Fig. 1. The measurement system calibration and the acquisition of seed point coordinate. (a)Vision ray model; (b) principle for determining seed point coordinate

Fig. 2. Iterative surface reconstruction principle

Fig. 3. The transformation of point cloud coordinate. (a) The yoz plane in the parent coordinate system; (b) the three-dimensional representation in the parent coordinate system

Fig. 4. Coordinate transformation of measurement data point cloud. (a) The three-dimensional representation in the element coordinate system; (b) the y'Sz' plane in the element coordinate system

Fig. 5. The position of measured data and theoretical data before and after transformation. (a) Position before transformation; (b) position after transformation

Fig. 6. Surface error. (a) True value of surface error; (b) surface error reconstruction obtained by point cloud matching; (c) difference between Fig. 6(b) and Fig. 6(a)

Fig. 7. Comparison of Zernike coefficients between true values and reconstruction results

Fig. 8. Experimental setup

Fig. 9. The sag of off-axis aspheric. (a) The measured sag in component coordinate system; (b) the measured sag in parent coordinate system

Fig. 10. Comparison of experimental results. (a) Experimental result (removing the piston and the tilt terms); (b) interferometer result (removing the piston and the tilt terms); (c) experimental result (removing the piston, tilt, defocus, astigmatism and coma terms); (d) interferometer result (removing the piston, tilt, defocus, astigmatism and coma terms)