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Frontiers of Mechanical Engineering

ISSN 2095-0233

ISSN 2095-0241(Online)

CN 11-5984/TH

邮发代号 80-975

2019 Impact Factor: 2.448

Frontiers of Mechanical Engineering  2021, Vol. 16 Issue (1): 1-31   https://doi.org/10.1007/s11465-020-0602-6
  本期目录
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
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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.

Key wordssurface topography    measurement    optical interferometry    coherence envelope    phase-shifting algorithm
收稿日期: 2020-04-28      出版日期: 2021-03-11
Corresponding Author(s): Fengzhou FANG   
 引用本文:   
. [J]. Frontiers of Mechanical Engineering, 2021, 16(1): 1-31.
Dongxu WU, Fengzhou FANG. Development of surface reconstruction algorithms for optical interferometric measurement. Front. Mech. Eng., 2021, 16(1): 1-31.
 链接本文:  
https://academic.hep.com.cn/fme/CN/10.1007/s11465-020-0602-6
https://academic.hep.com.cn/fme/CN/Y2021/V16/I1/1
No. Measurement principle Commercial instrument Performance Applications or accessible samples
1 Stylus profilometry Form Talysurf® PGI Optics [18] Gauge range: Up to 28 mm;
noise: <2 nm Rq;
measurement area: Up to 300 mm diameter;
form error: <100 nm
Plastic lenses;
small components;
diffractive optics;
infrared glass and crystals
2 AFM Bruker’s Dimension Icon [19] XY scan range: 90 µm × 90 µm;
Z range: 10 µm;
XY position noise: ≤0.15 nm RMS;
Z sensor noise: 35 pm RMS;
sample size: ≤210 mm diameter;
sub-nanometer resolution
Surface imaging;
surface roughness;
atomic mica lattice;
carbon nanotubes
3 Optical interferometry Zygo NewViewTM 9000 [20] Manual XY: 100 mm travel;
motorized XY: 150 mm travel;
tilt: ±4° tilt;
repeatability: 0.08 nm for all magnifications;
sub-nanometer vertical resolution
Materials characterization;
MEMS;
semiconductor;
consumer electro-optics;
optical surface manufacturing
4 Confocal scanning LEXT OLS5000 [21] Field of view: 16–5120 µm;
height resolution: 0.5 nm;
lateral resolution: 0.12 mm;
repeatability (50 ´): 0.012 µm;
measurement noise: 1 nm
Inner texture;
fuel injector nozzle;
bearing ball;
ultrasonic transducer;
micro needle
5 LVDT probe Moore Nanotech’s Workpiece Error Compensations System [22] Air bearing;
miniature;
accuracy of the probe: <25 nm;
slopes: Up to 60° per side;
desired form accuracy (after correction): 0.05–0.15 µm
On-machine part geometry measurement and form error correction
Tab.1  
Fig.1  
Fig.2  
Fig.3  
Principle Method Measurement range (z) Vertical resolution Measurement speed Repeatability Samples under test
PSI Profiling [36];
Areal [43,89,90]
OPD between two adjacent data points is less than l/2 [36]; 7.84 µm unambiguous range [45] Several nanometers [45]; 1/1000 of a fringe [91] 0.39 s for 10 interferograms at a resolution of 480 × 640 pixels [92] 2.5 nm RMS [36]; 0.5 nm RMS [90] Off-axis parabola [36]; stepped surface [43]; biological cells [45]; micro-sphere [89]; fused silica [90]
CSI Areal [49,53,56,61] Over a dynamic range of 10 µm [57]; 100 µm [53] Sub-nanometer [53] 8 s for 20 µm step height [53]; 115 s for two 10 µm step heights [93] 0.5 nm [53] Machined steel [49]; 921 nm-high grating [53]; etched silicon [56]; wavy transparent layer [57]; micro V-groove [61]
WSI Areal [72,74,76,77] 200 µm [72];±120 µm [76] Nanometric scale [77] 0.42 s for 128 captured frames [75]; 1.25 s for ±120 µm z-heights [76] Sub-nanometer [76] Stepped surface [72]; transparent film [74]; semiconductor daughterboard [75]; metallized prismatic film [77]
