Your IFFT phase results don't make sense to me. They seem to show a phase gradient across the plot that does not exist in the measured data. Do you have the origin in the right place for the IFFT? Also, I think that for near-field to far-field I would usually use the FFT, not the IFFT.

The NF_raw data that is plotted is interpolated. Is the phase data interpolated, and was interpolated data used in the transform? Interpolation at the 360 degree phase steps would result in badly wrong data - but not the sort of thing you are seeing, I think.

The phase gradient in the IFFT data is diagonal (in the main lobe), so I expected to see a pattern in the sampling that was offset in both theta and phi - however I am not sure what process you did to get that data so I can't really comment on it.

Dear Malcolm White thanks for your input. Sorry for the confusion I actually show the raw data, the plot label just says it is interpolated. (I tried to interpolate it and increase the data point, to check if it fixes my problem.)

As far as I understand the FFT and IFFT are chosen based on the contention of propagation exp(jkr) or exp(-jkr). I have to use ifftshift command on result so that the "DC" modal component is the center.

Now I do have to interpolate data in order to evaluate it in spherical coordinates. Since I use the conventions

kx = k0 * sin(theta)*cos(phi)

ky = k0 * sin(theta)*sin(phi)

I try to avoid phase jumps by interpolating in the magnitude, real-part and imaginary-part separately, and then combine them as:

z_new = z_int_abs * exp(j *phase(z_int_real+ j* z_int_imag))

As far as I see this yields very good complex interpolation results.

It may be a stupid question but did you use degrees or radians in your sine and cos functions? They will probably expect radians, so if you used degrees you will get wrong and highly undersampled results.

Excuse me if this is so stupid you would never do it, but this does happen from time to time.

I don't understand how the IFFT has resulted in the non-linear phase gradient diagonally across the main beam in the centre of each plot on the bottom row of the IFFT. I would expect a rectangular or circular phase pattern across the main lobe and side lobes with flat or slow phase variation within the lobe.

The rapid phase change that you have is very close to the wave travelling across the plot, (600 radians per m) rather than normal to it (0 radians per m)

I made sure that everything is in terms of radians. I actually think that something goes wrong before or during the FFT. As you mentioned the phase change is to big. If you want I can transform the NF data into a format of your choice and you can take a look yourself.

CSV or excel would be fine for me. I might be able to cope with whatever you have!

Malcolm White thank you very much for you help, I really appreciate it. I exported the data as CSV and standard Matlab files. (I use python myself)

Thanks.

I also need the exact wavelength and sample spacing - some of the numbers you give in the post are approximate, as the scanned surface is not an exact number of sample spacings across.

I can work with approximate numbers, it won't quite be right, but shouldn't affect things that you are trying to understand.

Everything was sampled at 28 GHz which corresponds to 0.0107068735 m. The antenna and probe are 50 mm apart. The sample points are 1.53543 mm apart.

I have the things I need, after all. The spacings and frequency only scale the output.

Here are four contour plots from MATLAB using FFT, with some fftshift to get the peak in the middle.

These plots are what I would expect to see, with a peak in the centre for x, lower values for y, and well defined phase in the main lobe and near sidelobes.

I think there must be a problem with your fft

I scaled the phase wrong!

Here are the correct ones (I think) and the input files as well

I just did an fft from the fields in the image plane, assuming those were the fields in a planar aperture. The fft will give the far-field angular distribution, I think. The ifft wouldn't be fatal!

If you can't read the matlab files I can do other formats.

I didn't need the spacings or wavelength to do this. They only affect the scale of the output figure. I think the edge of the figure corresponds to the angle when the phase between sample points is pi.

spacing*2*pi*sin(angle)/wavelength=pi

angle = asin(wavelength/2/spacing)

Thank you so much for your help. Sadly I have trouble to import the .fig files. Could you export them as PNGs? I think for now it is ok if I know how your results look like, so I can adjust my code. Thank you very much again

II have used the principal that I believe to be true, that the fields you have sent me can be regarded as the fields in a plane aperture, and I have calculated the far-field of an aperture with those fields in it.

I've checked, and the fft and ifft give nearly identical phase plots in the far field. The amplitude plots are also similar.

Your results should look something like mine. There must be a mistake somewhere in your processing

Dear Malcom, I made the same observation regarding the FFT and IFFT (only the factor of 2pi and the phase change). Sadly I can not reproduce your result. Could you share the Matlab commands you use to generate the data?

fftx = fft(NF_data_pol_x)

ifftx = ifft(NF_data_pol_x)

ffty=fft(NF_data_pol_y)

contour(20*log10(abs(fftx)))

contour(360/2/pi()*(angle(fftx)))

contour(flip(360/2/pi()*(angle(ifftx)),1))

contour(fftshift(360/2/pi()*(angle(fftx)),1))

The flip and shift are useful for getting the peak in the middle and the right way up.

1 or 2 refers to the axis that is shifted or flipped.

Dear Malcolm thank you for the clarification. You only performed a single FFT/iFFT, but to get the modal components in x (kx) and y (ky), we need to perform the two dimensional fft alogrithm (fft2 in Matlab https://www.mathworks.com/help/matlab/ref/fft2.html). I think once you do this your results should look more like mine.

Dear Malcolm White I gained some further insight into the problem in the last two days, that I would like to share with you. I found out that I can improof my results by padding the input to the FFT. I still get get phase aliasing (it looks like a chess pattern) but you can clearly see the correct phase. I also created plots that zoom into the modal space, so one can better inspect the modal components of interest. The red ring denotes k0 at 28 GHz in free space.

Padding the input to the FFT by adding zeros at the ends introduces interpolated points in between the original results and gives a much smoother looking result.

Although it may look better, I still think the pattern you are getting is not the correct one. I don't understand why the matlab FFT I did, and your IFFT do not give similar results. I am not sure what you are plotting in your modal space plots, so I can't comment on them.