Theoretical and experimental studies of the decorrelation residuals of the matrix-analysis three flat test

Lingqiang Meng; Zhigang Han; Xiaoqin Shan

doi:10.1117/1.OE.57.7.074108

23 July 2018 Theoretical and experimental studies of the decorrelation residuals of the matrix-analysis three flat test

Lingqiang Meng, Zhigang Han, Xiaoqin Shan

Author Affiliations +

Optical Engineering, Vol. 57, Issue 7, 074108 (July 2018). https://doi.org/10.1117/1.OE.57.7.074108

Abstract

A method utilizing matrix analysis has been presented for a full-area three-flat test. With the aid of the Moore–Penrose pseudoinverse of a circulant matrix, a set of closed mathematical formulas has been derived to obtain the absolute profiles of samples. According to the simulation results, the matrix analysis method shows better performances for determining the absolute profiles and suppressing the decorrelation residuals of the reconstructed wavefronts, compared to the iterative method. Three optical flats with 135-mm apertures are measured. The results obtained with the new method agree well with those obtained with the iterative algorithm and the classical three-flat test. Furthermore, the relationship between the decorrelation residual and the wavefront error introduced in the rotation measurement has been studied. Theoretical and experimental results show that the odd-symmetric component contributes significantly to the decorrelation residual.

Citation Download Citation

Lingqiang Meng, Zhigang Han, and Xiaoqin Shan "Theoretical and experimental studies of the decorrelation residuals of the matrix-analysis three flat test," Optical Engineering 57(7), 074108 (23 July 2018). https://doi.org/10.1117/1.OE.57.7.074108

Received: 25 April 2018; Accepted: 5 July 2018; Published: 23 July 2018

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