Optimized differential absorption radiometer for remote sensing of chemical effluents Gabriel Laufer and Avishai Ben-David
A differential absorption radiometer sensor that was optimized for near-perfect 共⬃2%兲 correction of the absorption by ambient atmospheric species 共e.g., water兲 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 共e.g., water vapor兲 at the sample filter frequency provides near-perfect correction for dominant background absorption effects. The net absorption 共emission兲 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兾m2 is possible from distances of ⬍6 km. © 2002 Optical Society of America OCIS codes: 010.1120, 280.1120, 120.5630, 120.1880, 120.0280, 040.1880.
1. Standoff Detection of Chemical Vapors
We describe a compact, large field-of-view 共FOV兲 infrared 共IR兲 remote sensor 共patent pending兲 of chemical vapors using a new differential absorption radiometer 共DAR兲 technology. The modular sensor can be configured as a passive remote sensor and packaged in numerous ways, including as a handheld device, in airborne applications such as unmanned air vehicles or as an unattended sensor. Remote detection of chemical vapors in the atmosphere depends mostly on optical techniques that can be classified into two groups: 共a兲 active techniques such as lidar, differential absorption lidar, or laserinduced fluorescence and 共b兲 passive techniques, such as Fourier-transform IR spectroscopy or multispectral or hyperspectral techniques such as gas filter correlation radiometry or tunable etalons. The main deficiency of differential absorption lidar systems is that they require a narrow-band, rapidly tunable laser system thereby introducing the need for long data-intensive spectral scans. Furthermore, such systems are typically complex, requiring highly trained
G. Laufer 共
[email protected]兲 and A. Ben-David are with the Department of Mechanical and Aerospace Engineering, University of Virginia, P.O. Box 400746, Charlottesville, Virginia 22904-4746. Received 7 May 2001; revised manuscript received 5 November 2001. 0003-6935兾02兾122263-11$15.00兾0 © 2002 Optical Society of America
personnel for operation, and provide a narrow FOV that is limited by the divergence of the laser beam. The performance of passive remote sensors operating in the far IR at 8 –13.3 m has been evaluated by Flanigan.1 In this spectral range, which spans one of the atmospheric windows, radiation is emitted mostly by objects at or near typical atmospheric temperatures. For example, at 275 K, blackbody emission peaks near 10.5 m.2 Thus a solid surface in the background at that temperature can provide the radiation source, and the target gas along the line of sight, when colder than that source, can be detected and identified by its absorption signature. Conversely when the background is colder 共e.g., the sky兲, the target gas can be detected by its emission signature. Clearly, passive detection in the longwavelength IR is possible only when there is a temperature differential ⌬T between the target gas and its surroundings. In one analysis1 the relationship between ⌬T and the detection limit of certain vapors was evaluated. For example, as little as 164 parts per million per meter 共ppm兾m兲 of SF6 can be detected with an integration time of 1兾60 s when a change is induced in the IR signal that is equivalent to ⌬T ⬎ 0.4 K. SF6 was selected for this and other studies as a simulant of toxic vapors because of its relatively nontoxic properties and for its strong absorption band at 930 cm⫺1. Of course use of a hot object as a source of blackbody radiation increases ⌬T. When ⌬T is sufficiently large 共e.g., ⬎ 1000 K兲, natural variations in the temperature of the detected 20 April 2002 兾 Vol. 41, No. 12 兾 APPLIED OPTICS
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gas may have a small or even a negligible effect on the detection sensitivity. Furthermore, the sensitivity and detectivity increase but, in return, the system loses much of its flexibility. Fourier-transform infrared spectroscopy is one of the most common passive remote sensing technologies 共for example, see Ref. 3兲. There, a wide range of the IR spectrum is recorded and analyzed to provide species identification, optical density, and temperature measurement. When certain assumptions are used regarding atmospheric properties, even depth resolution along the line of sight can be achieved. The main disadvantage is that these systems depend on a complete spectral scan with a highly refined interferometer that needs to be hardened for field, air, or space applications. Furthermore, data processing and interpretation require large computing storage and processing capabilities, particularly if Fourier-transform IR imaging is required. Finally, for high spectral resolution, the FOV of the interferometer must be limited 共e.g., to 5° for 5-cm⫺1 resolution4兲, thereby limiting light-gathering and wide-area search capabilities. In many applications, however, the target chemical and its spectroscopy are known in advance. Therefore full spectral scans may not be necessary for detection or even identification. Instead, radiometry in one or more dedicated bands may suffice. In one such technique, a filter consisting of strips of bandpass filters— each coincident with the absorption line of one species—is used to image the distribution of those chemicals.5,6 The gas filter correlation radiometer 共GFCR兲 is another example of such a band-specific detector.7,8 There, one radiometric measurement of the target through a gas cell containing the target gas is followed by a second measurement through a second cell, typically containing a spectrally inert gas or vacuum. Correlation between these two measurements is used to identify the presence of the target gas in the FOV and determine its optical density 共CL兲. The system normally includes a single detector, and alternated detection through either cell can be achieved optically by polarization modulation and switching.8 The GFCR is particularly attractive for detection or to image the distribution of light molecular gases having a fine spectral structure such as CO2, or CH4. There the correlation between the spectrum of the gas in the sample cell and the spectrum of the gas in the FOV provides high specificity that allows rejection of the signal even by spectrally similar gases. Heavier molecules such as SF6 or dimethyl methylphosphonate 共DMMP兲 do not have such fine structure in the long-wavelength IR, and therefore use of a GFCR for their detection does not provide the same specificity as for the lighter molecules. Thus use of bandpass filters similar to those of Refs. 5 and 6 can provide the same sensitivity and specificity as a GFCR but without the complexity associated with the integration of an often-toxic sample gas cell in the system. The DAR described here provides many of the ad2264
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Fig. 1. Configuration of the DAR for chemical vapor detection. Blackbody radiation Ib from the background medium at temperature Tb is passing through the vapor cloud that is at temperature Tv and transmission v and through two sections of the atmosphere at temperatures T1 and T2 having transmission coefficients 1 and 2, respectively.
