How to Simulate a Camera Using a Modulation Transfer Function?

[mgma]

Hello,

Homework Statement

and

Homework 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.

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:

MTF_i,j = h(f_x,f_y)

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 MTF_i,j of the two-dimensional MTF matrix from this MTF function f(x)?

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

Thanks in advance,
Miguel

 

[KataKoniK]

Dear Miguel,

Thank you for your question. It seems like you are on the right track with your approach to simulate the camera using the MTF polynomial. To obtain the frequency image corresponding to the MTF, you can use the following steps:

1. Calculate the spatial frequency values for a grid of points in the x direction, using the formula x = 1/fx, where fx is the number of cycles/mm.
2. Use the values from the x grid to calculate the MTF values, using the polynomial expression provided.
3. Repeat the same process for the y direction, using the formula y = 1/fy.
4. Multiply the MTF values obtained from the x and y directions to obtain the 2D MTF matrix.
5. Use the 2D MTF matrix as the frequency image in your algorithm.

I hope this helps. Let me know if you have any further questions.