An imaging Fourier transform spectrometer developed at TUHH was used for short-range remote detection and identification of liquids on surfaces. The method is based on the measurement of infrared radiation emitted and reflected by the surface and the liquid. A radiative transfer model that takes both the real and imaginary parts of the refractive index of the materials into account has been developed. The model is applied for the detection and identification of potentially hazardous liquids. Measurements of various liquids on diverse surfaces were performed. The measured spectra depend on the optical properties of the background surface. However, using the radiative transfer model, automatic remote detection and identification of the liquids is possible. The agreement between measured spectra and spectra calculated using the radiative transfer model is excellent.
© 2008 Optical Society of America
Infrared spectrometry is routinely used for the analysis of gases, liquids, and solids. In the conventional set-up for the analysis of surfaces, a sample is introduced into a sample chamber of a conventional or imaging spectrometer (e.g. a microscope). However, in some applications, such as the detection and identification of hazardous compounds, the preparation of the sample is not possible, dangerous, or time-consuming. Previous studies showed that infrared spectrometry allows remote detection and identification of liquid contaminants on surfaces [1,2]. In these studies, the determination of the presence of substances was performed by comparison of measured spectra with reference spectra of the linear absorption coefficient of the liquids. In order to model the detailed structure of the spectra, in particular the shape of the signatures, a comprehensive radiative transfer model is required. In this work, a radiative transfer model that takes both the real and imaginary parts of the refractive index into account is presented and applied to the detection and identification of organic liquid species deposited on a variety of surfaces.
In addition, the studies cited were performed with conventional spectrometers, i.e. instruments with a single detector element. One problem associated with the use of a spectrometer with a single detector element to detect liquids on surfaces is the choice of the spectrometer’s field of view. If a large field of view is chosen, it may not be filled by the liquid which may be present in the form of small droplets. This results in high limits of detection. If a small field of view is chosen, the investigation of an extended area is timeconsuming. In contrast, imaging spectrometry allows the inspection of extended areas (large field of view of the array) with a small instantaneous field of view (field of view of each pixel), resulting in low limits of detection.
2. Radiative transfer model
The set-up for the measurements is depicted in Fig. 1. Radiation emitted by the source is reflected by the surface under examination. The radiation reflected and emitted by the surface is measured by the spectrometer. In this work, an imaging Fourier transform spectrometer (IFTS) is employed.
Under the assumption that the atmosphere between the surface and the spectrometer is homogeneous, the spectral radiance measured by the spectrometer is given by 
B air is the spectral radiance of the black body at the temperature of the air between the surface and the spectrometer and τair is the transmission of the air between the surface and the spectrometer. The spectral radiance that enters the layer of air from the surface is modelled as the sum of two contributions, radiation emitted by the surface (L e), and radiation reflected by the surface (L r). If a spectral range within an atmospheric window (e.g. 800–1200 cm-1) is considered and if the distance l between the surface and the spectrometer is small, the measured spectral radiance is given by the sum of L e and L r (τair≈1). All quantities in Eq. (1) are frequency dependent. The contribution of emission is modelled by
Here R is the reflectance of the surface with the liquid film and B S is the radiance of the black body at the temperature of both the surface and the liquid, which are assumed to be in thermal equilibrium. In this work, the liquid and the background material are modelled as homogeneous absorbing dielectric materials with plane surfaces and the specular reflectance is used in the model. However, if non-specular reflection is not negligible, it is appropriate to calculate the radiation emitted by the surface based on the directional hemispherical reflectance. The reflected radiation is modelled by
L in is the incident spectral radiance. Figure 2 shows the system of the thin film on the surface.