vantages of the well-tested GFCR including high sensitivity, simple data analysis, and compactness but without the need for sample and reference gas cells. On the other hand, the overlap between the broadband lines of several gases and the lack of fine structure may prevent distinction between spectrally similar chemicals by a single DAR consisting of one pair of detectors. Multiple DARs are expected to improve the specificity. 2. Differential Absorption Radiometer
The DAR was designed to quickly detect a target gas by its absorption or emission spectra. IR radiation 共either the absorption attenuated or the direct emission兲 is collected by a telescope or a lens and analyzed by the DAR. A pair of bandpass filters allows this species-specific detection. The first is the sample filter, which transmits with a center frequency that coincides with an absorption line of one or more of the target species and a bandwidth that matches the absorption bandwidth 共e.g., 15 cm⫺1兲. The second is the reference filter with the same bandwidth and peak transmission but with a center frequency that does not coincide with any significant absorption of the target gas. In one implementation9 a single detector was used, and polarization modulation was used to direct radiation through one or the other filter. Alternatively, collected radiation can be simultaneously passed through the sample and reference filters that are mounted side by side with an IR detector behind each filter 共Fig. 1兲. The detectors can either be on the same wafer or be independently mounted and preselected to provide nearly identical responsivity 共V兾W兲 and detectivity 共D*兲. Clearly, any variation between the responsivities of the two detectors contributes directly to the measurement uncertainty if left uncalibrated. For a compact detector, where imaging is not required, additional species can be detected by a linear array. Chemical cloud imaging can be achieved by use of a focal-plane array similar to that used in Ref. 5. When the target is viewed through the sample filter, the detector senses radiation from the IR source 共natural or artificial兲 modified by absorption 共or emission兲 by the target species and by all atmospheric trace gases in the FOV that have spectral features at
that frequency. Absorption 共or emission兲 by other airborne trace species interferes with the detection and may completely obscure the presence of the target chemical. The reference detector with its reference filter are designed to correct for this interference by detecting only radiation that is modified by absorption 共or emission兲 by a trace specie. In typical DARs, the transmission line center of the reference filter is selected near that of the sample filter. This choice ensures that the irradiance as defined by the spectral distribution of the source incident on both detectors and their response as defined by their spectral response will be nearly identical. Through subtraction of the measurement of the reference detector from that of the sample detector, interferences by absorbers with bandwidths broader than that of the filters, by elastic scattering, and by variation of the source temperature and intensities can be corrected. Although this approach provides correction for most errors, it may not provide any correction for absorption by the atmospheric trace species whose bandwidth is narrower or comparable to the transmission bandwidth of the filters. Furthermore, for some species with a potentially large and rapidly varying optical density, e.g., water vapor, this error can exceed all other errors combined. Thus, to fully correct for absorption 共or emission兲 by those trace species, the line center of the reference filter must be selected at a wavelength r to coincide with the spectral features of those trace gases that provide a combined absorption coefficient ⌺␣w共r兲 ⫽ ⌺␣w共s兲, where s is the center wavelength of the sample filter and where the summation is over all the integrated absorption coefficients ␣w of the lines that overlap the filters’ transmission curves. When the sample signal is subtracted from the reference signal, the interfering effects of the trace gases are reduced, and the target species can be detected even at exceptionally low optical densities. Interferences by additional trace species can be corrected by the inclusion of other reference filters and detectors. Although this may require the reference filter transmission to be centered at a wavelength that is far removed from that of the sample filter, the slow variation in the spectral distribution of blackbody sources and of the spectral response of the filters ensures that the uncorrected errors associated with those distributions will be small relative to the corrected errors. A unique feature of this technique is that a rather complex spectral analysis is reduced to a simple differential measurement. This new system provides miniaturization beyond existing DARs 共for example, see Ref. 9兲, where a single detector is used and the two filters are switched in its FOV. The optical switching approach is necessary only for imaging by a single focal-plane array. However, for dual-detector sensors, eliminating the need for optical switching presents an obvious advantage. Furthermore, simultaneous detection along the sample and background paths provides more realistic background subtraction and potentially higher sensitivity.
To obtain continuous subtraction of background signal and of common noise components at exceptionally low noise levels, a commercially available electronic subtraction and normalization system, the balanced ratiometric detector 共BRD兲,10 can be used. The excellent performance of the BRD can permit use of uncooled detectors with relatively low D* 共of the order of 108 cm Hz⫺1兾2 W⫺1兲 such as thermopiles. This simple electronic circuit continuously subtracts the photocurrent of one detector from the other while providing a single output that corresponds to the normalized difference between the two signals. Simultaneous detection of several chemicals may be possible by a combination of several detectors with multiple BRD circuits. Because of the low cost and small size of all the components, such a combination will still result in a low-cost compact system but with much higher specificity. The DAR兾BRD technique is attractive for compact modular sensors because 共1兲 it allows an easy interpretation of its results thereby eliminating complex infield computation; 共2兲 its broadband detection and high throughput result in a low noise-equivalent spectral radiance even with uncooled detectors; 共3兲 it has a unique subtraction technique that provides low-noise detection and prevents saturation of the preamplifiers even in the presence of large emission by uncooled optical components; 共4兲 the electrical bandwidth is narrow 共⬍1000 Hz兲, which means that the transimpedance amplifier noise is relatively low; 共5兲 it has the potential for remote detection in the presence of various backgrounds 共daytime, night, cloudy skies兲; and 共6兲 it is highly modular and versatile with potential for packaging as an in situ or a remote sensor. 3. Spectroscopy of the Atmosphere and Molecular Pollutants
Remote sensing techniques of chemicals in the atmosphere use either their emission or absorption properties. In either mode, radiation propagates through the atmosphere between a source emitting a radiance Ib and the target species and then between the target species and the detector 共Fig. 1兲. Identifying a gas target must involve analysis of its spectrum and that of the atmosphere. Atmospheric transmission is a complex interplay between molecular absorption and scattering, aerosol absorption and scattering, and atmospheric index of refraction variations. Molecular absorption is mainly caused by H2O, CO2, O3, CH4, N2O, and NH3. To avoid excessive attenuation by atmospheric absorption, the DAR sensor must operate within an atmospheric window. Although the exact extent of these windows depends on the detection range and acceptable attenuation, the most significant are from ⬃300 nm to the near IR at ⬃1.5 m, from ⬃3 to 5.5 m, and then from 8 to 13.5 m.11 Aerosols in the atmosphere and in clouds and fog contribute significantly when their density is high. Turbulence may also affect some measurements. However, subtraction and normalization can correct most effects of aerosols 20 April 2002 兾 Vol. 41, No. 12 兾 APPLIED OPTICS
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Fig. 2. Variation of the absorption coefficients of DMMP and DIMP. The line centers of the sample and reference filters for two DMMP DARs are also shown. The primary DAR is aligned with the strongest absorption line whereas the secondary DAR is aligned with a weaker DMMP line.
