When the white light interferometry system is used to measure the multi-point roughness of smooth sample surface, because there is a little tilt between the sample surface and the measuring lens, one position measurement is completed and moved to the next, the surface of the sample can easily leave the interference interval. In order to solve this problem, a method of Z-axis compensation by the width and slope of white light interference fringes is proposed. First, the mathematical model of interference fringes and inclination angle of sample surface is established; second, the relationship between interference fringes width and inclination angle of sample surface is analyzed; Finally, the compensating amount of Z-axis is analyzed when moving horizontally for a distance. The experimental results show that when the slope of interference fringes is -0.73 and the width of interference fringes is 28.40 μm, the inclination angle of the sample surface relative to the measuring plane is 0.56°. When the system moving 1 mm for the X-axis, the amount of compensation required for the Z-axis was 5.73 μm; when moving 1 mm for Y-axis, the amount of compensation required for the Z-axis was 7.89 μm. The experimental results show that the relationship between horizontal moving distance and Z-axis compensation can be determined by calculating the width slope of interference fringes. It simplifies the measurement process of the system and avoids re-focusing when moving to the next point.
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