In modern optical processing and inspection, laser interferometers are widely employed to detect the surface shape of optical components. In the process of surface shape detection, due to the temporal coherence of the laser, the optical elements in the interferometer such as bubbles, scratches, defects, and surface dust will produce coherent noises. As a result, these noises will change the phase distribution of the interference signal, affect the results of the interferometry, and need to be suppressed. The ring light source can be produced by axicon, and it can reduce the influence of interferometer coherent noise. Additionally, with the development of optical technology, there is a growing demand for the ability of interferometers to detect surface errors at higher spatial frequencies. The instrument transfer function (ITF) of an interferometer can be utilized to evaluate the ability to resolve surface errors of different spatial frequencies and is an important performance index of an interferometer system. Meanwhile, this function is usually measured by a standard step plate. In our study, two sets of ring light source Fizeau interference systems with diameters of ?100 mm and ?810 mm are proposed.

The axicon is employed to generate a solid ring light source, and the design idea that ?100 mm and ?810 mm systems leverage common lens groups is adopted, which can lower the difficulty in the installation of ?810 mm systems. It is found that the coherent noise is suppressed well, but the ITF of the system measured by the step plate is poor. Additionally, part of the light reflected by the step plate can not enter the imaging lens group, and more light can pass through after replacing the imaging lens group with a larger aperture. Since the analysis of the imaging process of the interference system to the step plate shows that the interference optical path and imaging optical path of the system can be adopted for simulation, the scheme of optimizing the interference path and imaging path simultaneously is chosen to design the interference system with the ability to detect the middle-frequency surface shape errors.

We design the 100 mm and ?810 mm systems with a completely consistent ring light source, beam splitter prism, beam expanding lens group, and imaging lens group, which can greatly reduce the installation difficulty. During optimization, the angle between the edge rays and the normal lines of each lens surface is limited to more than 3° for reducing the stray light that is not ideally reflected by the surface of each lens of the beam expanding collimator group (Fig. 4). The peak valley (PV) and root mean square (RMS) values of wavefront difference of each system are better than 0.01λ and 0.002λ respectively (Fig. 5), with the tolerances of the system analyzed. A ?100 mm experimental system is built, and the coherent noise of the system in the ring light source mode is significantly suppressed compared with the point light source mode (Fig. 6). The ITF curve of the ?100 mm experimental system is poor (Fig. 7). After replacing the small-caliber imaging lens group with a large-caliber lens with worse wavefront quality, the ITF curve of the ?100 mm experimental system has been significantly improved (Fig. 8), and then the reason of this phenomenon is analyzed. In the design of the ?100 mm and ?810 mm systems with the detection ability of intermediate frequency surface shape error, the interference path and imaging path are optimized at the same time. The PV of each interference path is better than 0.01λ, and the RMS of the wavefront difference is better than 0.002λ. The modulation transfer function values of each imaging path at corresponding spatial frequencies are all higher than 0.67 (Figs. 10 and 11), and the tolerances of the system are analyzed.

Two sets of ring light source Fizeau interference systems with diameters of ?100 mm and ?810 mm are designed. The axicon is employed to produce a real ring light source. The two systems adopt the design idea of re-using parts of the lens group, which can reduce the difficulty in ?810 mm system installation. In optimization, the idea of a“small aberration complement”is adopted to reduce the tolerance sensitivity of the lens surface. The ?100 mm experimental system has a sound coherent noise suppression effect, but the ITF of the system decreases seriously in the middle-frequency band. The experiment indicates that some light reflected by the step plate has a large deviation from the normal light path and cannot enter the imaging lens group. The reason for this phenomenon is that diffraction occurs at the step of the step plate, and this part of the light will form a certain aperture angle and enter the ?100 mm experimental system. In the system, the first surface of the imaging lens group becomes the aperture stop due to its small aperture. Most of the diffracted light of the step plate is blocked to result in a significant decrease in the ITF of the system. Therefore, based on the original design, the interference path and imaging path of the interference system can be optimized simultaneously by setting a reasonable stop position and setting a paraxial plane on the camera sensor and the measured surface of the interference path. Finally, the ring light source Fizeau interference system able to detect the surface shape error of the intermediate frequency is designed.