CONFERENCE PROCEEDINGS
Advanced Search >
Home > Proceedings > Volume 10742 > Article
Translator Disclaimer
14 September 2018 Chebyshev gradient polynomials for high resolution surface and wavefront reconstruction
Maham Aftab; James H. Burge; Greg A. Smith; Logan Graves; Chang-jin Oh; Dae Wook Kim
Author Affiliations +
Proceedings Volume 10742, Optical Manufacturing and Testing XII; 1074211 (2018) https://doi.org/10.1117/12.2320804
Event: SPIE Optical Engineering + Applications, 2018, San Diego, California, United States
Abstract
A new data processing method based on orthonormal rectangular gradient polynomials is introduced in this work. This methodology is capable of effectively reconstructing surfaces or wavefronts with data obtained from deflectometry systems, especially during fabrication and metrology of high resolution and freeform surfaces. First, we derived a complete and computationally efficient vector polynomial set, called G polynomials. These polynomials are obtained from gradients of Chebyshev polynomials of the first kind – a basis set with many qualities that are useful for modal fitting. In our approach both the scalar and vector polynomials, that are defined and manipulated easily, have a straightforward relationship due to which the polynomial coefficients of both sets are the same. This makes conversion between the two sets highly convenient. Another powerful attribute of this technique is the ability to quickly generate a very large number of polynomial terms, with high numerical efficiency. Since tens of thousands of polynomials can be generated, mid-to-high spatial frequencies of surfaces can be reconstructed from high-resolution metrology data. We will establish the strengths of our approach with examples involving simulations as well as real metrology data from the Daniel K. Inouye Solar Telescope (DKIST) primary mirror.
Conference Presentation
© (2018) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Citation Download Citation
Maham Aftab, James H. Burge, Greg A. Smith, Logan Graves, Chang-jin Oh, and Dae Wook Kim "Chebyshev gradient polynomials for high resolution surface and wavefront reconstruction", Proc. SPIE 10742, Optical Manufacturing and Testing XII, 1074211 (14 September 2018); https://doi.org/10.1117/12.2320804
ACCESS THE FULL ARTICLE
PERSONAL SIGN IN
Full access may be available with your subscription
 
Forgot your username?
Forgot your password?
No SPIE account? Create an account
Institutional Access:
Sign in with your institutional credentials
PURCHASE THIS CONTENT
INTERESTED IN A FREE CORPORATE TRIAL?
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
Members: $17.00
Non-members: $21.00 ADD TO CART
PROCEEDINGS
 7 PAGES + PRESENTATION
DOWNLOAD PDF SAVE TO MY LIBRARY
WATCH
PRESENTATION
SHARE
GET CITATION
< Previous Article
|
Next Article >
Advertisement
Advertisement
KEYWORDS
RELATED CONTENT
Subscribe to Digital Library
Receive Erratum Email Alert
Back to Top