Algorithm for the simulation of ronchigrams of arbitrary optical systems and Ronchi grids in generalized coordinates

Alberto Cordero-Dávila; José Díaz-Anzures; Victor Cabrera-Peláez

doi:10.1364/AO.41.003866

Applied Optics
Vol. 41,
Issue 19,
pp. 3866-3873
(2002)
•https://doi.org/10.1364/AO.41.003866

Algorithm for the simulation of ronchigrams of arbitrary optical systems and Ronchi grids in generalized coordinates

Alberto Cordero-Dávila, José Díaz-Anzures, and Victor Cabrera-Peláez

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Alberto Cordero-Dávila, José Díaz-Anzures, and Victor Cabrera-Peláez, "Algorithm for the simulation of ronchigrams of arbitrary optical systems and Ronchi grids in generalized coordinates," Appl. Opt. 41, 3866-3873 (2002)

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Abstract

We present a simple algorithm that makes possible the simulation of ronchigrams for any optical system in which it is possible to make an exact ray tracing. We report the simulations for the following grids: the Ronchi classical, square, circular, radial, circular-radial, biparabolic, elliptic-hyperbolic, bipolar, and bielliptic ones.

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Parameter	Value
Distance of the object from the first surface	10²⁰
Object plane curvature	0
Conic constant, deformation coefficients	0, 0, 0, 0, 0
Refraction index	1, 1, 1, 1
First surface curvature	0.06164
Conic constant, deformation coefficients	0, 0, 0, 0, 0
Distance	0.40
Refraction index	1.649, 1.649, 1.649, 1.649
Curvature	0.19311
Conic constant, deformation coefficients	0, 0, 0, 0, 0
Distance	1.05
Refraction index	1.517, 1.517, 1.517, 1.517
Curvature	-0.135327
Conic constant, deformation coefficients	0, 0, 0, 0, 0
Distance	10.5
Refraction index	1, 1, 1, 1
Curvature	0
Conic constant, deformation coefficients	0, 0, 0, 0, 0
Distance	1
Refraction index	1, 1, 1, 1
Curvature of the image surface	0
Semidiameter, image height, pupil	2, 10^-20, 1

Parameter	Value
Distance from the object to the first surface	181
Object plane curvature	0
Refraction index	1, 1, 1, 1
Mirror surface curvature	-0.0166666
Conic constant, deformation coefficients	-1.02, 0, 0, 0, 0
Distance	35.5
Refraction index	-1,-1,-1,-1
Grid plane curvature	0
Distance	1
Refraction index	1, 1, 1, 1
Image surface curvature	0
Semidiameter, image height, pupil	7, 7, 1

Coordinate	T₁	T₂
Biparabolic	$\frac{T_{y}}{{[- T_{x} + {(T_{x}^{2} + T_{y}^{2})}^{1 / 2}]}^{1 / 2}}$	${[- T_{x} + {(T_{x}^{2} + T_{y}^{2})}^{1 / 2}]}^{1 / 2}$
Elliptic-hyperbolic	$log [{(M)}^{1 / 2} + {(1 + M)}^{1 / 2}]$	$\arctan {(\frac{N}{1 - N})}^{1 / 2}$
Bipolar	${Cot}^{- 1} (\frac{T_{x}^{2} + T_{y}^{2} + a^{2}}{2 {aT}_{y}})$	$\frac{1}{2} log [\frac{{(T_{x} + a)}^{2} + T_{y}^{2}}{{(T_{x} - a)}^{2} + T_{y}^{2}}]$
Bielliptic	$\frac{T_{x}^{2} - T_{y}^{2}}{a}$	$\frac{2 T_{x} T_{y}}{a}$

Parameter	Value
Distance of the object from the first surface	10²⁰
Object plane curvature	0
Conic constant, deformation coefficients	0, 0, 0, 0, 0
Refraction index	1, 1, 1, 1
First surface curvature	0.06164
Conic constant, deformation coefficients	0, 0, 0, 0, 0
Distance	0.40
Refraction index	1.649, 1.649, 1.649, 1.649
Curvature	0.19311
Conic constant, deformation coefficients	0, 0, 0, 0, 0
Distance	1.05
Refraction index	1.517, 1.517, 1.517, 1.517
Curvature	-0.135327
Conic constant, deformation coefficients	0, 0, 0, 0, 0
Distance	10.5
Refraction index	1, 1, 1, 1
Curvature	0
Conic constant, deformation coefficients	0, 0, 0, 0, 0
Distance	1
Refraction index	1, 1, 1, 1
Curvature of the image surface	0
Semidiameter, image height, pupil	2, 10^-20, 1

Parameter	Value
Distance from the object to the first surface	181
Object plane curvature	0
Refraction index	1, 1, 1, 1
Mirror surface curvature	-0.0166666
Conic constant, deformation coefficients	-1.02, 0, 0, 0, 0
Distance	35.5
Refraction index	-1,-1,-1,-1
Grid plane curvature	0
Distance	1
Refraction index	1, 1, 1, 1
Image surface curvature	0
Semidiameter, image height, pupil	7, 7, 1

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Equations (18)

Applied Optics