Spectral noise due to sampling errors in Fourier-transform spectroscopy

An assessment is made of the spectral noise in Fourier-transform spectroscopy caused by sampling errors in the interferogram acquisition. Numerical evaluations are performed in the case of the REFIR (radiation explorer in the far infrared) instrument developed for the measurement of the long-wavelength Earth emissions from satellite platforms. In this case the slow response of a room-temperature pyroelectric detector, the relatively short acquisition time, the broadband operation, and the wish for a relaxed requirement of the mirror drive accuracy make sampling error an important issue. Different sampling methods can be considered for reduction of the spectral noise induced by sampling errors. The effects of different sampling methods are quantified and discussed for the selection of the most-suitable option for this instrument. We find that only sampling methods that introduce some compensation (either analog or digital) of the frequency dependence of amplitude and phase components of the acquisition-system responsivity provide satisfactory results. In particular, the equal time sampling followed by a digital filter and numerical resampling has been examined minutely with a simulation model used to perform sensitivity tests of the main parameters that characterize the procedure.     

Performance degradation of a Michelson interferometer due to random sampling errors

The performance of a standard Michelson interferometer is degraded by disturbances that cause the interferogram signal to be sampled at nonconstant time intervals. A formula that shows how the power spectrum of the random disturbances interacts with the signal to contaminate different regions of the measured spectrum is derived for the spectral noise. The sampling noise does not look conventionally noiselike because it is correlated over large regions of the measured spectrum, and adjustment of the unbalanced background interferogram to match the size of the balanced background interferogram minimizes the sampling-noise amplitude.     

Retrieval of physical particle properties from lidar observations of extinction and backscatter at multiple wavelengths

Tropospheric height profiles of five particle backscatter coefficients between 355 and 800 nm and particle extinction coefficients at 355 and 532 nm measured with a multiple-wavelength backscatter lidar and a dual-wavelength Raman lidar are presented. From these data microphysical particle parameters are determined by a specifically designed inversion algorithm.     

Estimate of the incoherent-scattering contribution to lidar backscatter from clouds

Lidar backscatter from clouds in the Delft University of Technology experiment is complicated by the fact that the transmitter has a narrow beam width, whereas the receiver has a much wider one. The issue here is whether reception of light scattered incoherently by cloud particles can contribute appreciably to the received power. The incoherent contribution can come from within as well as from outside the transmitter beam but in any case is due to at least two scattering processes in the cloud that are not included in the coherent forward scatter that leads to the usual exponentially attenuated contribution from single-particle backscatter. It is conceivable that a sizable fraction of the total received power within the receiver beam width is due to such incoherent-scattering processes. The ratio of this contribution to the direct (but attenuated) reflection from a single particle is estimated here by means of a distorted-Born approximation to the wave equation (with an incident cw monochromatic wave) and by comparison of the magnitude of the doubly scattered to that of the singly scattered flux. The same expressions are also obtained from a radiative-transfer formalism. The ratio underestimates incoherent multiple scattering when it is not small. Corrections that are due to changes in polarization are noted.     

Potential of lidar backscatter data to estimate solar aerosol radiative forcing

The potential to estimate solar aerosol radiative forcing (SARF) in cloudless conditions from backscatter data measured by widespread standard lidar has been investigated. For this purpose 132 days of sophisticated ground-based Raman lidar observations (profiles of particle extinction and backscatter coefficients at 532 nm wavelength) collected during two campaigns [the European Aerosol Research Lidar Network (EARLINET) and the Indian Ocean Experiment (INDOEX)] were analyzed. Particle extinction profiles were used as input for radiative transfer simulations with which to calculate the SARF, which then was plotted as a function of the column (i.e., height-integrated) particle backscatter coefficient (beta(c)). A close correlation between the SARF and beta(c) was found. SARF-beta(c) parameterizations in the form of polynomial fits were derived that exhibit an estimated uncertainty of +/-(10-30)%. These parameterizations can be utilized to analyze data of upcoming lidar satellite missions and for other purposes. The EARLINET-based parameterizations can be applied to lidar measurements at mostly continental, highly industrialized sites with limited maritime influence (Europe, North America), whereas the INDOEX parameterizations rather can be employed in polluted maritime locations, e.g., coastal regions of south and east Asia.     