and turbulence, and, depending on the selection of the reference filter, also most of the atmospheric molecular absorption will be corrected. Therefore, as long as the signal induced by the target chemical itself exceeds all noise sources, detection even in the presence of precipitation, clouds, or fog may be possible albeit at reduced sensitivity. For passive detection of a molecular chemical, its optical absorption and emission must occur by transitions between its naturally populated states 共unlike laser-induced fluorescence where emission is by transitions between artificially excited states2兲. Therefore passive detection is mostly limited to the IR and long-wave length IR where vibrational and rotational transitions occur within the ground electronic state 共transitions between electronic states mostly occur in the solar blind UV兲. Many toxic chemicals have strong absorption features in the 3.3– 4.2-m and in the 8 –13.3-m ranges that also match two atmospheric windows.11 However, absorption bands of target chemicals that are in the 3.3– 4.2-m range also coincide with strong C-H stretches by hydrocarbons in the 3.1– 4.1-m range, which may interfere with positive identification. Thus the 8 –13.3-m range appears to be the most suitable for remote sensing of numerous toxic chemicals. Figure 2 illustrates the spectral variation of two gases that are used as spectral simulants of highly toxic gases, DMMP and diisopropyl methylphosphonate 共DIMP兲. Because both have band-peak frequency, bandwidth, and absorption coefficients that are similar to those of other highly toxic chemicals, they are often used as spectroscopic simulants to test remote sensors. The sensor described here was also modeled and evaluated by use of those highly toxic chemicals. The spectra shown in Fig. 2 are comparable to those illustrated in Ref. 12. It is evident that both chemicals have spectral lines that overlap each other at least partially. For example, the strongest 共or primary兲 line of DMMP that is peaked at 1050 cm⫺1 partially overlaps one of the weaker 共or secondary兲 lines of DIMP. There is no fine structure as is normally noticed in the spectra of lighter molecules such CO2, and the absorption coefficients of 2266
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these lines are exceptionally high. For example, the transmission by 100 mg兾m2 共16.6 ppm兾m at standard atmospheric conditions兲 at this primary line of DMMP is 0.72 and is 0.85 at the primary line for DIMP for similar density. The strong absorption and the lack of fine structure permit sensitive detection of these and similar toxic chemicals even by simple detectors such as the DAR. On the other hand, the overlap between the broadband lines of several gases and the lack of fine structure may prevent distinction between spectrally similar chemicals by a single DAR consisting of one pair of detectors. Employing one or more additional detector pairs combined with other bandpass filters may be desirable when distinction between species, i.e., specificity, is required. The results of a numerical evaluation of the performance of DARs designed for the detection of DMMP and DIMP are described in Section 6. 4. Simulation of the Differential Absorption Radiometer
A model describing the performance of a DAR consisting of two IR detectors, each equipped with a bandpass filter, was developed. The filters were assumed to have a Lorentzian-shaped spectral transmission curve f共兲 where is the frequency 共cm⫺1兲. The line shape, bandwidths, and peak transmissions were specified to match commercially available filters. Although DARs can detect either emission or absorption by the target gas, the simulation included only absorption. However, the effects of temperature difference ⌬T ⫽ Tv ⫺ Tb between the target vapor temperature Tv and the blackbody source temperature Tb were considered separately and are discussed in Section 5, including ⌬T ⬎ 0 and ⌬T ⬍ 0. The model included three spectral transmission components that were combined to form the total transmission s of thermal radiation emitted by a hot source in the FOV. Because the DAR provides normalization of the measured signal, the model did not need to account for the actual irradiance as long as the detectors operate below their saturation level, i.e., within the linear range of their response. The three transmission components of the model are 共a兲 by the atmosphere along the line of sight 共both before and after the target gas兲, 共b兲 by a possible target gas cloud, and 共c兲 with the bandpass filter in front of the detector. Parameters such as gain, quantum efficiency, or window transmissions were assumed to be identical for both detectors. Similarly the spectral emissivity ε共兲 of the source was assumed to be constant. This of course may not be met accurately when the difference between the sample and the reference filter frequencies is large. However, for most applications considered here, the error that is due to ε共兲 ⫽ const results in a constant zero offset. Thus, because of the DAR normalization, the source temperature and ε共兲 did not need to be included. Equation 共1兲 represents the integrated transmittance through a path of length L through the target gas having a concentration C, a horizontal path of length La ⫽ L1 ⫹ L2 through the atmosphere 共Fig. 1兲,
and a sample bandpass filter having a transmission sf: s ⫽
兰
sf共兲exp ⫺ 兵共␣ 共兲CL 兲 ⫹ 关D a共兲 L a兴其d,
(1)
where ␣共兲 is the mass absorption coefficient of the vapor12 and Da共兲 is the volume extinction coefficient of the atmosphere at sea level. Thus the optical depth of the target gas is defined by ␣ C L whereas its optical density is C L. The atmospheric absorption parameters were obtained from a HITRAN data set that includes spectroscopic data of 32 molecules. The concentration Ci of each of these molecules was defined by the standard atmosphere data. The data were processed to provide the volume extinction coefficient Da at sea level with 32 species, each having an absorption coefficient ␣i and concentration Ci: Da ⫽
兺␣ C . i
i
(2)
i
Ir ⫺ Is , Ir
I s ⫽ I b 1 v 2 ⫹ I共1 ⫺ 1兲 2 v ⫹ I v共1 ⫺ v兲 2 ⫹ I共1 ⫺ 2兲,
(4)
and the radiance reaching the reference detector is given by I r ⫽ I b 1 2 ⫹ I共1 ⫺ 1兲 2 ⫹ I共1 ⫺ 2兲 ⫽ I b 1 2
When altitude-dependent variations of atmospheric properties are not included, the results of the model are limited to horizontal line of sights at sea level. Equation 共1兲 is proportional to the signal detected by one of the DAR detectors. The signal of the reference DAR detector, which is proportional to the transmittance r, was modeled similarly with sf being replaced in Eq. 共1兲 with the transmission rf of the reference filter. The net normalized transmission detected by the DAR through a cloud of the target gas is obtained when we subtract the transmitted signal at the sample detector from the signal of the reference detector and divide the difference by the reference signal: I net ⫽
