It is shown that both surface tilting and translational motion can be independently estimated by use of the speckle photographic technique by capturing consecutive images in two different fractional Fourier domains. A geometric interpretation, based on use of the Wigner distribution function, is presented to describe this application of the optical fractional Fourier transform when little prior information is known about the motion.
© 2003 Optical Society of America
John T. Sheridan, Bryan Hennelly, and Damien Kelly, "Motion detection, the Wigner distribution function, and the optical fractional Fourier transform," Opt. Lett. 28, 884-886 (2003)