Assessment of lidar inversion errors for homogeneous atmospheres

Abstract

The inversion of lidar returns from homogeneous atmospheres has been done customarily through the well-known slope method. The logarithmic operation over the range-corrected and system-normalized received signal used in this method introduces a bias in the statistics of the noise-affected processed signal that can severely distort the estimates of the atmospheric attenuation and backscatter coefficients under measurement. It is shown that a fitting of the theoretically expected exponential signal to the range-corrected received one, using as the initial guess the results provided by the slope method and a least-squares iterative procedure, can yield enhanced accuracy under low signal-to-noise ratios and especially in moderate-to-high extinction conditions.

Statistics of the slope-method estimator

“…If the signal strength P͑R͒ is typically more than 50 photons over the integration time, as is always the case, the statistics of the observation-noise random variable N i , which merges into single-body signalinduced dark-current shot noises and electronic thermal noise, can be assumed continuous Gaussian ones 8 ͑computation of the system's total noise variance is also given in the same reference͒. Consequently there is some likelihood, particularly higher for decreasing SNR's, that a noise realization of N i approaching the noise floor ϪP i at the ith observation cell R i causes either a large noise spike in N i Ј or even a singularity in Eq.…”

“…Because for a given backscatter lidar system we can always relate the product K␤ in Eq. ͑1͒ ͓or, alternatively, K if the pair ͑␣, ␤͒ is related by means of some look-up visibility table 14,15 to the SNR at the starting point R min of full overlap between the laser beam and the telescope field of view 7,8 ͓hereafter SNR͑R min ͔͒, we can indistinctly parameterize our plots in terms of SNR͑R min ͒'s or K's. Selection of SNR͑R min ͒ instead of K in Fig.…”

Piece-wise variance method for signal-to-noise ratio estimation in elastic/Raman lidar signals

“…Observation noise corrupting measured elastic/Raman signals at the receiver output can be of different statistical origins, namely, shot photo-induced, shot dark-current, and thermal ( [2], Ap. A and [3], Ap.…”

Morphological tools for range-interval segmentation of elastic lidar signals

“…Spatial segmentation of elastic signals is also of application in the so-called slice method [2], in which the atmosphere is divided into layers where the well-known slope method or, alternatively, exponential-curve fitting methods [3] are successively applied to adjacent range-intervals of homogeneous characteristics in order to retrieve a piece-wise range-dependent extinction estimate. Likewise, inherent inhomogeneous inversion algorithms such as the Klett's method and its variants [4] can be applied to different range sub-intervals of the whole inversion range with different calibrations and correlating hypotheses in each one of these segments.…”