Measurement Of Aspheric Surfaces By Non-null Annular Subaperture Stitching Interferometry

Although the design, fabrication and assembly techniques of aspheres have made considerable developments, general and accurate measurement of aspheres is difficult and continues to be a challenge. I combined the two concepts of non-null testing and subaperture stitching and developed non-null annular subaperture stitching interferometry (non-null ASSI), which has much larger dynamic range and can be used to measure steep aspheres or aspheric wavefronts.The concept and principle of the non-null ASSI are proposed. Based on the Twyman-Green interferometer, aspheric wavefront emerging from the diverging lens (PCS) partially compensates for aberrations of normals of the asphere under test. Annular subaperture with different radii can be measured by translating the asphere along the optical axis. Simulation methods of the system based on optical design software or home-made raytracing codes are proposed. The boundaries and overlapping areas of subapertures of the asphere are determined by the slope of the wavefront on the detector. For multi-frame phase-shifted interferograms acquired, the well-known four step formula is used to demodulated the phase while for single-frame interferograms with closed fringes, the proposed path-independent regularized phase-tracking (PIRPT) or polynomial-based phase-fitting (PPF) techniques is employed. The extracted phase is decomposed by Zernike polynomials for further analysis.The calibration of retrace error of the non-null ASSI is extensively investigated. A transfer function model is proposed and the calibration procedure is understood as to find its inverse solution. Two practical algorithms are proposed, i.e., synthetically reverse optimization reconstruction (ROR) and theoretical reference wavefront (TRW). The former attempts to find the solution by nonlinear optimization while the latter by wavefronts subtraction. Residual wavefront errors after calibration by both methods are typically smaller than λ/1000(peak to valley, PV) and λ/20, respectively. The subaperture stitching process is introduced to reconstruct full-aperture figure shape of the asphere from subaperture data with retrace error removal. Numerical experiments show its accuracy is better than λ/1000.The errors of the non-null ASSI are systematically analyzed. Besides the retrace error and software errors mentioned above, four hardware errors are analyzed with emphasis, i.e.,1)model errors and2)alignment errors of the PCS,3)position error and4) alignment errors of the asphere. For1),(relative) errors of refractive indices, thicknesses and curvatures are required to be no greater than e-5,5um and0.005%, respectively. For2), adjustment methods based on auxiliary parallel plate and sphere are proposed, which can respectively minimize tilt and decenter errors of the PCS within10" and6μm. For3), two methods based on aplanatic lens or defocus of the wavefront are proposed, which can both control the error within10μm. For4), adjustment method based on tilt and coma of the wavefront is proposed and can reduce tilt and decenter errors to2" and5um.Finally, the correctness and measurement precision of the non-null ASSI are experimentally demonstrated. Three paraboloids (two with departure from the vertex sphere56.5um and one9.0um) were measured by the non-null ASSI with and without subaperture stitching. The results agree well with those by the stigmatic null test and Zygo Verifire interferometer. The PV and root mean square (RMS) values of the deviations of all the results are smaller than λ/10and λ/50, respectively. The results show the non-null ASSI has good measurement precision, strong measurement ability and great dynamic range.In summary, the paper investigated the non-null ASSI from both theory and experiment. Since aspheres are increasingly being used nowadays, the non-null ASSI has potential huge economic benefits and will greatly promote the progress of aspheric testing.