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. 2023 Feb 4;23(4):1762. doi: 10.3390/s23041762
LDS Laser displacement sensor
O1, O2, O3, O4 Origin points of the laser beam of the LDS1, LDS2, LDS3, LDS4
P1, P2, P3, P4 Laer projection points of the laser beam of the LDS1, LDS2, LDS3, LDS4
SLP Structured light probe
x0, y0, z0 Origin coordinates of the laser beam of the LDS
l,m,n Direction vector of the laser beam of the LDS coupling
the conversion coefficient of voltage to physical distance
d Thickness of the wafer used for calibration (from calibration)
A,B,C,D Planar equation parameters of the additionally measured plane
v Output voltage of the LDS
Q The coefficient matrix of the calibration system of equations
M Threshold for the number of deleted equations
Thresh Threshold for the distance between the solved d and measured d (i.e. d0)
d0 Thickness of the wafer used for calibration (from measurement)
d’ Iteration of d
Ratio Decrease ratio of difference between d and d0
α Maximum value limit of the angle between the laser beam and
the surface normal to be measured
β Minimum value limit of the angle between any two planes in the calibration
a,b,c,r The intermediate variables used to generate the plane parameter
λ The smallest angle between the newly generated plane normal (A, B, C)
and the existing ones
K The data volume (i.e. the number of equations)
RANSAC Random sample consensus
vector0 Surface normal of the wafer measured by LDSs when motors rotate
to an angle of 0
vector0’ Surface normal of the wafer measured by the SLP when motors rotate
to an angle of 0
θ Angle between the surface normal of the wafer measured by LDSs and
vector0 when motors rotate to random angles
θ Angle between the surface normal of the wafer measured by the SLP
vector0’ when motors rotate to random angles