another section of the atmosphere with temperature T2 and integrated transmittance 2. The integrated transmittance is computed over the spectral range of the sample or reference filters that are assumed to have identical line shapes but different centerline frequencies. Each of these gas elements i can also contribute its own blackbody emission of Ii, where Ii is described by Planck’s function,2 with a spectral emissivity of εi ⫽ 1 ⫺ i. Accordingly the radiance of layer 1 in Fig. 1 is I1共1⫺1兲. Thus, neglecting aerosol and multiple scattering, and assuming that the atmosphere is homogeneous through the entire line of sight 共i.e., T1 ⫽ T2 and I1 ⫽ I2 ⫽ I兲, the overall radiance reaching the sample and reference detectors of the DAR is given for the sample detector by
(3)
where both measurements and the normalization are obtained simultaneously. Generally, normalization is required to render the measurement independent of variations in the target temperature, its emissivity, detector temperature 共as long as both detectors are at the same temperature兲, and attenuation by atmospheric aerosols or albedo. 5. Effect of Temperature on the Differential Absorption Radiometer Signal
In most passive IR sensing tasks, a target species is detected by its absorption of radiation Ib emitted by a medium in the background 共Fig. 1兲 or by natural thermal emission by the target gas itself. The spectral distribution of the radiance of the medium in the background is typically described by the blackbody curve at its temperature Tb.That radiation is then transmitted through a path in the atmosphere at temperature T1 and spectrally integrated transmittance 1, through the target vapor at temperature Tv and integrated transmittance v, and then through
⫹ I共1 ⫺ 1 2兲,
(5)
where the integrated transmittance by the target gas at the reference filter frequency is assumed to be v ⫽ 1. Although the target gas does present a residual broadband absorption such that v ⬍ 1 at the reference detector, neglecting that absorption in Eq 共5兲 merely reduces the projected detection sensitivity. For a homogeneous atmosphere along the line of sight, the relative magnitudes of transmissions 1 and 2 depend on the distances 共Fig. 1兲 between the background medium to the target gas and from the target gas to the detector. When the background medium temperature is high 共i.e., Tb ⬎⬎ T1, Tv, T2兲 and the distances are relatively short, the sample and reference detectors’ radiances are given within a high degree of accuracy by the first terms in Eqs. 共4兲 and 共5兲: Is ⫽ Ib1v2 and Ir ⫽ Ib12. Thus when the emission by the hot source Ib is dominant, the normalization eliminates the dependence on Ib, and the net normalized DAR signal can be simply expressed by the integrated transmittances as I net ⫽
Ir ⫺ Is r ⫺ s ⬵ ⫽ 1 ⫺ v, Ir r
(6)
where r ⫽ 12 and s ⫽ 12v. For a background medium with a temperature of 1000 K 共which is easily achieved with a blackbody source兲 at 1 km, a homogeneous atmosphere with T1 ⫽ T2 ⫽ 300 K, 1 ⫽ 2 ⱖ 0.9 共e.g., at 1050 cm⫺1 the transmittance through ⬃500 m of atmosphere兲, and a target gas with v ⫽0.9 共e.g., ⬃30 mg m⫺2 of DMMP兲, the approximation 关Eq. 共6兲兴 is accurate to within 1%. Note that Eq. 共6兲 includes integrated transmittances. We obtained such integrated transmittances in the present simulation by numerical integrations using sf ⫽ rf and assuming that the blackbody emission at the sample filter frequency is 20 April 2002 兾 Vol. 41, No. 12 兾 APPLIED OPTICS
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DAR provides a well-corrected baseline irrespective of Tb or Tv. Equation 共7兲 can also be reduced to I net ⫽ 共1 ⫺ v兲,
(8)
where ⫽
Fig. 3. Variation of the atmospheric radiance with frequency for a 0 –1-km layer as measured from the detector and for the 1-km to ⬁ layer. All parameters are for the 1976 U.S. Standard Atmosphere.
identical to the emission at the reference filter frequency. The error associated with the latter assumption is estimated below. The approximation of Ib ⬎⬎ I, Iv lends itself quite well for the description of active sensing either with a laser or an incoherent source. Passive sensing on the other hand requires a natural source such as the atmosphere itself. Figure 3 illustrates the variation with frequency of the radiance of a 1-km atmospheric layer at 288.1 K and with 46% relative humidity just in front of the detector viewed at 1° to the horizon 共lower curve兲. The upper curve shows the radiance by the remainder of the atmosphere beyond that first 1-km layer, i.e., from 1 km to ⬁. We calculated both curves by MODTRAN using parameters of the 1976 U.S. Standard Atmosphere. The spectral distribution of the layer 1 km to ⬁ follows nearly the distribution of a blackbody source at 283.61 ⫾ 2.28 K whereas the temperature of the front layer 共0 –1 km兲 is 284.94 K. Furthermore, nearly the same radiance distribution with less than 1% difference is emitted by the background layer when it is spanning either from 1 km to ⬁, as in Fig. 3, or from 5 km to ⬁. Thus, irrespective of the distance to the target gas, if the atmosphere itself acts as the source, the source can be viewed as being in direct contact with the target gas, i.e., 1⫽1 共Fig. 1兲. With this simplification, the DAR equation 关Eq. 共3兲兴 for passive sensing is
I net ⫽
共I b ⫺ I v兲共1 ⫺ v兲 2 . I b 2 ⫹ I共1 ⫺ 2兲
(7)
Clearly when ⌬T ⫽ Tv ⫺ Tb ⫽ 0, and thus Iv ⫽ Ib, the net DAR signal is Inet⫽0 and passive detection is no longer possible.13 This is consistent with the second law of thermodynamics that precludes net energy exchange 共including radiation兲 between any two media at the same temperature. Similarly, when there is no target gas along the line of sight, i.e., v ⫽ 1, the net DAR signal is again Inet⫽0. This last result is consistent with Eq. 共6兲, thereby indicating that the 2268
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Ib ⫺ Iv . I b ⫹ I共1兾 2 ⫺ 1兲
(9)
Equation 共8兲 is similar to Eq. 共6兲 with the exception that the integrated absorbance 1⫺ v by the target vapor is reduced by a coefficient that depends on Tb and Tv and appears as a contrast term. The magnitude and spectral dependence of is defined primarily by Ib and Iv, which in turn vary with Tv and Tb and by 2. As the example of Fig. 3 illustrates, when the atmosphere provides the radiation source, the brightness temperatures of the front layer 共0 –1 km兲 and the background layer 共1 km to ⬁兲 are within 1 K to each other. Consequently their Planck functions are I ⬇ Ib 关of course the radiance of the front layer in Fig. 3 is I共1⫺2兲兴. Thus Eq. 共9兲 can be further simplified to ⫽
Ib ⫺ Iv 2. Ib
(10)
