For the data sampled in digital systems two conditions hold:
- The Signal must have a finite bandwidth: above a cutoff frequency all frequency components must be zero..
- The sampling frequency must be minimum twice the cutoff frequency of the signal.
These rules are called Shannon sampling theorem , or Nyquist Shannon Sampling Theorem.
This effect is called aliasing and results from mirroring of frequencies above into the frequencies below the cutoff limit..
In Optics the Nyquist-Frequency equals onle line per pixel = half a line pair per pixel.
At the Nyquist-Frequency the MTF reaches Zero. We don’t have contrast then.
The cutoff frequency depends on the FNumber and the wavelength.
One can resolve 70% of the Nyquist frequency = 0.7*Nyquist frequency = Nyquist frequency / 1.41
If you even want a chance to reach 50% contrast, you should even divide by 2.
This contrast is then reachend over a range of 4 pixels.
Lets say we have a sensor with 2.2um pixel pitch.Then the Nyquist frequency is 1/2 line pairs per Pixel.
On 1mm = 1000um fit 1000/2.2u = 454pixel.
So the Nyquist frequency = 0.5lp / pixel = (454/2) lp/mm = 227lp/mm.
there we have 0% Contrast.
To have a chance for 50% Contrast haben, we have to divide this value by 2 and get (227/2) lp/mm = 113.5 lp/mm.