Quantum fluctuations in traveling-wave amplification of optical images

We investigate amplification of optical images by means of a traveling-wave optical parametric amplifier. As shown recently by Kolobov and Lugiato [Phys. Rev. A 52, 4930 (1995)] for a cavity-based geometry, such a scheme can amplify images without deteriorating their signal-to-noise ratio thus working as a noiseless amplifier. Here we consider a configuration without cavity which is more realistic for a possible experimental realization. We investigate in detail the quantum fluctuations of the amplifier and formulate criteria for its noiseless performance. The spatial resolution power which guarantees noiseless amplification is estimated. We demonstrate how the optimum phase matching of a phase-sensitive wavefront of the image can improve the noise performance of the amplifier and bring it to the ultimate value achievable under given physical conditions. We discuss the effect of improvement of the signal-to-noise ratio in the case of observation of both the input and the amplified image with an ideal photodetector of small area (i.e. much less than the coherence area of the amplifier). This improvement is due to the fact, that the signal-to-noise ratio in the input is deteriorated by the observation with the photodetector of small area.