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Multimode Imaging in the Thermal Infrared for Chemical Contrast Enhancement. Part 2: Simulation Driven Design Heather Brooke, Megan R. Baranowski, Jessica N. McCutcheon, Stephen L. Morgan, and Michael L. Myrick* Department of Chemistry and Biochemistry, 631 Sumter Street, University of South Carolina, Columbia, South Carolina 29208 We present a simulation-driven process to design an infrared camera system that is tuned to specific analytes of interest based on “molecular factor computing”. There are many factors involved in optimizing discrimination using optical filtering aids, including, but not limited to, the detector response, optical throughput of the system, optical properties of the samples, and optical properties of the materials for sensitizing films/filters. There are nearly infinite possible setups for the system, which means it is neither cost nor time efficient to physically test each one. In lieu of this, we developed routines in MATLAB (The Mathworks, Natick, MA) that simulate the camera output, per pixel, given specific conditions. Beginning with measured spectra of calibration samples or standards and using an objective function or figure of merit (FOM) to measure simulated performance, these routines evaluate large numbers of combinations of chemical films as filters for discrimination based on linear discriminant analysis (LDA). In this study, the FOM was the Fisher ratio between a neat fabric and one stained with either a polymer film or blood. Molecular factor computing (MFC) was first described by Fong et al.1 and has been reported several times over the past 15 years.2-6 It consists of the nonspectroscopic detection of an analyte by detection through multiple filters whose spectra are defined by the absorption properties of a polymer or solution. To this extent, MFC is similar to a multiplexed spectral correlator in which the correlation between the spectrum of a sample with the spectrum of a filtering compound is measured. In a general application, a group of filtering compounds or filters is selected and light transmitted through the sample in question is measured by interposing all of the filters in sequence into the light path. The pattern of intensities then forms a sort of “spectrum in miniature”, in which only a few spectrally convoluted measurements are used as a basis for analysis. * To whom correspondence should be addressed. Phone: 803-777-6018. (1) Fong, A.; Hieftje, G. M. Appl. Spectrosc. 1995, 49, 493–498. (2) Dai, B.; Urbas, A.; Douglas, C. C.; Lodder, R. A. Pharm. Res. 2007, 24, 1441–1449. (3) Fong, A.; Hieftje, G. M. Appl. Spectrosc. 1995, 49, 1261–1267. (4) Fischer, M. R.; Hieftje, G. M. Appl. Spectrosc. 1996, 50, 1246–1252. (5) Tarumi, T.; Amerov, A. K.; Arnold, M. A.; Small, G. W. Appl. Spectrosc. 2009, 63, 700–708. (6) Workman, J. J. Appl. Spectrosc. Rev. 1999, 34, 1–89. 10.1021/ac101108z 2010 American Chemical Society Published on Web 09/23/2010
Our recent work with infrared imaging using chemical or polymer filtering films is a form of MFC. Since the measurements being made are spectrally convoluted, the question remains of what the optimal single or set of filtering elements would be to achieve a particular purpose. As we found in our previous work with multivariate optical computing,7-15 any sensing system that makes use of filtering elements arrives at much the same question. In addition, any optical or spectroscopic system for which multiple choices of components can be made faces a similar issue when the performance of the system as a whole is not a linear summation of the performances of individual elements. Fong and Hiefjte1,3 selected liquid chemical filters with the goal of making an instrument with sensitivity to a wide range of chemical functional groups because they were interested in a general-purpose system. In our case, we are interested in designing instruments with very specific and optimized properties for the detection of known analytes. Further, we have the capability of creating a wide range of possible filtering elements, and for each filter element, we have the capability of producing them in various optical thicknesses. At a minimum, hundreds of thousands of different filter selections are possible, and it would be ruinous to try to measure them each experimentally for optimal performance. In such cases, simulation of the instrument performance can provide a computer system with a means of testing large numbers of elements to arrive at optimized designs in relatively short order.16 We report our efforts to produce simulation-driven designs for two analytes on fabric samples, measured by diffuse reflectance: a polymer (Acryloid B67, commonly used in airbrushing) and blood. Lacking a means of effectively simulating the spectra of (7) Haibach, F. G.; Greer, A. E.; Schiza, M. V.; Priore, R. J.; Soyemi, O. O.; Myrick, M. L. Appl. Opt. 2003, 42, 1833–1838. (8) Haibach, F. G.; Myrick, M. L. Appl. Opt. 2004, 43, 2130–2140. (9) Myrick, M. L.; Soyemi, O.; Karunamuni, J.; Eastwood, D.; Li, H.; Zhang, L.; Greer, A. E.; Gemperline, P. Vib. Spectrosc. 