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Abstract
Plastic identification is a fundamental step in material and chemical recycling. Overlap between plastics is a common limitation of existing identification methods, and it is necessary for plastic waste to be shredded and spread over an area to avoid overlapping between flakes. However, this process decreases sorting efficiency and also increases the risk of misidentification. This study specifically focuses on plastic sheets and aims to develop an efficient identification method for overlapping plastic sheets, by using short-wavelength infrared hyperspectral imaging. The method is based on the Lambert–Beer law and is simple to implement. We consider a practical situation with a reflection-based measurement system and demonstrate the identification performance of the proposed method. The tolerance of the proposed method against error sources of measurement is also discussed.
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1. Introduction
Plastic recycling has been posing a challenge to developing a sustainable society [1,2]. Material and chemical recycling is an attractive option for overcoming the environmental impact caused by the disposal or thermal reuse of plastic waste and has an important role to tackle with the ever increasing amount of such waste [3,4]. Plastic identification is its fundamental step, since in most cases, a high purity of plastics is required for their material and chemical recycling.
The achievable purity of sorted plastics varies depending on the composition of plastic products [5], and specific strategies are required to identify materials. Of these materials, we focus on see-through plastic sheets used for various products, of which consumption has recently increased everywhere to guard us from infections, and such waste, after use or replacement, has become a crucial issue [6–8]. These plastic sheets are in general composed of the same, uniform material and thus considered to be a feasible candidate for material and chemical recycling. Industries have been devoted to developing scalable chemical recycling technologies for such resources and to overcome difficulties due to the degradation of or additives in plastics [9–12]. For this reason, the development of efficient and accurate methods for identifying of plastic sheets is now of great importance.
Hyperspectral imaging (HSI) allows noninvasive, instant, on-site identification of plastics that are difficult for the human eye to distinguish from each other to a certain level of categorization [13–33]. It has also been studied as a promising candidate for reducing the environmental impact of heavy water usage or media that physically interact with plastics, which are needless for spectroscopic measurement. However, existing plastic identification or sorting systems, irrespective of whether they use HSI or other approaches, have a common limitation, namely that plastic wastes are crushed into mixed flakes and categorized into registered materials, at which time overlapping plastics are misclassified or discarded as outliers. Although the overlap of flakes is avoided by spreading them over an area, this limits the amount of waste that can be processed within a unit time and the area of a system. In the first place, crush-and-mix makes it inefficient to sort plastic sheets that were originally composed of uniform materials, and worse, could increase the possibility of misclassification.
The motivation of this study is to circumvent this limitation to facilitate material uniformity of plastic sheets and enable identification using HSI even when sheets are overlapping and then to provide a practical option to increase the efficiency and accuracy of identifying plastic sheets. More specifically, if we could identify roughly stacked and overlapping plastic sheets without crushing them into flakes, both the system efficiency, including manual sorting of the identified plastics, and the purity of the sorted plastics would increase.
There are some discussions with a shared motivation to address the classification problem of overlapping plastics. Hollstein et al. [18] discussed this problem; however, it was assumed that reflectance spectra from overlapping plastic sheets are the linear summation of each reflectance spectrum from the single plastic sheet. Martinez et al. [34] introduced an idea that regards the overlapping plastic classification problem as a weighted regression problem on a neural network. However, the method requires a number of overlapping combinations of plastic flakes as its training dataset. In contrast, our approach is described with light absorption and requires no dataset with various combinations of plastics.
