## Abstract

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.

©2003 Optical Society of America

## 1. Introduction

Infrared spectroscopy and in particular spectroradiometry with infrared Fourier transform spectrometers has demonstrated immense potential and success in the last few decades for monitoring air pollution, industrial stack emissions and routine measurements of trace gas constituents in the atmosphere [1,2]. In the last few years there has been significant interest in the possibility of detection and identification of bacterial spores in an open-air environment with a passive infrared (IR) sensor (spectroradiometer). Many in the scientific community have doubted the possibility of passive IR remote bio-aerosols sensing (*e.g.*, [3]) due to the lack of instrument sensitivity and the overwhelming problem of faint thermal emission (or absorption) by the bacterial spores superimposed on a temporally fluctuating ambient thermal radiance background. In our experiment we used a state-of-the-art Fourier Transform InfraRed (FTIR) Michelson spectrometer [4] where the measured interferograms were converted to spectra [5] and analyzed with advanced hyperspectral detection, identification and estimation algorithms [6]. The sensor acquired data at 5.5 Hz with a noise equivalent spectral radiance of 1·10^{-9} to 2·10^{-9}
*watt*/(*cm*
^{2}
*sr cm*
^{-1}), wavenumber resolution of 3.85 *cm*
^{-1} and a field of view (FOV) of 0.5°. The integration time for each measurement was 0.1 *s*.

Previously [6] we showed excellent detection and identification of a bio-aerosol cloud containing dry *Bacillus subtilis* var. *niger* (BG) and of a kaolin dust cloud. In that experiment the cloud, at a distance of 50 *m*, was contained in a large open chamber (in the shape of a tunnel) which reduced the effect of scattering of sky radiance by the bio-aerosols. The thermal contrast was ~ 5 *K*. The identification of the BG bio-aerosols was excellent (correlation coefficient value of 0.97 between the deduced spectrum and a BG library spectrum). In this study we show a successful attempt to remotely detect a cloud of dry *Bacillus subtilis* var. *niger* aerosol spores at a 3 *km* distance in an open-air environment where the thermal contrast was low (~ 1 *K*) and the cloud drifted with the wind direction. The results of this study are encouraging as they suggest for the first time the feasibility of detecting biological aerosols with passive FTIR sensors.

## 2. Algorithm

Based on a simple three-layer radiative transfer model for a nearly horizontal line of sight where the ambient temperature *T* is assumed to be constant along the line of sight we have developed detection, identification and estimation algorithms [6]. We assume that the aerosol cloud is at equilibrium with the ambient atmosphere and thus its temperature is also *T*. Usually a thermal equilibrium is established very rapidly in the atmosphere. With theses assumptions the spectral measurements *M*(λ) at a wavenumber λ are given by

where *M*
_{0} are the background measurements in the absence of the aerosol cloud (i.e., for ρ=0), *T* is the ambient atmospheric temperature, *B*(λ, *T*) is the Planck function describing the radiance of a blackbody at a temperature *T*, α is the mass extinction coefficient (*m*
^{2}
*mg*
^{-1}) of the bio-aerosol cloud and ρ(*mg m*
^{-2}) is the aerosol cloud mass-column density.

The algorithm estimates the spectral statistics of the background measurements and employs advanced signal processing techniques to statistically “subtract” the background spectra *M*
_{0} from the measurements by employing an orthogonal subspace projection (*OSP*) operator (where the wavenumber dependence is omitted for clarity):

The *OSP* operator projects the measurements into a subspace which is orthogonal to the space spanned by the background measurements. This projection decorrelate the measurements from the background and leave out that portion of the measurements which is expected to be strongly dependent on the signal due to the presence of the bio-aerosol cloud. We view this process as an effective subtraction process where significant part of the background contribution to the measurements is removed (i.e., the first term in Eq. (1)). It is implicitly assumed that the measured background prior to the presence of the cloud within the sensor’s FOV is the same as the background (that can not be measured) when the cloud is present in the FOV. Thus, the subtraction process can be regarded as statistical subtraction.

