Signal-to-noise ratio in direct-detection mid-infrared Random-Modulation Continuous-Wave lidar in the presence of colored additive noise

We have derived the signal-to-noise ratio in direct-detection Random-Modula tion Continuous-Wave (RM-CW) lidar in the presence of colored additive nois e. In contrast to a known formula derived for the photon shot-noise regime, which may adequately describe experimental conditions in the near-infrared , our result is applicable mainly at longer, mid-infrared wavelengths. Unli ke the former formula, our result is explicitly dependent on the pseudorand om code (PRC) used for modulation. Three known modulation codes, the M-, A1 -, and A2-sequence are compared and shown to have practically equivalent si gnal and noise properties (provided that clutter inherent in the A1- and A2 -sequence is neglected), except that the M- sequence has a near-zero-freque ncy noise pickup that degrades its performance in real measurement systems. This difference provides an alternative explanation of a better performanc e of the A1-/A2-sequence in a previous experiment [3], carried out in the n ear-infrared. It suggests the presence of an additive noise component and t hus some applicability of our result also in near-infrared lidar. A need fo r balanced sequences-particularly in the mid-infrared-is explained, althoug h in a different way than previously suggested in near-infrared, photon sho t noise-limited lidar. Additional, sinusoidal carrier modulation is conside red and shown to have significant drawbacks. Our results allow comparison o f given modulation sequences, and construction of improved ones. Interestin gly, the improved sequences will possess less "random" characteristics, see mingly against the underlying concept of random modulation. (C) 2001 Optica l Society of America.