} {\bar{h}}_{y, j} Δ n_{j}$

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Applied Optics