We produce a spectrum for each of the measurements and correlate it with a library reference spectrum (*e.g.*, a BG absorption spectrum). We declare a detection event when the correlation coefficient exceeds a pre-selected threshold (a measure of a match). We are exploring whether other measures of a match can be superior to the use of a correlation coefficient. The mass-column density of the bio-aerosol cloud is estimated by computing a maximum-likelihood (*ML*) solution (which is the well known minimum least-squares solution when the noise is a white noise) for each of the possible realizations of the measured background spectra (we may have hundreds of background spectra) and then computing an expectation (a weighted average) of the mass-column density for each of the measurements. In the *ML* solution we have many wavenumbers for each measured spectrum and only one unknown (the mass-column density for that measurement). Thus, the estimate of mass-column density is very robust and the system of equations is over-determined.

To assess the probabilities of detection and false alarm we assume that the desired signal, noise and background all follow a Gaussian mixture model (normally distributed statistics). A detection threshold computed with the probability model is used (Section 4) to divide the estimated mass-column density for each of the measurements into two distinct classes: (1) cloud is present or (2) cloud is absent.

Detection models are based on constructing a test statistic derived from the probability density function (*pdf*) of the data (mass-column density, ρ), which is contaminated with noise. The noise may consist of random instrument noise and interference (structured noise) components from “look alike” targets that are unwanted and can obscure the desired target. The objective of the test statistic is to choose between two hypotheses; *H*
_{0} and *H*
_{1} regarding the data. In our experiment the desired target-signal, *H*
_{1}, is induced by the mass-column density of a BG cloud when the cloud is within the sensor’s FOV in addition to the presence of noise in the measurements. The null hypothesis *H*
_{0} is that the data does not contain the target-signal of interest (i.e., the BG cloud is not within the sensor’s FOV) and consists of only noise and interference (background). A *pdf* model for the two hypotheses enables us to compute probabilities of detection and false alarm and to set a threshold for detection that separates the two hypotheses.

We assume a mixture model for the *pdf* of ρ given by

where *pdf* (ρ | *H*
_{0}) and *pdf* (ρ | *H*
_{1}) are the conditional probabilities for the mass-column concentration ρ under the *H*
_{0} and *H*
_{1} assumptions, and *w*
_{0} is the prior probability *P*(*H*
_{0}). We assume normal (Gaussian) *pdf*

where µ and σ are the mean and standard deviation of a normal *pdf*. Thus, the *pdf* for the two hypotheses in the Gaussian mixture model (Eq. 3) are given by

$$\mathit{pdf}(\rho \mid {H}_{1})=N\left(\rho ;{\mu}_{1},{\sigma}_{1}^{2}\right)$$

We estimate the five parameters (ω_{0}, µ_{0}, σ_{0}, µ_{1}, σ_{1}) with an Expectation-Maximization (*EM*) algorithm [7]. The *EM* algorithm is based on two stages; expectation and maximization. In the expectation stage we formulate our “expectation” that the sampled data ρ behave according the model Eq. (3) with initial guess for the parameter set (ω_{0}, µ_{0}, σ_{0}, µ_{1}, σ_{1}). Thus, in the expectation stage we construct the probabilities (Eq. 6) that the sampled data belong to category *H*
_{0} and to category *H*
_{1} respectively

$$\mathit{pdf}({H}_{1}\mid \rho )=\frac{\mathit{pdf}\left({H}_{1},\rho \right)}{\mathit{pdf}\left(\rho \right)}=\frac{\left(1-{w}_{0}\right)\mathit{pdf}(\rho \mid {H}_{1})}{\mathit{pdf}\left(\rho \right)}$$

