# Computation of real MTF and comparison with theoritical MTF

Before explaining my problem I have to explain the context: I want to modelize a detector. I assume that the PSf of this detector is an Airy disk. Knowing the characteristics of the detector, I can compute the analytic MTF.

But this analytic MTF will not be observed, because the detector is made up of pixels. To modelize it, I intergate the PSF over the pixels. It gives me a discrete PSF, as it can be seen below:

From this discrete PSF I calculate the MTF (the discrete MTF, or as it will be called later in another image, the numerical MTF).

(and to be very precise, I compute 2 MTFs, one for each direction)

Here is the discrete (numeric) MTF (blue curve) and the analytic MTF (red curve) the other curves represent the discrete MTF multiply by different analytic MTF taking diffraction into acount.

So here are my problems, the blue curve does not goes to 0 amplitude at 1 cy/pix, for the high spatial frequencies. I think it is due to the discretization but I do not really understand why. I would be very glad if someone could explain me the physical meaning of this. I have seen some experimental MTF doing the same on some websites.

My second problem is that as you can see, the discrete MTF is better than the analytical one for high spatial frequency. Do you think my calculations are wrong because of this?

For the calculation of the MTF, I do the discrete fourier transform of a row (or a line) of the PSF, with one point per pixel.

PSF stands for point spread function and MTF for Modulation transfer function.

Please tell me if something is not clear so I can update my post.

Thank you