Handbook of Biomedical Optics

26 Handbook of Biomedical Optics

to perform a 2D Fourier transform almost instantaneously

(Figure2.24), in the time for light to travel a distance 2f.

Note that if U

1

is a constant, assuming the pupil P is very big,

U

3

is a delta function. If the pupil is nite, we get the point spread

function. If U

1

is a circular function, a constant value within a

circle, smaller than the pupil P, then the nal amplitude is its

Hankel function, that is the Airy disk 2J

1

(v)/v.

We have seen that if U

1

is a delta function, then U

3

is a constant.

Two of these units may be coupled together, as in Figure 2.25.

But the Fourier transform of the Fourier t