Hideki FUNAMIZU, Jun UOZUMI¹, and Yukihiro ISHII

Department of Applied Physics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku, Tokyo 162-8601, Japan
¹Faculty of Engineering, Hokkai-Gakuen University, Sapporo 064-0926, Japan

(Received September 25, 2009; Accepted December 12, 2009)

When a diffuser is illuminated by the coherent light with a negative power-law distribution, fractal speckles are produced in the far-field diffraction region. Fractal speckles have extremely long spatial correlation functions of the intensity distributions in comparison with ordinary speckles, which implies that they may extend measurement ranges in various metrological applications based on the spatial correlation of speckles. To have fractal speckles with satisfactory statistical properties, it is required to produce a power-law illumination profile with high quality. In this paper, we report on the computer-generated holograms for producing power-law intensities on the basis of the method of stationary phase, with the error-reduction algorithm combined with to suppress strong ringing of the intensity.

Key words: fractal, fractal speckle, computer-generated hologram, the method of stationary phase, error-reduction method