We present an identification method based simply on Lambert–Beer law. In our experiment, we use short-wavelength infrared HSI (SWIR-HSI) that measures spectral image data over 900–1700 nm. Compared with infrared imaging and the other systems measuring the spectra of longer wavelengths or Raman shifts, SWIR-HSI enables installation costs to be reduced while also having sufficient ability to inform us of the distinct optical features of various plastic materials, which are difficult to obtain from the visible wavelength region. Note that the “see-through” property of plastic sheets is assumed for the SWIR wavelength region, but the proposed method may be extended to wider targets by using the other wavelength regions that transmit sufficient flux of light. While reflection spectra are used for plastic sorting in most practical situations, the principle behind plastic identification using spectroscopy relates to the light absorption by the molecular vibration of polymers. When considering plastic sheets on a conveyor belt, since they are transparent, trans-reflection describes the measured spectra. That is, we analyze reflected light from the surface of the conveyor belt after transmission through plastic sheets. Lambert–Beer law describes how light is absorbed over the transmission path. We formulate the estimation of the transmission paths as weights on a linear regression problem that correspond to the thicknesses of the sheets. As the algorithm is simple, based purely on Lambert–Beer law, it is possible to estimate the thickness distribution of overlapping sheets by a fast computation of a single matrix multiplication. From the estimated thicknesses, we can interpret that the nonzero thicknesses of the registered plastics have been identified to exist. In practice, the presented identification approach ignores outliers due to measurement error and outlier reflection mainly from the edges (or scratches and cracks on the surface, if they exist) of sheets. The outliers on measured spectra cause estimation error of thickness. We also consider a simple technique to mitigate such errors using a conventional image processing technique. The simple technique worked in our test because non-crushed sheets have sufficient surface area, compared with the area of the edges, and they have sufficient thickness in general (the tested materials had thicknesses of 2 and 3 mm), being dominant in measured spectra, compared with the outliers. We discuss a strategy to detect unregistered plastics, which may exist in practical situations. We end by discussing another cause of error due to light interference between overlapping sheets.
2. Materials and methods
We describe the plastic sheets tested in this study (Section 2.1), the SWIR-SHI system for measurement (Section 2.2), and the proposed method to estimate the thickness distribution of plastics based on Lambert–Beer law (Section 2.3).
2.1 Tested plastic sheets and reflectors
We tested the proposed method against sheets made from the following four different plastics: polyethylene terephthalate (PET), acrylic (AC), polycarbonate (PC), and polyvinyl chloride (PVC). Each were 2 and 3 millimeters of thickness and measured $50 \times 50$ millimeters in square size (Fig. 1).
Fig. 1. (a) Photo of overlapping plastic sheets on the green belt and (b) its annotation. (c) Photo of overlapping plastic sheets on the polytetrafluoroethylene sheet and (d) its annotation. The labels in (b) and (d) were abbreviated as “plastic name–thickness” (mm).
The following characterizations are essential for the proposed method to work: First, the sheets have characteristic absorption bands in the SWIR region; second, the transmittance is sufficient, and thus we assume that a sufficient light intensity is observed for the trans-reflection through the sheets (these properties are shown in Section 3.1, Fig. 4); third, there is no diffuse-like reflection due to back-scattering. If such diffuse reflection exists, a nonlinear equation is required, which is not straightforward to solve. Plastic sheets used as see-through sheets generally have these properties.
We tested two reflectors placed under the sheets, namely a green belt, which is a common option for industry (Fig. 1(a)), and a polytetrafluoroethylene sheet (Fig. 1(c)), which is often used as a reference board to calibrate hyperspectral imaging systems due to its uniform reflectance over wavelengths. Aluminum plate is also often used for conveyor belts, but it was not tested here. The texture of the polytetrafluoroethylene sheet is more uniform, compared with that of the green belt. As a reflection from the belt is assumed to be uniform over regions, such a texture affects thickness estimation; nevertheless, we will confirm that the influence is small and can be mitigated by the simple image processing techniques used in this study.
2.2 Measurement system
We used a SWIR-HSI system (RESONON Inc.) provided by KLV Co., Ltd. This is a line sensor that takes 320 pixels every line and has a spectral sensitivity over wavelength ($\lambda$) of 900–1700 nm with 164 spectral bands, 4.9 nm of the full width at half maximum.
