Quantum limits in the measurement of very small displacements in optical images.

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.