Estimation method for serial dilution experiments.

Titration of microorganisms in infectious or environmental samples is a corner stone of quantitative microbiology. A simple method is presented to estimate the microbial counts obtained with the serial dilution technique for microorganisms that can grow on bacteriological media and develop into a colony. The number (concentration) of viable microbial organisms is estimated from a single dilution plate (assay) without a need for replicate plates. Our method selects the best agar plate with which to estimate the microbial counts, and takes into account the colony size and plate area that both contribute to the likelihood of miscounting the number of colonies on a plate. The estimate of the optimal count given by our method can be used to narrow the search for the best (optimal) dilution plate and saves time. The required inputs are the plate size, the microbial colony size, and the serial dilution factors. The proposed approach shows relative accuracy well within ±0.1log10 from data produced by computer simulations. The method maintains this accuracy even in the presence of dilution errors of up to 10% (for both the aliquot and diluent volumes), microbial counts between 10(4) and 10(12) colony-forming units, dilution ratios from 2 to 100, and plate size to colony size ratios between 6.25 to 200.

Probability theory for 3-layer remote sensing in ideal gas law environment.

We extend the probability model for 3-layer radiative transfer [Opt. Express 20, 10004 (2012)] to ideal gas conditions where a correlation exists between transmission and temperature of each of the 3 layers. The effect on the probability density function for the at-sensor radiances is surprisingly small, and thus the added complexity of addressing the correlation can be avoided. The small overall effect is due to (a) small perturbations by the correlation on variance population parameters and (b) cancellation of perturbation terms that appear with opposite signs in the model moment expressions.

Regression model for estimating inactivation of microbial aerosols by solar radiation.

The inactivation of pathogenic aerosols by solar radiation is relevant to public health and biodefense. We investigated whether a relatively simple method to calculate solar diffuse and total irradiances could be developed and used in environmental photobiology estimations instead of complex atmospheric radiative transfer computer programs. The second-order regression model that we developed reproduced 13 radiation quantities calculated for equinoxes and solstices at 35(°) latitude with a computer-intensive and rather complex atmospheric radiative transfer program (MODTRAN) with a mean error <6% (2% for most radiation quantities). Extending the application of the regression model from a reference latitude and date (chosen as 35° latitude for 21 March) to different latitudes and days of the year was accomplished with variable success: usually with a mean error <15% (but as high as 150% for some combination of latitudes and days of year). This accuracy of the methodology proposed here compares favorably to photobiological experiments where the microbial survival is usually measured with an accuracy no better than ±0.5 log10 units. The approach and equations presented in this study should assist in estimating the maximum time during which microbial pathogens remain infectious after accidental or intentional aerosolization in open environments.

Probability theory for 3-layer remote sensing radiative transfer model: univariate case.

A probability model for a 3-layer radiative transfer model (foreground layer, cloud layer, background layer, and an external source at the end of line of sight) has been developed. The 3-layer model is fundamentally important as the primary physical model in passive infrared remote sensing. The probability model is described by the Johnson family of distributions that are used as a fit for theoretically computed moments of the radiative transfer model. From the Johnson family we use the SU distribution that can address a wide range of skewness and kurtosis values (in addition to addressing the first two moments, mean and variance). In the limit, SU can also describe lognormal and normal distributions. With the probability model one can evaluate the potential for detecting a target (vapor cloud layer), the probability of observing thermal contrast, and evaluate performance (receiver operating characteristics curves) in clutter-noise limited scenarios. This is (to our knowledge) the first probability model for the 3-layer remote sensing geometry that treats all parameters as random variables and includes higher-order statistics.

A model for inactivation of microbes suspended in the atmosphere by solar ultraviolet radiation.

Solar ultraviolet (UV) light within 280-320 nm (UVB) is the primary cause for virus inactivation in the atmosphere. Only the effect of the direct component has been previously evaluated. We developed a simple regression model to estimate the inactivation of a virus due to direct (unscattered), diffuse (scattered) and total (direct + diffuse) components of solar UV (daily integrated irradiances). The model predicts the maximum number of radiation-days a virus will survive at a given altitude above the ground in rural and urban environments under clear skies. We explored the effect of several environmental variables: visibility, altitude and ground reflectivity. We found that the effect of diffuse radiation on virus inactivation was larger than the direct component. The diffuse irradiance increased with ground albedo (mainly due to reflection of the direct attenuated solar off the ground) and decreased with increased visibility (proportional to aerosol loading in the atmosphere). The diffuse component increased with altitude, but the ratio of diffuse to the total decreased with increased altitude, highlighting the importance of the diffuse component of UV near the ground. Our model may help public health studies in predicting and understanding the effect of environmental parameters on the survival of germs.

