Measurement of Axial and Off-Axis Geometrical Aberrations of Microscope Objectives

W. M. Vaidya; M. K. Sen Gupta

doi:10.1364/JOSA.50.000467

Journal of the Optical Society of America
Vol. 50,
Issue 5,
pp. 467-477
(1960)
•https://doi.org/10.1364/JOSA.50.000467

Measurement of Axial and Off-Axis Geometrical Aberrations of Microscope Objectives

W. M. Vaidya and M. K. Sen Gupta

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W. M. Vaidya and M. K. Sen Gupta, "Measurement of Axial and Off-Axis Geometrical Aberrations of Microscope Objectives," J. Opt. Soc. Am. 50, 467-477 (1960)

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Abstract

An apparatus incorporating several improvements for direct measurement of aberrations in microscope objectives is described. In principle, it is similar to that of Kingslake, who by shifting a pinhole across the aperture of a microscope objective measured the resultant transverse aberration from which spherical aberration could be readily calculated. By using a different pinhole system, accuracy of setting has been improved, as also the brightness of image. Sensitivity of measurement of transverse aberration has been increased by the addition of a separate magnifying system.

The theory of measurements has been extended to extra axial aberrations and the methods of measurements of spherical aberration, offence against sine condition, tangential and sagittal curvatures have been described with aberration graphs for a typical microscope objective.

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Equations (15)

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G′pr→	0 mm (axial)			2 mm (tangential)			2 mm (sagittal)
y (mm)	Readings for T=R (mm)	R/m	Corrected Y, by Eq. (1a) (mm)	Readings for T=R (mm)	R/m	Corrected Y, by Eq. (1) (mm)	Microm. readings ζ (mm)	ζ/m	Corrected Y, by Eq. (1a) (mm)
−4.75	4.855	0.809	−4.85	4.425	0.735	−4.81	4.760	0.790	−4.85
−4.25	4.935	0.882	−4.34	4.615	0.766	−4.81	4.800	0.797	−4.34
−3.75	5.060	0.843	−3.83	4.715	0.783	−3.79	4.900	0.813	−3.83
−3.25	5.025	0.837	−3.32	4.755	0.789	−3.28	4.860	0.807	−3.32
−2.75	4.965	0.827	−2.81	4.725	0.784	−2.77	4.845	0.804	−2.81
−2.25	4.950	0.825	−2.30	4.695	0.779	−2.26	4.785	0.794	−2.30
−1.75	4.855	0.813	−1.79	4.665	0.774	−1.75	4.795	0.796	−1.79
−1.25	4.905	0.817	−1.28	4.660	0.774	−1.24	4.755	0.789	−1.28
−0.75	4.930	0.821	−0.77	4.610	0.765	−0.73	4.800	0.797	−0.77
−0.25	4.950	0.825	−0.26	4.575	0.759	−0.22	4.820	0.800	−0.26
0.25	4.990	0.831	0.26	4.635	0.769	0.30	4.810	0.798	0.26
0.75	5.065	0.844	0.77	4.625	0.768	0.81	4.800	0.797	0.77
1.25	5.085	0.847	1.28	4.605	0.764	1.32	4.825	0.801	1.28
1.75	5.080	0.846	1.79	4.625	0.768	1.83	4.845	0.804	1.79
2.25	4.990	0.831	2.30	4.600	0.764	2.34	4.780	0.793	2.30
2.75	5.025	0.837	2.81	4.550	0.755	2.85	4.795	0.796	2.81
3.25	4.965	0.827	3.32	4.500	0.747	3.36	4.725	0.784	3.32
3.75	4.995	0.832	3.83	4.440	0.737	3.87	4.740	0.787	3.83
4.25	5.070	0.845	4.34	4.425	0.735	4.37	4.770	0.793	4.34
4.75	5.270	0.878	4.85	4.540	0.754	4.89	4.815	0.799	4.85

G′pr→	0 mm (axial)		2 mm (tangential)				2 mm (sagittal)
Y (mm)	T (mm)	L by Eq. (2) (mm)	G′_U (mm)	G′_L (mm)	OSC′ by Eq. (3)	X′_T by Eq. (4) (mm)	Δζ_S₊ (mm)	Δζ_S₋ (mm)	X′_S by Eq. (5)
0.0	0.000	?	⋯	⋯	⋯	⋯	⋯	⋯	⋯
0.5	−0.007	−2.130	1.993	2.001	0.0005	−1.280	0.002	0.000	0.320
1.0	−0.013	−1.975	1.996	1.994	0.0007	0.160	0.000	0.003	−0.240
1.5	−0.016	−1.617	1.998	1.987	0.0012	0.586	−0.003	0.005	−0.426
2.0	−0.015	−1.133	1.996	1.988	0.0013	0.320	0.001	0.005	−0.160
2.5	−0.008	−0.481	2.001	1.982	0.0013	0.608	0.007	0.001	0.192
3.0	0.000	0.000	2.010	1.977	0.0010	0.880	0.011	−0.005	0.426
3.5	0.005	0.213	2.019	1.975	0.0005	1.005	0.013	−0.011	0.548
4.0	0.003	0.112	2.027	1.985	−0.0010	0.840	0.011	−0.006	0.340
4.5	−0.010	−0.334	2.025	2.008	−0.0028	0.302	0.004	0.007	0.195
5.0	−0.030	−0.905	2.007	2.042	−0.0050	−0.560	−0.005	0.011	−0.256

