Singular-value decomposition (SVD) of a linear imaging system gives information on the null and measurement components of object and image and provides a method for object reconstruction from image data. We apply SVD to through-focus imaging systems that produce several two-dimensional images of a three-dimensional object. Analytical expressions for the singular functions are derived in the geometrical approximation for a telecentric, laterally shift-invariant system linear in intensity. The modes are evaluated numerically, and their accuracy confirmed. Similarly, the modes are derived and evaluated for a continuous image representing the limit of a large number of image planes.
© 2006 Optical Society of America
Original Manuscript: December 2, 2005
Revised Manuscript: March 23, 2006
Manuscript Accepted: May 1, 2006
Anna Burvall, Harrison H. Barrett, Christopher Dainty, and Kyle J. Myers, "Singular-value decomposition for through-focus imaging systems," J. Opt. Soc. Am. A 23, 2440-2448 (2006)