Impact of atmospheric boundary layer turbulent temperature fluctuations on remote detection of vapors by passive infrared spectroscopy.

A computational model to simulate the effects of boundary layer isotropic atmospheric turbulence on the radiative transfer process is presented. We perform a large number of simulations with stochastic ambient conditions to estimate the statistics necessary to predict the detection limit of a given trace gas. We find that the radiance and transmittance variability are primarily determined by the optical depth of the emitting atmosphere, and that the relative variability of the transmittance is an order of magnitude smaller than that of the radiance. We estimate that the atmospheric detection limit of a DMMP vapor cloud at 30 meters altitude for a ground-based observer ranges from 3.5 to 12 ppb-m, depending on the horizontal range to the cloud. Addition of uncorrelated detector noise has a disproportionate effect on the detection limit over the spectrally correlated turbulence noise. These calculations appear to be the first predictions of vapor detection limits that explicitly incorporate the effects of turbulence.

Simultaneous estimation of aerosol cloud concentration and spectral backscatter from multiple-wavelength lidar data.

We present a sequential algorithm for estimating both concentration dependence on range and time and backscatter coefficient spectral dependence of optically thin localized atmospheric aerosols using data from rapidly tuned lidar. The range dependence of the aerosol is modeled as an expansion of the concentration in an orthonormal basis set whose coefficients carry the time dependence. Two estimators are run in parallel: a Kalman filter for the concentration range and time dependence and a maximum-likelihood estimator for the aerosol backscatter wavelength and time dependence. These two estimators exchange information continuously over the data-processing stream. The state model parameters of the Kalman filter are also estimated sequentially together with the concentration and backscatter. Lidar data collected prior to the aerosol release are used to estimate the ambient lidar return. The approach is illustrated on atmospheric backscatter long-wave infrared (CO2) lidar data.

Radiative transfer model for aerosols at infrared wavelengths for passive remote sensing applications: revisited.

We introduced a two-dimensional radiative transfer model for aerosols in the thermal infrared [Appl. Opt.45, 6860-6875 (2006)APOPAI0003-693510.1364/AO.45.006860]. In that paper we superimposed two orthogonal plane-parallel layers to compute the radiance due to a two-dimensional (2D) rectangular aerosol cloud. In this paper we revisit the model and correct an error in the interaction of the two layers. We derive new expressions relating to the signal content of the radiance from an aerosol cloud based on the concept of five directional thermal contrasts: four for the 2D diffuse radiance and one for direct radiance along the line of sight. The new expressions give additional insight on the radiative transfer processes within the cloud. Simulations for Bacillus subtilis var. niger (BG) bioaerosol and dustlike kaolin aerosol clouds are compared and contrasted for two geometries: an airborne sensor looking down and a ground-based sensor looking up. Simulation results suggest that aerosol cloud detection from an airborne platform may be more challenging than for a ground-based sensor and that the detection of an aerosol cloud in emission mode (negative direct thermal contrast) is not the same as the detection of an aerosol cloud in absorption mode (positive direct thermal contrast).

Lidar detection algorithm for time and range anomalies.

A new detection algorithm for lidar applications has been developed. The detection is based on hyperspectral anomaly detection that is implemented for time anomaly where the question "is a target (aerosol cloud) present at range R within time t(1) to t(2)" is addressed, and for range anomaly where the question "is a target present at time t within ranges R(1) and R(2)" is addressed. A detection score significantly different in magnitude from the detection scores for background measurements suggests that an anomaly (interpreted as the presence of a target signal in space/time) exists. The algorithm employs an option for a preprocessing stage where undesired oscillations and artifacts are filtered out with a low-rank orthogonal projection technique. The filtering technique adaptively removes the one over range-squared dependence of the background contribution of the lidar signal and also aids visualization of features in the data when the signal-to-noise ratio is low. A Gaussian-mixture probability model for two hypotheses (anomaly present or absent) is computed with an expectation-maximization algorithm to produce a detection threshold and probabilities of detection and false alarm. Results of the algorithm for CO(2) lidar measurements of bioaerosol clouds Bacillus atrophaeus (formerly known as Bacillus subtilis niger, BG) and Pantoea agglomerans, Pa (formerly known as Erwinia herbicola, Eh) are shown and discussed.

Radiative transfer model for aerosols in infrared wavelengths for passive remote sensing applications.

