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

We consider the problem of the measurement of very small displacements in t he 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 u sed in the measurement, cannot be overcome by use of ordinary single-mode s queezed light. We give the form of possible multimode nonclassical states o f light, enabling us to enhance by orders of magnitude the resolution of su ch a measurement beyond the standard quantum limit. (C) 2000 Optical Societ y of America.