What does this paragraph mean? I'm reading this paper about about an algorithm to measure image sharpness, and am confused by these sentences in the 6th paragraph:

It is well known that the attenuation of high-frequency content can lead to an image that appears blurred. One way to measure this effect is to examine the image’s magnitude spectrum $M(f)$, which is known to fall inversely with frequency, i.e. $M(f)\propto f^{-\alpha}$, where $f$ is the frequency and $-\alpha$ is the slope of the line $\log{M}\propto-\alpha \log{f}$.

I don't know what frequency this is referring to as the images this paper and algorithm are concerned with are grayscale, does anyone have a clue?
Detail in images require higher frequency basis functions.  The frequency in this case is measuring fluctuations in intensity as a distance is traversed.  With a lot of detail, a lot of fluctuations, thus higher frequency.
Tamp down the higher frequency and you lose detail, i.e. the image blurs.
The dampening is measured (described) best on a log scale.
Consider this answer Honey Mustard.