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Abstract
Miniaturized mid-infrared spectrometers present opportunities for applications that range from health monitoring to agriculture. One approach combines arrays of spectral filters with infrared photodetectors, called filter-array detector-array (FADA) microspectrometers. A paper recently reported a FADA microspectrometer in tandem with machine learning for chemical identification. In that work, a FADA microspectrometer with 20 filters was assembled and tested. The filters were band-pass, or band-stop designs that evenly spanned the microspectrometer’s operating wavelength range. However, given that a machine learning classifier can be trained on an arbitrary filter basis, it is not apparent that evenly spaced filters are optimal. Here, through simulations with noise, we use a genetic algorithm to optimize six bandpass filters to best identify liquid and gaseous chemicals. We report that the classifiers trained with the optimized filter sets outperform those trained with evenly spaced filter sets and those handpicked to target the absorption bands of the chemicals investigated.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Mid-infrared (MIR; 2.5-25 µm) spectroscopy is widely used to identify materials in science and industry. Each year, novel uses of MIR spectroscopy are found, for example to identify counterfeit bank notes [1], perform micro-archaeology [2], sort plastic waste [3] and to distinguish tree species using leaf spectra [4]. The current standard tool for MIR spectroscopy is the Fourier Transform Infrared (FTIR) spectrometer. FTIR spectrometers offer high resolution and high sensitivity but are generally bench-top tools. While this is not problematic for many applications, there is increasing interest in miniaturizing MIR spectrometers to enable them to be used in applications where size, power consumption, and weight are more important than optical performance. The integration of chip-scale MIR spectrometers, called microspectrometers, into smartphones, tablets, smart watches, and lightweight unattended vehicles may open up new applications in health care [5], chemical and hazard detection [6], environmental control and food quality evaluation [7].
At the shorter end of the MIR (<5 µm), several microspectrometers based on micro-electromechanical systems (MEMS) have been demonstrated [8]. These include microspectrometers that consist of MEMS-tunable Fabry-Perot filters integrated with broadband detectors [9,10]. Similarly, IR microspectrometers have been demonstrated that consist of Michelson interferometers with micro-actuated mirrors in one arm for Fourier Transform spectroscopy [10,11]. However, adapting these systems to target longer wavelengths (i.e 5–15 µm) is challenging as the longer optical path lengths (OPL) required are hard to obtain with MEMS actuators, as these have limited travel distances. Other FTIR spectrometers using thermo-optical [12] or electro-optical [13] systems require large device footprints because these phenomena produce small refractive index modulations. Another FTIR design simplifies analog modulation with discrete OPL changes using optical switches and waveguides of different lengths [14] to reconstruct spectra between 1550 nm to 1570 nm. It is not clear however whether this approach could be used at MIR wavelengths and over a wider spectral range.
An alternative microspectrometer architecture is the filter-array detector-array (FADA) spectrometer. Compared to the aforementioned approaches, FADA spectrometers have the advantage of simplicity. In a FADA spectrometer, an array of filters selectively transmit light to an array of detectors, the readouts of which are then used to reconstruct the input spectrum. The use of planar filters and no moving parts ensures that the device is as thin as possible. As it does not depend on OPL modulation, it is simpler to fabricate and is less susceptible to mechanical vibration or temperature fluctuations. Detector arrays are commercially available at relatively low cost at both visible and MIR wavelengths, being originally developed for color photography and thermal imaging, respectively. In the visible to near infrared region, filters used have included bandpass plasmonic filters [15], photonic crystals [16] and dielectric metasurfaces [17]. Thus far, nanopatterned metal filters [18,19] have been used for sensing in the ∼5–15 µm region. These consist of a thin metallic layer on top of a substrate like silicon with a periodic lattice of apertures which have a transmission spectra that depends on hole geometry and materials [20]. These can be tuned to operate from visible to MIR, be densely packed together, and only require a single lithography step. Although FADA spectrometers based on these technologies that are fully integrated and also reconstruct MIR spectra have not yet been reported, preliminary work emulating expected spectrometer operation with fabricated filter arrays have shown longer wavelengths sensing (∼5–15 µm) is feasible [18,19,21].
