  We consider a method of high-fidelity, spatially resolved position
measurement of ultracold atoms in an optical lattice. We show that the
atom-number distribution can be nondestructively determined at a spatial
resolution beyond the diffraction limit by tracking the progressive evolution
of the many-body wavefunction collapse into a Fock state. We predict that the
Pauli exclusion principle accelerates the rate of wavefunction collapse of
fermions in comparison with bosons. A possible application of our principle of
surpassing the diffraction limit to other imaging systems is discussed.