The reflection coefficient r 123 of the film on the substrate is given by 
where r 12 is the reflection coefficient of the interface between air and the liquid film, t 12 is the transmission coefficient of the surface, r 21 is the reflection coefficient of the interface between the liquid film and air, t 21 is the transmission coefficient of the interface between the liquid film and air, r 23 is the reflection coefficient of the bottom interface of the film, and
Here, σ is the frequency (wavenumber) of the radiation, d is the thickness of the film, and n and κ are the real and imaginary parts of the refractive index of the liquid. φin is the angle of incidence. Using t 12 t 12=1-r 2 12 and r 12=-r 21, a compact expression for the reflectance R may be derived :
The reflection coefficients r 12 and r 23 are given by the Fresnel equations (see for example reference 4). The calculation requires knowledge of both the real and imaginary parts of the complex refractive index of the liquid and the substrate. In this work, the Kramers-Kronig transform is used to calculate the real part of the refractive index of the liquid based on a spectrum of the linear absorption coefficient. For details regarding the practical implementation of the Kramers-Kronig transform, see for example Ref. 5. Equations (4) and (6) are valid for both s- and p-polarised radiation. For unpolarised incoming radiation, the mean of the reflectance for s- and p-polarised radiation is calculated (Eq. 6).
3. Identification of liquids
The identification method is based on the approximation of a measured spectrum with reference spectra. First, the spectrum of the brightness temperature TBr(σ) is calculated . This spectrum is analysed sequentially for all target compounds contained in a spectral library. The analysis is performed in three steps. In the first step, the mean brightness temperature is subtracted and the signatures of one target compound, atmospheric gases (e.g. H2O), and potential interferents are fitted to the resulting spectrum using a least squares fitting procedure. The signature of the target compound is calculated using the radiative transfer model described above. The brightness temperature spectrum corresponding to the resulting radiance spectrum is calculated. For the calculation of the refractive index, a spectrum of the linear absorption coefficient is used. The real part of the refractive index is calculated using the Kramers-Kronig transform. The refractive index of the background surface is calculated using reflectance spectra and the Kramers-Kronig transform. Reflectance spectra of solids are available in spectral libraries such as the ASTER spectral library . The fitting procedure includes an approximation of the baseline. In the second step, the contributions of all fitted signatures (i.e. atmospheric species and baseline) except the signature of the target compound are subtracted from the measured spectrum.
Then, in order to decide if the target compound is present, the coefficient of correlation between the corrected spectrum, i.e. the result of the subtraction, and a reference spectrum is calculated in a compound-specific number of spectral windows. The signal-to-noise ratio is calculated by division of the maximum brightness temperature difference caused by the target compound (determined by the least squares fitting procedure) by the noise equivalent temperature difference of the spectrum. If all coefficients of correlation and the signal-to-noise ratio are greater than compound-specific threshold values, the target compound is identified. A modified version of the algorithm for the identification of gases has been described in reference  and the reader is directed to this article for further detail.
An imaging Fourier transform spectrometer (IFTS) developed at TUHH was used . The interferometer of the IFTS is a modified Michelson interferometer with cube-corner mirrors (Bruker Optics, Karlsruhe, Germany). The detector material of the focal plane array (AIM 128 LW, 128×128 pixels, AIM Infrarot-Module, Heilbronn, Germany) is HgCdTe (MCT). The pitch of the array is 40 µm, the spectral range is 960–1330 cm-1. In this work, an optical path difference that corresponds to a spectral resolution of ΔσFWHM=5 cm-1 is used.
Due to the relatively small area of each pixel, the power incident on each detector element is small compared to the power incident on the single detector element of a conventional Fourier transform spectrometer. Thus, longer integration times or spatial filtering procedures are necessary to achieve signal-to-noise ratios of the same order of magnitude as the signal-to-noise ratio of a conventional system. In this work, spatial filtering is performed by convolution of the image with a weighting function, a two-dimensional rectangular function of 5×5 pixels.
A measurement set-up (Fig. 1) employing a radiant heater (600 W) as source of radiation was implemented. The distance l between the IFTS and the surface under examination was approximately 1 m. The materials used as background surfaces were clay, wood, pressboard, and steel. Prior to all measurements, a radiometric calibration using a black body at two different temperatures was performed.
5. Results and discussion
As an example, results of measurements of 50 µL methyl salicylate applied to a clay tile are presented and discussed. Measurements were performed using the set-up shown in Fig. 1.
Figure 3 shows a video image of the tile and the liquid on the surface of the tile as well as spectra of different areas of the tile. The area covered by methyl salicylate is observable in the video image. Spectrum (a) is the brightness temperature spectrum of an area covered with methyl salicylate. Spectrum (b) is the brightness temperature spectrum of an area which is not covered by methyl salicylate. The emissivity of the clay surface is high and only a slowly varying function in the spectral range of the IFTS. Thus, in contrast to spectrum (a), the brightness temperature spectrum (b) exhibits little structure, the brightness temperature T Br is almost constant. The measurements of methyl salicylate on pressboard and wood resulted in similar spectra, as shown in Figs. 4 and 5.