Spectral reconstruction is dependent upon, and scales with, the number of independent spectral channels i.e the number of filters. For example, in [19], good agreement between reconstructed and measured transmission spectra is shown to be possible using an array of 101 plasmonic bandpass filters that are evenly-spaced in the spectral domain. In [18], a wavelength range similar to Ref. [19] is spanned by 30 plasmonic filters. This leads to lossy spectral reconstruction with only the most prominent features of spectra being recovered.
Most previous microspectrometer works have aimed to reconstruct transmission spectra. One could then use these spectra for chemical or material identification, i.e using a spectral library. Meng et al [22] proposed a different approach in which chemicals and materials are identified directly from the sensor readouts using machine learning classifiers (MLC). In other words, the intermediate step of spectral reconstruction is omitted. The MLC is trained to distinguish between chemicals directly from the sensor readout. In their follow-up work with a fully-assembled prototype [23], the work referenced in the Abstract of this letter, Meng et al used a basis of 20 filters (bandpass and bandstop) that were tuned to probe the wavelength region of interest (7 µm to 14 µm) in equal intervals.
An evenly-spaced filter set is a sensible basis for spectral reconstruction, but an MLC can be used with any filter basis. The training process takes the input readout data and optimizes the MLC to deliver the best classification model. This raises several questions. Is it possible to optimize the filter basis to maximise MLC performance? If so, what enhancement can be expected? Furthermore, can this be used in situations where the number of investigated chemicals exceeds the number of filters?
Spectral filter selection seeks out an optimal subset of spectral filters that can accurately capture important discriminating information, whilst removing noise and sampling redundancy. Having fewer filter channels distills the data collection down to only the bands that give useful information and thus improve data acquisition speed and processing efficiency. This optimization has shown promising advantage over generic filter configurations (i.e evenly-spaced narrowband filters) in applications such as multi-spectral land imaging for ground object detection [24], environmental montoring [25] and mineralogical mapping [26]. Spectral filter optimization has been explored in biomedical imaging to improve recovery of histological skin parameters [27] as well as more recently to improve oxygen content monitoring in tissue [28,29]. However, there have been few instances of computational spectral band optimization for longwave infrared chemical detection. If bands are chosen, this typically involves manually targeting the main absorption features of a single target chemical (i.e non-dispersive gas sensors [30]), repeating the process for each additional chemical to be sensed.
In this paper, we use a genetic algorithm [31,32] to optimize a set of six bandpass filters, with the goal of maximizing the accuracy with which an MLC identifies up to 14 chemicals (six gases and eight liquids). Through MLC simulations that include noise, we find that the filters optimized by the genetic algorithm identify six liquid chemicals with a mean accuracy (92.6%, standard error: S.E = 0.21%) higher than that achieved with evenly spaced filter sets (87.8%, S.E = 0.21%) or filter sets handpicked to target key absorption features (89.9%, S.E = 0.20%). Of those six liquids, hexane is found to be the most challenging to classify, with the genetically optimized filter set reporting a higher accuracy (86.1%) than the other two hand-picked filter sets, at 71.4% and 74.6% respectively. When optimized to identify the combined batch of 15 liquid and gaseous chemicals (including void), we report that the genetic optimization achieves a mean accuracy (89.6%, S.E = 0.07%) higher than that obtained with six evenly spaced filter sets (86.6%, S.E = 0.08%). Of the combined batch, benzene is the most challenging to classify, with the genetically optimized filter set reporting 77.6% accuracy, compared to the 63.8% achieved by the evenly spaced filter set. In both cases, the optimization strongly enhances the classification accuracies of the chemicals that the evenly spaced filter sets struggle with.
The paper is structured as follows. In Section 2, we describe the simulation of our filter-array detector-array (FADA) spectrometer. The readouts of our spectrometer are modelled (Fig. 1) and used to generate interpolated data (Fig. 2) to train the machine learning classifier for chemical identification. The accuracy of the MLC is evaluated by classifying unseen test data. Classifiers are trained to identify seven liquid chemicals (including void) using two generic handpicked filter sets (each containing six bandpass filters) and the results are shown in Fig. 3. In Section 3, we describe the genetic algorithm used to find optimal filter sets (Fig. 4 & 5) with the optimized filter set results shown in Fig. 6. The effect of noise and different filter numbers is examined in Fig. 7. Next, the genetic algorithm is used to optimize six bandpass filters to identify a larger collection of 15 liquid and gaseous chemicals (including void). The baseline results for the evenly spaced filter sets are shown in Fig. 8 with the results from the optimization shown in Fig. 9. In section 4, we discuss the work’s limitations. In Section 5, the conclusion of this simulation study is provided. Additional details (Fig. 10–13) about the simulation modelling is provided in the Appendix at the end.
