Measurement of the flatness or the shapes of mirrors by one-shot projection of structured light dot pattern

Abstract

No existing methods could measure the 3D shapes of mirrors accurately enough for inverse engineering. Consequently, manufacturing highly accurate mirrors remains challenging in space optics. For mirror flatness measurement, the best accuracy state-of-the-art methods have achieved so far is nanometer. In this paper, we propose an approach for mirror measurement with a single shot projection of structured light dot pattern. The proposed approach is not only capable of measuring the mirror flatness with femtometre height resolution (10−13 mm), but also capable of measuring the 3D shapes of mirrors more accurately than many state of the art methods. This approach first computes the projected dot pattern in the world coordinate system and gets the measured points. Then, it computes the dot pattern in the ideal coordinate system and gets the true points. After the system is re-calibrated with the true points, the flatness or the 3D shapes of the mirrors could be measured robustly. Experimental results showed that the proposed approach is significantly more accurate than state-of-the-art methods in measuring the flat mirror or mirror flatness with femtometre height resolution under laboratory conditions and it also the potential to achieve similar accuracy in measuring the 3D shapes of mirrors. Thus, it might benefit the manufacturing industry of space optics significantly in the future.. Keywords: Mirror flatness, Measurement, Image processing, True point, Measured point