I don't understand your question at all. Can you put it in a different way please.
thank you for your reply.
I will ask the question as follows: what is the influence of the calculations on the the space transformation on the design of planar focusing antennas design using quasi-conformal maping
I am not sure about this but this is what I think
If you conformally map the antenna and use metamaterials to similarly map the surrounding space and materials then the performance should remain the same in the transformed space (I think). Otherwise conformally mapping the antenna without transforming the medium it is in will change its impedance and hence its operating frequency. Array performance depends on electrical distances from the antenna to the illumination point so unless material properties in this path is also transformed then the antenna pattern will change. This won't just change the shape of the pattern but also relative sidelobe levels. Feed line lengths will also change if the properties of the material they are in is not transformed.
There is a fourier transform relation between the excitation pattern and the far-field pattern, and there may be a way of taking the conformal transformation across too, but I don't know. Watch out for feed lengths and so relative phases in your transformed array.
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