2002, 28, 73–81. (10) Myrick, M. L.; Soyemi, O.; Li, H.; Zhang, L.; Eastwood, D. Fresenius’ J. Anal. Chem. 2001, 369, 351–355. (11) Priore, R. J.; Haibach, F. G.; Schiza, M. V.; Greer, A. E.; Perkins, D. L.; Myrick, M. L. Appl. Spectrosc. 2004, 58, 870–873. (12) Profeta, L. T. M.; Myrick, M. L. Spectrochim. Acta, Part A 2007, 67, 483– 502. (13) Simcock, M. N.; Myrick, M. L. Appl. Opt. 2007, 46, 1066–1080. (14) Soyemi, O.; Eastwood, D.; Zhang, L.; Li, H.; Karunamuni, J.; Gemperline, P.; Synowicki, R. A.; Myrick, M. L. Anal. Chem. 2001, 73, 4393–4393. (15) Soyemi, O.; Eastwood, D.; Zhang, L.; Li, H.; Karunamuni, J.; Gemperline, P.; Synowicki, R. A.; Myrick, M. L. Anal. Chem. 2001, 73, 1069–1079. (16) Russell, R. H. Comput.-Aided Eng. 1995, 14, 76–80.
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the analytes on fabrics, we begin our simulation by experimentally determining the reflectance properties of the neat and reproducibly stained fabrics. The next step involved the development of MATLAB programs to calculate the expected camera response for a given setup (e.g., single filter and single calibration sample). We show results of this simulation are comparable to experimental results using the modeled setup and that the simulation can be used to determine an optimal setup for a given analyte on a known substrate (e.g., blood on fabric). The spectra of possible filtering elements are determined by estimating the spectral absorption coefficients of the filtering materials and then simulating the filters at a range of filter thicknesses. A computer routine is then used to simulate each measurement of the neat and stained fabrics when viewed through the chemical filters. In this simplified simulation, the Fisher ratio17 between the neat and stained responses (a ratio of variability between groups divided by the pooled variability within groups) is calculated by linear discriminant analysis (LDA), which is used as the figure of merit (FOM) for the predicted contrast in an image. EXPERIMENTAL SECTION Source/Detector System for Imaging. Optical components were characterized by their spectral profiles. These included the fixed components of the system, i.e., the spectral emission of the light source, spectral responsivity of the detector, and the throughput of the lens. All these profiles were stored and read directly in Excel format. Instrument setup and data analysis is described in ref 18. The product of the spectral profiles of these fixed components is shown in Figure 1(Top). The light source for these measurements was located approximately 1 m from the fabric sample along the fabric normal. Reflected/scattered light was measured by the camera at an angle of approximately 30° from the fabric normal. Fabric orientations were determined relative to a predetermined fiber axis in the fabric for all studies, as other work in our laboratories has shown this approach to give the most reproducible spectra of fabrics.19 The predetermined fiber axis in the fabric was always aligned normal to the plane determined by the angles of light incidence and scattering/reflection. Neat and doped fabric samples were made as described below, and data was collected via LabVIEW (version 8.5 w/Machine Vision, National Instruments, Austin, TX) and processed offline in MATLAB using lock-in amplifier techniques, as described in ref 18. Due to variations in illumination across the images, we took five images of each set of neat and doped fabrics with the neat sample pinned above the doped and five images with the doped fabric pinned above the neat. The average response for each in-phase (AC-0) image was calculated for four different cropped areas, resulting in 20 replicates for each sample. The doped/neat ratios were calculated from pairs of images as described in eq 1, generating 10 replicate D/N values for each fabric sample. This equation was derived to eliminate the variations in the overall intensity of the light source that might occur (17) Fisher, R. A. Ann. Eugenics 1936, 7, 179–188. (18) Brooke, H.; Baranowski, M. R.; McCutcheon, J. N.; Morgan, S. L.; Myrick, M. L. Anal. Chem., in press, DOI: 10.1021/ac101109w. (19) McCutcheon, J. N. Forensic Discrimination, Age Estimation, and Spectral Optimization for Trace Detection of Blood on Textile Substrates using Infrared Spectroscopy and Chemometrics. University of South Carolina, Columbia, SC, 2010.