The contrast term represents the degradation of the DAR signal when ⌬T is reduced. When ⌬T3⬁ 共e.g., when the source is a laser beam兲, 31. But as the simulations below show, when ⌬T ⬍ 5 K, ⬍⬍ 1. Thus, although Equations 共8兲 to 共10兲 may appear as simple algebraic manipulations of Eq. 共7兲, they are convenient and powerful for simulation and system performance analysis. By contrast to Eq. 共6兲, Eq. 共8兲 still contains an uncorrected term 2 of attenuation effects by atmospheric trace species. It is introduced by the radiative effects of the front atmospheric layer 共0 –1 km in Fig. 3兲. However, even if left uncorrected, its primary role is to influence the normalization. Thus, if 2 ⫽ 0.9, the error in measurement of the net DAR difference will be 10%. By comparison, if both v ⫽ 0.9 and 2 ⫽ 0.9, then measurement of the absorption of the target gas by a single detector will result in a 100% error. Thus, despite this uncorrected effect, this DAR is still immune to false alarms by varying densities of certain trace species, e.g., water vapor. Equations 共8兲 and 共9兲 also demonstrate that although the DAR can ideally provide a perfectly corrected baseline, accurate measurements of the optical density of the target gas that also account for the radiative effects of the atmosphere require a separate measurement of 2 and correction of its effect. This is typical to most passive sensors where integration along the line of sight of both atmospheric and target gas absorptions provides an uncertainty that can be corrected only by triangulation. For passive sensing, where Tb ⬇ Tv, the magnitude of may introduce a larger uncertainty than the uncorrected effect of 2. This condition can be expected when the vapor cloud is formed by ordinary
evaporation that initially results in Tv ⬍ T2 and after a brief period of equilibration Tv ⬇ T2. However, after equilibration when the atmosphere is the source, Tb ⬍ Tv and ⬍⬍ 兩1兩. Thus, when ⌬T ⬍⬍ Tb, the transmission appears as if it were reduced uniformly across the entire band ⌬ by the fixed contrast term . For example, when Tb ⫽ 300 K, ⌬T ⫽ 5 K, and 2 ⫽ 0.9, the contrast term ⫽ 0.089 at 1050 cm⫺1 or the DAR output is only ⬃9% of its value when measured against an infinitely hot source. At ⌬T ⫽ 2 K the contrast term ⫽ 0.035, and at ⌬T ⫽ 1 K, ⫽ 0.017. Again, accurate measurements by passive means of the optical density of the target gas will require an independent measurement of T and Tv. When ⌬T ⬎ 0, i.e., when the vapor is warmer than its background source, the effective transmission is ⬍ 0 and the spectral signature is dominated by vapor emission 共rather than absorption兲. For ⌬T ⬍⬍ Tb and for an optically thin medium, the absorption and emission processes can be linearized, and consequently the absolute magnitude of the emission at a given spectral line equals that of the absorption. 6. Results
Water vapor is one of the strongest interferents in almost all remote sensing experiments, even for measurements within the atmospheric windows. Furthermore, the strong temporal and spatial variations in its density make accounting for its effect difficult. Therefore designing a DAR that corrects nearly exactly for these effects is highly desirable. The model was used to optimize a DAR to detect DMMP by selecting filter properties that provide the highest mitigation of interferences by atmospheric water vapor over a wide range of temperatures and to predict its performance. In a typical calculation, the line center of the sample filter was selected to coincide with a strong absorption by DMMP at 1050 cm⫺1. The bandwidth and peak transmission of both the sample and the reference filters were set at 12.9 and 0.64 cm⫺1, respectively, which are typical of commercially available filters. This bandwidth is also consistent with the absorption bandwidth of numerous toxic chemicals in this spectral range.12 To optimize the center frequency of the reference filter 共i.e., to find a reference filter that provides optimal mitigation of absorption by water vapor兲, we calculated the net normalized absorption 关Eq. 共6兲兴 repeatedly while varying that reference filter’s center frequency. Figure 4 presents the result of such an iterative calculation. It is a comparison of the outputs of a series of DARs, all with the same sample filter but with reference filters at line-center frequencies varying from 800 to 1150 cm⫺1. To ensure that the correction for absorption by atmospheric water vapor is optimized, the spectral properties of air were modified in this modeling to include only the absorption lines of water. Effectively, this is as if the atmosphere contained only water vapor. The partial pressure was set at 0.02325 atm corresponding to a relative humidity14 of 83% at a temperature of 23°C where Fig. 4
Fig. 4. Variation of the DMMP DAR signal with the centerline frequency of the reference filter, assuming that atmospheric absorption of radiation by a hot source 共⬎1000 K兲 is induced only by water vapor at 296 K and 0.02325 atm and through a distance of 5 km. The upper curve is with 100-mg兾m2 DMMP in the near field 共2⬇1兲 whereas the lower curve is without DMMP. The sample filter frequency is held constant at 1050 cm⫺1, a selected reference filter is marked at 955 cm⫺1.
was modeled. Additional modeling was also made for temperatures of 40°C where the same partial pressure represents a relative humidity of 31% and at 5°C where one third of this partial pressure corresponds to a relative humidity14 of 89%. The upper curve in Fig. 4 shows the net normalized absorption signal with 100 mg兾m2 of DMMP in the near field 共i.e., 2 ⬇ 1兲 and with a hot source 共e.g., 1000 K兲 at 5 km. The lower curve shows the net normalized absorption without a target gas in the FOV. The presence of a target gas in Fig. 4 is noted by an increase in the normalized signal as expected for a subtraction order r ⫺ s 关Eq. 共6兲兴. At these two conditions, i.e., with and without target gas, the difference between two such absorption measurements is ⬎16% of the normalizing signal. Obviously, both curves go through zero when the reference filter is at 1050 cm⫺1 because then s ⫽ r 关Eq. 共6兲兴. Note that, because of the normalization, there is no need to calibrate the source when the emissivity ε ⬍ 1 or when it is uniformly attenuated over the relevant spectral range by aerosol. The difference between the spectral emissivities ε共兲 at the reference filter frequency and the sample filter frequency is a fixed parameter that for most gray and black bodies 共e.g., the atmosphere兲 depends only on the source temperature. At 293 K and for ε ⫽ 1, the uncorrected error is ⬍1.5% of the total signal. At other reference filter frequencies, e.g., at 990 cm⫺1, the effect of water-vapor absorption is not fully mitigated and introduces an uncorrected signal of Inet ⫽ 0.076. Thus, if the unmitigated signal by water vapor is considered noise, the measurement with 100 mg兾m2 of DMMP in the near field provides on humid days a signal-to-noise ratio approximately equal to 3. When we apply the DAR described here, DMMP at much lower optical densities can be detected at all levels of humidity. The pronounced structure of both curves in Fig. 4 is induced by atmospheric water vapor. The effect of 20 April 2002 兾 Vol. 41, No. 12 兾 APPLIED OPTICS
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Fig. 5. Variation of the net normalized DMMP DAR signal with distance from a hot source 共⬎1000 K兲. The sample filter is at 1050 cm⫺1 and the reference filter is at 955 cm⫺1. The partial pressure of water vapor is 0.02325 atm corresponding to 83% humidity at 23°C.