In the maximization stage we compute a maximum likelihood estimate of the parameters (ω_{0}, µ_{0}, σ_{0}, µ_{1}, σ_{1}) for the expected *pdf’s* (Eq. 6) given by

$${\mu}_{0}={w}_{0}^{-1}\int \mathit{pdf}({H}_{0}\mid \rho )\rho d\rho $$

$${\mu}_{1}={\left(1-{w}_{0}\right)}^{-1}\int \mathit{pdf}({H}_{1}\mid \rho )\rho d\rho $$

$${\sigma}_{0}^{2}={w}_{0}^{-1}\int \mathit{pdf}({H}_{0}\mid \rho ){\left(\rho -{\mu}_{0}\right)}^{2}d\rho \text{}$$

$${\sigma}_{1}^{2}={\left(1-{w}_{0}\right)}^{-1}\int \mathit{pdf}({H}_{1}\mid \rho ){\left(\rho -{\mu}_{1}\right)}^{2}d\rho $$

The solution (ω_{0}, µ_{0}, σ_{0}, µ_{1}, σ_{1}) in Eq. (7) is a function of our initial guess that was used in constructing Eqs. (4–6). Thus, an iterative process between the expectation stage (Eq. 6) and the maximization stage (Eq. 7) is required until a satisfactory convergence for (ω_{0}, µ_{0}, σ_{0}, µ_{1}, σ_{1}) is achieved. The threshold γ is computed from the solution of

The threshold γ minimizes the sum of the probability of false alarm (i.e., deciding *H*
_{1} when *H*
_{0} is true) and the probability of a missed detection (i.e., deciding *H*
_{0} when *H*
_{1} is true).

## 3. Experiment and results

An open-air instantaneous release (a 5 s puff) of 800 *g* of BG was conducted at Dugway Proving Ground, Utah on July 23, 2002 at 2:02:45 AM (local time) ~3 *km* from the FTIR sensor. At 1:59:00, prior to the BG puff release, road dust was generated by two vehicles driven on a 1 *km* dirt road for 45 s. The temperature difference Δ*T* (thermal contrast) between the atmospheric background and the BG aerosols was small (~ 1 *K*) and thus the (observable) absorption of energy by the BG aerosol cloud was very small. The thermal contrast is the difference in brightness temperature computed from spectra at wavenumber ~1300 *cm*
^{-1} (large water vapor absorption) and ~1100 *cm*
^{-1} (maximum absorption of BG). The large absorption from water vapor is effectively a blackbody and thus its brightness temperature gives the ambient air temperature. If Δ*T*=0 a thermo-dynamical equilibrium exists and if we neglect all scattering by the bio-aerosols (*e.g.*, sky radiance and desert thermal emitted radiance), and consider only absorption and emission mechanisms, then no spectral information from the bio-aerosols would be observable. When Δ*T* < 0 (the ambient temperature, which is the cloud temperature is higher than the background brightness temperature) the cloud will emit energy. When Δ*T* > 0 the cloud’s temperature is lower than the background brightness temperature and thus the cloud will absorb energy.

We started to collect measurements at 01:59 and collected a total of 6750 measurements (~21 minutes of data). The sensor was placed on a small scanner to enable manual tracking of the BG cloud while collecting the measurements. The cloud moved with the wind at a speed of ~3 *m s*
^{-1} close to the ground. An elastic-backscatter (aerosol) lidar (XM94) mapped the cloud in real-time showing a drift and wind related variations in peak concentration. At a distance of 3 *km* the footprint of the sensor FOV is about 24 *m* and thus tracking a moving cloud is difficult even for a relatively large cloud (~ 100 *m*). Since the sensor could be moved only manually, the cloud was within the sensor’s FOV for a small fraction of the total number of measurements. The lidar mapping display was used as information for pointing the sensor; pointing that amounted to (literally) blind shots in the dark (~2 AM local time). The lidar information on the cloud dimension and bio-aerosol concentration was used to assist and validate the analysis of the passive sensor measurements.