In explaning the system, the $XYZ$-coordinate system in Fig. 2(a) is associated with the fixed body (the camera and the pole) of the system and not associated with the motorized plane. In this experiment, a target object is placed on a motorized stage (parallel to the $XY$-plane) lit by line-focused halogen illumination. The hyperspectral image data of $XY \lambda$-dimensions is stored by concatenating $X \lambda$-dimensional snapshot data over the orthogonal direction ($Y$), along which the stage is motorized.
2.3 Identification algorithm of overlapping sheets
Figure 2(b) illustrates how trans-reflection is observed from overlapping sheets. We assume total $M$ ($=4$, specifically in this study) sheets of the four different plastics, namely PET ($m=1$), AC ($m=2$), PC ($m=3$), PVC ($m=4$), with absorption coefficients per 1 mm thickness $\sigma _m(\lambda )$ overlapping with total $L_m$ of thicknesses $(m = 1, \ldots, M)$. These sheets are placed nearly parallel to the reflector conveyor stage ($XY$-plane). Note that we cannot distinguish the stacking order of the sheets and can only estimate the total sheet thickness $L_m$ of each plastic $m$. $L_m=0$ means that the plastic labeled $m$ does not exist.
We assume that the tilt angles from perfectly parallel stacking on the reflector and the change of path length from refraction are small. Since specular reflection from the surface of a sheet disturbs trans-reflection spectra, we assume the sheets are stacked with off-the-specular reflection approximately determined by the incident angle $\theta$ between the optical axis ($Z$) and the light source (Fig. 2(b)). As the sheets are placed nearly parallel to the conveyor, specular reflections can be avoided by letting the light source be sufficiently tilted against the optical axis.
Under these assumptions, and by using Lambert–Beer law, an observed spectrum $I(\lambda )$ at a point $(X, Y)$ is approximately written as
where $I_0(\lambda )$ is the illumination spectrum and $R(\lambda )$ is the reflectance of the conveyor table, which is assumed to be uniform over all the observed points. Note that we could always measure $I_0(\lambda ) R(\lambda )$ in a calibration step, but it would be better to allow ambiguity of the light intensity, which is the constant $A_0$ over wavelength. This ambiguity allows a change of the light intensity after calibration or a change of conveyor speed that changes exposure time. $\sigma _m'(\lambda ) = (1 + 1/{\rm cos}\theta ) \sigma _m(\lambda )$ is the absorption coefficient per trans-reflection through 1 mm thickness, considering the incident angle $\theta$.Provided the spectral calibration of the sensor, we calculate
In the form of matrix-vector multiplication, given $B$ spectral bands as input, we have
The estimated thicknesses of the sheets are affected by the edges of the sheets (Section 1), the nonuniformity of the reflector (Section 2.1), observation error, and so on. To mitigate the nonuniformity of the reflector and noise, we conduct spatial binning over $2 \times 2$ pixels. Against the influences from the edges of the sheets, we use the closing and opening operators used in image processing. The closing operator modifies erroneous estimation due to the sheet edges appearing on a sheet, and the opening operator eliminates the false segments due to the edges elsewhere (Section 3.2, Fig. 5).
Figure 3 is the flow chart of our identification scheme. The strategy to detect unknown, unregistered plastics is discussed experimentally in Section 3.3.
Fig. 3. Flow chart of the proposed identification scheme (four or three registered plastic sheets out of four).
3. Results and discussion
We show transmission spectra of the tested plastics in Section 3.1, demonstrate the identification of overlapping sheets in Section 3.2, outline a strategy to detect unregistered plastics in Section 3.3, and discuss the interference effect between overlapping sheets in Section 3.4.
3.1 Transmission spectra of tested sheets
Figure 4 shows the SWIR transmission spectra of the four tested sheets, obtained by the HSI system. All the spectra are normalized w.r.t. their Euclidean norms. The solid lines are the mean spectra averaged within each plastic sheet, and the shaded regions around the solid lines show the standard deviations. The standard deviations are relatively large at the short and long wavelength regions. This is considerably due to the lower spectral sensitivity of the sensor at the wavelength regions. Thus, we used the wavelength region with the small standard deviations.
