| Recently, considerable attention has been paid to the parametric image amplifier in the nonlinear optics and quantum optics. It is one of the most important contents for the quantum optics and nonlinear optics to study on the quantum properties and physical applications of the parametric image amplifier. In this paper, the important properties of the parametric image amplifier, such as the noiseless amplification of optics images and the squeezing effect of the input image, are studied ,and a series of significant results are obtained.In chapter 1, a simple history overview of the parametric image amplifier is studied, and the schematic presentation of the optical parametric amplifier, the physical realization of the ring-cavity parametric image amplifier are introduced generally.In chapter 2, the linear schemes of the ring-cavity optical parametric amplifier and ring-cavity parametric image amplifier are presented and relation between the input image and the output image of the ring-cavity parametric image amplifier is derived by using of the theory of the ring-cavity optical parametric amplifier, which privide a besis for the following investigations.In chapter 3, the noiseless amplification of optical images in the parametric image amplifier is discussed. Taking the coherent states as the input image of the parametric image amplifier, we compare the power signal -to-noise ration of the output image with the one of the input image. The result show that the noiseless amplification of optical images can be realized in the parametric image amplifier when the parametric image amplifier satisfy some specifical conditions.
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