Handbook of Biomedical Optics

16 Handbook of Biomedical Optics

Fresnel’s zones in the following way. Contributions from succes-

sive zones (Figure 2.11) tend to cancel as the phases are dierent

by 180°. If the number of zones is N, then a

2

= nr and

N

a

r

=

2

λ

,

(2.32)

that is, it is equal to the Fresnel number, dened earlier

(Equation2.8).

Note that for a general axially symmetric U

1

, along the axis,

the amplitude is

U r

ik

r

ikr U R

ikR

r

R R

a

2 0

0

0 1

0

1

1

2

0

1 1

0

2

, exp exp .

( )

= −

(

)

(

)

⎛

⎝

⎜

⎞

⎠

⎟

∫

d (2.33)

Let R a t

1

2 2

/ = , and put U

1

(R

1

) = V

1

(t). We have

2

1 1

2

R R a td d= ,

and thus

U r i N ikr V t i Nt t

2 0 0 1

0

1

0, exp exp .

( )

= −

(

)

(

)

(

)

∫

π π d

(2.34)

So the intensity is given by ...