We present a design method for diffractive axicons in spatially partially coherent Gaussian Schell-model illumination. The method of stationary phase applied to the Fresnel diffraction integral for on-axis intensity leads, on requiring a uniform axial image profile, to a second-order differential equation for the optimal axicon phase function. The first integral can be formally performed, and the phase function is subsequently obtained numerically. The correctness of the synthesized phase profiles is confirmed by numerical simulations using partially coherent Fresnel diffraction theory. The effects of input-beam spot size and coherence width are assessed, and influences of different forms of apodization, including asymmetric functions for narrow incident beams, in annular-aperture diffractive axicons are examined.
© 2002 Optical Society of America
Original Manuscript: May 29, 2001
Revised Manuscript: August 27, 2001
Manuscript Accepted: August 27, 2001
Published: March 1, 2002
Anna Thaning, Ari T. Friberg, Sergei Yu. Popov, and Zbigniew Jaroszewicz, "Design of diffractive axicons producing uniform line images in Gaussian Schell-model illumination," J. Opt. Soc. Am. A 19, 491-496 (2002)