Mathematical model of contacting aspheric surface profile measurement

Gu-feng Qiu

doi:10.1117/12.828713

20 May 2009 Mathematical model of contacting aspheric surface profile measurement

Gu-feng Qiu

Proceedings Volume 7283, 4th International Symposium on Advanced Optical Manufacturing and Testing Technologies: Optical Test and Measurement Technology and Equipment; 72832T (2009) https://doi.org/10.1117/12.828713
Event: AOMATT 2008 - 4th International Symposium on Advanced Optical Manufacturing, 2008, Chengdu, Chengdu, China

Abstract

This paper proposes a new mathematical model to simplify the measurement process in high precision contacting aspheric surface profile measurement.This model will unwind the requirement to position adjustment of aspheric mirror while providing high precision measurement results. After a throughout analysis of the possible causes for the measurement mirror of contacting profile measurement instruments, we suggest a new mathematical model based on Least square method to correct the errors caused by the inclination in X, Y direction, eccentricity in X, Y, Z direction that exists in the positioning of aspheric mirror, inaccuracy of curvature radius, and the random micro-excursion between the circumrotating center and the detecting header of profile measurement instrument. By mathematical simulation, it is proved that this model could achieve high precision in correcting those errors stated above. For eccentricity less than 1 cm and inclination less than 0.1 degree, this model could completely correct these errors. It is also very effective in correcting the errors of curvature radius. The results of practical engineering implementation indicate that this model is reliable and effective.

Citation Download Citation

Gu-feng Qiu "Mathematical model of contacting aspheric surface profile measurement", Proc. SPIE 7283, 4th International Symposium on Advanced Optical Manufacturing and Testing Technologies: Optical Test and Measurement Technology and Equipment, 72832T (20 May 2009); https://doi.org/10.1117/12.828713

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