Fig. 1. Schematic of filter-array detector-array (FADA) implementation with a machine learning chemical classifier
2. Simulation details
2.1 FADA chemical classifier
A schematic diagram of chemical identification with the filter-array detector-array (FADA) spectrometer is provided as Fig. 1. The source illuminates the sample, with the transmitted light passing through the filter array before being collected by the sensor. Each raw readout ${i_m}$ from the sensor can be modeled as follows:
The liquid and gaseous chemicals we consider in this study are chosen because they are commonly used in scientific laboratories and industry. The six liquid chemicals chosen are: acetic acid (CH3COOH), acetone (C3H6O), chloroform (CHCl3), ethanol (C2H5OH), hexane (C6H14), and toluene (C7H8). The eight gaseous chemicals chosen are: ammonia (NH3), benzene (C6H6), ethane (C2H6), ethene (C2H4), ethyne (C2H2), nitrous oxide (N2O), ozone (O3), and sulfur dioxide (SO2). The chemicals are included in our model as follows. The molecular absorption cross-section data, taken from HITRAN database [34], is used to calculate the transmittances of the chemicals from the Beer-Lambert Law (Fig. 2(a)). The optical path lengths assumed for the liquid and gaseous measurements are 0.01 cm and 10 cm, respectively as these are common values for liquid membrane cells and gas cells. For convenience, the concentrations are expressed as percentages in units of normalized molarity (N.M), which is defined as the molar concentration (M; molarity) divided by the analyte’s molarity when in pure form. The concentration range considered here is from 1% to 100%. For example, the molarity of pure acetic acid (at 298 K and 1 atm pressure) is 17.5 M. This means that a diluted acetic acid solution of 0.175M has a normalized molarity of 1%.
Fig. 2. a) Beer-Lambert Law calculated transmittances of the six liquid chemicals (and void) for normalized molarities (N.M) of 1%, 10% and 100%. b) to f) show the process of generating training data for acetic acid using six evenly spaced filters. b) Raw readouts, with noise, for acetic acid for 1% (blue curve), 10% (red curve) and 100% (yellow-gold curve) N.M according to Eq 1. c) Readouts, with noise, for void class, d) Reference normalized readouts, corresponding to raw readouts divided by void readouts. e) Intermediate concentrations readouts modeled by interpolation. There are 19 interpolated concentrations between 1% – 10% N.M and another 19 between 10% – 100% N.M (for a total of 41 concentrations). f) Exemplary training data for acetic acid comprises of 20 instances of readouts for each of the 41 different concentrations, for a total of 820 sets of data.
As discussed, an important motivation for FADA microspectrometers is their simplicity, which presents the opportunity for miniaturization. To make our study consistent with the latter, in our model we take the normalized sensor response R to be that of a lightweight (mass < 1g) thermal camera that is available at low cost (FLIR Lepton, [33]) at the time of writing. We assume that each camera frame has a signal to noise ratio (SNR) of 10 dB. Our model also assumes frame-averaging (FA) to further reduce image noise: $\left\langle {{i_m}} \right\rangle $. Each readout models FA over three seconds, by averaging data collected over 27 frames (which would comprise data collection for three seconds at nine frames-per-second, the maximum frame rate of the FLIR Lepton). The raw readouts (Fig. 2(b)) are normalized by a reference readout $\left\langle {{o_m}} \right\rangle $ (Fig. 2(c)) to give a reference normalized readout: ${I_m} = \frac{{\left\langle {{i_m}} \right\rangle }}{{\left\langle {{o_m}} \right\rangle }}$. The reference readouts correspond to readout measurements made when there is no sample present (i.e void; assume ${T_c} = 1$). From here on, the term “readouts” will be used as shorthand for reference normalized frame-averaged readouts.
