Calibration of numerical aperture effects in interferometric microscope objectives

Katherine Creath

doi:10.1364/AO.28.003333

Applied Optics
Vol. 28,
Issue 16,
pp. 3333-3338
(1989)
•https://doi.org/10.1364/AO.28.003333

Calibration of numerical aperture effects in interferometric microscope objectives

Katherine Creath

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Katherine Creath, "Calibration of numerical aperture effects in interferometric microscope objectives," Appl. Opt. 28, 3333-3338 (1989)

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Abstract

The numerical aperture (N.A.) of a microscope objective can affect the measurement of surface profiles. Large N.A. objectives measure smaller heights than the actual values. An experiment to calibrate these effects on objectives with N.A.s of 0.1–0.95 is described using four traceable step height standards and a computer-controlled interferometric optical profiler utilizing phase-measurement interferometry techniques. The measured N.A. scaling factors have good agreement with a theory developed by Ingelstam. N.A. scaling factors are determined to an uncertainty of ± 1% for N.A.s ≤0.5 and ± 2% for N.A.s ≥0.9.

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Magnification	N.A.	Tilt angle (rad)	Effective N.A.
5	0.10	0.0323	0.068
10	0.25	0.0101	0.240
20	0.40	0.0074	0.393
40	0.50	0.0090	0.492
100	0.90	0.0035	0.898
200	0.95	0.0045	0.949

Objective magnification	N.A.	Num. obj. measured	Total meas. each step
5	0.10	1	5
10	0.25	5	25
20	0.40	6	30
40	0.50	4	20
100	0.90	1	40
200	0.95	2	80

Step height (nm)	Magnification	Measured step (nm)	Standard deviation (%)
43.50	5	39.35	—
	10	39.46	0.62
	20	39.11	1.29
	40	38.92	1.16
	100	33.49	3.50
	200	32.89	1.71
48.00	5	48.18	—
	10	48.10	0.72
	20	47.12	1.08
	40	47.08	0.78
	100	39.93	1.01
	200	39.44	1.08
83.40	5	83.63	—
	10	83.18	0.83
	20	81.46	0.64
	40	79.26	0.84
	100	68.00	0.59
	200	66.98	0.87
85.50	5	83.99	—
	10	83.07	0.79
	20	82.03	0.49
	40	80.95	0.96
	100	69.23	2.37
	200	69.67	3.24

Magnification	N.A.	N.A. factors					Standard deviation
Magnification	N.A.	43.5	48.0	83.4	85.5	Average	Standard deviation
5	0.10	1.010	1.001	0.991	0.999	1.000	0.008
10	0.25	1.008	1.003	0.997	1.010	1.004	0.006
20	0.40	1.017	1.024	1.018	1.023	1.021	0.003
40	0.50	1.023	1.025	1.046	1.037	1.033	0.011
100	0.90	1.205	1.207	1.220	1.217	1.212	0.007
200	0.95	1.228	1.222	1.239	1.209	1.225	0.012

N.A.	N.A. factors					Effective N.A.
N.A.	Schulz	Gates	Bruce and Thornton	Ingelstam	Measured (adjusted)	Effective N.A.
0.10	1.003	1.003	1.003	1.003	1.003	0.10
0.25	1.016	1.016	1.016	1.016	1.007	0.17
0.40	1.044	1.044	1.042	1.040	1.024	0.31
0.50	1.072	1.074	1.069	1.063	1.036	0.38
0.90	1.393	1.472	1.313	1.203	1.215	0.93
0.95	1.524	1.692	1.571	1.226	1.228	0.95

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Applied Optics