GRIN lens profile measurement by ray trace analysis

Toyokazu Sakamoto

doi:10.1364/AO.22.003064

Applied Optics
Vol. 22,
Issue 19,
pp. 3064-3069
(1983)
•https://doi.org/10.1364/AO.22.003064

GRIN lens profile measurement by ray trace analysis

Toyokazu Sakamoto

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Toyokazu Sakamoto, "GRIN lens profile measurement by ray trace analysis," Appl. Opt. 22, 3064-3069 (1983)

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Abstract

A fifth-order algebraic formula is derived for the axial deviation of the ray observed behind the GRIN lens exit face, whose expansion coefficients characterize the coefficients up to sixth-order in the index profile of a GRIN lens with arbitrary length; the index coefficients up to sixth-order of a near one-quarter pitch lens are estimated with the formula. The proposed technique would be useful for the evaluation of a GRIN lens with larger spherical aberrations and a longer GRIN rod.

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Observed data		Solution of Eqs. (10′)	Refractive-index coefficients

			Exact solution	Approximate solution ^a
$∑ x_{k}^{2} = 14.35$	$∑ x_{k}^{4} = 9.033$	â = −155.7 ± 1.8	g = 0.223 ± 0.002 mm⁻¹	0.223 ± 0.002 (0.223 ± 0.002)
$∑ x_{k}^{6} = 6.764$	$∑ x_{k}^{8} = 5.511$	$\hat{b} = 15.2 \pm 1.2$	ĥ₄ = 6.1 ± 0.3	6.3 ±0.3 (4.2 ±0.2)
$∑ x_{k}^{10} = 4.719$	$∑ x_{k} y_{k} = - 2172$	ĉ = −11.1 ± 1.3	ĥ₆ = −122 ± 6	−108 ±7 (−54 ±3)
$∑ x_{k}^{3} y_{k} = - 1365$	$∑ x_{k}^{5} y_{k} = - 1022$

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Applied Optics