Criteria for derivation of e-beam emittances using undulator radiation

We present general considerations on the possibility of extracting the e-beam emittance values from the undulator brightness data. The most important result of the present analysis is that it is not possible to obtain a one-to-one correspondence between the point values of the brightness and emittances. Nevertheless, it is shown that there exists an uncertainty region of emittance values which can be connected to give the interval of the perturbed brightness. The extension of this region depends on the accuracy of the brightness estimation. per is devoted to such an analysis and to a discussion of the intrinsic limitations of the method.