Microscope Image Processing

The Shannon sampling theorem [1, 4, 5] states that a continuous function

can be reconstructed, without error, from evenly spaced sample points, provided

that two criteria are met. First the function must be band-limited. That means

that its Fourier spectrum is zero for all frequencies above some cutoff frequency,

which we call f

c

. This means the function can have no sinusoidal components of

frequency greater than f

c

. Second, the sample spacing must be no larger than

Dx ¼ 1=2f

c

. This means there will be at least two sample points per cycle of the

highest-frequency sinusoidal component of the function. If these two criteria are

met, the function can be recovered from its samples by the process of interpol-

ation, if that is properly done.

If Dx < 1=