other strong atmospheric absorbers such as CO2 or O3 is discussed below. An important observation is that the lower curve in Fig. 4, which represents the DAR signal when there is no target gas in the FOV and for a water-only atmosphere, crosses the zero net signal line several times. Thus a DAR designed for the detection of DMMP with a reference filter with a line center that coincides with any of these zero crossings will show no net signal when there is no target gas in the FOV. Such a DAR can provide nearly perfect correction for absorption or emission by a 5-km column of atmospheric water. However, because some of the strongest absorption lines become optically thick for columns ⬎5 km 共i.e., the attenuation no longer varies linearly with distance兲, Inet viewed through longer columns may be ⫽0 and can significantly exceed the signal induced by the target gas itself. But as was shown by this simulation, when the reference filter is centered at 955 cm⫺1 共marked in Fig. 4兲, the sum of the absorption coefficients ⌺␣w of all the overlapping lines of water vapor seen through that filter closely match ⌺␣w seen through the filter at 1050 cm⫺1. Thus, at that frequency, the absorption by water vapor meets a unique condition that renders the correction by the DAR independent of the optical density CL: exp共⫺␣ w CL兲 955 ⫽ exp共⫺␣ w CL兲 1050.
(11)
Consequently the net DAR signal associated with measurements through these two filters is corrected nearly perfectly for absorption by water vapor irrespective of the humidity level and the path length between the source and the detector. We demonstrated this by calculating Inet 关Eq. 共6兲兴 for transmission of radiation from a hot source through a water-only atmosphere with a partial pressure of 0.02325 atm with horizontal path lengths 0 ⬍ L ⬍ 6 km 共Fig. 5, lower curve兲, corresponding to 0 ⬍ C L ⬍ 139.5 atm-m. It is striking to note that, despite the large variation in C L, the variation of Inet as predicted by the bottom curve is limited to ⬍0.005. Furthermore, when a cloud of 100 mg兾m2 of DMMP is in the line of sight, the variations in the overall signal are also limited to ⬍0.005. Thus, with the selection of this reference filter, the effects of 2270
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water-vapor absorption are corrected to within 0.3% of the detected signal. Although Fig. 5 may suggest that DMMP can be detected by this DAR from L ⬍ 6 km, the detection range is ultimately defined by imaging parameters such as resolution and by attenuation effects such as 2 or aerosol scattering 共which was neglected here兲. To determine the detection sensitivity, the calculation was repeated with 100 mg兾m2 of DMMP. It can be seen in Fig. 5 that, for the water-only atmosphere, the change in Inet is ⬎0.16, or 16% of the total signal detected by the reference detector. This is nearly 50 times the projected uncorrected effect of atmospheric water vapor 共lower curve兲. Thus if the measurement is limited only by that effect 共e.g., detector or amplifier noise is ⬍⬍0.5%兲, sensitivities of approximately 3 mg兾m2 共⬃0.5 ppm-m兲 are possible. Of course actual remote sensing takes place through an atmosphere that contains at a minimum all its natural species. The upper and the second from the bottom curves in Fig. 5 represent the variation of the net DAR signal with L through a standard atmosphere as described by HITRAN, with and without DMMP in the FOV, respectively. With the source at a short distance, e.g., ⬍0.1 km, these two curves nearly coincide with those that represent detection through the hypothetical water-only atmosphere. Thus, for short range, a DMMP DAR that was designed to correct only for absorption by water vapor is nearly insensitive to interferences by other atmospheric species as well. Furthermore, unlike water vapor, the spatial and temporal density distributions of the remaining major absorbing species CO2 and O3 vary slowly. Thus the error that is introduced when we do not correct for their absorption effects is nearly constant in any given setting and represents a slowly varying bias. With the hot source at a moderate range of L ⬍ 6 km, the DAR signal induced by DMMP in the FOV is ⬇1.5 larger than the signal induced by the standard atmosphere. Therefore detection of DMMP at an optical density greater than or equal to 100 mg兾m2 is possible unambiguously even without correction of absorption effects by other atmospheric species. At longer distances, such correction may be necessary. The results of Figs. 4 and 5 were obtained with the atmosphere at 23°C. To determine the effect of the atmosphere temperature on the optimization of the reference filter, the analysis was repeated for a temperature of 40°C where the same partial pressure of water vapor represents a relative humidity of 31% and for 5°C where one third of this partial pressure corresponds to a relative humidity14 of 89%. At temperatures lower than 5°C the atmospheric content of water vapor diminishes rapidly and its effect is minimal. In both models, the uncorrected effect of water vapor remained at ⬍2% when L ⬍ 6 km. Furthermore, similar modeling where the sample filter was centered at 918 cm⫺1 to coincide with a second line of DMMP and the reference filter was at 1006.5 cm⫺1, the uncorrected effect of water vapor was ⬍1% for the same atmospheric conditions.