In Fig. 1 we show the mean correlation coefficient of the detection events as a function of time (upper *x*-axis) and measurement number (lower *x*-axis). The identification portion of the algorithm produced no detection events in regions (d) and (f). The standard deviation (0.0144, 0.0268, 0.0207 and 0.0107) of the mean correlation coefficient (0.8148, 0.8405, 0.8221 and 0.8158) for regions (a), (b), (c) and (e) are quite small (not shown). In Table 1 we summarize the number of detection events for each of the six time regions (a to f) that are noted in the figure. The pre-release region (a) consisted of 1250 measurements of which 8 yielded (false) detection events that may be due the presence of the road dust. Thus, the probability of a false alarm, *P _{FA}*, for region (a) is 8/1250=0.0064. We should note that at measurement number ~2300 (close to the end of region (b)) we changed the elevation angle of the sensor (by -0.2 degrees), a change that may have caused the line of sight to intersect the ground.

We strongly believe that the cluster (noted in Fig. 1) of detection events (total of 25 out of the 33 detection events) in region (b) consists of valid (*i.e.*, real) cloud-detection events due to the fact that this cluster consists of (almost) instantaneous measurements for which either the cloud was within the sensor’s FOV for all the measurement in the cluster or not. We do not think that the detection events (total of 7 out of 1250 measurements) in region (c) are plausible and we think that they are false alarms based on the pointing direction of the sensor and the very similar frequency (7/1250) and spread of events as the false alarm events (8/1250) in the pre-release region (a). It is very probable that the detection events (total of 5 out of 1250 measurements) in region (e) are also false alarm events. The cause of false alarms is partially due to the change of background atmospheric conditions during the measurements for which the statistical background subtraction in the algorithm is not perfect.

We want to emphasize that the probability of detection *P _{D}* in region (b) cannot be stated to be 33/1250 because we do not know for how many measurements

*n*

_{1}(out of the total

*n*measurements) the BG cloud was within the sensor FOV. The number of detection events (

*n*) in region (b) is given by

_{det ections}and one can reasonably assume that the known probability of false alarm for region (a) is the same as the unknown probability of false alarm for region (b). The probability of detection and number of measurements *n*
_{1} is estimated (section 4) with a probability model where the statistical significance of the detection is demonstrated. It is also entirely possible that even in the case of perfect pointing, some measurements will not contain the expected BG spectrum due to sensitivity limitations of the sensor. The statistics of the measurements show (section 4) that while the number of detection events was small, the detection is statistically meaningful.

In Table 2 we give the BG cloud-mapping data from the XM94 lidar measurements. The XM94 gives a radar-type display (a pie-chart) where the radial distance is along the lidar pulse propagation and the azimuth is a distance relative to a fixed reference line (the line of sight to the point of release). For the corresponding times in Table 2 (detection events in time region (b) of Fig. 1) the sensor pointed at azimuthal distances of 125 *m*, 200 *m*, 0 *m* and 0 *m*. These azimuthal distances are within ±100 *m* due to the parallax effect of the distance between the sensor location and the XM94 lidar location (~ 20 *m*) and the accuracy of our pointing. The azimuthal width of the cloud is ~100 *m* and the depth (radial distance) of the cloud is ~200 *m* (XM94 video display). Thus, our detection events in region (b) are reasonably consistent with the location of the BG cloud - a fact that enhances the confidence of our detection claim.

We do not know the size distribution of the bio-aerosols and thus we cannot convert the mean cloud concentration (*cm*
^{-3}) in Table 2 to mass-column density (*mg m*
^{-2}) which is deduced [6] with our detection & estimation algorithm. However, we can get a rough idea of the expected mass-column density if we assume for the bio-aerosols (density 1.45 g *cm*
^{-3}) a log-normal size distribution with mean diameter µ=ln(1.74µ*m*) and standard deviation of σ=ln(2.09µ*m*). In this size distribution 99% of the aerosols are with diameter less than 10 µ*m* and the total mass for aerosol number density of 1 *cm*
^{-3} is 4·10^{-11}
*g*. Given this size distribution, a cloud with depth of 200 *m* and a mean concentration of 50 *cm*
^{-3} (Table 2) the mass-column density of the cloud is 400 *mg m*
^{-2}.

