Abstract
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.
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Abbreviations
- A:
-
Analyzer
- AFM:
-
Atomic force microscope
- AIA:
-
Advanced iterative algorithm
- AOM:
-
Acousto-optical modulator
- AOTF:
-
Acousto-optic tunable filter
- ASSF:
-
Advanced spatial spectrum fitting
- BS:
-
Beam splitter
- CCD:
-
Charge coupled device
- CGH:
-
Computer generated hologram
- CLSM:
-
Confocal laser scanning microscopy
- CNC:
-
Computer numerical control
- CPS:
-
Coherence peak sensing
- CSI:
-
Coherence scanning interferometry
- CWT:
-
Continuous wavelet transform
- DAQ:
-
Data acquisition card
- DHI:
-
Digital holographic interferometry
- DNR:
-
Dynamic noise reduction
- DRI:
-
Dispersed reference interferometry
- DTM:
-
Diamond turning machine
- FDA:
-
Frequency domain analysis
- FFT:
-
Fast Fourier transform
- FOV:
-
Field of view
- FT:
-
Fourier transform
- GP:
-
Gaussian process
- GPU:
-
Graphics processing unit
- HHT:
-
Hilbert-Huang transform
- HI:
-
Heterodyne interferometry
- HT:
-
Hilbert transform
- IMAQ:
-
Image acquisition board
- IR:
-
SLED Near-infrared superluminescent light-emitting diode
- L1:
-
Collimating lens
- L2:
-
L3 Microscope objectives
- LED:
-
Light emitting diode
- LVDT:
-
Linear variable differential transformer
- MEMS:
-
Micro-electromechanical systems
- MO:
-
Microscope objectives
- MSSM:
-
Mid-band spatial spectrum matching
- NA:
-
Numerical aperture
- OPD:
-
Optical path difference
- P:
-
Polarizer
- PC:
-
Personal computer
- PCA:
-
Principal component analysis
- PD:
-
Photodiode
- PSA:
-
Phase-shifting algorithm
- PSI:
-
Phase-shifting interferometry
- PV:
-
Peak-to-valley
- PZT:
-
Piezoelectric transducer
- QW1:
-
QW2 Quarter wave plates
- REF:
-
Reference mirror
- RMS:
-
Root mean square
- SD-OCT:
-
Spectral domain optical coherence tomography
- S2H2PM:
-
Single-shot Hilbert-Huang phase microscopy
- SNR:
-
Signal-to-noise ratio
- SWLI:
-
Scanning white-light interferometry
- TKEO:
-
Teager-Kaiser energy operator
- USFP:
-
Ultra-sparse fringe pattern
- VSI:
-
Vertical scanning interferometry
- WFF:
-
Windowed Fourier filtering
- WFR:
-
Windowed Fourier ridges
- WFT:
-
Windowed Fourier transform
- WLI:
-
White light interferometry
- WLPSI:
-
White-light phase-shifting interferometry
- WLSI:
-
White-light scanning interferometry
- WS-DHM:
-
Wavelength scanning digital holographic microscope
- WSI:
-
Wavelength scanning interferometry
- WT:
-
Wavelet transform
- ZOPD:
-
Zero optical path difference
- λ :
-
Wavelength
- \(\overline \lambda \) :
-
Mean wavelength
- γ(x,y :
-
z) Cross correlation
- ϕ[(z−z 0(x,y)]:
-
Phase variation
- ξ :
-
Frequency center
- ω :
-
Angular frequency
- ψ a,b(z):
-
A complete set of daughter wavelets
- φ :
-
Interferometric phase
- φ(z):
-
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
- f b :
-
Bandwidth of the mother wavelet
- f c :
-
Center frequency
- f(z):
-
Modulation function
- G :
-
Group velocity OPD
- h norm(n):
-
Normalized impulse response
- H(e jco):
-
Frequency response
- i xy(n):
-
Unbiased image
- i xy*(n):
-
π/2 phased-shifted image from ixy(n)
- I(x :
-
y, z) Output signal from the CCD camera
- I ab :
-
Correlation term
- I{skAB/d}:
-
Demodulated correlation term
- I 0 :
-
Constant background intensity
- I xy (n) :
-
Input image
- I(z):
-
Interferogram
- I i(z)(i :
-
=1,2, ⌦, 7) Consecutive fringe intensities
- I(Z i):
-
Interference function
- j :
-
Imaginary unit
- k :
-
Angular wavenumber of the light source
- k 0 :
-
Mean wavenumber
- k z :
-
Spatial frequency
- l :
-
Fringe order
- M(z):
-
Fringe visibility (also called modulation)
- N :
-
Step number
- P(k j):
-
For a particular wavenumber kj, the jth component of the FT
- Rq :
-
Root mean square deviation
- Sf(u :
-
ξ) WFT spectrum
- u :
-
Translated coordinate
- V xy(n):
-
Demodulation function
- w(x):
-
Window function
- W i(a,b):
-
Correlation coefficient of one-dimensional CWT
- (x :
-
y) Spatial coordinates
- z :
-
Scanning position
- z 0(x :
-
y) Surface profile height
- Δz :
-
Step size
- Z :
-
OPD
- Z i :
-
Equally-spaced OPD positions
- *:
-
Complex conjugate
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Acknowledgements
This work received funding from the Enterprise Ireland and from the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie grant agreement (Grant No. 713654), the National Natural Science Foundation of China (Grant No. 51705070), and the Science Foundation Ireland (SFI) (Grant No. 15/RP/B3208). The authors appreciate the fruitful discussions and suggestions from Szymon Baron of DePuy Synthes. The authors would also like to thank Chengwei Kang of University College Dublin for his comments on the paper.
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Wu, D., Fang, F. Development of surface reconstruction algorithms for optical interferometric measurement. Front. Mech. Eng. 16, 1–31 (2021). https://doi.org/10.1007/s11465-020-0602-6
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DOI: https://doi.org/10.1007/s11465-020-0602-6