  The synchrotron radiation is commonly known to be completely linearly
polarized when observed in the orbital plane of the synchrotron motion. Under
actual experimental conditions, however, the degree of polarization of the
synchrotron radiation may be lower than the ideal 100%. We demonstrate that
even tiny impurities of polarization of the incident radiation can drastically
affect the polarization of the elastically scattered light. We propose to use
this effect as a precision tool for the diagnostics of the polarization purity
of the synchrotron radiation. Two variants of the diagnostics method are
proposed. The first one is based on the polarization measurements of the
scattered radiation and relies on theoretical calculations of the transition
amplitudes. The second one involves simultaneous measurements of the
polarization and the cross sections of the scattered radiation and is
independent of theoretical amplitudes.