HI Profiling [87,94]; Areal [95] 27 µm [94] 0.31 nm [82]; 0.2 nm [94] 0.2 µm scanning speed of PZT [86] 0.5 nm [94] Semiconductor [82]; stepped surface [87]; corneal surface profile [95]
Tab.2  
Fig.4  
Fig.5  
Fig.6  
Fig.7  
Fig.8  
Fig.9  
No. Author Principle Algorithm Performance Object Remark
1 Ai and Novak [113] VSI Centroid method Consistent repeatability even when the modulation function exhibited multiple peaks 3D surface topography Free of the ambiguities in multi-peak modulation functions, suitable for rapid online applications
2 Dong and Chen [144] Laser interferometer (Fizeau type) FFT Phase retrieval from a single-shot spatial carrier fringe pattern Flat mirror Highly efficient and timesaving for dynamic or real-time measurement
3 Vo et al. [93] WLSI FFT and PSA Nanometric resolution and good repeatability Step height; spherical surface The batwing effects and positioning error in the maximum modulation were reduced
4 Ma et al. [145] WLSI WFT Good noise immunity and a more accurate ZOPD position CGH diffractive element A smoothened and continuous profile of sharp step surface was obtained
5 Trusiak et al. [160] Mach–Zehnder interferometry HHT Single-frame fast acquisition and processing time around 5–10 s Static and flowing microbeads; red blood cells Robust, fast, and accurate single-shot quantitative phase imaging for dynamic objects
6 Serizawa et al. [149] SD-OCT CWT Measurement repeatability of 65.1 nm for 2D surface, RMS measurement error of 0.17 µm for 3D surface profile Step height High measurement accuracy without resampling the wavenumber or linear interpolation
7 de Groot and Deck [62] WLSI FDA Measurement repeatability of 0.5 nm RMS, scanning rate of 2 µm/s Sensing head; moth’s eye Without relying on fringe contrast, all data processing occurred in the spatial-frequency domain
8 Kim et al. [179] Wavelength-tuning Fizeau interferometer 13-sample PSA RMS phase error under 3 nm, even for a phase-shift miscalibration of ±30% Transparent fused silica plate Compensation for miscalibration and first-order nonlinearity of phase shift, coupling errors, and bias modulation of intensity
9 Cao et al. [190] Mach–Zehnder-type PSI ASSF RMS phase error less than 0.05 rad Macrophage cell; light guide panel Stable self-calibration phase retrieval with few interferograms containing fewer than one fringe
Tab.3  
Fig.10  
Fig.11  
Fig.12  
Fig.13  
Fig.14  
Fig.15  
Fig.16  
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
Symbols
λ Wavelength
λ ¯ Mean wavelength
γ(x, ?y,?z) Cross correlation
ϕ [(z z0(x, ?y)] Phase variation
ξ Frequency center
ω Angular frequency
ψa,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
fb Bandwidth of the mother wavelet
fc Center frequency
f( z) Modulation function
G Group velocity OPD
hnorm(n) Normalized impulse response
H( e jω) Frequency response
ixy(n) Unbiased image
ixy(n) p/2 phased-shifted image from i xy(n)
I( x,?y, ?z) Output signal from the CCD camera
IAB Correlation term
IAB d Demodulated correlation term
I0 Constant background intensity
Ixy(n) 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
kz Spatial frequency
l Fringe order
M(z) Fringe visibility (also called modulation)
N Step number
P( kj) For a particular wavenumber kj, the jth component of the FT
Rq Root mean square deviation
Sf (u,?ξ ) WFT spectrum
u Translated coordinate
Vxy(n) Demodulation function
w(x) Window function
WI(a,b) Correlation coefficient of one-dimensional CWT
(x, y) Spatial coordinates
z Scanning position
z0 (x,?y ) Surface profile height
Δz Step size
Z OPD
Zi Equally-spaced OPD positions
Complex conjugate
  
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