In Fig. 2 we show the averaged deduced spectra for each of the regions (a), (b), (c), and (e) of Fig. 1 (of all spectra that have correlation with the library reference spectrum greater than 0.8) and the library reference spectrum for BG. The deduced spectrum in region (a) is a look-alike spectrum (probably due to the road dust) that is responsible for the false alarm events. The spectrum in region (b) is due to the **presence** of the BG cloud within the sensor’s FOV. The difference between the library spectra and the deduced spectra may be due to the effect of scattering by the bio-aerosols - an effect that is not addressed by our simple radiative model where only emission and absorption are considered. In addition the effect of the fluidizer Cab-O-Sil (primarily fine silica particles), which is added to the BG prior to the release (in order to prevent clumping) is to shift the peak wavenumber (1078 *cm*
^{-1}) to a longer wavenumber around 1098 *cm*
^{-1} (due to the silica). It is important to remember that the presence of BG and Cab-O-Sil is a joint event in this experiment. We do not know the amount of Cab-O-Sil that was added. The BG library spectrum (without Cab-O-Sil) that was used in the algorithm was measured separately ahead of this test using a sample material.

In Fig. 3 we show the results of our estimation algorithm [6] for the BG cloud masscolumn density for the first 2300 measurements (*i.e.*, the pre-release region (a) and region (b) of Fig. 1) and the location (circles) of detection events from Fig. 1. The sharp contrast between the estimated mass-column density at the cluster of detection events (measurements 1550 to 1750) and the remainder of the measurements suggests that the cluster of detection events consists of valid detection events. A moving average of 5 samples (*i.e.*, ~ 1 second averaging) is employed in the figure. As the thermal contrast becomes smaller, the estimated mass-column density is more difficult and is subject to more uncertainty. The accuracy of the estimate can not be verified but is reasonable; the mean mass-column density is 451.2 *mg m*
^{-2} (µ_{1} in section 4) and the overall range (~1600 *mg m*
^{-2}) is within factor 4 of the computed mass-column density (400 *mg m*
^{-2}) for the assumed lognormal size distribution and a 200 *m* cloud with mean concentration of 50 *cm*
^{-3} (Table 2).

The negative values of mass-column densities in Fig. 3 are due to background variations and measurement error which are translated into non-physical negative mass-column densities (by the algorithm) in the absence of the BG cloud within the sensor’s FOV. In addition when the thermal contrast is small (~ 1 *K* in this experiment) fluctuations in the background temperature (or its emissivity) can easily result in a change of sign in the thermal contrast Δ*T* for which in turn would result in apparent negative mass-column density (i.e., the bio-aerosols are detected through emission and absorption). The mean of the mass-column density in the absence of the BG cloud is 39.7 *mg m*
^{-2} (µ_{0} in section 4), a magnitude which is quite small though is not exactly zero as we would have liked.