Y (mm)	G′_S₊ (mm)	G′_S₋ (mm)	OSC′ by Eq. (6)
3.5 (zonal)	6.007	6.003	−0.0008
5.0 (marginal)	6.034	6.020	−0.0045

G′pr→	0 mm (axial)			2 mm (tangential)			2 mm (sagittal)
y (mm)	Readings for T=R (mm)	R/m	Corrected Y, by Eq. (1a) (mm)	Readings for T=R (mm)	R/m	Corrected Y, by Eq. (1) (mm)	Microm. readings ζ (mm)	ζ/m	Corrected Y, by Eq. (1a) (mm)
−4.75	4.855	0.809	−4.85	4.425	0.735	−4.81	4.760	0.790	−4.85
−4.25	4.935	0.882	−4.34	4.615	0.766	−4.81	4.800	0.797	−4.34
−3.75	5.060	0.843	−3.83	4.715	0.783	−3.79	4.900	0.813	−3.83
−3.25	5.025	0.837	−3.32	4.755	0.789	−3.28	4.860	0.807	−3.32
−2.75	4.965	0.827	−2.81	4.725	0.784	−2.77	4.845	0.804	−2.81
−2.25	4.950	0.825	−2.30	4.695	0.779	−2.26	4.785	0.794	−2.30
−1.75	4.855	0.813	−1.79	4.665	0.774	−1.75	4.795	0.796	−1.79
−1.25	4.905	0.817	−1.28	4.660	0.774	−1.24	4.755	0.789	−1.28
−0.75	4.930	0.821	−0.77	4.610	0.765	−0.73	4.800	0.797	−0.77
−0.25	4.950	0.825	−0.26	4.575	0.759	−0.22	4.820	0.800	−0.26
0.25	4.990	0.831	0.26	4.635	0.769	0.30	4.810	0.798	0.26
0.75	5.065	0.844	0.77	4.625	0.768	0.81	4.800	0.797	0.77
1.25	5.085	0.847	1.28	4.605	0.764	1.32	4.825	0.801	1.28
1.75	5.080	0.846	1.79	4.625	0.768	1.83	4.845	0.804	1.79
2.25	4.990	0.831	2.30	4.600	0.764	2.34	4.780	0.793	2.30
2.75	5.025	0.837	2.81	4.550	0.755	2.85	4.795	0.796	2.81
3.25	4.965	0.827	3.32	4.500	0.747	3.36	4.725	0.784	3.32
3.75	4.995	0.832	3.83	4.440	0.737	3.87	4.740	0.787	3.83
4.25	5.070	0.845	4.34	4.425	0.735	4.37	4.770	0.793	4.34
4.75	5.270	0.878	4.85	4.540	0.754	4.89	4.815	0.799	4.85

G′pr→	0 mm (axial)		2 mm (tangential)				2 mm (sagittal)
Y (mm)	T (mm)	L by Eq. (2) (mm)	G′_U (mm)	G′_L (mm)	OSC′ by Eq. (3)	X′_T by Eq. (4) (mm)	Δζ_S₊ (mm)	Δζ_S₋ (mm)	X′_S by Eq. (5)
0.0	0.000	?	⋯	⋯	⋯	⋯	⋯	⋯	⋯
0.5	−0.007	−2.130	1.993	2.001	0.0005	−1.280	0.002	0.000	0.320
1.0	−0.013	−1.975	1.996	1.994	0.0007	0.160	0.000	0.003	−0.240
1.5	−0.016	−1.617	1.998	1.987	0.0012	0.586	−0.003	0.005	−0.426
2.0	−0.015	−1.133	1.996	1.988	0.0013	0.320	0.001	0.005	−0.160
2.5	−0.008	−0.481	2.001	1.982	0.0013	0.608	0.007	0.001	0.192
3.0	0.000	0.000	2.010	1.977	0.0010	0.880	0.011	−0.005	0.426
3.5	0.005	0.213	2.019	1.975	0.0005	1.005	0.013	−0.011	0.548
4.0	0.003	0.112	2.027	1.985	−0.0010	0.840	0.011	−0.006	0.340
4.5	−0.010	−0.334	2.025	2.008	−0.0028	0.302	0.004	0.007	0.195
5.0	−0.030	−0.905	2.007	2.042	−0.0050	−0.560	−0.005	0.011	−0.256

Abstract

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Figures (11)

Tables (3)

Equations (15)

Journal of the Optical Society of America