近年來，材料科學致力於定量描述材質的屬性，其中透明度作為評估材質光學特性的重要參數備受關注。本研究提出了一種影像式材質透明度測量方法，利用彩色偏光相機、光學和影像處理技術，克服了傳統方法在測量材料透明度方面的限制。我們通過提取41個具有不同穿透率和霧度的材料的偏光資訊進行模型迴歸，並使用52個光學樣品進行驗證，與傳統光學儀器的測量結果進行比較和分析。此外，為探討顏色是否會影響穿透率和霧度模型的迴歸結果，我們量測了15個彩色壓克力進行評估。
實驗結果表明，該方法能夠準確測量光學樣品的穿透率，其決定係數R²為0.95，平均誤差小於5 %。對於霧度，迴歸效果良好，決定係數R²為0.94，平均測量誤差為5.08 %。
另外，本研究發現顏色對迴歸模型的影響與入射光的光譜特性相關。由於我們使用的近平行平板燈在紅色和紫色波長範圍內的光源能量較低，這對於驗證樣品中的紅色壓克力的穿透率和霧度迴歸結果的準確性產生了影響。儘管如此，我們仍然觀察到其他彩色壓克力的穿透率迴歸結果是有效的，其決定係數R²為0.97，平均測量誤差為5.03 %。
同時，為了評估全域視角下透明度測量的有效性，我們使用彩色漸層壓克力、隱形眼鏡、塑膠滴管和全鋯人造假牙進行了影像式透明度量測實驗。結果顯示，該方法能夠有效解決複雜材料測量的問題，不再受限於材料的形狀和尺寸。然而，該研究方法仍受偏光特性的限制，例如無法對存在殘留應力的材料進行透明度測量，原因是光學延遲現象對光線的傳播方向和相位產生改變。

In recent years, materials science has been devoted to quantitatively describe the transparency properties of materials, which is an important parameter for evaluating the optical characteristics of materials. This study proposes an image-based measurement method for material transparency, which overcomes the limitations of the traditional method by utilizing a color-polarized camera, optics, and image processing. We performed the model regression using the polarized information which was extracted from 41 materials with different transmittance and haze. And we validated the method using 52 optical samples, comparing and analyzing the results with those obtained from optical instrument. Additionally, to investigate the influence of color on the regression results of transmittance and haze models, we measured 15 color acrylics for evaluation.
The experimental results demonstrated that the proposed method accurately measures the transmittance of optical samples, with a coefficient of determination (R²) of 0.95 and an average error of less than 5 %. For haze, the regression results are favorable, with a R² of 0.94 and an average measurement error of 5.08 %.
Furthermore, this study found that the influence of color on the regression model is related to the spectral characteristics of the incident light. Due to the lower energy of the light source in the red and purple wavelength ranges emitted by the near-parallel flat light used in our experiment, affects the accuracy of the regression results for the transmittance and haze of red acrylic in the verification samples. Nevertheless, we still observe that the regression results for transmittance of other color acrylics are effective, with a R² of 0.97 and an average measurement error of 5.03 %.
Moreover, in order to evaluate the effectiveness of transparency measurement from a global perspective, we conducted imaging-based transparency measurement experiments using color gradient acrylics, contact lenses, plastic droppers, and full zirconia artificial teeth. The results demonstrated that the method is capable of effectively addressing the challenges of measuring complex materials, and overcoming limitations related to material shape and size. However, the method is still limited to the characteristics of polarization, such as the inability to measure transparency in materials with residual stress due to changes in the propagation direction and phase of light caused by optical retardation.

[1]C. Eugène, “Measurement of ‘total visual appearance’: a CIE challenge of soft metrology,” in 12th IMEKO TC1 & TC7 Joint Symposium on Man, Science & Measurement, IMEKO Budapest, pp. 61–65, 2008.
[2]M. H. Brill, “Physical and informational constraints on the perception of transparency and translucency,” Computer Vision, Graphics, and Image Processing, vol. 28, no. 3, pp. 356–362, 1984, doi: 10.1016/S0734-189X(84)80013-4.
[3]H. Shahbazi, M. Tataei et al., “Structure-transmittance relationship in transparent ceramics,” Journal of Alloys and Compounds, vol. 785, pp. 260–285, 2019, doi: 10.1016/j.jallcom.2019.01.124.
[4]S. Qi, H. Zeng et al., “Energy–saving performance evaluation of photochromic glass in buildings,” Bulletin of the Chinese Ceramic Society, vol. 41, no. 4, pp. 1177, 2022.
[5]X. Fang and H. Xia, “Comparison among three translucency parameters,” West China Journal of Stomatology, vol. 35, no. 3, pp. 281–285, 2017.
[6]F. Manoochehri, E. Ikonen et al., “Comparison measurements on regular spectral transmittance,” Color Research & Application, vol. 21, no. 6, pp. 440–447, 1996, doi: 10.1002/(SICI)1520-6378(199612)21:6<440::AID-COL6>3.0.CO;2-W.
[7]H. L. Yu, C. C. Hsiao et al., “New apparatus for haze measurement for transparent media,” Measurement Science and Technology, vol. 17, no. 8, pp. N29–N36, 2006, doi: 10.1088/0957-0233/17/8/N01.
