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The small signal-to-noise ratio (SNR) of conventional laser induced fluorescence (LIF) measurements using a continuous wave laser, either diode or dye, is typically overcome by amplitude modulating the laser at a specific frequency and then using lock-in amplification to extract the signal from measurement noise. Here, we present LIF measurements of the neutral helium velocity distribution function in an rf plasma using frequency modulated (FM) laser injection. A pulse train of 100% amplitude modulation is generated synthetically with a random sequence of pulse lengths. The FM signal then drives an acoustic optic modulator placed in the path of the injection beam in an LIF measurement. The signal from a fast photomultiplier tube is digitized and cross-correlated with the known modulation signal. The resultant FM-based LIF signal outperforms a conventional lock-in-based LIF measurement on the same plasma in terms of SNR and precision.