Spectral variations associated with the emission curve of the blackbody source can also contribute to the uncertainty, particularly when the center frequency of the sample filter is far removed from that of the sample filter. For example, for a perfect blackbody at 296 K viewed by a DMMP DAR that includes a sample filter at 1050 cm⫺1 and a reference filter at 955 cm⫺1, the source irradiance viewed by the reference filter is 0.75% below the irradiance at the sample filter frequency. However, this reading is merely a nonzero baseline offset. The results of Figs. 4 and 5 were obtained with the assumption that the source is hot. However, when ⌬T is reduced, the net DAR signal is expected to decline significantly. For example, Eqs. 共8兲 and 共10兲 describe Inet for passive detection along a horizontal line of sight with the sky and the atmosphere as the background source. In both equations the contrast term was introduced to allow adjustment of the results obtained for active sensors that use a hot source 共e.g., Figs. 4 and 5兲 to passive sensors where ⌬T ⬍⬍ Tb. Thus when the source is at 23°C and when ⌬T ⫽ 5°C, the contrast term is 关Eq. 10兴 ⫽ 0.089, and thus the transmission by the DMMP cloud is only 8.9% of its transmission when Tb ⬎ 1000 K. At ⌬T ⫽ 2°C, the contrast term is ⫽ 0.035, and when ⌬T ⫽ 1°C, the contrast term is ⫽ 0.017. Accordingly, the net normalized DMMP signal of the optimized DAR is only Inet ⫽ 0.014 when ⌬T ⫽ 5°C, it is Inet ⫽ 0.005 when ⌬T ⫽ 2°C, and only Inet ⫽0.0022 when ⌬T ⫽ 1°C. Of course, the contrast term must also be applied to the absorption by the atmosphere itself. Therefore the uncorrected interferences by all atmospheric species, including water, are reduced at the same rate as the signal by the target gas. Consequently at sufficiently low ⌬T, the noiseequivalent power of the detector becomes the ultimate detection-limiting parameter. With this projection, a DAR having a signal-to-noise ratio of at least 200 can provide a detection limit of at least 100-mg兾m2 DMMP 共16 ppm-m兲 with a natural or artificial source with ⌬T ⱖ 2°C at L ⬍6 km. With a signal-to-noise ratio of at least 400, detection at the same sensitivity is possible when ⌬T ⫽ 1°C. For comparison, the noise-equivalent temperature difference15 for a 2-mm uncooled detector with a noiseequivalent power of 4⫻10⫺9 W兾公Hz, operating at a bandwidth of 100 Hz, is 0.032°C. A similar variation 共but with a reversed sign兲 is projected when the vapor cloud is slightly warmer than its surroundings, i.e., the detection is by emission. The results of Figs. 4 and 5 may appear as a unique coincidence. However, because of the rich spectrum of water and the wide range of the absorption coefficients of its various lines, numerous other combinations of sample and reference filters were identified by the model for methanol, several toxic gases, and for additional lines of DMMP and DIMP. Table 1 lists the frequencies of such pairs for the strongest and weaker absorbing lines of DMMP and DIMP and for methanol. Thus several matched detector pairs can be assembled to detect simultaneously a multi-
Table 1. Sample and Matched Reference Filter Frequencies of DARs That Were Optimized to Provide Sensitive Detection of the Listed Species While Minimizing Interference by Water-Vapor Absorption
Chemical Specie
Sample Filter Frequency 共cm⫺1兲
Reference Filter Frequency 共cm⫺1兲
DMMP DMMP DIMP DIMP Methanol
1050 918 994.4 919.2 1033
955 1006.5 933.5 1006.5 978
tude of species while at the same time correct the background effects that are unique for each of the detected species. Furthermore, when more than one detector pair is assigned to each of the detected species, the specificity of the system can be enhanced. Similarly, correction for other background species that are determined to be critical in a specific environment can be achieved by additional reference detectors when filters are selected to match the absorption by atmospheric species such as CO2, O3, or hydrocarbons to the absorption by those atmospheric species as seen through the sample filter. 7. Enhancement of System Specificity
The specificity of a single DAR pair is limited. For example, because of the overlap between a weak line of DIMP and a strong line of DMMP, a DAR with a sample filter at 1050 cm⫺1 cannot distinguish between an optically dense cloud of DIMP and a thin cloud of DMMP. Specificity can be significantly improved by the addition of matched DAR pairs with sample filter line centers coinciding with the absorption of other lines of the same species or lines of yet other target or interfering species. The following example 共Fig. 6兲 illustrates how a quadrant detector can be configured to distinguish between two spectrally similar species by detecting simultaneously the absorption by two lines of DMMP at 1050 and 918 cm⫺1 共Fig. 2兲. The two remaining quadrants are equipped with reference filters at 955 and 1006.5 cm⫺1, respectively, that were matched to the other two quadrants for near-perfect correction for absorption 共emission兲 by water vapor, i.e., ␣w兩1050 ⫽ ␣w兩955 and ␣w兩918 ⫽ ␣w兩1006.5. Thus, by detecting background-corrected normalized absorption by two separate DMMP line pairs, the detector is able to distinguish between DMMP and at least one potential interferant. We demonstrated this by calculating the effect induced by a cloud of 100 mg兾m2 of DMMP in the presence of a cloud of DIMP at the significantly higher density of 1000 mg兾m2. The detector is expected to distinguish between these two chemicals even in the face of large disparity in their densities. The normalized net signal by the two DARs of Fig. 6 was calculated for absorption of radiation from a hot source, e.g., T⬎ 1000 K 共Table 2兲. It can be seen that the change in the net normalized signal when 100 mg兾m2 of DMMP are in the FOV is 17% of the 20 April 2002 兾 Vol. 41, No. 12 兾 APPLIED OPTICS
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piles, with filter arrays can result in a compact, sensitive, and highly specific sensor. 8. Conclusions
Fig. 6. Quadrant detector designed as a dual-DAR sensor for positive identification of DMMP by simultaneous detection of two of its strongest lines while providing for each line near-perfect correction for interference by atmospheric water vapor. The center frequencies of the sample and reference filters are indicated. All filters were assumed to have a bandwidth of 12.9 cm⫺1 and a peak transmission of 64%.