In an experimental implementation, the machine learning classifier (MLC) would be trained through supervised learning. For each chemical, the readouts from several standard concentrations (e.g 1%, 10% and 100%) would be collected. To reduce the number of experiments that need to be conducted, training at intermediate concentrations would be performed by interpolation of the experimental results. This would enable the MLC to identify chemicals at many concentrations. We emulate this process via simulations as follows. The transmittances for the chemicals considered (Fig. 2(a)) and the “void” class are calculated at standard concentrations (of 1%, 10% and 100%) and the frame-averaged raw readouts (Fig. 2(b)), reference readouts (Fig. 2(c)) and corresponding reference normalized readouts (Fig. 2(d)) are all modeled. The readouts that would be obtained for intermediate concentrations are approximated by interpolating between the three readouts at the standard concentrations (Fig. 2(e)). These steps are repeated multiple (20) times to generate sufficient readout data with which to train the MLC (Fig. 2(f)).
Fig. 3. Transmission matrices for typically used filter sets. a) evenly spaced filter set, c) handpicked filter set, with its corresponding confusion matrices respectively in b) and d). Each row represents the true label of an instance of test data, and the corresponding column represents the MLC’s predicted classification.
We evaluate the accuracy of our trained MLCs by classifying unseen test data. The test comprises 1000 randomly chosen concentrations for each chemical class, totaling 7000 when the MLC is used only for liquid chemicals, or 15000 when it used for both liquid and gaseous chemicals (both inclusive of “void” class). Once selected, the 1000 test concentrations remain fixed for all subsequent simulations (Fig. 12). The test consists of randomly picking 500 concentrations from each of two ranges, namely 1% to 10% and 10% to 100%. The random selection follows a uniform probability distribution. The classification accuracy is taken to be the total proportion correct, i.e the average accuracy of all classes. A trained MLC will report accuracies that vary from test to test due to the random nature of the white noise model. To account for this, the accuracies reported in the manuscript are the mean of 10 tests with the uncertainty reported as the standard error (S.E). The test results are presented as confusion matrices which show the percentage of correct classifications along the diagonal and misclassifications elsewhere for the tests all together.
2.2 Supervised machine learning classifier
We next discuss the details of the supervised classifier. We perform chemical classification using a multi-class, linear kernel, support vector machine (SVM) classifier (fitcecoc; MATLAB R2020b [35]) with error-correcting outputs. We compare the following methods: k-nearest neighbors, decision trees, discriminant analysis and SVM. We find that SVM provides the highest accuracy (Fig. 13). An SVM learns to classify data by projecting it into a higher dimensional space and calculating decision boundary hyperplanes that give best data separation. The kernel specifies the projection of the original data to the new feature space (e.g linear, quadratic, Gaussian etc). For the chemicals investigated, we find no significant difference between using linear, quadratic and Gaussian kernels. We thus choose linear kernel due to its simplicity. A single SVM is only capable of binary classification. We therefore combine it with error-correcting output codes to transform the original multiclass classification into a system of multiple, binary classification problems. This is done by training an SVM for each unique chemical pair, and then comparing the outputs to determine the final classification.
As discussed in the next section, we use genetic optimization to design filters for our FADA system. We benchmark the effectiveness of these filters by their classification performance to that achieved with two other filter sets. The first is termed the “evenly spaced filter set” and comprises bandpass filters that cover the investigated wavelength range (7 µm – 14 µm) in equally spaced intervals, with minimal overlap (Fig. 3(a)). This approach has been frequently used in previous FADA microspectrometer investigations [18,19,22,23,36]. An MLC trained with this filter set delivers an accuracy of 87.8% (S.E = 0.21%) (Fig. 3(b)) and struggles to classify hexane. Hexane have relatively weaker absorption features (Fig. 2(a)) thus low concentrations are frequently misclassified as “void”.
