[OPTICAL REVIEW Vol. 2, No. 5 (1995) 347-351]

## Spectrum Invariance for a Particular Class of Optical Fields Propagated in Far Zone

Yoshihiro OHTSUKA

*Department of Engineering Science, Faculty of Engineering, Hokkaido University, Sapporo, 060 Japan*

(Received June 30, 1995; Accepted August 1, 1995)

This paper describes invariance of the normalized optical spectrum for a particular class of optical fields propagated in the far zone from a secondary, spatially, partially coherent source. The optical field across the secondary planar source is inhomogeneous to give the complex degree of spectral coherence such that Eľ=*h*{αω(ρ_{1}?ρ_{2})}exp{*i*εω(ρ_{1}^{2}?ρ_{2}^{2})}, where α, ε are constants, ω is optical frequency, and ρ_{1}, ρ_{2} denote two points in the secondary source. This expression for Eľ is the same as obtained in the Fresnel zone from a primary, spatially incoherent source. The invariance law does not hold for the spectrum of the light propagated from the primary source.

Key words : spectrum invariance on propagation, inhomogeneous optical fields, particular complex degree of spectral coherence