Freeform surfaces have drawn intensive attention in optical imaging and illumination field because of its great flexibility in optical design. However, the fabrication and testing of freeform surfaces remain a great challenge due to the arbitrary shape. Interferometry is among the high-accuracy testing method of optical surfaces. How to generate a non-rotationally symmetric wavefront similar with the surface under test and retrieve the phase from dense interferogram are hotspot issues. In this paper, we introduce two key technologies in non-null interferometry to solve the above-mentioned problems. The first is the design method of an off-axis catadioptric non-null compensator including a deformable mirror. The second is phase retrieval of single dense interferogram with digital moiré phase shifting interferogram and wavelet analysis. Simulations demonstrate the feasibility of the proposed method.
Deformable mirror (DM) is a flexible wavefront modulator with a changeable surface. It is traditionally adopted in adaptive optical system for aberration correction. Recently applications in zoom imaging system and interferometer for freeform measurement have been proposed because the improvement in fabrication technique makes larger stroke amount and faster response possible. The order and accuracy of aberration correction are typical wavefront correction characteristics of DMs. Due to the non-linearity, hysteresis and creep characteristic of piezoelectric ceramics, accurate control of piezoelectric type DM remains a challenge. Generally, the surface shape of a DM is changed by altering the voltages applied to different actuators below the DM film. And the shape of the DM can be fitted with Zernike polynomial to better characterize the aberration. So accurate control of the DM surface shape requires a relationship between the control voltage vector and the Zernike coefficients of the surface shape. We adopt neural network for the foundation of the relationship. 3000 set of control-voltage-vector and Zernike-coefficient pairs are experimentally collected based on the data measured with an interferometer and fitted with Zernike polynomials. The neural network is constructed and trained, and the control voltage vectors of new surface shapes can be retrieved with the network. The accuracy of shape realization is finally demonstrated by comparison between measured and predicted voltages.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
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.