Figure 4 shows results of the automatic identification algorithm. On the left of Fig. 4, a measured spectrum and a reference spectrum fitted to the measured spectrum are depicted. The reference spectrum was calculated using the radiative transfer model as described in sections 2 and 3. A measured absorption spectrum of methyl salicylate and a reflectance spectrum of clay  were used for the calculation of the complex refractive indices. A linear baseline correction was applied. Note that the reference spectrum contains the specific signatures of the measured spectrum. In particular, asymmetric shapes of the signatures that are not observed in the spectrum of the linear absorption coefficient can be observed. On the right of Fig. 4, the identification result (yes/no decision) is shown and highlighted by an overlay of a false colour image on a video image.
Figure 5 shows results of the same reference spectrum applied to a measurement of methyl salicylate on wood. The agreement between the measured and fitted spectra is excellent, although the reference spectrum was calculated for clay as the background surface. Because the reflectance of many materials that may serve as the background is low and only a slowly varying function of frequency, the same radiative transfer model may be used for the identification of liquids on these materials.
Figure 6 shows results of a measurement of 150 µL methyl salicylate on a steel plate. Because of the high reflectance of the steel surface, multiple reflections within the film occur and the strong absorption bands of methyl salicylate in the range 1165–1315 cm-1 cause a saturated signal. Thus, the analysis is performed in a different spectral range (980–1090 cm-1). Note the difference between this spectrum and the spectra of methyl salicylate on the poorly reflecting surfaces shown earlier.
Figure 7 depicts two measurements of triethyl phosphate. One is performed on a clay tile, the other on a steel plate. Again, the two measured spectra differ significantly. Thus, the analysis using the modelled spectra for triethyl phosphate on the different surfaces were performed using different spectral ranges. In the case of the poorly reflecting clay tile as substrate, the range for identification was set to both 990–1070 cm-1 and 1090–1300 cm-1, whereas for the highly reflective steel plate the identification was only performed in the range 1060–1250 cm-1.
6. Summary and conclusions
The results demonstrate the feasibility of remote detection and automatic identification of liquids on surfaces by active imaging Fourier transform infrared spectrometry. The method may be used for the identification of hazardous substances. Moreover, potentially the method may be used for the identification of trace amounts of explosives on surfaces.
The radiative transfer model described in this work may be used for automatic identification of liquids on various surfaces. Generally, the spectrum is dependent on both the properties of the liquid and the properties of the background. Due to the low and only slowly varying reflectance in the spectral range considered of many surfaces that may serve as the background of a measurement, the same reference spectra may be used for the identification of liquids on different surfaces. These reference spectra may be calculated under the assumption of a constant reflectance of the background. The dependence of the spectra on the thickness of the liquid film potentially allows quantification of the liquid contamination. The accuracy of the model may be increased by taking diffuse reflectance into account.
The model may also be applied to a modified active set-up in which the radiation source is replaced by a tunable laser source. For the detection of the reflected radiation, an imaging spectrometer or an infrared camera may be employed. This experimental set-up potentially allows measurements from longer distances due to the possibility of a higher spectral radiance of the laser source compared to the thermal source employed in this work.
In addition, the model may be applied to passive measurements . In this case the incident radiation is given by radiation from the sky. In contrast to the active set-up, the dominating contribution to the signal is the emission by the surface. An advantage of the passive set-up is that there is no strong dependence of the signal on the distance allowing identification from longer distances. In comparison to the active set-up, automatic identification is more complicated due to the influence of the spectrum of the radiation from the sky. However, in combination with a model for the radiation from the sky (or a measured spectrum of the radiation of the sky), the radiative transfer model presented in this work allows automatic identification.
The work described in this paper was partially financed by the UK Ministry of Defence and is published with the permission of the Defence Science and Technology Laboratory on behalf of the Controller of HMSO. The authors thank Bruker Daltonics, in particular Andreas Beil and Holger Skupin for their cooperation.
References and links
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7. ASTER spectral library, http://speclib.jpl.nasa.gov/