A free-form surface sub-aperture stitching interferometry (FSSI) is proposed for aspheric and free-form surfaces testing. Different from normal annular and circular sub-aperture stitching method, non-null interferometric configuration and irregular sub-apertures are employed to make the best use of the resolved fringes. Meanwhile, a multi-aperture simultaneous reverse optimizing reconstruction (MSROR) process is proposed for full aperture figure error reconstruction. With the multi-configuration model, full aperture figure error would be extracted in form of Zernike polynomials from sub-apertures wavefront data by the MSROR method. This method concurrently accomplishes sub-aperture retrace error and misalignment correction, requiring neither complex mathematical algorithms, nor sub-aperture overlaps. The experiments show that, the aspheric annular sub-aperture stitching accuracy with the proposed FSSI is more than 1/50λ (rms) comparing with the result of ZYGO Verifier Asphere interferometer. The bi-conic surface sector sub-aperture stitching accuracy is about 1/ 50λ (rms) comparing with result of Taylor Hobson contourgraph in longitudinal section contour.
Aspheric non-null test achieves more flexible measurements than the null test. However, the precision calibration for retrace error has always been difficult. A reverse optimization reconstruction (ROR) method is proposed for the retrace error calibration as well as the aspheric figure error extraction based on system modeling. An optimization function is set up with system model, in which the wavefront data from experiment is inserted as the optimization objective while the figure error under test in the model as the optimization variable. The optimization is executed by the reverse ray tracing in the system model until the test wavefront in the model is consistent with the one in experiment. At this point, the surface figure error in the model is considered to be consistent with the one in experiment. With the Zernike fitting, the aspheric surface figure error is then reconstructed in the form of Zernike polynomials. Numerical simulations verifying the high accuracy of the ROR method are presented with error considerations. A set of experiments are carried out to demonstrate the validity and repeatability of ROR method. Compared with the results of Zygo interferometer (null test), the measurement error by the ROR method achieves better than 1/10λ.
A model-based phase-shifting interferometer (MPI) is developed, in which a novel calculation technique is proposed instead of the traditional complicated system structure, to achieve versatile, high precision and quantitative surface tests. In the MPI, the partial null lens (PNL) is employed to implement the non-null test. With some alternative PNLs, similar as the transmission spheres in ZYGO interferometers, the MPI provides a flexible test for general spherical and aspherical surfaces. Based on modern computer modeling technique, a reverse iterative optimizing construction (ROR) method is employed for the retrace error correction of non-null test, as well as figure error reconstruction. A self-compiled ray-tracing program is set up for the accurate system modeling and reverse ray tracing. The surface figure error then can be easily extracted from the wavefront data in forms of Zernike polynomials by the ROR method. Experiments of the spherical and aspherical tests are presented to validate the flexibility and accuracy. The test results are compared with those of Zygo interferometer (null tests), which demonstrates the high accuracy of the MPI. With such accuracy and flexibility, the MPI would possess large potential in modern optical shop testing.
A non-null annular subaperture stitching interferometry (NASSI), combining the subaperture stitching idea and non-null test method, is proposed for steep aspheric testing. Compared with standard annular subaperture stitching interferometry (ASSI), a partial null lens (PNL) is employed as an alternative to the transmission sphere, to generate different aspherical wavefronts as the references. The coverage subaperture number would thus be reduced greatly for the better performance of aspherical wavefronts in matching the local slope of aspheric surfaces. Instead of various mathematical stitching algorithms, a simultaneous reverse optimizing reconstruction (SROR) method based on system modeling and ray tracing is proposed for full aperture figure error reconstruction. All the subaperture measurements are simulated simultaneously with a multi-configuration model in a ray-tracing program, including the interferometric system modeling and subaperture misalignments modeling. With the multi-configuration model, full aperture figure error would be extracted in form of Zernike polynomials from subapertures wavefront data by the SROR method. This method concurrently accomplishes subaperture retrace error and misalignment correction, requiring neither complex mathematical algorithms nor subaperture overlaps. A numerical simulation exhibits the comparison of the performance of the NASSI and standard ASSI, which demonstrates the high accuracy of the NASSI in testing steep aspheric. Experimental results of NASSI are shown to be in good agreement with that of Zygo® Verifire<sup>TM</sup> Asphere interferometer.
Careful alignment of optical elements is essential in interferometric tests. Misalignments of the key element largely influence the testing accuracy. For aspheric figure error testing, non-null tests achieve more flexible and economical measurements than the null ones. However, retrace error is induced due to the violation of null configuration, making the alignment difficult. In aspheric partial compensation testing, the partial compensating lens (PCL) as the key component needs careful adjustment. The aplanat alignment method is effective for the PCL adjusting with high accuracy employing a removable lens, which combined with the PCL as an aplanat. But its structure is complex. After describing this method, a PCL computer-aided alignment (CAA) method is posed basing on system modeling in a ray tracing software. The structure is simplified with computer calculations. The PCL tilt and decentration are easily aligned with a plane and a standard spherical mirror respectively, according to linear relations with wavefront coma aberrations on the detector. Alignment of the PCL was implemented with these two methods in an aspheric partial compensation testing experimental apparatus. Adjustment and aspheric testing results were presented in order. The CAA method is a generalized approach with simpler structure, while the aplanat alignment method is easy to carry out and suitable for industrial application.