Development of surface reconstruction algorithms for optical interferometric measurement
Dongxu WU1,2, Fengzhou FANG1,3()
1. Centre of Micro/Nano Manufacturing Technology (MNMT-Dublin), University College Dublin, Dublin 4, Ireland 2. School of Control Engineering, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China 3. State Key Laboratory of Precision Measuring Technology and Instruments, Centre of Micro/Nano Manufacturing Technology (MNMT), Tianjin University, Tianjin 300072, China
Optical interferometry is a powerful tool for measuring and characterizing areal surface topography in precision manufacturing. A variety of instruments based on optical interferometry have been developed to meet the measurement needs in various applications, but the existing techniques are simply not enough to meet the ever-increasing requirements in terms of accuracy, speed, robustness, and dynamic range, especially in on-line or on-machine conditions. This paper provides an in-depth perspective of surface topography reconstruction for optical interferometric measurements. Principles, configurations, and applications of typical optical interferometers with different capabilities and limitations are presented. Theoretical background and recent advances of fringe analysis algorithms, including coherence peak sensing and phase-shifting algorithm, are summarized. The new developments in measurement accuracy and repeatability, noise resistance, self-calibration ability, and computational efficiency are discussed. This paper also presents the new challenges that optical interferometry techniques are facing in surface topography measurement. To address these challenges, advanced techniques in image stitching, on-machine measurement, intelligent sampling, parallel computing, and deep learning are explored to improve the functional performance of optical interferometry in future manufacturing metrology.
Wavelength scanning digital holographic microscope
WSI
Wavelength scanning interferometry
WT
Wavelet transform
ZOPD
Zero optical path difference
Symbols
Wavelength
Mean wavelength
Cross correlation
Phase variation
Frequency center
Angular frequency
A complete set of daughter wavelets
Interferometric phase
Wavefront phase
a
Scaling factor of CWT
b
Shift factor of CWT
A(x, y)
Amplitudes of the signals reflected from the sample
B
Amplitudes of the signals reflected from the reference mirror
f
NA factor of the interference objective
fb
Bandwidth of the mother wavelet
fc
Center frequency
Modulation function
G
Group velocity OPD
Normalized impulse response
Frequency response
Unbiased image
p/2 phased-shifted image from
Output signal from the CCD camera
Correlation term
Demodulated correlation term
I0
Constant background intensity
Input image
I(z)
Interferogram
Ii(z) (i=1, 2, …, 7)
Consecutive fringe intensities
I(Zi)
Interference function
j
Imaginary unit
k
Angular wavenumber of the light source
k0
Mean wavenumber
Spatial frequency
l
Fringe order
M(z)
Fringe visibility (also called modulation)
N
Step number
For a particular wavenumber kj, the jth component of the FT
Rq
Root mean square deviation
WFT spectrum
u
Translated coordinate
Demodulation function
Window function
Correlation coefficient of one-dimensional CWT
(x, y)
Spatial coordinates
z
Scanning position
Surface profile height
Step size
Z
OPD
Zi
Equally-spaced OPD positions
Complex conjugate
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