TY - JOUR

T1 - Analysis of 3rd order spherical aberration with the continuous wavelet transform

AU - Sheu, Jin Yi

AU - Lin, Ching Huang

AU - Chang, Rong Seng

PY - 2000

Y1 - 2000

N2 - There are several numerical techniques to solve the value of aberration coefficients. One classical technique is the Gaussian elimination method, which has been described in most standard numerical analysis textbooks, such as Ralston's text, the conventional direct inversion method is numerically unstable. To obtain the Zernike coefficients from a sampled wavefront with inherent measurement noise, the classical least-squares matrix inversion method and the Gram-Schmidt orthogonalization method would become ill-conditioned due to an improper data sampling. In this paper, we present the continuous wavelet transform (CWT) technique to find the defocus aberration and 3rd order spherical aberration coefficients. The technique we proposed is superior to the conventional methods in two ways. (1) Our method is much faster than the conventional methods, especially in applications with only a fewer number of sampling points. (2) Our method is also more accurate in fitting aberration coefficients than the conventional methods, particularly in applications involving noise. Furthermore, the aberration coefficients determined through the CWT are independent of the order of the polynomial expansion. So we can find a true value from the datum of fitting.

AB - There are several numerical techniques to solve the value of aberration coefficients. One classical technique is the Gaussian elimination method, which has been described in most standard numerical analysis textbooks, such as Ralston's text, the conventional direct inversion method is numerically unstable. To obtain the Zernike coefficients from a sampled wavefront with inherent measurement noise, the classical least-squares matrix inversion method and the Gram-Schmidt orthogonalization method would become ill-conditioned due to an improper data sampling. In this paper, we present the continuous wavelet transform (CWT) technique to find the defocus aberration and 3rd order spherical aberration coefficients. The technique we proposed is superior to the conventional methods in two ways. (1) Our method is much faster than the conventional methods, especially in applications with only a fewer number of sampling points. (2) Our method is also more accurate in fitting aberration coefficients than the conventional methods, particularly in applications involving noise. Furthermore, the aberration coefficients determined through the CWT are independent of the order of the polynomial expansion. So we can find a true value from the datum of fitting.

UR - http://www.scopus.com/inward/record.url?scp=0033690508&partnerID=8YFLogxK

M3 - 會議論文

AN - SCOPUS:0033690508

SN - 0277-786X

VL - 4056

SP - 507

EP - 514

JO - Proceedings of SPIE - The International Society for Optical Engineering

JF - Proceedings of SPIE - The International Society for Optical Engineering

T2 - Wavelet Applications VII

Y2 - 26 April 2000 through 28 April 2000

ER -