How to find the x-axis of modulation transfer function of a gaussian curve in MATLAB?

I am trying to find modulation transfer function of a gaussian curve by using MATLAB. The gaussian curve is as below:

x- axis is distance(form -15mm to 15mm) and y axis is count(Magnitude). I used the following code to find find fourier transfrom of gaussian curve.

FFT_y = fft(y); %take fourier transform
  
FF_mag = abs(FFT_y )/(length(FFT_y )); %find magnitude
  
FF_mag = (FF_mag-min(FF_mag))./(max(FF_mag)-min(FF_mag)); %normalize magnitude

I cropped FF_mag by using the following codes

FF_mag_nw = FF_mag(1:(length(FF_y)/32));

plot(FF_mag_nw);

I used 32 in above code to get main portion of graph and I got MTF plot as below:

I am confused about X-axis. What will be the range of X-axis in per mm? Can anyone help me give an idea to calculate X-axis of MTF plot?

Thanks in Advance! Manu

[Cinzia Emmanuello]

Dear Manu and whoever comes to this question while googling stuff,

I do not know in which field you are working in (you could have specified it) but anyway the x-axis is in the spatial frequency domain (line pairs/mm). The axis is not in mm anymore, you just applied a Fourier transformation.

Regards,

Cinzia

[Signal Express]

@Cinzia Emmanuello ; @madhan ravi and @Nikhil Sonavane Hello sirs/madam, Is it possible to determine the point spread function and modulation transfer function of an image using matlab? If so, could you guide me through it? I have an image from a microscope, I have determined the resolution by camparing it with the USAF 1951 resolution test chart but I dont know how to proceed further. I must confess, I am a novice in matlab!

Answer 1

[Nikhil Sonavane]

Referring to the last plot function used-

plot(FF_mag_nw); 

The above command will plot FF_mag_nw which is a one-dimensional matrix against its row number as its x co-ordinate. X-axis in the plot will span from 1 to length(FF_y)/32. Hence, x-axis in your plot will only signify the total number of data points in FF_mag_nw.

[madhan ravi]

https://in.mathworks.com/help/matlab/ref/plot.html#description [see under plot(Y)]- exactly as mentioned in the doc, which is what Nikhil describes in his answer.