6. Conclusion

In this chapter, the application of PDI system in the wavefront and surface testing is introduced. Various PDI setups, including the fiber PDI and pinhole PDI, have developed for highaccuracy optical testing, and the measurement accuracy up to subnanometer was reported. Different from the pinhole PDI, the adjustable fringe contrast is easily realized with fiber PDI, and it can be applied to test the surface with various reflectivities. To realize the adjustable fringe contrast with pinhole method, the polarizing elements with special structure is needed to transform the polarization states and adjust the relative intensities of the interfering testing and reference beams. High measurable NA can be achieved with the pinhole; however, the light transmission is quite low; high light transmittance can be obtained with single-mode fiber; however, the measurable NA is limited by the NA of the fiber. To obtain both the high diffraction light power and high-NA spherical wavefront, a SMA fiber with cone-shaped exit end has been proposed, and it is considered as a feasible way to extend the measurement range of the system. Based on the SMA fiber, a PDI system for the absolute 3D coordinate measurement was proposed. The system utilizes the SMA fiber to get spherical wave with both high NA and high light intensity, and large measurable range is achieved.

The numerical study of point-diffraction wavefront both with pinhole and SMA fiber is performed, which is based on the FDTD method. The aperture angle, light transmittance, and wavefront error are analyzed. According to simulation results, the ideal spherical wavefront with the accuracy better than subnanometer can be obtained both with pinhole and SMA fiber, and the increase in NA range and diffraction aperture size could lead to the growth of diffracted wavefront error. It can be seen from the comparison of pinhole diffraction and SMA fiber diffraction, the light transmittance in both the methods grows with the increase in aperture size, and the similar aperture angles can be obtained with the same diffraction aperture size. However, the light transmittance in SMA fiber diffraction is far larger than that in pinhole diffraction. Thus, the SMA fiber provides a feasible way to obtain the high light intensity required in the optical testing, enabling the extension of measurement range with PDI system.

The experimental measurement of SMA fiber point-diffraction wavefront is carried out to evaluate its accuracy in practical application, which is based on shearing interferometry. To realize the high-precision calibration of the systematic error introduced by the lateral displacement between SMA fibers, a double-step calibration method based on three-dimensional coordinate reconstruction and symmetric lateral displacement compensation is used to remove the geometric aberration from the shearing wavefront. Besides, the differential Zernike polynomials fitting method is used to reconstruct the point-diffraction wavefront. The spherical wavefront with the accuracy reaching the order of 10<sup>−</sup><sup>4</sup> λ is obtained in the experiment. The calibration method can be performed without any preknowledge about the measurement system configuration. It realizes the high-accuracy measurement of point-diffraction wavefront and also provides a feasible method for geometric aberration calibration in interferometric system.
