One of the important applications of aspheric mirror is the camera lens. Compared with spherical mirror, aspheric mirror has the advantage of improving the optics imaging quality, decreasing the optics weight, elevating its stability and reducing its cost. Although the process of aspheric mirror is becoming mature, the measurement of aspheric mirror still remains a problem.
The Hilbert Transform is very useful in the communications systems and the digital processing system. In this article, a method is proposed for interferometric phase's demodulation with a discrete Hilbert Transform. First, a Hilbert Transform demodulated phase principle is represented and the phase information of aspheric mirror is evaluated only from one interferogram. The sine and cosine components are calculated from a single interference signal, whose ratio of arc tangent is called interferometric phase demodulation. In addition, wave-front reconstruction is achieved by using Zernike polynomial fitting. Furthermore, the phase-extraction algorithm, error correction and some applications to the measurement of the surface shape are discussed so that on-line measurement of aspheric mirror is realized.