Characteristic abrosption bands were observed near 1100–1250 nm, 1350–1450 nm, and over 1600 nm. These absorption bands can be used for identifying plastics. In this study, however, we used the whole spectra, except for short and long wavelength regions of less sensitivity, as a dictionary to estimate overlapping plastic sheets by linear regression using the absorption coefficients.
3.2 Identification and thickness estimation results of overlapping sheets
We begin by discussing the effect of the opening and closing operations introduced to mitigate estimation errors near the sheet edges. Figure 5(a) and (b) are the estimated thickness distributions before and after the processing. Comparing the cross-section plots in (a1) and (b1), the opening and closing operators averaged the erroneous estimation due to the edges that appeared on the sheet near $X=50$ pixel and eliminated the false estimation near $X=90$ pixel, respectively. Although such operations somewhat blur spatially the estimation, we consider that it is not problematic for the purpose of this study, which seeks a method to identify and find bulky plastic sheets.
Fig. 5. Estimated thickness distribution of (a) PC, (b) AC, (c) PVC, (d) PET measured on the green belt. The color bars have millimeter units. The dotted lines and the corresponding plots of thickness (mm)/X (pixel) are the cross-sections of the estimated distributions.
Figures 6 and 7 show the estimated distribution of the four overleapping plastic sheets, (a) PC, (b) AC, (c) PVC, and (d) PET, measured on the green belt and the polytetrafluoroethylene reflector, respectively. All the results were processed by the opening and closing operations. The distributions are shown with pseudocolors, and the scale bars correspond to the thickness of the sheets. The results were consistent with the annotated images in Fig. 1(b) and (d). Each sheet with 2 and 3 mm of thickness was approximately estimated for all the plastics. We show cross sections of the estimated distribution of the thickness of the sheets. In Fig. 6, the sheets with a thickness of 2 mm (a1, b1, c1, d1) and 3 mm (a2, b2, c2, d2) were approximately estimated. Also in Fig. 7, the sheets with a thickness of 2 mm (a1, b1, c1:60–100 pixels on X-axis, and d1) and 3 mm (a1, b1, c1:0–40 pixels on X-axis, and d2) were approximately estimated. These results suggest that both the green belt and the polytetrafluoroethylene reflector can be used, and the ambiguity of the light intensity is also estimated simultaneously. Note that the dips or bumps found in the cross-section plots (near $X=70$ of Fig. 6(a2), $X=40$ of Fig. 6(c2), $X=40$ of Fig. 6(d2), $X=70$ of Fig. 6(d1), $X=50$ of Fig. 7(a2), $X=40$ of Fig. 7(b2), and $X=100$ of Fig. 7(d1)) are the results of the opening and closing operations to mitigate erroneous estimation near the edges, but such spiky errors shown in Fig. 5(a) were removed. Another type of deviation in the estimated thickness is in the slopes, such as in Fig. 6(c1) and Fig. 7(c1). They are considerable because of the difference of incident light intensity due to bending of the reflectors, especially near their edges. Although nonzero thickness was found at points without corresponding plastics, these errors can be discarded by setting a threshold such that a thickness below 0.3 mm might be an error against these samples. Note that this thresholding value should depend on cases. Such errors could be dealt with by setting a threshold to discard, or it could be judged mechanically whether there actually exist materials.
Fig. 6. Estimated thickness distribution of (a) PC, (b) AC, (c) PVC, and (d) PET measured on the green belt. The color bars have millimeter units, and the maps are in the pseudo color. The light blue colored lines and the corresponding plots of thickness (mm)/X (pixel) are the cross-sections of the estimated distributions.
Fig. 7. Estimated thickness distribution of (a) PC, (b) AC, (c) PVC, and (d) PET measured on the polytetrafluoroethylene reflector. The color bars have millimeter units, and the maps are in the pseudo color. The light blue colored lines and the corresponding plots of thickness (mm)/X (pixel) are the cross-sections of the estimated distributions.