The second filter set considered is termed the “handpicked filter set” and comprises bandpass filters. The spectral position and width of the filters’ passbands are chosen based on the absorption spectra of the chemicals. We investigate classification performance for a set of filters with passband widths equal to the full width at half-maximum (FWHM; Fig. 3(c)) values of the strongest absorption peak of each of the chemicals considered, at a normalized molarity of 10%. This approach draws inspiration from that used in commercial non-dispersive infrared (NDIR) gas sensors that pair a detector and bandpass filter tuned to sense the target gas’ key absorption band. For example, a carbon dioxide NDIR gas sensor [30] has a single filter with its passband tuned to the gas’ prominent absorption band at a wavelength of 4.3 µm. Using the handpicked filter set, the trained MLC delivers better classification accuracy (89.9%, S.E = 0.20%) than the evenly spaced filter set (87.8%, S.E = 0.21%). The handpicked filter set (Fig. 3(c)) outperforms the evenly-spaced filter set for hexane classification (74.6% vs 71.4%) and has superior accuracy for the other chemicals. This provides early indication that tuning filters to the chemicals being examined can enhance the performance of a chemical classifier.
2.2 Genetic algorithm
A genetic algorithm is a stochastic approach to finding solutions to problems that is inspired by biological evolution [31,32]. It involves manipulating a large population of candidate solutions, assigning a fitness quality to each, and then using evolutionary strategies such as selection, cross-over and mutations to generate an improved population of candidate solutions. Sifting through solutions in large populations effects parallelism which explores many solutions simultaneously. Additionally, the conceptual simplicity of the algorithm makes it adaptable to solving a broad range of problems where sufficiently good solutions suffice. In effect, it enables good solutions to be found, even though only a small fraction of possibilities are investigated. This makes it suitable for problems where the solution space is too expansive to search and poorly-understood. Genetic algorithms have previously been used in nanophotonics, including to design metasurfaces to achieve desired transmission spectra [37–39] and for polarization control [40].
Fig. 4. Diagram visualizing the genetic optimization cycle; child (subsequent) generations are made up of three subsets: elite, crossing-over and mutations. Once the child generation is completed it then becomes the new parent generation and the cycle repeats.
Fig. 5. Diagrams visualizing the three child subsets in the genetic optimization algorithm. a) The elite subset consists of the top ten performing filter sets from the parent (prior) generation. b) A color-coded visualization of the crossing-over process used to mix pairs of parent filters together to generate children. c) The mutations subset consists of 45 parent filter sets which have had the spectral location and width of all its bandpass filters randomly altered (within 10% of original values). The mutations are exaggerated for visibility and grey dashed lines provide visual guidance.
The genetic algorithm we use to optimize our filter sets can be summarized as follows (Fig. 4). An initial population of 100 random filter sets (each containing six filters) is generated. Each filter has a single passband with a random center wavelength and with a spectral width between 7 nm and 7 µm. The latter is chosen randomly, following a uniform probability distribution. Each filter set is used to train an MLC and the accuracy is evaluated. This parent population of filter sets is then used to generate the subsequent child population via three subsets. The first subset is elite selection wherein the top ten performing filter sets from the parent generation are directly carried over to the child population (Fig. 5(a)). The second subset consists of 45 filter sets generated by mixing random pairs of parents (Fig. 5(b)). The mixing emulates chromosomal cross-over as the new filter set is built by randomly selecting, with equal probability, unmodified filters from either parent. The final subset consists of filter sets that have had the passbands of all filters randomly mutated (Fig. 5(c)). Of the top 80 parents, 45 filter sets are randomly chosen. Both the spectral position and width of the passband of each filter contained in the latter are randomly modified. The change is picked from a uniform distribution and limited to being no more than 10% of the initial value to ensure the tweaking is not excessive. This principle follows from biological evolution’s preference for change over longer time scales. The random mutations introduce new variation into the filters of each population. Once the child population is complete, new MLCs are trained and the corresponding averaged classification accuracies are recorded. Afterwards, the algorithm proceeds with the next iteration and the filter sets just produced becomes the parent population. The algorithm is repeated 100 times to produce a final run of 101 populations of filter sets. The genetically optimized filter set is thus the best performing filter set of the final generation.
