title: Fast fine-pixel aerial image calculation in partially coherent imaging by matrix representation of modified Hopkins equation.
abstract: A fast computation algorithm for fine-pixel aerial images is presented that modifies the transmission cross coefficient approach of Hopkins as a product of two matrices. The spatial frequency of the image is calculated by the sum of diagonal and off-diagonal elements of the matrix. Let N, N(F), and M be the number of the point sources, the sampling number for fast Fourier transform, and the sampling number in the spatial frequency domain ranging twice the pupil size, respectively. The calculation time of this method is proportional to BN[(M-1)/2](4), while that of a conventional source integration method is 2ANN(F)log(2)N(F), where A and B are constants and generally B < A. If N(F) is sufficiently greater than M or M is small enough, which is the fine-pixel condition, this method runs faster than the source integration method. If the coherence factor is 0.9 and M < or = 55, this method runs faster than the source integration even under the Nyquist sampling condition.
authors.affiliation: 231 Cory Hall, Department of Electrical Engineering and Computer Science, University of California, Berkeley, California 94720-1770, USA. kenjiy@eecs.berkeley.edu
authors.forename: Kenji
authors.initials: K
authors.lastname: Yamazoe