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between the measurement of the doped and neat samples in the two geometries.
D/N )
( ) D2D1 N1N2
(1)
In this equation, D and N represent signals from a cropped region of the neat and doped fabric samples, respectively, and the subscript denotes the position of the sample. The subscript 1 denotes the sample in the top position in the image, and 2 represents the sample in the bottom position in the image. Filters. Filters were composed of a coating deposited on KBr windows. One filter composed of Acryloid B67 was selected for studies of Acryloid B67-stained fabrics and was used to validate the simulation approach. This filter is the same one whose fabrication was described in ref 18, and its mid-infrared transmission spectrum is shown in Figure 1(Top). Because a goal of our work is to use simulation to identify the optimum filter for the analysis of blood on fabrics in infrared forensic imaging, we restricted our simulations to films that could actually be prepared in our laboratory. One task was to begin identifying potential candidate films and to develop film-coating methods for them. Priority was given to those materials that were (a) easy to prepare as films, (b) inexpensive to test, or (c) suspected as being of potential use in the analysis of blood. This latter criterion was necessarily subjective; it led us to examine materials that were known infrared interferences with blood or
Figure 1. (Top) Response curve of Merlin uncooled microbolometer camera, as given by manufacturer (black). Transmission spectrum of ∼50 µm filter of Acryloid B67 (red). (Bottom) Transmission spectra of two materials used in the optimization program: albumin (black) and nylon (blue). The left axis is correct for albumin; the nylon profile has been offset by -40% T for clarity.
that were proteins. Film deposition methods, such as dip coating and spin coating, were studied and chosen so that a suitable thin film could be deposited on a window to create a chemical filter. Preliminary testing of coatings for thin films prioritized four materials that met these simple criteria: albumin, aprotinin, nylon, and polystyrene. Films were cast on KBr or ZnSe windows (depending on the solvent) by dip-coating as described previously,18 with tape applied to one face of the window to ensure only one face was coated. Gravimetry was used to estimate the masses of these materials deposited on the windows, and the bulk densities of the materials were then used to estimate the physical thickness of the films. Those thicknesses were 7.6 ± 1.9, 7.8 ± 2.0, 7.0 ± 3.0, and 6.4 ± 1.1 µm, respectively, where the uncertainties represent 95% confidence intervals. Five replicate transmission spectra of were taken of each filter (Figure 1(Bottom)) with a Nexus 470 infrared spectrometer (Thermo Electron, Madison, WI), over the spectral range of 4000-525 cm-1 (128 scans per spectrum at a resolution of 4 cm-1 with Happ Genzel apodization), and a background spectrum of the salt plate was acquired before each sample. The absorption coefficient spectrum for each sample was calculated by dividing the measured absorption spectrum of the films by the film thickness. These coefficient spectra were then used to simulate spectra of any thickness. Polymer-on-Fabric Samples. Acrylic, cotton, nylon, and polyester fibers are among the most common textile samples found at crime scenes.20 Samples of each of these fabrics were obtained from textile manufacturers and dyed with three dyes: acrylic with basic violet 16, basic yellow 28, and basic blue 159; cotton with reactive red 239, reactive orange 72, and reactive violet 5; nylon 6,6 with