How to interpolate complex array (FT)? I do Fourier Transform for an image, then consider line(slice) in FFT image. When that slice isn't parallel neither x- not y-axis, coordinates are not integer.
E.g. slice can hold indices {(0,0), (0.25,1), (0.5,2), (0.75,3), (1,4)...}.
When using nearest-interpolation, quality of whatever I do is pure.

What techniques can you suggest to improve interpolation in Fourier grid?
The usual way to do this is to interpolate using surrounding points.  There is a simple 6-point mechanism that uses:



This question on the Mathematics SE site has some more details. Note the answer's correction to the equation in the question.