Self-calibrated subaperture stitching test of hyper-hemispheres using latitude and longitude coordinates

Abstract

Limited by the f-number of the transmission sphere, it is impossible to test the whole surface of a hyper-hemisphere using a standard interferometer directly. This paper presents an extension of the subaperture stitching test method to hyper hemispheres. The stitching algorithm is based on the coordinate mapping from local measurement frame to a global frame, and overlapping correspondence is calculated by virtue of coordinates of latitude and longitude. The reference surface error is represented by Zernike polynomials and self-calibrated during the stitching to achieve higher accuracy. Then the stitched surface error distribution is presented by map projection. To realize accessibility to the whole surface of a hyper-hemisphere, we also propose a design for the subaperture test platform, according to the subaperture lattice design. Finally, a hemisphere and a full sphere are tested and figured, respectively, to validate the method and the experimental setup.

Subaperture stitching interferometry based on digital holography

“…Afterward, a stitching algorithm is utilized to synthesize a full aperture phase map by estimating and correcting relative alignment errors of adjacent subapertures [26]. First, based on initial position parameters, the subaperture phase maps are synthesized into a full aperture phase map in a general coordinate frame.…”

“…A significant improvement was realized by simultaneously fitting rigid-body alignment terms among multiple overlapping subapertures [18][19][20][21][22][23][24][25]. Recently, Shanyong Chen et al proposed a self-calibrated subaperture stitching algorithm for hyper-hemispheres tests, based on the alternating optimization technique and the successive linearization method [26][27][28]. To our best knowledge, the existing SSI utilizes a commercial phase-shifting interferometry to acquire the subaperture phase maps.…”

Sensitivity coefficient for monitoring residual surface error in plane subaperture stitching interferometry

“…However, the main disadvantages of the absolute test are its complexity and time-consuming nature. Another method involves the use of a special algorithm with interlocked compensators (components such as piston and tilt that are included to minimize various alignment errors), and the approach can be used to stitch the subapertures and simultaneously remove the reference surface error [21][22][23][24][25]. The interlocked compensators correspond to a set of Zernike polynomials, and they are used to simulate the reference surface error [21].…”

“…The interlocked compensators correspond to a set of Zernike polynomials, and they are used to simulate the reference surface error [21]. The eight lower-order terms [20,21] and 36 Zernike polynomials [24,25] are always used to fit the reference surface error, and these are subsequently are removed from each subaperture surface.…”