It was shown some time ago that the space-time and the space-frequency degrees of polarization of a stochastic electromagnetic beam are not equivalent to each other. It is not possible, in general, to obtain a formal relationship between them. In this Letter, we discuss certain conditions under which they are directly related. These conditions lead to the concept of polarization-purity. If an optical beam obeys these conditions, its space-frequency degree of polarization has the same value at all frequencies present in the spectrum, and the value is equal to the space-time degree of polarization.
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