  A binary matrix can be scanned by moving a fixed rectangular window
(submatrix) across it, rather like examining it closely under a microscope.
With each viewing, a convenient measurement is the number of 1s visible in the
window, which might be thought of as the luminosity of the window. The
rectangular scan of the binary matrix is then the collection of these
luminosities presented in matrix form. We show that, at least in the technical
case of a smooth m x n binary matrix, it canbe reconstructed from its
rectangular scan in polynomial time in the parameters m and n, where the degree
of the polynomial depends on the size of the window of inspection. For an
arbitrary binary matrix, we then extend this result by determining the entries
in its rectangular scan that preclude the smoothness of the matrix.
