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Two-photon fluorescence traces used for picosecond pulse-width measurement are analyzed and described by intensity correlation functions, also known as second-order coherence functions. The correlation functions and the fluorescence traces are discussed for three special types of light emission and calculated in detail for a three-mode laser model in free-running, mode-locking, and FM-like operation. A rigorous calculation for the fluorescence intensity excited by a laser oscillating in a large number of modes with arbitrary amplitudes and phases is also given. The shapes of the fluorescence traces are found to be essentially the same for both, free-running and ideally mode-locked emission, but with different contrast ratios of 1.5 : 1 and 3 : 1, respectively.