Farfield pattern reconstruction using 2D interpolation in matlab

I am trying to use fourier transform based approach for near field to farfield transformation of E-fields. I have my sampling plane in xy with following coordinates -120mm <X<120mm and -120mm<Y<120mm. My operating frequency is 2.5 GHz to 4GHz. I have taken fourier transform for the E-field complex data and have converted my FFT indices into wavenumbers. In order to do the Near field to farfield transformation, I have to then interpolate the FFT values to the stationary observation points in spherical coordinates. So, i used interp2 function to do this. The following is my code for this interpolation.

Ex_interp(:,:,i)= interp2(Fx_grid1, Fy_grid1, Exff_z0(:,:,i), kx(:,:,i), ky(:,:,i), 'spline',0);

Ey_interp(:,:,i)= interp2(Fx_grid1, Fy_grid1, Eyff_z0(:,:,i), kx(:,:,i), ky(:,:,i), 'spline',0);

i= number of frequecies in my code. The Fx grid1 and Fy grid are the wavenumbers in cartesian coordinates already in gridded format. Their size is 1024 x 1024. (FFT size=1024). The kx and ky are the observation points in cartesian coordinates calculated from the spherical coordinates. The code works for me and it gives a farfield which closely matches the data from a Electromagnetic solver. But, the catch is that it matches only at lower frequencies, and as the frequency increases, the spline fit is giving me lot of inflections in my antenna beam pattern. I beleive this is related to the interpolation error. Because, when i change the interpolation type to 'cubic' it gives lot of ripples in my beam pattern. So, basically with the different types of interplation the final beam varies drastically at higher frequencies. I did not find any method better than spline in interp2 function. I do not know how to solve this issue. Are there any other methods available for 2D interpolation where we can also control the spline fitting parameters? Looking for some suggestions here.. I am new to these interpolation techniques, so i am not able to understand the problem completely here.

[Umar]

Hi Keerthipriya,

When dealing with interpolation errors affecting the beam pattern at higher frequencies during near field to far field transformation, it's crucial to explore alternative interpolation methods beyond 'spline' and 'cubic' in MATLAB's interp2 function. One approach is to consider using custom interpolation functions or techniques that offer more control over the fitting parameters.

One option is to implement a custom interpolation function using MATLAB's griddedInterpolant class, which allows for more flexibility in defining interpolation behavior. By creating a custom interpolant, you can tailor the interpolation method to better suit the characteristics of your data and mitigate issues like inflections or ripples in the beam pattern.

For more information regarding griddedInterpolat, please refer to https://www.mathworks.com/help/matlab/ref/griddedinterpolant.html

Another strategy is to experiment with different interpolation algorithms available in MATLAB, such as 'linear' or 'nearest', to assess their impact on the beam pattern at higher frequencies. By systematically testing various interpolation methods and parameters, you can optimize the interpolation process to achieve more accurate results across different frequency ranges.

I hope that answers your question.