Fig. 3 clearly shows that for 175 measurements (around measurement number 1600) the deduced mass-column density exceeded a 1 *s* co-adding-detection-threshold γ=332 *mg m*
^{-2} (Fig. 4), and 135 measurements exceeded the single-measurement-detection-threshold γ=569 *mg m*
^{-2} (section 4). This is very different number of detection events than the number of detections (25) given in Fig. 1 for the cluster location and the discrepancy needs to be explained. In Fig. 1 detection events are declared based on a spectral match (the value of the correlation coefficient) between the deduced spectrum and a library spectrum. Whereas in Fig. 3 detection is declared when the deduced mass-column density exceeds a given threshold. These two criteria for detection are not the same. Nevertheless, Fig. 3 shows that the two detection criteria point to the same location and the cluster location is well within the location of the peaks of the estimated mass-column density. The parameter for spectral match is a very sensitive parameter. Based on our experience we choose a conservative value (*r* =0.8) as the minimum required correlation coefficient for which (Table 1) the number of false detections in region (a) is 8 and the number of detection events in region (b) is 33 (*i.e.*, ratio of 33/8~4 between detection and false alarm). The value of *r*
^{2} gives the fraction of the total variation (information) in the deduced spectrum that can be explained (predicted) with a minimum least-squares regression fit to the library spectrum. For *r* =0.75 the number of false detections in region (a) increased to 44 and the number of detection events in region (b) increased to 88 (the ratio decreased to 88/44=2). For *r* =0.7 the number of false detection and the number of detection events are 115 and 153 respectively and the ratio decreased further to 1.3. In addition we should note again that the mass-column density estimate is very robust due to the fact that in the maximum likelihood solution (which is a minimum least-squares solution when the *pdf* is normal) we have 209 wavenumbers (for the range 800 *cm*
^{-1} to 1200 *cm*
^{-1}) for each measured spectrum and only one unknown (ρ). Thus, the estimate of ρ is very robust. The important point in Fig. 3 is that the two different criteria of detection result in a consistent location of detection events for the two.

## 4. Probability model and statistical evaluation

In Fig. 4 we show the probability model (Eqs. 3–8) for the estimated mass-column concentrations (Fig. 3). The model shows the statistical significance of the detection events (*i.e.*, the separation of the two hypotheses). The threshold γ=322 *mg m*
^{-2} is the location (noted in the figure) of the intersection of *pdf* (ρ | *H*
_{0}) and *pdf* (ρ | *H*
_{1}). Thus, mass-column density ρ>γ belongs to the hypothesis *H*
_{1} (BG cloud is within the sensor’s FOV). The parameters for the *pdf* model are *w*
_{0}=0.805, µ_{0}=39.7 *mg m*
^{-2} and σ_{0}=120.3 *mg m*
^{-2} for *pdf* (ρ | *H*
_{0}). For *pdf* ( ρ | *H*
_{1}) the parameters are µ_{1}=451.2 *mg m*
^{-2} (the mean masscolumn density of the BG cloud) and σ_{1}=438.8 *mg m*
^{-2}.

The detection probability is given by

and the false alarm probability is given by

where *erf* (•) is the error function

These probabilities are for one second of averaging (i.e., a moving average for 5 measurements). For a single measurement (*i.e.*, non averaging) the probability model results (not shown) are less favorable (a lower *P _{D}* and a higher

*P*): γ=569

_{FA}*mg m*

^{-2}(a higher threshold),

*P*(γ)=0.48 and the probability of false alarm is

_{D}*P*=0.0192.

_{FA}(γ)With the given probabilities of detection and false alarm (for a single measurement) we can estimate (Eq. 9) the number of measurements (*n*
_{1}) for which the BG cloud was within the sensor’s FOV in time region (b) of Fig. 1 to be

where *n _{det ections}*=135 (section 3),

*P*=0.0192,

_{FA}*P*=0.48 and

_{D}*n*=1250. Thus, for the detection based on spectral match detection criterion (Fig. 1 and Table 1) the probability of detection is

*n*(~10%, where

_{det ections}/*n*_{1}*n*=25 for the cluster). This probability is much lower than the ~60% probability of detection computed for the (one second) deduced masscolumn density exceeding a given threshold (Figs. 3,4), and the ~50% probability of detection for the deduced mass-column density from a single measurement.

