Rigorous accuracy analysis of the fiber point diffraction interferometer

The fiber phase shifting point-diffraction interferometer (FPS/PDI) has recently been designed to measure spherical surface with high precision. The wavefront shape emerging from the fiber, which acts as the referenced wave in FPS/PDI, must be controlled precisely in design. The rigorous theory model of fiber point diffraction is studied for instrument realization. To execute such high accurate (10-4λ) simulation, vector diffraction method must be adopted because conventional scalar diffraction theory is unsuitable when the fiber core size is comparable to wavelength. Based on the model, the influence of fiber core diameter, end-face figure and so on is studied. Some important conclusions are inferred. Firstly, the residual aberration is reduced with decreasing of fiber core size, so that the available numerical aperture decreases. Secondly, when the end face of the optical fiber is ellipse, the effect of the ellipticity should be considered. Thirdly, the oblique fiber, like ordinary fibers cut with zero face angle, generates a high quality spherical wave, but the propagation direction changes with the oblique angle. Finally, the residual aberration of diffraction wavefront becomes larger when the surface error of the end-face figure increases. The result shows that the single mode fiber used in experiment is available for instrument design and its influence over systematic error is negligible within certain numerical aperture.