Principles of interference microscopy for the measurement of surface topography

Peter de Groot

doi:10.1364/AOP.7.000001

Advances in Optics and Photonics
Vol. 7,
Issue 1,
pp. 1-65
(2015)
•https://doi.org/10.1364/AOP.7.000001

Principles of interference microscopy for the measurement of surface topography

Peter de Groot

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Peter de Groot, "Principles of interference microscopy for the measurement of surface topography," Adv. Opt. Photon. 7, 1-65 (2015)

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- Microscopy
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About this Article
History
- Original Manuscript: September 25, 2014
- Revised Manuscript: December 10, 2014
- Manuscript Accepted: December 22, 2014
- Published: February 2, 2015

Abstract

Interference microscopy plays a central role in noncontact strategies for process development and quality control, providing full 3D measurement of surface characteristics that influence the functional behavior of manufactured parts. Here I briefly review the history and principles of this important technique, then concentrate on the details of hardware, software, and applications of interference microscopy using phase-shifting and coherence scanning measurement principles. Recent advances considered here include performance improvements, vibration robustness, full color imaging, accommodation of highly sloped surfaces, correlation to contact methods, transparent film analysis, and international standardization of calibration and specification.

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Magnification	Type	NA ( $A_{N}$ )	Lateral Resolution (μm)	Working Distance (mm)
$0.5 \times$	Wide field^a	0.015	17.2	40
$1 \times$	Michelson	0.03	8.62	40
$2.5 \times$	Michelson	0.08	3.45	40
$5 \times$	Michelson	0.13	1.99	40
$10 \times$	Michelson	0.28	0.92	18
$10 \times$	Mirau	0.30	0.86	7.4
$20 \times$	Mirau	0.40	0.65	4.7
$50 \times$	Mirau	0.55	0.47	3.4
$100 \times$	Mirau	0.85	0.30	0.5

Frames	Reference	Step	$\tan (θ)$
3	[128]	$π / 2$	$\frac{(\begin{matrix} - 1 & 0 & 1 \end{matrix})}{(\begin{matrix} - 1 & 2 & - 1 \end{matrix})}$
4	[116]	$π / 2$	$\frac{(\begin{matrix} \begin{matrix} 1 & 1 \end{matrix} & \begin{matrix} - 1 & - 1 \end{matrix} \end{matrix})}{(\begin{matrix} \begin{matrix} - 1 & 1 \end{matrix} & \begin{matrix} 1 & - 1 \end{matrix} \end{matrix})}$
7	[118,129]	$π / 2$	$\frac{(\begin{matrix} - 1 & 0 & 7 & 0 & - 7 & 0 & 1 \end{matrix})}{(\begin{matrix} 0 & - 4 & 0 & 8 & 0 & - 4 & 0 \end{matrix})}$
12	[122]	$π / 3$	$\frac{\sqrt{3} (\begin{matrix} 0 & - 3 & - 3 & 3 & 9 & 6 & - 6 & 9 & - 3 & 3 & 3 & 0 \end{matrix})}{(\begin{matrix} 2 & 1 & - 7 & - 11 & - 1 & 16 & 16 & - 1 & - 11 & - 7 & 1 & 2 \end{matrix})}$

Part	Title	Status	Date
1	Areal surface texture drawing indications	CD	2014
2	Terms, definitions, and surface texture parameters	PS	2012
3	Specification operators	PS	2012
4	Comparison rules	NS	—
5	Verification operators	NS	—
6	Classification of methods for measuring surface texture	PS	2010
70	Measurement standards for areal surface texture measurement instruments	PS	2014
71	Software measurement standards	PS	2012
72	Software measurement standards, XML file format	CD	2012
600	Nominal characteristics of areal surface topography instruments	WD	2014
601	Nominal characteristics of contact (stylus) instruments	PS	2010
602	Nominal characteristics of non-contact (confocal chromatic probe) instruments	PS	2010
603	Nominal characteristics of non-contact (phase-shifting interferometric microscopy) instruments	PS	2013
604	Nominal characteristics of non-contact (coherence scanning interferometry) instruments	PS	2013
605	Nominal characteristics of non-contact (point autofocus) instruments	PS	2014
606	Nominal characteristics of non-contact (variable focus) instruments	CD	2012
607	Nominal characteristics of non-contact (imaging confocal) instruments	WD	2014
700	Calibration of areal surface measuring instruments	WD	2013
701	Calibration and measurement standards for contact (stylus) instruments	PS	2010

Metrological Characteristic	Instrument Specifications	Notes
Amplification coefficient (z)	Step height repeatability Step height accuracy	Expressed in height units and/or as a percentage of the measured height
Linearity deviation (z)	Height response linearity	Expressed as a maximum permissible error (MPE)
Measurement noise	Surface topography repeatability Repeatability of the rms	Expressed as a standard deviation for each specification
Topographic lateral resolution	Optical lateral resolution Lateral sampling	The specifications are for influence factors that relate to lateral resolution
Residual flatness	(not specified)	Calibrated and adjusted in situ using a system error subtract procedure
Field amplification and linearity (xy)	(not specified)	Calibrated and adjusted in situ

Specification	Value	Footnotes
Surface topography repeatability	0.1 nm	Repeatability ( $1 σ$ ) for PSI mode, 1 second data acquisition, 1 million image points, $3 \times 3$ pixel surface filtering
Repeatability of the rms	0.005 nm	Repeatability ( $1 σ$ ) of the ISO Sq parameter, same conditions as for the surface topography repeatability
Optical lateral resolution	0.33 μm	$100 \times$ , 0.85 NA objective, Sparrow criterion
Lateral sampling	0.04 μm	$100 \times$ objective, $2 \times$ tube lens
Step height accuracy	0.8%	Instrument contribution to the uncertainty ( $k = 1$ ) for step height measurement in extended scan mode (0.15 mm to 20 mm range)
Height response linearity	$\leq 20 nm$	Maximum deviation with respect to the best fit linear response
Step height repeatability	0.1%	Repeatability ( $1 σ$ ) in reported step height as verified using 1.8 and 24 μm standard artifacts

Abstract

Supplementary Material (4)

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Equations (57)

Advances in Optics and Photonics