Fluorescence excited in CaF by fixed-frequency lines of a krypton-ion laser has been recorded at high resolution by Fourier transform spectrometry. The main aim-to characterize the lowest 2 Delta state-was realized, following the analysis of lines of transitions between levels of C2 Pi , excited by the laser, and B'2 Delta . The spectra also provide some new information about C2 Pi , and the results confirm recent work which shows that the accepted vibrational numbering in D2 Sigma + must be increased by one. Constants, cm-1, for B'2 Delta are as follows: Te, 21573.93; Ae, 12.34; omega e, 528.57; Be, 0.32950.