Fringe analysis with Hilbert transform and its application to the measurement of aspheric mirror

Jie Lv; Ming Wang; Hai Huan; Bin Zhang

doi:10.1117/12.783175

27 November 2007 Fringe analysis with Hilbert transform and its application to the measurement of aspheric mirror

Jie Lv, Ming Wang, Hai Huan, Bin Zhang

Proceedings Volume 6723, 3rd International Symposium on Advanced Optical Manufacturing and Testing Technologies: Optical Test and Measurement Technology and Equipment; 67231D (2007) https://doi.org/10.1117/12.783175
Event: 3rd International Symposium on Advanced Optical Manufacturing and Testing Technologies: Large Mirrors and Telescopes, 2007, Chengdu, China

Abstract

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.

Citation Download Citation

Jie Lv, Ming Wang, Hai Huan, and Bin Zhang "Fringe analysis with Hilbert transform and its application to the measurement of aspheric mirror", Proc. SPIE 6723, 3rd International Symposium on Advanced Optical Manufacturing and Testing Technologies: Optical Test and Measurement Technology and Equipment, 67231D (27 November 2007); https://doi.org/10.1117/12.783175

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available