3. Results
3.1 6 Filters: Seven liquid chemical classes (including void)
We next describe the results achieved by using our genetic algorithm to produce a filter set for classifying the six liquid chemicals chosen for our study. The filter set obtained from the genetic algorithm is illustrated in Fig. 6(a). We later explore how the accuracy evolves with iteration number and present its classification performance. The accuracy of the filter set versus population generation is shown in Fig. 6(b). As the process advances, the 95% confidence interval and the interquartile range shrink. As each population is generated and probes the solution search space, elite selection and cross-over help direct the algorithm’s search effort closer to regions with promising results (i.e. to filter sets with higher accuracies). This naturally causes the population accuracy to increase, and for successive generations of filter sets to look more similar. The random mutations introduce variation to individual filters which otherwise remain untouched by the selection and crossing-over process. By the last generation (101), the top performing filter sets are very similar. The six filters contained within each set are almost identical, with the only notable difference being ordering. The classification accuracy of the optimized filter set is 92.6% (S.E = 0.21%, Fig. 6(c)) whilst it is 87.8% (Fig. 3(b)) for evenly spaced filter set and 89.9% for handpicked filter set (Fig. 3(d)). The optimization delivers favorable performance gains because it improves the accuracy of hexane to 86.1%, acetone to 93.6% and toluene to 91.5%, compared to 71.4%, 86.8% and 84.0% for evenly-spaced filters. Incorrect classifications of hexane as “void” nearly halve (from 25.7% for evenly-spaced filters down to 13.9%) but are not completely removed. At low concentrations (∼1% N.M) of hexane, subtle fluctuations in readouts from absorption becomes indistinguishable against the background of white noise in void measurements, indicating a potential limitation of the FADA platform.
Fig. 6. a) Genetically optimized set of six filters for six liquid chemicals (and void). b) Accuracy vs evolution generation for six filter optimizations. Rectangular shaded box indicates middle 50% of data (interquartile range) that sits around the median (black line). Whiskers (protruding lines) indicate 95% confidence interval, i.e. range of values that contains 95% of recorded accuracies. Outliers are indicated by unfilled circles. Average accuracy is represented by the yellow line. c) Confusion matrix of genetically optimized filter sets, indicating average of 92.6% and standard error of 0.21%. d) Surface plots of mean accuracies of classifiers trained with the genetically optimized filter set (GA) and evenly-spaced filter set (ES) under various image SNR and frame average conditions. Bottom-most surface plot indicates the difference between the GA and ES results (GA$- $ES).
It is useful to compare the optimized filter set with the transmittances of the chemicals studied (Fig. 2(a)). The genetically optimized filters are seen to cluster around spectral regions where the investigated chemicals have rich absorption features. The genetic algorithm is better than handpicking filters to match chemical’s absorption bands because it also considers the effect of each filter on identifying all the other investigated chemicals. Hence it adjusts filter parameters accordingly for optimal performance. Filters 1 and 2 probe the $\lambda = \; $ 7–8.5 µm region where most of the chemicals have notable spectral features, except for toluene. Filter 3 overlaps with ethanol’s 11 µm absorption band. Filters 4–6 cover the $\lambda = $ 13 - 14 µm region where toluene and chloroform have absorption features.
Next, we compare the performance of MLCs trained with the optimized filter set and the evenly-spaced filter set, in various noise conditions. We consider a range of image SNR values from 2 to 20 and frame averaging values from 3 to 54. The mean accuracy recorded for each condition is shown as a surface plot in Fig. 6(d). The top surface is the performance of the optimized filter set (GA); the middle surface corresponds to that of the evenly-spaced filter set (ES); and the bottom-most surface corresponds to the absolute difference between the two sets. In the noise cases examined, the classification accuracy of the optimized filter set is consistently higher than that of the evenly-spaced filter set. The optimized filters strongly outperforms the evenly-spaced filters in noisier environments, with the greatest difference recorded to be 21.2% (for image SNR = 4 and frame average = 3). But it should be noted that the improved accuracy of 73.8% (up from 52.6%) is still poor. When noise is lowest (image SNR = 20 and frame average = 54), the performance difference shrinks to 2.4%, with the optimized filter set returning 94.1% accuracy compared to the 91.7% of the evenly-spaced filter set.
Fig. 7. a) Surface plots of classification accuracies for optimized filter set (GA) and evenly-spaced filter set (ES) as a function of filter numbers and SNR. Bottom-most surface plot indicates the difference between the GA and ES results (GA$- $ES). b) Genetically optimized filter sets for 3, 7, 12 and 24 filters (for SNR = 10 and FA = 27).
