The two-step persistent spectral hole burning (PSHB) of a hole in the inhomogeneous distribution function (IDF) of the zero-phonon line (ZPL) optical transition frequencies in a three-level system by two successive light pulses, in the case of an exponentially increasing and decreasing first coherent pulse and an infinitely short second pulse, is considered. The time-dependent ZPL in the luminescence spectrum in the recording scheme with the time gate in front of the spectrometer with high resolution in the case of exponential opening and closing of the time gate is calculated. It is shown that the time-dependent ZPL in the luminescence spectrum is described by a formula which is analogous to the formula describing the spectral hole in IDF. The effect of compensation of the natural linewidth of the excited level and the parameter describing the exponential increase of the transparency of the time gate is presented.
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