Three-degree-of-freedom simultaneous measurement based on Fourier transform dispersive interferometry using an optical frequency comb.

High-precision and multi-degree-of-freedom geometric measurement holds significant importance in feature detection for large-scale equipment manufacturing. The measurement process demands the qualities of absoluteness, simultaneity, and traceability, especially in the face of attitude compensation, target monitoring, and the construction of length references. The measurement range of commonly used high-precision optical interferometry is constrained by the wavelength of light and the size of diffraction grating, thus limiting its applicability to long distances. The optical frequency comb (OFC), with an ultra-short pulse characteristic of a periodic sequence, can be traced back to a length reference so that specific points can be determined for long-distance measurements. When integrating OFC with optical interferometry, it enables the achievement of absolute high precision distance measurements. It is essential to address the design issue which demands simultaneous multi-group distance measurements to achieve multiple-degree-of-freedom expansion. In this study, we presented a technique for three-degree-of-freedom (DOF) simultaneous measurements based on dispersive interferometry using an optical frequency comb by improving the optical structure. To solve the nonlinear problem of frequency sampling in dispersive spectrum broadening, two non-even Fourier transform algorithms are improved as a method of phase calculation. By incorporating phase ω information into the non-uniform fast Fourier transform (NUFFT) method, we achieved effective calculation of non-uniform discrete Fourier transform (NUDFT). At the same time, it can reduce the mitigate mutual interference during the extraction of multiple sets of interference peaks. The experimental findings indicate that when compared with an autocollimator, there is a consistent agreement within 3 arcsec for angles up to 1000 arcsec. This absolute measurement scheme is almost not affected by time and other factors, which provides potential for angle information monitoring.