Traceable methods for vertical scale characterization of dynamic stroboscopic scanning white-light interferometer measurements

V. Heikkinen; I. Kassamakov; J. Seppä; T. Paulin; A. Nolvi; A. Lassila; E. Hæggström

doi:10.1364/AO.54.010397

Applied Optics
Vol. 54,
Issue 35,
pp. 10397-10403
(2015)
•https://doi.org/10.1364/AO.54.010397

Traceable methods for vertical scale characterization of dynamic stroboscopic scanning white-light interferometer measurements

V. Heikkinen, I. Kassamakov, J. Seppä, T. Paulin, A. Nolvi, A. Lassila, and E. Hæggström

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V. Heikkinen, I. Kassamakov, J. Seppä, T. Paulin, A. Nolvi, A. Lassila, and E. Hæggström, "Traceable methods for vertical scale characterization of dynamic stroboscopic scanning white-light interferometer measurements," Appl. Opt. 54, 10397-10403 (2015)

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Table of Contents Category
- Instrumentation, Measurement, and Metrology
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About this Article
History
- Original Manuscript: September 9, 2015
- Revised Manuscript: November 9, 2015
- Manuscript Accepted: November 9, 2015
- Published: December 9, 2015
Virtual Issues
Virtual Journal for Biomedical Optics Vol. 11, Iss. 2

Abstract

Stroboscopic scanning white-light interferometry (SSWLI) can be used for 3D imaging of oscillating samples. It allows measurement of micrometer to millimeter size samples with nanometer vertical precision. Unlike coherent light source systems the SSWLI can measure unambiguously samples with vertical steps. Traceability of the vertical displacement measurement is important with SSWLI since the height measurement is not related to any specific monochromatic light wavelength. For static measurements SSWLI can be calibrated using, e.g., step height standards, but to characterize dynamic measurements traceable samples with accurate motion are needed due to error sources related to the frequency response of the SSWLI. In the presented method, SSWLI measurements are performed on dynamic transfer standards, which are characterized using a laser interferometer traceable to the SI meter. In this work dynamic SSWLI measurements at subkilohertz to 10.7 kHz frequencies with micrometer range displacement are characterized. The expanded uncertainty ( $k = 2$ ) was 9.6 nm for a measured displacement of 766 nm at 10.7 kHz. The methodology can be used up to the frequency limits of the SSWLI using suitable samples.

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Repeatability of LFTS Motion Amplitude/nm
Amplitude/Frequency	50 Hz	100 Hz	200 Hz	400 Hz
100 nm	0.2	0.77	1.19	2.64
500 nm	1.02	3.57	1.76	8.08
1000 nm	1.34	1.79	5.39	19.16
2000 nm	1.80	3.71	23.31	—
4000 nm	2.49	6.78	—	—

Source of Uncertainty	Symbol	Uncertainty	Distribution	Sens. Coeff.	Uncertainty Contribution
Repeatability	$Z_{meas}$	$4.2 nm / μm$	normal	$Z$	0.0042 $Z$
Cosine error	$Δ α$	$\pm 0.01 rad$	rectangular	$(1 - \cos (Δ α)) Z$	0.00003 $Z$
Focusing/NA	$Δ NA$	$\pm 0.02 rad$	rectangular	$(1 - \cos (Δ NA)) Z$	0.0002 $Z$
Phase detection	$Δ Φ$	$\pm 0.2 nm$	normal	1	0.2 nm
Wavelength	$Δ λ$	$< \pm 1 \times 10^{- 7}$	normal	$Z$	$< 1 \times 10^{- 7}$ $Z$
Measurement position	$δ_{pos}$	$\pm 5 μm$	rectangular	$(b \times Δ x) Z$	0.0014 $Z$
Residual periodic nonlinearity of interferometer	$δ_{lin}$	$\pm 1.0 nm$	normal	1	1 nm
Total standard uncertainty $\pm \sqrt{1.0 {nm}^{2} + {(4.4 Z nm / μm)}^{2}}$

Difference between SSWLI Reading and Reference/nm
Amplitude/frequency	50 Hz	100 Hz	200 Hz
100 nm	—	—	0.54
500 nm	—	−3.6	−2.3
1000 nm	5.8	−9.8	—
2000 nm	−4.5	—	—

Standard Uncertainty of Characterization/nm
Amplitude/Frequency	50 Hz	100 Hz	200 Hz
100 nm	—	—	6.3
500 nm	—	8.2	2.8
1000 nm	7.9	14.4	—
2000 nm	9.0	—	—

TS Amplitude/nm	Standard Uncertainty/nm	SSWLI Amplitude/nm	Standard Uncertainty/nm	Difference from Reference/nm	Expanded Uncertainty $(k = 2) / nm$
325.1	1.7	323.1	2.7	−2.0	6.4
644.0	3.0	644.0	2.7	−1.8	8.3
766.2	3.5	761.6	3.3	−4.6	9.6

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