How to find PSD (Power spectral density) of spatial data
A spectrum estimation method that works well in many cases is Welch's method. The MATLAB implementation is pretty straight forward to use, even when not knowing about the math behind it. Following Marcus' recommendations, you could try:

if norm(diff(X,2)) &lt; sqrt(eps) % is X evenly spaced ?
    Fs = 1/mean(diff(X)); % find the step size of X
    [Pyy,F] = pwelch(Y,[],[],[],Fs,'onesided','PSD'); % compute the PSD
    plot(log10(F),log10(Pyy)), xlabel('log [\mum^{-1}]'), ylabel('log[PSD[\mum^2/\mum^{-1}]]')
    axis tight, grid on
end