How do you measure "detail" of a signal?
What you are referring to is typically known as "Image Sharpness". A quick scan, as well as some prior knowledge, comes to the following:


Fourier analysis- Using this has 2 key disadvantages. First of all, noise would tend to show up no matter what, and thus higher frequency components would tend to show up. Secondly, sharpness tends to be a local phenomena, and thus might not show up if you do a transform of the entire image.
Eigenvalue analysis- I haven't actually read this paper, but it proposes using eigenvalue analysis to determine the sharpness of an image.
Edge detection algorithms depend on a certain amount of sharpness. One could use different values for edge detection parameters to determine the amount of sharpness. 
Kurtosis Measurement of wavelet coefficients- Again, I haven't read the entire paper, but this seems to suggest calculating wavelet coefficients, performing an FFT of the entire set of coefficients, and measuring the kurtosis. This should be relatively immune to noise.


I'm sure there are many more. This is a very active field of study currently. If none of these methods suits you, then continue to search through academic papers, and see if you can find a better method.