Analysis of lidar backscatter profiles in optically thin clouds

The solution of the lidar equation for profiles of backscatter and extinction in optically thin clouds is constrained by values of the cloud transmittance determined from the elastically scattered lidar signals below and above the cloud. The method is extended to those cases in which an aerosol layer lies below or above the cloud layer. Examples are given in both cases. An analytical expression for the average lidar ratio in the cloud is derived for those cases in which molecular scattering is significant.     

Principal component analysis applied to multiwavelength lidar aerosol backscatter and extinction measurements

The use of powerful Raman backscatter lidars enables one to measure the stratospheric aerosol extinction profile independently of the backscatter, thereby obtaining additional information to aid in retrieving the physical characteristics of the sampled aerosol. We used principal component analysis to construct a self-consistent method for the retrieval of aerosol bulk physical and optical properties from multiwavelength elastic and/or inelastic Raman backscatter lidar signals. The procedure is applied to synthetic and actual lidar signals. We found that aerosol surface area and volume can be usefully estimated and that the use of Raman-derived extinction data leads to a notable improvement in the accuracy of the estimations.     

Target-plane intensity approximation for apertured Gaussian beams applied to heterodyne backscatter lidar systems

With an application in lidar systems in mind, we investigate the effects of transmit-aperture truncation of Gaussian beams by employing the extended Huygens-Fresnel principle. We derive an approximation to the top-hat aperture-transmission function by defining an abstract Gaussian aperture-transmission function. The two fitting parameters of the latter are found when the beam radius and the on-axis intensity for both aperture cases are equated in the observation plane. Bounds for the applicability of the approximation are established, and its accuracy and usefulness is demonstrated through application to the calculation of the return signal of a heterodyne lidar system.     

Bounds on least-squares four-parameter sine-fit errors due toharmonic distortion and noise

Least-squares sine-fit algorithms are used extensively in signal-processing applications. The parameter estimates produced by such algorithms are subject to both random and systematic errors when the record of input samples consists of a fundamental sine wave corrupted by harmonic distortion or noise. The errors occur because, in general, such sine-fits will incorporate a portion of the harmonic distortion or noise into their estimate of the fundamental. Bounds are developed for these errors for least-squares four-parameter (amplitude, frequency, phase, and offset) sine-fit algorithms. The errors are functions of the number of periods in the record, the number of samples in the record, the harmonic order, and fundamental and harmonic amplitudes and phases. The bounds do not apply to cases in which harmonic components become aliased     

Sensitivity of a lidar inversion algorithm to parameters relating atmospheric backscatter and extinction

A solution of the single-scattering lidar equation requires a relationship between the coefficients of backscatter beta(r) and extinction sigma(r) to be of the form beta(r) = C2sigma(r)k, where C2 and k are parameters independent of range r. The sensitivity of a particular lidar inversion algorithm to uncertainties in C2 and k is investigated using a measured lidar return which indicated the atmosphere to be essentially horizontally homogeneous during a reduced visibility condition. Starting with the measured power returned as a function of range, extinction coefficients and average visibilities are calculated using the inversion algorithm for different values of C2 and k and compared with those inferred from the lidar return using the slope method. The calculated extinction coefficients (and visibilities) were found to be extremely sensitive to uncertainties in C2. This questions the usefulness of the lidar inversion algorithm for aerosol extinction applications when the air mass characteristics change along the measurement path.     

Particle backscatter, extinction, and lidar ratio profiling with Raman lidar in south and north China

Aerosol Raman lidar observations of profiles of the particle extinction and backscatter coefficients and the respective extinction-to-backscatter ratio (lidar ratio) were performed under highly polluted conditions in the Pearl River Delta (PRD) in southern China in October 2004 and at Beijing during a clear period with moderately polluted to background aerosol conditions in January 2005. The anthropogenic haze in the PRD is characterized by volume light-extinction coefficients of particles ranging from approximately 200 to 800 Mm(-1) and lidar ratios mostly between 40 and 55 sr (average of 47+/-6 sr). Almost clean air masses were observed throughout the measurements of the Beijing campaign. These air masses originated from arid desert-steppe-like regions (greater Gobi area). Extinction values usually varied between 100 and 300 Mm(-1), and the lidar ratios were considerably lower (compared with PRD values) with values mostly from 30 to 45 sr (average of 38+/-7 sr). Gobi dust partly influenced the observations. Unexpectedly low lidar ratios of approximately 25 sr were found for a case of background aerosol with a low optical depth of 0.05. The low lidar ratios are consistent with Mie-scattering calculations applied to ground-based observations of particle size distributions.     