acid yellow 49, acid blue 45, and acid green 27; and polyester with disperse violet 77, disperse yellow 114, and disperse red 60. These samples were then coated with Acryloid B67 (Talas, Inc., New York, NY), an acrylic ester resin known to make good thin films, using an airbrush that had a calculated flow rate of 1 mL/min. The front side of each fabric was sprayed for 4 min, with a solution of 11.035 g of Acryloid B67 dissolved in 100 mL of toluene. The film coverage on the fabrics was determined to be equivalent to ∼20 µm total average thickness (2.1 mg/cm2) based on flow rate of the airbrush, density of the polymer (1.04 g/cm3), and coated area of the fabric sample (184 cm2). Diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS) spectra were taken using a Thermo-Nicolet (Waltham, MA) Nexus 670 FT-IR system (cooled DTGS detector with a CsI beamsplitter) with the U-Cricket, a diffuse reflectance accessory (Harrick Scientific Products, Ossining, NY) with angles of incidence and scattering of ∼60°, and an angle between the incident and reflected/scattered rays of ∼120°. Twenty replicate spectra of each neat fabric sample (Figure 2) were collected using the following parameters: 610-3000 cm-1 spectral range, 128 scans, 4 cm-1 resolution, mirror velocity of 0.6329 cm/ sec, and a gain of 8. The orientation of the fabrics for DRIFTS was such that a predetermined fiber axis of each fabric sample was aligned normal to the plane defined by the angles of incidence and scattering/reflection. (20) Saferstein, R. Criminalistics: An Introduction to Forensic Science, 9th ed.; Pearson Education: Saddle River, NJ, 2006.
Figure 2. DRIFTS of two different fabrics with the maximum camera response range highlighted in blue. (Top) Cotton neat (black) and doped with Acryloid B67 (red). Doped samples exhibit a distinct peak near 1700 cm-1, which is apparent in the transmission spectrum of Acryloid B67. There are also spectral differences in the highlighted region. (Bottom) Acrylic neat (black) and doped with 25× dilution of blood (red). Doped samples exhibit intensity differences from the neat fabric samples in the highlighted region, as well as an absorbance near 1600 cm-1.
Blood-on-Fabric Samples. Fresh rat blood, stabilized with ethylenediaminetetraacetic acid (EDTA), was acquired from the University of South Carolina School of Medicine’s Animal Resource Facility. Samples of the four fabrics were cut into 2 × 2 in. swatches. Each swatch of fabric was coated with a 5× dilution of blood (8 mL of whole blood mixed in 32 mL of an isotonic solution, described in ref 21) on a Gilson 223 sample changer utilizing a dip coating application with Trilution LH software (Middleton, WI), in order to ensure a uniform coating on the fabric. The sample was lowered into and withdrawn from the solution at a rate of 100 mm/s and remained in the solution for 3 s. Twenty replicate spectra (Figure 2(Bottom)) were obtained for each blood-doped sample, under the same spectral sampling conditions as for neat fabrics. All replicate spectra of neat and doped fabrics were acquired using a defined orientation and face of the fabric. Simulations and Multivariate Analyses. Spectral simulations and data analysis were performed using MATLAB. Linear discriminant analysis was carried out using a MATLAB program by Michael Kiefte of Dalhousie University that is available for free download.22 Standard deviations for performance are calculated by propagation of errors. (21) Brooke, H.; Baranowski, M. R.; McCutcheon, J. N.; Morgan, S. L.; Myrick, M. L. Anal. Chem., in press, DOI: 10.1021/ac101107v. (22) Kiefte, M., http://www.mathworks.com/matlabcentral/fileexchange/18discrim.
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RESULTS AND DISCUSSION Simulating a Single Response. Simulation began by importing the series of spectral data sets. The response of the camera system to a single sample, i, when viewing the sample through a filter j, was computed using eq 2:
Table 1. Simulated and Experimental Results for the Ratios of Signals Measured on Fabrics for Validation Purposesa ratio
simulated
experimental
D/N Df/Nf
Acrylic 0.810 ± 0.009 0.868 ± 0.008
0.771 ± 0.016 0.849 ± 0.020
(2)
D/N Df/Nf
Cotton 0.927 ± 0.010 0.982 ± 0.010
0.85 ± 0.03 0.862 ± 0.029
Many of the quantities in eq 2 are relative spectral values, and thus, it describes a calculation of the relative signal, Sij, which is given by a summation over the wavelengths detected by the system represented by initial and final wavelengths λ1 and λ2. The terms in the summation include the reflectance, Ri(λ), of calibration sample i at each wavelength, λ; the efficiency, ηc(λ), of the camera system for detecting wavelength, λ; and the actual or simulated transmittance, Tj(λ), of filter j at each wavelength λ. The spectral efficiency of the camera system (Figure 1(Top)) is the product of the several fixed sensitivity parameters: the relative spectral response of the camera detector element, Rd(λ); the relative spectral efficiency of the light source, Φp(λ); and the approximate spectral transmittance of the 7-12 µm antireflection-coated lens, TAR(λ). Quantities assumed to have negligible influence on the spectra (e.g., the transmittance of germanium, the difference between the throughput of our particular lens and that of a “typical” lens provided by the manufacturer, etc.) were not included in the calculations. Tj(λ) in eq 2 was taken as either the actual, measured transmittance spectrum of a real filter (used when experimental data with a real filter was to be compared directly to the result of calculation) or a simulated spectrum (when the purpose was to determine the best filter material and thickness for a particular application). The unfiltered camera response was defined by assigning Tj ) 1. Validating the Single Response Simulation. The camera system was tested to validate that simulations based on eq 2 gave reasonable results. Although no images are provided here, intensities from images of the validation samples (described above) were extracted for quantitative comparisons. Table 1 shows data for both experimental and simulated responses. The simulations compare intensities measured for doped fabric reflectances relative to the neat fabrics (D/N ratios) when viewed directly (no subscript) or viewed through a filter (subscripted “f”). We also calculated and measured ratios of signals such as Nf/N, the ratio of signals for neat fabric viewed through a filter to those measured directly. Those ratios are not presented in Table 1 because the reflectance and scattering of the filter are not simulated. A two-sided F-test showed that the pooled variance in the simulated data is significantly different (p < 0.01) and lower than in the experimental data. In all cases, simulation suggested the fabric samples would have lower reflectances when doped than when neat. This trend is also found in the experimental data. In general, for a particular fabric, we find that the effect of a coating on the fabric is modeled with reasonable accuracy, despite the fact that differences found between simulated and experimentally determined response ratios
D/N Df/Nf
Nylon 0.774 ± 0.014 0.844 ± 0.013
0.912 ± 0.029 0.97 ± 0.03
D/N Df/Nf
Polyester 0.680 ± 0.005 0.784 ± 0.005
0.82 ± 0.04 0.86 ± 0.04
λ2
Sij )
∑ R (λ) × η (λ) × T (λ) i
c
j
λ1
where
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ηc(λ) ) Φp(λ) × TAR(λ) × Rd(λ)
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a D and N represent the reflected intensity of light from doped and neat fabrics, respectively, and the subscript “f” denotes the response is either simulated or measured with the Acryloid B67 filter in place. Uncertainties in the table are 95% confidence intervals (19 and 9 degrees of freedom, respectively, for simulated and experimental results), calculated by error propagation.
are statistically significant at the 95% level of confidence when compared for each fabric/filter condition pair of data sets. The average difference in the D/N ratio (experimental minus simulated response) was +0.029 ± 0.11, where the positive sign means that on average the simulation underestimated the experimentally determined response ratio. For two of four fabrics, the ratio differences between simulation and experiment were positive, while for two the differences were negative. When two-sided twosample t tests are conducted for each of the row comparisons in Table 1, the differences in response ratios are statistically significant at the 95% level of confidence. These differences between model and experiment are fairly small and not entirely unexpected due to the difference between the scattering angles detected by the camera system (∼30° between incidence and scattering) and the U-Cricket diffuse scattering accessory (∼120° between incidence and scattering) with which the fabric standards were measured. In addition, the modeled spectral throughput of the lens is taken from a “typical” spectral profile provided by the camera manufacturer and that is not necessarily the same as the actual lens used in our experiments. The remaining source of ratio offsets is due to errors in the actual reflectance spectra, such as baseline offsets, etc., relative to the effective reflectance spectrum of the fabric when measured with the camera system. The fabric samples were not measured with a “backing” in the diffuse reflectance accessory, while the thermal imaging measurements were recorded on fabric samples attached to a plywood board. Any light penetrating through the fabric samples could be reflected from the board and returned to the camera. Although likely a very small fraction, this could create a minor discrepancy between the simulated and experimental ratios. More important to the usefulness of simulation in instrument design is the ability to simulate the relative effects of viewing through filters. In each case analyzed, simulation shows that the D/N ratio should increase when viewed through the Acryloid B67 filter; experimental results confirm this trend. The simulated D/N ratio when filtered increases by an average 0.07 ± 0.03 (compared to unfiltered ratios, the experimental D/N ratio increases by 0.05
± 0.04 from unfiltered to filtered outcomes (values ±95% confidence interval, based on 3 df)). There is a general similarity of the modeled ratios themselves to their experimentally determined values and an even greater resemblance of the changes due to viewing through a filter of known composition. These results suggest that simulation is a reasonable approach to optimizing an experimental system of the type used here, an infrared camera with sequential filters, for chemical measurements. Optimizing Filter Selection. Accepting that simulation of the reflectance measurement of a sample is a valid approach to the design and selection of filter elements for a “molecular factor”type instrument, we constructed a MATLAB program that determines the optimal filter selection for the discrimination of a specific analyte. The first step in the program is the importing of DRIFTS spectra of calibration samples. Transmission spectra of possible molecular factor filters, as well as throughput or efficiency curves for all fixed elements of the system, are also assumed. The molecular factor filter spectra are themselves calculated from a single transmission spectrum of a thin film whose thickness is estimated gravimetrically (vide supra). The original measured transmission spectrum on a film near 6 µm thickness is used to estimate the spectral absorption coefficients, which are then used to estimate spectra for films at discrete thicknesses of 2, 4, 6, 8, and 10 µm to be imported in this step. No effort is made to make or simulate continuously variable molecular factor filters, as we have found the effect of a filter is a smoothly varying function with thickness. These data sets are arranged on different sheets of the same EXCEL file for ease of access and revision. A sheet is dedicated for each substrate’s calibration DRIFTS spectra (four sheets for four fabrics), with a single separate sheet containing the group assignments (1 for neat, 2 for doped), under the assumption that all fabric data sheets are organized the same way and contain the same number of samples. A single sheet holds the estimated spectra of all the possible molecular factor filters. Separate sheets hold data on the optical throughput of the lens, response of the detector, and spectral efficiency of the light source. The fixed system component spectral data use a common vibrational frequency vector (in wavenumbers), which is found on another sheet of the file and becomes the active spectral wavenumber vector for the entire calculation. Sheets containing DRIFTS and transmission spectra of filters and calibration samples include a wavelength vector in the first column of each sheet, which need not be the same as the wavelength vector for the fixed elements. If it is not, the spectra are interpolated onto the wavelength vector of the fixed components above. When this data file is read, the sheet labels and column titles are read and a structured variable is created with the native MATLAB “importdata” function in which each sheet becomes a variable named by the sheet label given in the EXCEL file. Another element of the structured variable is a vector of the column names for the possible molecular factor films. At the conclusion of this load operation, the computer will have stored the calibration spectra, group labels, and full instrument response, plus the (calculated) spectrum of each possible molecular factor filter.
A filter could be any available material and thickness provided in the EXCEL file. The program can then simulate the relative response of the camera for doped versus neat fabrics when viewed through each filter. These responses are calculated for the entire wavenumber range provided, as well as for user-defined subset spans of the entire spectrum as entered in the MATLAB command line. For example, if the user requests spans of 500 cm-1, then the outputs will be calculated for 500 cm-1 blocks of the spectrum, starting at the smallest wavenumber in the wavenumber vector. If the spectrum is not evenly divisible by the user-defined span, the final value is calculated for a 500 cm-1 block that ends with the highest wavenumber value in the wavenumber vector and overlaps with the previous one. These responses, plus the response simulation of viewing without a filter, are calculated for each individual spectral region and are treated as response vectors that can be used to discriminate between doped and neat fabrics using LDA. Discrimination between these two classes is characterized by a Fisher ratio which is calculated separately for each fabric and used as the FOM for optimization. Selection of an optimum filter is performed by “brute force.” FOMs are generated for every possible filter in each wavenumber region separately. The optimum (i.e., largest) FOM for each individual fabric is identified, and the filter and wavenumber region that produced this optimal FOM is recovered. The program produces the name and thickness of the filter with the highest FOM and the optimal wavelength range, for each type of fabric. A structured variable is also generated that contains the spectral and camera responses for each calibration sample when viewed through each possible filter and without a filter, the names of each potential filter, the wavelength subsets, the LDA scores and variates, the PCs chosen for compression, the FOM for each filter, the camera responses for the optimal filter for each fabric, the optimal wavelength vector for each fabric, and a variable with the indices for the optimal filter along with its FOM. This structured variable preserves the calculated data in case any further analysis is desired. For 20 possible filters, with 500 cm-1 sections, the total calculation time for this program is roughly 25 s on a single PC (3 GHz Intel Core2 Duo CPU, E8400 with 2.96 GB of RAM). Figures of Merit. To permit expansion of this method to larger numbers of filters, the first step in analysis is to consider the simulated set of responses and reduce them through principal components analysis. In the case of a single filter, the responses consist of the unfiltered and the filtered response. This dimension reduction is done as a prelude to reducing the dimensionality of the data in the event of covariance in the responses. However, the number of principal components (PCs) chosen to represent the data is never less than two (required by the linear discriminants engine being used, vide infra). For a single filter, the number of principal components selected is exactly two at all times, and the information that drives the LDA engine is exactly the same as if the raw simulation was provided to the engine. Once the principal components representing the filter set are chosen, scores for those principal components are multiplied by the eigenvalues for the corresponding PCs and then subjected to linear discriminant analysis for neat vs blood-doped sample spectra. The classification output is compared to the known classes Analytical Chemistry, Vol. 82, No. 20, October 15, 2010
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of the targets that were provided as an input, and if they disagree for any sample, a notation is made that the classification result was imperfect. The linear discriminant vectors (LDs) are then recovered and the scores of each spectrum on the LDs are computed. Scores of the two classes on the LDs are used as the basis for calculating a Fisher ratio. The Fisher ratio requires the mean scores of each class, the mean score of all samples, numbers of samples in each class, and the variances of the scores in each class.17 In our initial work, the variance of the doped sample data was larger than the variance of the neat fabric data, and we assumed the additional contribution to variance for doped samples was due to inhomogeneous coating. The true Fisher ratio should reflect the precision of the method as well as possible and be as little dependent on sample preparation as possible. Since the most reproducible samples in the initial phase of this project were those of neat fabric, we used the variance of the measurement on neat fabric to represent the variance of an idealized blood-doped sample as well. For data in this report, the two variances are essentially identical because of improvements in the reproducibility of coating developed as another part of our project.19 The Fisher ratio based on the selected principal components for the discrimination of the doped vs neat fabric classes is stored as a figure of merit. At the end of this stage of the simulation, all the filters are represented by a Fisher ratio for discriminating doped from neat fabric. The filter corresponding to the largest simulated Fisher ratio is then identified. This entire simulation process can be run for different spectral windows by assuming a top-hat spectral filter to restrict the camera system to a particular band. In this way, it is possible to narrow down the regions of greatest spectral importance for a given discrimination. CONCLUSIONS In an accompanying paper,21 experimental data for blood discrimination using a single-filter imaging system is provided. With 20 discrete filters consisting of four film materials and five thicknesses, even a single-filter imaging system is laborious to evaluate experimentally. Simulation provides a more convenient tool for determining the optimum filter, even when only a single filter is desired, because it does not require that all 20 filters be fabricated. It is also not susceptible to errors in filter fabrication, variable haziness in the filter substrates, or differences in the atmospheric humidity, detector temperature, etc. that could obscure the true optimum result in an experimental setting. In short, while simulation of the camera system response may be imperfect, we often forget that experiments are also imperfect and can be misleading. Simulation is at least consistent in its imperfections. The program described above was used to determine what single filter would allow for the best separation between doped and neat acrylic samples, using the full spectral range of the Merlin uncooled-microbolometer camera. For a doped sample with a 5× dilution of blood (dip-coated), the best filter was determined to be 2 µm of albumin, with a FOM of 1683; however, increasing the filter thickness did not decrease the FOM significantly as it remained above 1600 for thicknesses up to 10 µm. This setup is experimentally tested in another paper in this series.21 8426
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Molecular factor computing has been proposed in the past as a “poor man’s” version of hyperspectral spectroscopy or imaging. It has the advantage that simple chemical filters take the place of more complex spectroscopic components such as acousto-optical tunable filters, liquid crystal tunable filters, imaging spectrometers, and imaging interferometers. A positive aspect of molecular factor computing is that the range of filter elements is almost inexhaustible, and in principle, a system tailored to particular applications could be developed. The drawbacks associated with the wide range of potential components are that selection of an optimal set for any particular application is experimentally impractical. Simulation of the full system enables a complete, if approximate, analysis of all possible combinations of available system elements in rapid order. Although we have not done so, it is possible to include “hypothetical” system components, such as materials for which film-forming techniques are not yet developed, to ascertain whether a time investment in developing those components is worthwhile. One can propose filter components based on estimated spectral features derived from computational analysis, if the actual material is unavailable, to give a rough idea of the performance of a particular material, provided a reasonable computation method is available. Given the wide range of real, hypothetical, and theoretical filter elements that can be conceived of and the speed with which a reasonable simulation can be run, the design of a molecular-factortype imaging system is probably best driven by simulation. An advantage of this approach is that it is amenable to rapid recomputation if an additional filter set member becomes available or if a new target (e.g., explosive residues; fingerprint residues; oil stains; etc.) for analysis presents itself. We have shown in this report that it is possible to predict, by simulation, changes in system response that are reasonable reflections of true experimental measurements. Uncertainties estimated from simulations based on a spectral database of real spectra were found to be smaller than estimated experimental uncertainties. This is no doubt due to the noise characteristics of the infrared camera detector relative to a cooled laboratory infrared detector with long integration times used for collecting the reference spectral database from carefully standardized fabric samples. Consequently, simulation provides not just greater speed but better precision in selecting among system components than an experiment can provide. ACKNOWLEDGMENT This project was supported by Award No. 2007-DN-BX-K199 awarded by the National Institute of Justice, Office of Justice Programs, U.S. Department of Justice. The opinions, findings, and conclusions or recommendations expressed in this publication are those of the author(s) and do not necessarily reflect those of the Department of Justice. H.B. thanks the Graduate School of the University of South Carolina (Columbia) for travel and other support during this project. We also acknowledge James E. Hendrix for fabric acquisition and dyeing.
Received for review April 27, 2010. Accepted August 4, 2010. AC101108Z
