Figure of merit and fundamental range limitations in surface sensing direct-detection mid-infrared random-modulation continuous-wave lidar

We perform maximum range calculations for surface sensing direct-detection mid-infrared Random-Modulation-Continuous-Wave (RM-CW) lidar, and propose a system's figure of merit. In this type of lidar, noise can be additive and determined by detector's noise given by its specific detectivity D, area, and integration time. Fundamental limits of the sensing range are then imposed by diffraction, provided that the Background-Limited Infrared Photodetection (BLIP) limit (controlled by the field-of-view) is not exceeded. There is no dependence on a specific pseudorandom code (PRC) used since noise spectral density is assumed to be independent of frequency. Under most favorable conditions, including no losses due to optics or atmospheric attenuation, an object of angularly uniform unity reflectance and size not less than the laser beam can be detected within 1s with a 20 cm-diameter telescope and a signal-to-noise ratio of one from a distance of ∼200 km if a cooled detector and a laser emitting 500 mW cw at 5 μm are used. For an integration time of 0.1 ms (which is well below a typical atmospheric correlation time), or a room-temperature detector, the maximum range reduces to ∼20 km. As the technology of Quantum-Cascade lasers (QCLs) advances, the maximum range of several tens of kilometers can be expected in this type of lidar with all-thermoelectrically-cooled semiconductor components, and - perhaps after some modifications in the technique - about 1km with all-room-temperature components. To enable an absolute or relative overall performance evaluation of individual systems, we propose a lidar figure of merit, L_B*, analogous to specific detectivity (D*) commonly used in infrared detectors. Its fundamental limit (given by the laser power, wavelength, and detector's detectivity) and relation to the maximum sensing range are derived.