Current status of aplanatic gradient-index lens systems

Ichiro Kitano

doi:10.1364/AO.29.003992

Applied Optics
Vol. 29,
Issue 28,
pp. 3992-3997
(1990)
•https://doi.org/10.1364/AO.29.003992

Current status of aplanatic gradient-index lens systems

Ichiro Kitano

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Ichiro Kitano, "Current status of aplanatic gradient-index lens systems," Appl. Opt. 29, 3992-3997 (1990)

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Abstract

A gradient index (GRIN) lens, when processed by a spherical curvature at its endface, yields the equivalent aspheric effect, if the curvature is adequately optimized with refractive index distribution coefficients. Aplanatic lens systems of infinite or finite conjugates can be made by utilizing the new type of GRIN lens.

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GRIN	Single	Compound	Formulae
GIH(mm)	0.075	0.080	A_nm :Zernike’s Coefficient 8≥n≥m>0, n-m: even
W.F.E.	waves RMS		A_nm :Zernike’s Coefficient 8≥n≥m>0, n-m: even
OPDrms	0.07154	0.05111	$\sqrt{\frac{1}{2} \sum_{n = 1}^{8} \sum_{m = 0}^{n} [\frac{A_{n m}^{2}}{n + 1}]}$
Spherical SA	0.04521	0.00691	$\sqrt{\frac{1}{2} (\frac{A_{40}^{2}}{5} + \frac{A_{60}^{2}}{7} + \frac{A_{80}^{2}}{9})}$
Coma CM	0.02964	0.00992	$\sqrt{\frac{1}{2} (\frac{A_{31}^{2}}{4} + \frac{A_{51}^{2}}{6} + \frac{A_{71}^{2}}{8})}$
Astigmatism AS	0.04683	0.01472	$\sqrt{\frac{1}{2} (\frac{A_{22}^{2}}{3} + \frac{A_{42}^{2}}{5} + \frac{A_{62}^{2}}{7} + \frac{A_{82}^{2}}{9})}$
Residual	0.02812	0.04723	$\sqrt{{O P D}_{r m s}^{2} - ({S A}^{2} + {C M}^{2} + A S^{2})}$

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Applied Optics