Analysis of the optical center position of an optical system of a camera lens

Antonín Mikš; Jiří Novák

doi:10.1364/AO.57.004409

Applied Optics
Vol. 57,
Issue 16,
pp. 4409-4414
(2018)
•https://doi.org/10.1364/AO.57.004409

Analysis of the optical center position of an optical system of a camera lens

Antonín Mikš and Jiří Novák

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Antonín Mikš and Jiří Novák, "Analysis of the optical center position of an optical system of a camera lens," Appl. Opt. 57, 4409-4414 (2018)

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Abstract

A theory of an optical center of a camera lens is described. The concept of an optical center (a camera center) is used widely in various methods dedicated to the calibration of optical imaging and measuring systems in photogrammetry, computer vision, triangulation sensors, fringe projection techniques, surveying, and machine vision, where the so-called pinhole camera model is used as the camera’s basic model. It is shown that the optical center of the optical system with a fixed position does not exist generally, even for an ideal optical system. The optical center can be defined unambiguously for an ideal lens only for one specific object distance in general. Moreover, equations are derived for the calculation of initial design parameters of the three-element optical system composed of thin lens elements having the identical position of object and image principal planes. Such optical systems will have a fixed-position optical center, which does not depend on the object distance. The analysis was presented on several examples of the calculation of parameters of these optical systems.

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Equations (20)

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$m$	$m_{P} = 0$	$m_{P} = 0.5$	$m_{P} = 1$	$m_{P} = 1.5$	$m_{P} = \infty$
0	–	0.000	0.000	0.000	0
−2	0.125	0.020	−0.083	−0.173	−1
−4	0.125	0.037	−0.100	−0.256	−4
−6	0.125	0.044	−0.107	−0.300	−9
−8	0.125	0.048	−0.111	−0.327	−16
−10	0.125	0.051	−0.114	−0.345	−25

$f^{'} = 1$ , $S_{IV} \approx 0$ , $d = 0$
$f_{1}^{'}$	$f_{2}^{'}$	$f_{3}^{'}$	$d_{1}$	$d_{2}$	$s_{P}$	$s_{P^{'}}^{'}$	$s_{F^{'}}^{'}$
0.7810	−0.2236	0.3133	0.10	0.10	0.3339	0.1339	1.1339
1.2405	−0.3162	0.4244	0.20	0.20	0.6080	0.2080	1.2080
1.6424	−0.3873	0.5068	0.30	0.30	0.8678	0.2678	1.2678
2.2889	−0.4140	0.5055	0.40	0.30	0.9921	0.2921	1.2921
1.4687	−0.4140	0.5766	0.30	0.40	0.9921	0.2921	1.2921

$f^{'} = 1$ , $S_{IV} \approx 0$ , $d = 0$ , $d_{1} = 0.2$
$f_{1}^{'}$	$f_{2}^{'}$	$f_{3}^{'}$	$d_{2}$	$s_{P}$	$s_{P^{'}}^{'}$	$s_{F^{'}}^{'}$
0.4199	−0.3705	3.1500	0.4376	−0.2624	−0.9000	0.10
0.4198	−0.3573	2.4000	0.3530	−0.2470	−0.8000	0.20
0.4210	−0.3393	1.7500	0.2715	−0.2285	−0.7000	0.30
0.4249	−0.3138	1.2000	0.1940	−0.2060	−0.6000	0.40
0.4355	−0.2755	0.7500	0.1224	−0.1776	−0.5000	0.50

$m$	$m_{P} = 0$	$m_{P} = 0.5$	$m_{P} = 1$	$m_{P} = 1.5$	$m_{P} = \infty$
0	–	0.000	0.000	0.000	0
−2	0.125	0.020	−0.083	−0.173	−1
−4	0.125	0.037	−0.100	−0.256	−4
−6	0.125	0.044	−0.107	−0.300	−9
−8	0.125	0.048	−0.111	−0.327	−16
−10	0.125	0.051	−0.114	−0.345	−25

$f^{'} = 1$ , $S_{IV} \approx 0$ , $d = 0$
$f_{1}^{'}$	$f_{2}^{'}$	$f_{3}^{'}$	$d_{1}$	$d_{2}$	$s_{P}$	$s_{P^{'}}^{'}$	$s_{F^{'}}^{'}$
0.7810	−0.2236	0.3133	0.10	0.10	0.3339	0.1339	1.1339
1.2405	−0.3162	0.4244	0.20	0.20	0.6080	0.2080	1.2080
1.6424	−0.3873	0.5068	0.30	0.30	0.8678	0.2678	1.2678
2.2889	−0.4140	0.5055	0.40	0.30	0.9921	0.2921	1.2921
1.4687	−0.4140	0.5766	0.30	0.40	0.9921	0.2921	1.2921

Abstract

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Figures (4)

Tables (3)

Equations (20)

Applied Optics