To evaluate the effect of filter numbers on accuracy, we optimize sets with 3, 6, 7, 12 and 24 filters under various noise levels (SNR = 1, 5, 10 and 20, FA = 27) and compare its performance with its evenly-spaced counterparts. The results are shown as a surface plot in Fig. 7(a). The top surface corresponds to the performance of the optimizations (GA); the middle surface corresponds to the performance of the evenly-spaced counterparts (ES); and the bottommost surface shows the difference between the two (GA-ES). As shown, the optimized filter sets consistently outperforms the evenly-spaced configuration. Adding more filters to the optimized sets does improve performance in noisy environments (from 53.7% with 3 filters, to 75.4% with 24 filters at SNR = 1), but with smaller effect at higher SNR values (from 91.4% with 3 filters, to 94.5% with 24 filters at SNR = 20). As image SNR and filter number increases, the absolute difference between the optimized and evenly-spaced filters diminishes, from a maximum of 20.9% at SNR = 1 with 3 filters (GA = 53.7%, ES = 32.8%) to a negligible 0.1% at SNR = 20 with 24 filters (GA = 94.5%, ES = 94.4%). At SNR = 10, having more filters than six has little benefit and would increase the size and cost of the device. As shown in the transmission matrices for 3, 7, 12 and 24 filters (Fig. 7(b)), the additional filters considerably overlap each other. This is a combination of avoiding spectral regions that offer limited discriminating information or add extra noise. Alternatively, sampling from three filters is enough to achieve 88.7% accuracy and indicates the possibility of identifying more chemicals than number of filters available.
3.2 6 Filters: 15 liquid & gaseous chemical classes (including void)
Without further modifications, the genetic algorithm performs filter choice optimization in cases where the number of filters and chemical classes considered are not equal. The standard handpicking strategy of choosing the filter passband to match the main absorption lines of the liquids/gases only works when the number of said filters is equal to the number of target chemicals. Since handpicking is unavailable, we only compare the evenly spaced filter set (Fig. 8(a)) to the genetically optimized filter set (Fig. 9(a)). Here we consider the case where we still have six filters, but now include gases into the sample selection for a total of 15 chemical classes (void included). With still six evenly spaced filters, the new classifier has an average accuracy of 86.6% (S.E = 0.08%, Fig. 8(b)), where worst performance occurs for benzene and hexane, at 63.8% and 71.3% respectively. The genetically optimized filter set for this problem is shown in Fig. 9(a). The confusion matrix indicates an average accuracy of 89.6% (Fig. 9(b)), where the worst performers are still benzene and hexane, but have accuracies boosted to 77.6% and 79.5% respectively. Across the 15 classes, the optimization improves upon the accuracies of 10 of the chemicals with the greatest increase of 13.8% for benzene. This benefit comes at a slight accuracy compromise to the remaining five classes, with the steepest decline capped at a modest 2.2% for acetic acid.
Fig. 8. a) Transmission of six evenly spaced filters. b) Confusion matrix of corresponding trained MLC for a selection of 15 chemical classes.
Fig. 9. a) Transmission of six genetically optimized filters. b) Confusion matrix of corresponding trained MLC for a selection of 15 chemical classes.
4. Discussions
In this work, we show that a genetic algorithm represents a fairly simple means to select filters for chemical identification. We have identified several limitations to our study. The first is the zero-mean Gaussian white noise assumption about the FADA spectrometer. The actual experimental noise will depend on the source, the detector, samples, and performance of the fabricated filters. Secondly, the readout modelling does not account for temperature and pressure variations. These parameters may affect the stability of the device beyond that accounted for by our simple Gaussian white noise approximation. These may induce drifts in the readouts that would require suitable controls for monitoring, stabilization, and compensation, all of which are not included in this simplified model. The third limitation is that we currently only consider idealized bandpass filters. In practice, fabricated bandpass filters will invariably have different lineshapes and these will change the readout values expected. But our results show that filter optimization has greatest effect in noisier environments. Thus, it is expected that spectral band optimization involving realistic filter functions should still prove superior at chemical detection over generic filter sets. The fourth limitation of the model is that it does not consider humidity, and by extension, chemical mixtures. This may require adding training data of standardized sample mixtures, and require additional modelling, but that is beyond the current scope of this work.
