# Lens simulation with MTF

1. Oct 16, 2013

### mgma

Hello,

1. The problem statement, all variables and given/known data
and
2. Relevant equations

I need to simulate a camera given it's Modulation Transfer Function (MTF), which is a polynomial f(x). The expression for the MTF is:

y = 2E-08x4 + 0.0008x2 - 0.464x + 1.0076

(with x the spatial frequency in number of cycles/mm).

In order to simulate the effect of the lens in each image, I have to apply the following algorithm:

• Compute the 2D Fast Fourier Transform (FFT) of the input image
• Compute the frequency image corresponding to the MTF (I think this should be done only once, at the beginning)
• Multiply the two frequency images obtained (Complex FFT * MTF)
• Inverse the image obtained (with inverse FFT) to compute the final image
This is equivalent to a frequency convolution of the original image with the MTF.

3. The attempt at a solution

I don't understand how I should obtain the frequency image corresponding to the MTF. I think I should calculate a matrix with horizontal and vertical frequencies:

MTFi,j = h(fx,fy)

However, the polynomial expression that I have for the MTF is a function of only one variable, the spatial frequency x.

f(x) = 2E-08x4 + 0.0008x2 - 0.464x + 1.0076

How should I build the elements MTFi,j of the two-dimensional MTF matrix from this MTF function f(x)?

I think I should have two spatial frequencies fx and fy to calculate the MTF frequency image, but the MTF is given as function of a single spatial frequency by camera manufacturers.

Miguel
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution