Free-vibration modes of an annular mirror for the optical aberration representation

Abstract. The free-vibration modes of an annular mirror (FVMAM), reflecting the natural properties of the physical phenomenon of resonance, are proposed to represent the optical aberrations. A realistic dynamics model is presented to investigate the physical properties of an annular mirror on the natural frequencies of FVMAM. An explicit solution is derived from the analytic method based on the thin plate theory. Taking the primary mirror of the 2.5-m-wide field survey telescope as an example, the FVMAM is numerically calculated and studied. The results have shown that the mode shapes resemble the optical aberrations, and there is almost a one-to-one match between each free-vibration mode and each optical aberration. In addition, the results of the analytic method are validated by the finite-element method. The conclusions suggest that the results obtained by the two methods are in good agreement with each other. Moreover, we present a comparative study for FVMAM and annular Zernike polynomials which are very well known to be widely used to represent optical aberrations. The results show that the free-vibration modes can not only be used to replace annular Zernike polynomials but also can be more effective.