5. Conclusion
The results we present indicate that spectral band optimization can have a tangible improvement to the performance of a FADA chemical classifier. Through simulations, we demonstrate that a genetic optimization algorithm can select a set of filters that improves the accuracy with which a filter-array detector-array (FADA) chemical classifier identifies chemicals. A genetic optimization uses large populations of candidate filter sets and iteratively improves upon them with mechanisms inspired by biological evolution, namely selection, cross-over and mutations. We first use the genetic algorithm to optimize a set of six bandpass mid-infrared (MIR) filters to identify six liquid chemicals (and the void class). The machine learning classifier trained with this genetically optimized filter sets achieves 92.6% accuracy and out-performs evenly spaced filters (87.8%) and handpicked filters tuned to main absorption bands (89.9%). The optimization significantly improves the classification accuracies of the most difficult-to-identify chemicals (e.g toluene and hexane) as well as the void class. Furthermore, without modification, we use the genetic algorithm to optimize six filters but tasked with identifying an additional eight gaseous chemicals for a total of 15 chemical classes (including “void”). The genetically optimized filter set achieves an accuracy of 89.6% whilst the evenly spaced filter set manages 86.6%. Again, the optimization significantly improves the classification of the most difficult chemicals (e.g benzene and hexane) and improves the accuracy of most other chemicals investigated. Future developments of this work could involve using realistic filters (i.e that are not idealized and have finite optical densities, etc.), its application to other classification problems (e.g concentration detection) and its experimental demonstration.
Appendix
A1. Blackbody illumination ${B_T}$
The infrared illumination source is assumed to be a blackbody at T = 373.15K. The radiance is given by Planck’s Law:
A2. Normalized response of thermal camera
The infrared detector in this study is assumed to be the FLIR Lepton microbolometer. The normalized responsivity R of a typical pixel is taken from the engineering datasheet [33].
A3. Calculating transmission spectra of chemicals from Beer-Lambert Law
The transmission spectra Tc of the investigated chemicals are modelled from the Beer-Lambert Law:
where $\tau $ is the optical depth, ${\sigma _{cs}}$ is absorption cross-section (cm2 molecule−1) of the chemical, $\eta $ is the number density of the chemical (molecules cm−3) and l is the optical length (cm). The transmittance of the sample (i.e transmission spectra of the sample) is calculated as: The absorption cross-section of the chemicals investigated were taken from the HITRAN database (https://hitran.org/xsc/). The number density is calculated as $\eta = \frac{\rho }{m}c$ where $\rho $ is the density (g cm−3), m is the molecular weight (g mol−1) and c is the concentration as normalized molarity (unitless; concentration as a proportion of the sample’s molarity in pure form). Both $\rho $ and m were obtained from PubChem database (https://pubchem.ncbi.nlm.nih.gov/).A4. Testing concentrations used for classification evaluation
The 1000 random concentrations used for classification accuracy testing, ordered from lowest to highest, are plotted below. There are 500 concentrations between 1% – 10% N.M and another 500 concentrations between 10% – 100% N.M. These remain fixed for all simulations.
A4. Performance comparison between different classification models
Below, we show the show and compare the performance of different classification models. The models considered are Binary Decision Tree (BDT; fitctree, MATLAB R2020b), Discriminant Analysis (DA; fitcdiscr, MATLAB R2020b), K-Nearest Neighbour (KNN; fitcknn, MATLAB R2020b) and Support Vector Machines (SVM; fitcecoc, MATLAB R2020b) with various kernels.
Each model is tasked with using the six evenly-spaced filter set to identify 7 liquid chemical classes (including void). The histograms of the output accuracies of 100 test evaluations are shown in Fig. 13. The SVM models outperform the other classifiers for this scenario. The performance differences between different kernels is minor. Thus, the SVM with a linear kernel was chosen for its simplicity.
Funding
Australian Research Council (CE200100010); Defence Science Institute.
Disclosures
The authors declare no competing financial interests.
Data availability
Data may be obtained from the authors upon reasonable request.
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