3.3 Identification of unregistered plastics
In the previous chapter, we demonstrated that we could estimate thickness distributions when all the plastic materials are registered in the spectral dictionary $\mathbf {S}$. We discuss here cases of estimating scenes with unregistered plastics. For a demonstration, we registered three out of four plastics to create the spectral dictionary, and then applied the method. We then computed the error between the observed spectra $\tilde {\mathbf {I}}$ and the estimation $\mathbf {S} \mathbf {L}^\ast$ as $\| \tilde {\mathbf {I}} - \mathbf {S} \mathbf {L}^\ast \|_F^2$. We set an empirical value to threshold this error as 0.3 and then visualized the unregistered plastics. Figures 8 and 9 visualize the unregistered (a) PC, (b) AC, (c) PVC, and (d) PET on the green belt and the polytetrafluoroethylene reflector, respectively. Although some areas of unregistered PET are not identified in Fig. 8(d), the other plastics are successfully detected as unregistered ones. Conceptually, we can use these results to update the spectral dictionary, as shown in the flow chart (Fig. 3).
Fig. 8. Estimated unregistered plastics measured on the green belt for the same scene as Fig. 6. In each case, (a) PC, (b) AC, (c) PVC, and (d) PET is unregistered. The color bars are $\| \tilde {\mathbf {I}} - \mathbf {S} \mathbf {L}^\ast \|_F^2$, and the maps are in the pseudo color.
Fig. 9. Estimated unregistered plastics measured on the polytetrafluoroethylene reflector for the same scene as Fig. 7. In each case, (a) PC, (b) AC, (c) PVC, and (d) PET is unregistered. The color bars are $\| \tilde {\mathbf {I}} - \mathbf {S} \mathbf {L}^\ast \|_F^2$, and the maps are in the pseudo color.
3.4 Influence of interference between sheets
Finally, we discuss the influence of light interference between sheets, another source that disturbs observation. Light interference is observed for dielectric materials with the thickness scale of the wavelength of incident light and adds oscillatory behaviour on spectra. Koinig et al. discussed the influence of interference against thin plastic waste [35]. Although the plastic sheets considered in this study have thickness of a few millimeters, overlapping areas could cause interference between the sheet surfaces. Figure 10(e) shows an observed spectrum at a point where a PC sheet and a PET sheet are overlapping. We observed the influence of interference at some wavelengths with relatively flat regions of the spectrum (three boxes colored in red), but the influence is small compared with the absorption. Figure 10(a)–(d) shows the identification results for another example measured on the polytetrafluoroethylene reflector against this case with interference. We show the results before the opening and closing operations to see the influence of interference. The thickness distributions were also well estimated in this case. Although the experiment was limited to confirming the method’s robustness, this result suggests that light interference caused by overlapping sheets would have a small influence on the plastic identification.
Fig. 10. Estimated thickness distribution of (a) PC, (b) AC, (c) PVC, and (d) PET measured on the polytetrafluoroethylene reflector. The color bars have millimeter units. The spectrum (e) from the illustrated point is contaminated from the interference between sheets (red squared regions).
4. Conclusion
We have presented an identification method for overlapping, see-through plastic sheets using short-wavelength infrared hyperspectral imaging. The exprimental results suggest that the Lambert–Beer law-based method can identify overlapping plastic sheets and estimate their thickness. Possible error sources in measurement were discussed and practical techniques were demonstrated to mitigate these erroneous effects. We expect that this study will extend the applicability of hyperspectral imaging toward efficient, accurate plastic identification.
Disclosures
The relationship related to this study is as follows. The author is employed by DENSO IT Laboratory. The hyperspectral imaging system is a product of RESONON Inc. and was provided by KLV Co., Ltd. for research purpose. The plastic sheets used for the experiment were commercial products. The author does not hold any patents related to this study. Keisuke Ozawa is the corresponding author, conceived the study, developed the method, conducted the experiments, and wrote and reviewed the manuscript.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the author upon reasonable request.
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