  We consider the problem of the measurement of very small displacements in the
transverse plane of an optical image with a split photodetector. We show that
the standard quantum limit for such a measurement, which is equal to the
diffraction limit divided by the square root of the number of photons used in
the measurement, cannot be overcome by use of ordinary single-mode squeezed
light. We give the form of possible multimode nonclassical states of light,
enabling us to enhance by orders of magnitude the resolution of such a
measurement beyond the standard quantum limit.