_{det ections}## 5. Summary

In previous work [6] we demonstrated detection, identification and estimation of dry *Bacillus subtilis* var. *niger* (BG) bio-aerosol (and kaolin dust) cloud at a distance of 50 *m*. In this study an attempt to detect remotely an open-air puff release of BG aerosol spores at a distance of 3 *km* using a passive FTIR sensor (spectroradiometer) was conducted and the measurements were analyzed with hyperspectral detection, identification and estimation algorithms [6]. The algorithms are based on a simple radiative transfer theory and advanced statistical signal processing methods that statistically subtract the background spectra from the measurements and employ maximum likelihood theory to estimate the mass-column density of the cloud for each of the possible realizations of background measurements. Then, the mass-column density for each measurement is computed using an expectation (averaging) process. The thermal contrast (background brightness temperature to ambient air temperature) was small (~ 1 *K*) and thus the effect of the bio-aerosol absorption on the measured signals was weak and the detection as well as the estimation of the cloud mass-column density was difficult. Our estimate of the bio-aerosol mass-column density is reasonable but cannot be verified; the mean mass-column density is 451.2 *mg m*
^{-2} and the overall range (~1600 *mg m*
^{-2}) is within factor 4 of the computed mass-column density (400 *mg m*
^{-2}) for the assumed lognormal bioaerosols size distribution and a 200 *m* cloud with mean concentration of 50 *cm*
^{-3} (lidar measurements, Table 2).

Since only manual tracking was available, the BG cloud was within the sensor’s FOV only for only small fraction (~ 240 measurements) of the total number of measurements (a few thousands). The location of our detection events in time region (b) of Fig. 1 is reasonably consistent with cloud mapping data given by the XM94 aerosol-lidar and gives further confidence to our detection claim. The number of detection events (based on the estimation of the mass-column density in Figs. 3–4) was small (~175) but statistically significant.

Using a Gaussian-mixture probability model for these results (*i.e.*, for this experiment and the specific generic FTIR spectroradiometer) the probability of false alarm is 0.0095 and the probability of detection is 0.61 when we choose a threshold of detection that minimizes the sum of the probabilities of false alarm and of missed detection. These probabilities are for one second of averaging (5 measurements) and can be improved (*i.e.*, increase *P _{D}* and decrease

*P*) if the field test scenario enabled us to co-add more measurements. The probability of detection based on a criterion of spectral match to a library spectrum (correlation coefficient > 0.8 in Fig. 1) for a single measurement is 0.1 whereas the probability of detection based on the estimation of the mass-column density for a single measurement is much higher; 0.48. In the maximum likelihood solution for the mass-column density we have many wavenumbers for each measured spectrum and only one unknown (the mass-column density for that measurement). Thus the estimate of mass-column is robust and the detection probability is higher.

_{FA}The results are encouraging and suggest for the first time the feasibility for remotely detecting biological aerosols with passive FTIR sensors. It is an important first step and more controlled experiments are planned where the effect of different meteorological conditions and distances will be studied. These results pertain only to this experiment (*i.e.*, 3 *km* range, a given thermal contrast and the noise characteristics of the sensor).

## Acknowledgements

The *Bacillus subtilis* var. *niger* (BG) spectrum was measured by Alan Samuels of Edgewood Chemical Biological Center (ECBC). The administrative support of Bill Loerop (ECBC) is greatly appreciated. The author is grateful for continuous encouragement by Jim Jensen (ECBC). The comments, editorial help and discussions with Alan Samuels, the stimulating discussions with Ernie Webb and especially Rich Vanderbeek of ECBC whose insight to the data statistics was invaluable are all greatly appreciated. I thank Darren Emge (ECBC), Fran D’Amico (ECBC) and Thomas Gruber (MESH Inc.) for their help and conversations during the experiment. The XM94 lidar system was developed and operated by Robert R. Karl Jr. of Los Alamos National Lab. The constructive and insightful suggestions of the anonymous reviewer were extremely useful in revising the manuscript. The author was supported by the U.S. Army Soldier and Biological Chemical Command, Edgewood Chemical Biological Center under Contract No. DAAM01-94-C-0079

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