As e.g. shown in this Matlab Central page, the sharpness can be estimated by the average gradient magnitude.
I used this in Python as
from PIL import Image
import numpy as np
im = Image.open(filename).convert('L') # to grayscale
array = np.asarray(im, dtype=np.int32)
gy, gx = np.gradient(array)
gnorm = np.sqrt(gx**2 + gy**2)
sharpness = np.average(gnorm)
A similar number can be computed with the simpler numpy.diff instead of numpy.gradient. The resulting array sizes need to be adapted there:
dx = np.diff(array)[1:,:] # remove the first row
dy = np.diff(array, axis=0)[:,1:] # remove the first column
dnorm = np.sqrt(dx**2 + dy**2)
sharpness = np.average(dnorm)