A comprehensive analytical radiative transfer model for isothermal aerosols and vapors for passive infrared remote sensing applications (ground-based and airborne sensors) has been developed. The theoretical model illustrates the qualitative difference between an aerosol cloud and a chemical vapor cloud. The model is based on two and two/four stream approximations and includes thermal emission-absorption by the aerosols; scattering of diffused sky radiances incident from all sides on the aerosols (downwelling, upwelling, left, and right); and scattering of aerosol thermal emission. The model uses moderate resolution transmittance ambient atmospheric radiances as boundary conditions and provides analytical expressions for the information on the aerosol cloud that is contained in remote sensing measurements by using thermal contrasts between the aerosols and diffused sky radiances. Simulated measurements of a ground-based sensor viewing Bacillus subtilis var. niger bioaerosols and kaolin aerosols are given and discussed to illustrate the differences between a vapor-only model (i.e., only emission-absorption effects) and a complete model that adds aerosol scattering effects.

Improving the linearity of infrared diffuse reflection spectroscopy data for quantitative analysis: an application in quantifying organophosphorus contamination in soil.

Diffuse reflection data are presented for ethyl methylphosphonate in a fine Utah dirt sample as a model system for organophosphate-contaminated soil. The data revealed a chemometric artifact when the spectra were represented in Kubelka-Munk units that manifests as a linear dependence of spectral peak height on variations in the observed baseline position (i.e., the position of the observed transmission intensity where no absorption features occur in the sample spectrum). We believe that this artifact is the result of the mathematical process by which the raw data are converted into Kubelka-Munk units, and we developed a numerical strategy for compensating for the observed effect and restoring chemometric precision to the diffuse reflection data for quantitative analysis while retaining the benefits of linear calibration afforded by the Kubelka-Munk approach. We validated our Kubelka-Munk correction strategy by repeating the experiment using a simpler system--pure caffeine in potassium bromide. The numerical preprocessing includes conventional multiplicative scatter correction coupled with a baseline offset correction that facilitates the use of quantitative diffuse reflection data in the Kubelka-Munk formalism for the quantitation of contaminants in a complex soil matrix, but is also applicable to more fundamental diffuse reflection quantitative analysis experiments.

Comparison between orthogonal subspace projection and background subtraction techniques applied to remote-sensing data.

The basic measurement equation r = B + alphad + n is solved for alpha (the weight or abundance of the spectral target vector d) by two methods: (a) by subtracting the stochastic spectral background vector B from the spectral measurement's vector r (subtraction solution) and (b) by orthogonal subspace projection (OSP) of the measurements to a subspace orthogonal to B (the OSP solution). The different geometry of the two solutions and in particular the geometry of the noise vector n is explored. The angular distribution of the noise angle between B and n is the key factor for determining and predicting which solution is better. When the noise-angle distribution is uniform, the subtraction solution is always superior regardless of the orientation of the spectral target vector d. When the noise is more concentrated in the direction orthogonal to B, the OSP solution becomes better (as expected). Simulations and one-dimensional hyperspectral measurements of vapor concentration in the presence of background radiation and noise are given to illustrate these two solutions.

Measurements of atmospheric brightness temperature fluctuations and their implications on passive remote sensing.

Passive remote sensing of airborne chemicals at infrared wavelengths may be limited by temporal fluctuations in atmospheric brightness temperatures deltaT(t). Brightness temperatures in two infrared spectral bands were simultaneously measured on clear and cloudy days along three lines of sights. For time windows t < 3-5 s, deltaT(t) remained constant at the sensor noise level and rapidly increased as t increased. The fluctuation time scale for the cloudy day was longer than for the clear day. The long correlation time for T(t) limits the utility of signal averaging in improving detection signal-to-noise ratio (SNR). The simultaneous outputs of the two spectral channels during the clear day exhibited no spectral coherence at t < 3 s and limited coherence at t > 30 s. Measurements during the cloudy day were largely coherent. Consequently, band-by-band subtraction may have limited benefits.

Noise assessment of a Fourier transform infrared spectroradiometer subject to the stability of a conventional laboratory blackbody source.

A method is described for the measurement of the noise-equivalent spectral radiance (NESR) of Fourier transform infrared (FTIR) spectroradiometers at all wave numbers of a selected range. The method requires minimal detailed knowledge of the sensor and no support equipment beyond a blackbody source. The NESRs of the FTIR spectroradiometer are determined at every wave-number increment in the 700-1300 cm(-1) range, for six resolutions, with a conventional blackbody source and ensembles of differential spectra. The NESRs are well behaved and consistent with the expected dependence on resolution; however, they depend on source temperature at the highest (1 cm(-1)) and lowest (32 cm(-1)) resolutions, with little or no statistical dependence at intermediate resolutions. Residual source drift is shown to be the likely cause of the dependence at 1 cm(-1); the dependence on the source at 32 cm(-1) resolution is shown to be most probably due to photon noise. At intermediate resolutions the sensor noise is dominant.

