Tilt error analysis for laser triangulation sensor based on ZEMAX

A simulation model for laser triangulation sensor is given based on the non-sequential mode of ZEMAX, and the Lambertian scattering model is adopted to simulate the light intensity received by the detector while the object is tilting. The simulation model includes the power , divergence angle and energy distribution of the laser, as well as the scattering characteristics and construction features of the detector. The simulation results indicate that the tilt error increases when the tilt angle becomes larger under the same displacement, which shows a linear relationship. The tilt error also increases as the displacement increases under the same tilt angle. The maximum tilt error around the X-axis is -22.58μm, while the maximum tilt error around the Y-axis is -1.09 μm. When tilting around the X-axis, the tilt errors caused by positive rotation and negative rotation are the same, but opposite in sign. When tilting around Y-axis, both the value and the sign of the positive and negative tilt errors are the same. The minimum tilt error appears near the reference position. The farther away from the reference position, the greater of tilt error. According to the simulation results, reasons for tilt error are analyzed. Because of the existing of the tilt angle, the scattered field of the laser beam changes, which give rise to the asymmetry of the energy distribution received by the detector. The greater the tilt angle, the larger the spot diameter, which leads to the offset of the centroid and causes the tilt error. Three correction methods for tilt error are proposed. The first method is to install the sensors with the tilt axis paralleling to the receiving plane. The second one is to carry out the measurement near the reference position. The third is to compensate the tilt error with both simulation data and experimental data. The simulation model and one of the correction methods were verified by experiments. A high precision laser triangulation sensor based on our simulation results was developed to verify the simulation model. The object was placed on a rotary platform, and the rotary platform was fixed on a linear guideway in order to obtain an axial displacement. The measured data for different displacements and tilt angles were obtained by our experimental device. A grating scale with the resolution of 0.1 μm was adopted to serve as the standard instrument. The tilt errors were the difference between the measured data and the reference data. The displacement change from -50 mm to 50 mm with a step of 10 mm. The tilt angle change from -30 degrees to 30 degrees with a step of 10 degrees. The centroid of the laser spots with different displacements and tilt angles were calculated to obtain the tilt error by our simulation model. The experimental results show that the characteristics and tendencies of the tilt error were consistent with the simulation results. After error compensation, the tilt error dropped about 57.6%. The simulation model can also analyze the measuring errors caused by many other factors, such as the power variation of the laser source, the color and the roughness of the surface. Our simulation model is of certain significance for analyzing the measuring error of laser triangulation sensor.