Handbook of Biomedical Optics

Diffraction Optics 31

We introduce the object intensity spectrum, given by the

Fourier transform of its intensity, which is in contrast with

Equation 2.124,

V m n U x y i mx ny x y

1 1 1 1

2

1 1 1 1

2, , exp .

(

)

=

( )

− +

( )

⎡

⎣

⎤

⎦

−∞

+∞

−∞

+∞

∫∫

π d d

(2.149)

en we can show by exactly the same method as in Section 2.16

that

I x y V m n C m n i

mx

M

ny

M

m n

3 3 1

3 3

2, , , exp

( )

=

( ) ( )

− +

⎛

⎝

⎜

⎞

⎠

⎟

⎡

⎣

⎢

⎤

⎦

⎥

∫∫

π d d

(2.150)

where the OTF, C(m,n), is given by the Fourier transform of the

intensity point spread function |h|

2

. As for the coherent case we

had P(mf, nf ) = F(h), where F(.) represents the Fourier trans-

form, now we have

C m n F h

P m f n f P m f n f

,

,

*

,