Detection, identification, and estimation of biological aerosols and vapors with a Fourier-transform infrared spectrometer.

Two experiments were conducted with a Fourier-transform infrared (FTIR) spectrometer. The purpose of the first experiment was to detect and identify Bacillus subtilis subsp. niger (BG) bioaerosol spores and kaolin dust in an open-air release for which the thermal contrast between the aerosol temperature and background brightness temperature is small. The second experiment estimated the concentration of a small amount of triethyl phosphate (TEP) vapor in a closed chamber in which an external blackbody radiation source was used and where the thermal contrast was large. The deduced BG (TEP) extinction spectrum (identification) showed an excellent match to the library BG (TEP) extinction spectrum. Analysis of the time sequence of the measurements coincided well with the presence (detection) of the BG during the measurements, and the estimated concentration of time-dependent TEP vapor was excellent. The data were analyzed with hyperspectral detection, identification, and estimation algorithms. The algorithms were based on radiative transfer theory and statistical signal-processing methods. A subspace orthogonal projection operator was used to statistically subtract the large thermal background contribution to the measurements, and a robust maximum-likelihood solution was used to deduce the target (aerosol or vapor cloud) spectrum and estimate its mass-column concentration. A Gaussian-mixture probability model for the deduced mass-column concentration was computed with an expectation-maximization algorithm to produce the detection threshold, the probability of detection, and the probability of false alarm. The results of this study are encouraging, as they suggest for the first time to the authors' knowledge the feasibility of detecting biological aerosols with passive FTIR sensors.

Remote detection of biological aerosols at a distance of 3 km with a passive Fourier transform infrared (FTIR) sensor.

Bio-aerosols containing Bacillus subtilis var. niger (BG) were detected at a distance of 3 km with a passive Fourier Transform InfraRed (FTIR) spectrometer in an open-air environment where the thermal contrast was low (~ 1 K). The measurements were analyzed with a new hyperspectral detection, identification and estimation algorithm based on radiative transfer theory and advanced signal processing techniques that statistically subtract the undesired background spectra. The results are encouraging as they suggest for the first time the feasibility of detecting biological aerosols with passive FTIR sensors. The number of detection events was small but statistically significant. We estimate the false alarm rate for this experiment to be 0.0095 and the probability of detection to be 0.61 when a threshold of detection that minimizes the sum of the probabilities of false alarm and of missed detection is chosen.

Optimized differential absorption radiometer for remote sensing of chemical effluents.

A differential absorption radiometer sensor that was optimized for near-perfect (to approximately 2%) correction of the absorption by ambient atmospheric species (e.g., water) is described. A target gas is detected remotely by its IR signature viewed through a bandpass filter centered at one of its strongest lines. A second radiometric measurement obtained through a bandpass filter centered at a frequency optimized to match the absorption by an atmospheric trace species (e.g., water vapor) at the sample filter frequency provides near-perfect correction for dominant background absorption effects. The net absorption (emission) by the target gas was obtained through subtraction of the reference signal of the second measurement from that of the target gas measurement. For multiple species detection, additional sample and reference filter pairs can be configured. Predictions show that detection of strong absorbers such as dimethyl methylphosphonate at an optical density below 100 mg/m2 is possible from distances of < 6 km.

Computation of a spectrum from a single-beam fourier-transform infrared interferogram.

A new high-accuracy method has been developed to transform asymmetric single-sided interferograms into spectra. We used a fraction (short, double-sided) of the recorded interferogram and applied an iterative correction to the complete recorded interferogram for the linear part of the phase induced by the various optical elements. Iterative phase correction enhanced the symmetry in the recorded interferogram. We constructed a symmetric double-sided interferogram and followed the Mertz procedure [Infrared Phys. 7,17 (1967)] but with symmetric apodization windows and with a nonlinear phase correction deduced from this double-sided interferogram. In comparing the solution spectrum with the source spectrum we applied the Rayleigh resolution criterion with a Gaussian instrument line shape. The accuracy of the solution is excellent, ranging from better than 0.1% for a blackbody spectrum to a few percent for a complicated atmospheric radiance spectrum.