Handbook of Biomedical Optics

260 Handbook of Biomedical Optics

wide-sense-stationary random process is the Fourier transform

of the corresponding autocorrelation function, that is,

S

xx

f r e

j f

xx

( ) ( )=

−

−∞

∞

∫

τ

π τ

τ

2

d

where

r x t x t

xx

( ) E[ ( ) * ( )]τ τ= −

is the autocorrelation function. According to the Wiener–

Khinchin theorem, the temporal coherence function V

tc

is actu-

ally the Fourier transform of the power spectral density S( f )

of the light source, which is fully characterized by its shape,

its spectral bandwidth, and its center wavelength (Gilgen et al.

1989, Schmitt 1999, Wang 1999, Akcay et al. 2002, Wang and

Tuchin 2004):

V S k S f j f f

tc

(