normalized signal for the first DAR and 3.4% for the second DAR. The ratio between these two outputs is consistent with the ratio of absorption coefficients ␣ 兩1050兾␣ 兩918 ⫽ 3.78 of these two DMMP lines 共Fig. 2兲, and thus by itself can be a positive identifier of this chemical. When DIMP at ten times the optical density of DMMP is introduced into the FOV, the absolute value of the signal at the primary DAR is nearly zero and so is the ratio between the two absorptions 兩 ␣1050兾␣918 兩, thereby providing a strong indication that the chemical in the FOV is not DMMP. Finally, note that the signs of the signals induced by DMMP and DIMP are reversed. Because in passive detection the signal can be induced either by emission or by absorption, the sign of the output of an individual DAR cannot be used as an identifier. But the sign of the ratio between two DAR outputs can be an indicator. In the active mode, i.e., when a hot source is available, the sign of the signal itself can be used to discriminate between DMMP and DIMP. Thus this simple combination of DARs is already capable of unambiguously distinguishing between these two chemicals. Higher specificity is possible with use of additional detector pairs. Integrating detector arrays, either mercury cadmium telluride or thermo-
A DAR sensor that was optimized for near-perfect correction of the absorption by natural atmospheric species such as water vapor is described. The highly sensitive sensor operates without moving parts and at high collection efficiency that offers the potential for passive remote sensing with uncooled detectors. Although the sensor can operate at all spectral ranges, it was analyzed for passive detection in the 8 –12-m range. A target gas is detected by its IR absorption signature when it is colder than the background and by emission when it is warmer. The analysis of the remote detection of DMMP shows that, when the target gas is viewed against a hot source through a bandpass filter centered at one of its strongest absorption lines at 1050 cm⫺1 and then through a bandpass filter centered at 955 cm⫺1, the effect of water-vapor absorption can be corrected to within 2% of the signal for a horizontal column of 6 km of water at a partial pressure of 0.02325 atm 共83% humidity at 296 K兲 and for an atmospheric temperature varying from 5°C to 40°C. By comparison, 100 mg兾m2 of DMMP in the FOV introduces a change in the signal of ⬎16% because of absorption. A contrast term was developed to estimate the degradation of the DAR signal when ⌬T is reduced. When ⌬T 3 ⬁ 共e.g., when the source is a laser beam兲, 3 1. But in passive sensing, i.e., when ⌬T ⬍ Tb, the contrast term ⬍⬍ 1. The contrast term was used to evaluate the DAR when the temperature of the source is near the target gas temperature; when ⌬T ⫽ 5 K, the absorption by DMMP is only 1.4% of the DAR signal, it is only 0.5% when ⌬T ⫽ 2 K, and only 0.2% ⌬T ⫽ 1 K. But with reduced temperature contrast, the contrast term needs to be applied also to the absorption by other atmospheric species, thereby reducing their interferences. Ultimately, the detectivity limit at low temperature contrasts is determined by system and detector parameters such as the noise-equivalent power. This filter pair does not correct the effect of other atmospheric species. But from distances of ⬍6 km, their uncorrected effect is well below the signal induced by DMMP. DARs designed to detect other lines of DMMP or other species can also be optimized to correct for absorption 共emission兲 effects by water vapor. Because of the overlap between some spectral lines
Table 2. Change in Net Normalized Signal of a Two-Line DMMP DAR Sensor Induced by either DMMP or DIMP in the FOV 共Absorption from 1 km and T > 1000 K兲
2272
Type of Detector
Sample兾Reference Filters’ Center Frequencies
Species in the FOV and CL 共mg兾m2兲
Change in Net Normalized Signal
Main line DMMP DAR Second line DMMP DAR Main line DMMP DAR Second line DMMP DAR
1050 cm⫺1兾955 cm⫺1 918 cm⫺1兾1006.5 cm⫺1 1050 cm⫺1兾955 cm⫺1 918 cm⫺1兾1006.5 cm⫺1
DMMP, 100 DMMP, 100 DIMP, 1000 DIMP, 1000
0.17 0.034 ⫺0.006 ⫺0.3
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of one chemical with the lines of another, the specificity of a single-pair DAR is limited. For example, a DAR sensor configured to detect DMMP by use of a sample filter centered at 1050 cm⫺1 may detect absorption by DIMP that is associated with the shoulder at 1017.3 cm⫺1 共Fig. 2兲, particularly if the optical density of DIMP is much higher than that of DMMP. The consequence of this interference can be reduced when additional DARs are introduced consisting of detector pairs that are either optimized to detect absorption by one or more additional lines of DMMP, one or more lines of DIMP, or combinations thereof. For example, a quadrant detector 共Fig. 6兲 consisting of four separate detectors can be configured to operate as a dual DAR. When bandpass filters at 1050 and 955 cm⫺1 are attached to two of these detectors, they can serve as a primary DMMP DAR sensor optimized for correction of interfering effects by water vapor. A third detector with a bandpass filter centered 918 cm⫺1 to coincide with one of the secondary lines of DMMP and a fourth detector with a bandpass filter centered at 1006.5 cm⫺1 to correct for absorption or emission effects by water vapor can form a secondary DMMP DAR sensor. With simultaneous readings of both DARs, DMMP can be distinguished from DIMP. Additional DAR pairs can provide further specificity or correction for other atmospheric species. This research was partially funded by a Challenge Award from the Virginia Center for Innovative Technology under CIT award MAT-01-010 and by Avir, LLC, Charlottesville, Va. It is the basis for a Patent Cooperation Treaty 共PCT兲 application PCT兾US00兾 04027 entitled “Passive Remote Sensors of Chemicals” filed 18 February 2000. References 1. D. F. Flanigan, “Prediction of the limits of detection of hazardous vapors by passive infrared with the use of MODTRAN,” Appl. Opt. 35, 6090 – 6098 共1996兲.
2. G. Laufer, Introduction to Optics and Lasers in Engineering 共Cambridge U. Press, Cambridge, UK, 1996兲, p. 326. 3. W. L. Smith, H. E. Revercomb, R. O. Knuteson, F. A. Best, R. Dedecker, H. B. Howell, and H. M. Woolf, “Cirrus cloud properties derived from high spectral resolution infrared spectrometry during FIRE II. Part I: The High Resolution Interferometer Sounder 共HIS兲 system,” J. Atmos. Sci. 52, 4238 – 4245 共1995兲. 4. P. R. Griffiths and J. A. de Haseth, Fourier Transform Spectroscopy 共Wiley, New York, 1986兲, p. 656. 5. M. L. G. Althouse and C. I. Chang, “Chemical vapor detection with a multispectral thermal imager,” Opt. Eng. 30, 1725– 1733 共1991兲. 6. F. Lopez and J. de Frutos, “Multispectral interference filters and their application to the design of compact non-dispersive infrared gas analyzers for pollution control,” Sens. Actuators A 37–38, 502–506 共1993兲. 7. T. V. Ward and H. H. Zwick, “Gas cell correlation spectrometer: GASPEC,” Appl. Opt. 14, 2896 –2904 共1975兲. 8. G. W. Sachse and L.-G. Wang, “Non-mechanical optical path switching and its application to dual beam spectroscopy including gas filter correlation radiometry,” U.S. patent 5,128,797 共7 July 1992兲. 9. G. W. Sachse, “Optical path switching based differential absorption radiometry for substance detection,” U.S. patent 6,057,923 共2 May 2000兲. 10. P. C. D. Hobbs, “Ultra sensitive laser measurements without tears,” Appl. Opt. 36, 903–920 共1997兲. 11. W. B. Grant and R. T. Menzies, “A survey of laser and selected optical systems for remote measurements of pollutant gas concentrations,” J. Air Pollut. Control Assoc. 33, 187–194 共1983兲. 12. L. D. Hoffland, R. J. Piffath, and J. B. Bouck, “Spectral signatures of chemical agents and simulants,” Opt. Eng. 24, 982– 984 共1985兲. 13. S. S. Penner, Quantitative Molecular Spectroscopy and Gas Emissivities 共Addison-Wesley, Reading, Mass., 1959兲. 14. R. E. Sonntag, C. Borgnakke, and G. J. Van Wylen, Fundamentals of Thermodynamics, 5th ed. 共Wiley, New York, 1998兲, p. 664. 15. P. W. Kruse, ed., Uncooled Thermal Imaging, Arrays, Systems, and Applications, Vol. TT51 of the Tutorial Texts 共SPIE Press, Bellingham, Wash., 2001兲, p. 8.
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