The point diffraction interferometer (PDI), which generates the nearly ideal spherical wavefront with the pinhole method, is realized the absolute interferometric measurement without the use of reference surface. But it is hard to detect the diameter of the pinhole and hard for use of phase shifting interferometers in PDI. However the advanced fiber point diffraction interferometer (FPDI) not only replaces the pinhole with the fiber, but also makes it possible to implement phase shifting and maintain advantage of traditional PDI. In this paper, the different methods of measuring surface are proposed according to different experimental conditions and different targets (such as concave spherical surface, convex spherical surface, flat surface) with the fiber point diffraction interferometer built in the laboratory. Base on these experiments, there are several key factors in the measurement process such as measurement configuration, laser source, polarization beamsplitter, optical fiber. And these factors, affecting the experiment accuracy, were analyzed seriously.