Estimating errors in design sensitivities

Design sensitivities are useful quantities that may be efficiently computed by finite element analysis, from the field solution and its adjoint. However, the computed sensitivities are subject to discretization error. A method is described for the a posteriori estimation of this error, making use of the properties of hierarchal finite elements. The method is applied to the sensitivities of microwave scattering parameters, computed with three-dimensional tetrahedral elements. Results for a waveguide filter, a waveguide transformer, and a magic T demonstrate the quality of the estimator.     

Influence of daylight and noise current on cloud and aerosol observations by spaceborne elastic scattering lidar

The influence of daylight and noise current on cloud and aerosol observations by realistic spaceborne lidar was examined by computer simulations. The reflected solar radiations, which contaminate the daytime return signals of lidar operations, were strictly and explicitly estimated by accurate radiative transfer calculations. It was found that the model multilayer cirrus clouds and the boundary layer aerosols could be observed during the daytime and the nighttime with only a few laser shots. However, high background noise and noise current make it difficult to observe volcanic aerosols in middle and upper atmospheric layers. Optimal combinations of the laser power and receiver field of view are proposed to compensate for the negative influence that is due to these noises. For the computer simulations, we used a realistic set of lidar parameters similar to the Experimental Lidar in-Space Equipment of the National Space Development Agency of Japan.     

The errors due to mismatch in high-frequency channels

The values of the correction factor in the theoretical formula for the overall error when partial components are summed geometrically, are validated. Translated from Izmeritel'naya Tekhnika, No. 12, pp. 42–43, December, 1998.     

Aerosol lidar intercomparison in the framework of the EARLINET project. 3. Raman lidar algorithm for aerosol extinction, backscatter, and lidar ratio

An intercomparison of the algorithms used to retrieve aerosol extinction and backscatter starting from Raman lidar signals has been performed by 11 groups of lidar scientists involved in the European Aerosol Research Lidar Network (EARLINET). This intercomparison is part of an extended quality assurance program performed on aerosol lidars in the EARLINET. Lidar instruments and aerosol backscatter algorithms were tested separately. The Raman lidar algorithms were tested by use of synthetic lidar data, simulated at 355, 532, 386, and 607 nm, with realistic experimental and atmospheric conditions taken into account. The intercomparison demonstrates that the data-handling procedures used by all the lidar groups provide satisfactory results. Extinction profiles show mean deviations from the correct solution within 10% in the planetary boundary layer (PBL), and backscatter profiles, retrieved by use of algorithms based on the combined Raman elastic-backscatter lidar technique, show mean deviations from solutions within 20% up to 2 km. The intercomparison was also carried out for the lidar ratio and produced profiles that show a mean deviation from the solution within 20% in the PBL. The mean value of this parameter was also calculated within a lofted aerosol layer at higher altitudes that is representative of typical layers related to special events such as Saharan dust outbreaks, forest fires, and volcanic eruptions. Here deviations were within 15%.     

Turbulence-induced measurement errors in coherent differential absorption lidar ground systems

The presence of atmospheric refractive turbulence makes it necessary to use simulations of beam propagation to examine the uncertainty added to the differential absorption lidar (DIAL) measurement process of a practical heterodyne lidar. The inherent statistic uncertainty of coherent return fluctuations in ground lidar systems profiling the atmosphere along slant paths with large elevation angles translates into a lessening of accuracy and sensitivity of any practical DIAL measurement. This technique opens the door to consider realistic, nonuniform atmospheric conditions for any DIAL instrument configuration.     

Aerosol observations by lidar in the nocturnal boundary layer

Aerosol observations by lidar in the nocturnal boundary layer (NBL) were performed in Potenza, Southern Italy, from 20 January to 20 February 1997. Measurements during nine winter nights were considered, covering a variety of boundary-layer conditions. The vertical profiles of the aerosol backscattering coefficient at 355 and 723.37 nm were determined through a Klett-modified iterative procedure, assuming the extinction-to-backscattering ratio within the NBL has a constant value. Aerosol average size characteristics were retrieved from almost simultaneous profiles of the aerosol backscattering coefficient at 355 and 723.37 nm, the measurements being consistent with an accumulation mode radius not exceeding 0.4 mum. Similar results in terms of aerosol sizes were obtained from measurements of the extinction-to-backscattering ratio profile at 355 nm performed on six nights during the measurement campaign. Backscattering profiles at 723.37 nm were also converted into profiles of aerosol liquid water content.