[8]American Society for Testing and Materials 2003 Standard Test Method for Haze and Luminous Transmittance of Transparent Plastics ASTM D 1003.
[9]Japanese Industrial Standard 1997 Plastics—Determination of the Total Luminous Transmittance of Transparent Materials—Part 1: Single Beam Instrument JIS K 7361–1.
[10]International Organization for Standardization 1997 Plastics—Determination of Haze of Transparent Materials ISO 14782.
[11]H. L. Yu and C. C. Hsaio, “Comparison of different measurement methods for transmittance haze,” Metrologia, vol. 46, no. 4, pp. S233–S237, 2009, doi: 10.1088/0026-1394/46/4/S19.
[12]O. da Pos and L. Burigana, “Qualitative inference rules for perceptual transparency,” in Handbook of Experimental Phenomenology, L. Albertazzi, Ed., Chichester, UK: John Wiley & Sons, Ltd, 2013, pp. 343–367. doi: 10.1002/9781118329016.ch14.
[13]O. da Pos, “Psychophysics and phenomenology of perceptual transparency,” Psychology of Consciousness: Theory, Research, and Practice, vol. 10, no. 1, pp. 17–32, 2023, doi: 10.1037/cns0000318.
[14]J. W. Shirley, “An early experimental determination of snell’s law,” American Journal of Physics, vol. 19, no. 9, pp. 507–508, 1951, doi: 10.1119/1.1933068.
[15]M. Saito, Y. Sato et al., “Measurement of surface orientations of transparent objects by use of polarization in highlight,” Journal of the Optical Society of America, vol. 16, no. 9, p. 2286, 1999, doi: 10.1364/JOSAA.16.002286.
[16]S. G Puyol, J. J. Benítez et al., “Transparency of polymeric food packaging materials,” Food Research International, vol. 161, p. 111792, 2022, doi: 10.1016/j.foodres.2022.111792.
[17]R. Apetz and M. P. B. Bruggen, “Transparent alumina: A light–scattering model,” Journal of the American Ceramic Society, vol. 86, no. 3, pp. 480–486, 2003.
[18]F. Ferraris, S. Diamantopoulou et al., “Influence of enamel composite thickness on value, chroma and translucency of a high and a nonhigh refractive index resin composite,” The International Journal of Esthetic Dentistry, vol. 9, no. 3, pp. 382–401, 2014.
[19]Y. K. Lee, “Translucency of human teeth and dental restorative materials and its clinical relevance,” Journal of Biomedical Optics, vol. 20, no. 4, p. 045002, 2015, doi: 10.1117/1.JBO.20.4.045002.
[20]A. Islam, H. N. Hansen et al., “Process chains for the mass production of transparent crowns for posterior teeth,” CIRP Annals, vol. 68, no. 1, pp. 591–594, 2019, doi: 10.1016/j.cirp.2019.04.015.
[21]M. M. Gad, R. Abualsaud et al., “Translucency of nanoparticle-reinforced PMMA denture base material: An in-vitro comparative study,” Dental Materials Journal, vol. 40, no. 4, pp. 972–978, 2021, doi: 10.4012/dmj.2020-296.
[22]B. Yu, J. S. Ahn et al., “Measurement of translucency of tooth enamel and dentin,” Acta Odontologica Scandinavica, vol. 67, no. 1, pp. 57–64, 2009, doi: 10.1080/00016350802577818.
[23]W. M. Johnston, “Review of translucency determinations and applications to dental materials: Translucency of dental materials,” Journal of Esthetic and Restorative Dentistry, vol. 26, no. 4, pp. 217–223, 2014, doi: 10.1111/jerd.12112.
[24]Z. Velinov, M. Papas et al., “Appearance capture and modeling of human teeth,” ACM Transactions on Graphics, vol. 37, no. 6, pp. 1–13, 2018, doi: 10.1145/3272127.3275098.
[25]J. Yao, S. Li et al., “Evaluation of three transmission parameters of dental opal porcelains and the correlations among parameters,” West China Journal of Stomatology, vol. 26, no. 3, pp. 279–283, 2008.
[26]A. Della Bona, A. D. Nogueira et al., “Optical properties of CAD–CAM ceramic systems,” Journal of Dentistry, vol. 42, no. 9, pp. 1202–1209, 2014, doi: 10.1016/j.jdent.2014.07.005.
[27]Z. Fang, H. Zhu et al., “Development, application and commercialization of transparent paper,” Translational Materials Research, vol. 1, no. 1, p. 015004, 2014, doi: 10.1088/2053-1613/1/1/015004.
[28]H. Zhu, Z. Fang et al., “Transparent paper: Fabrications, properties, and device applications,” Energy & Environmental Science, vol. 7, no. 1, pp. 269–287, 2014, doi: 10.1039/C3EE43024C.
[29]S. Munera, J. Blasco et al., “Use of hyperspectral transmittance imaging to evaluate the internal quality of nectarines,” Biosystems Engineering, vol. 182, pp. 54–64, 2019, doi: 10.1016/j.biosystemseng.2019.04.001.
[30]M. H. Hu, Q. L. Dong et al., “Estimating blueberry mechanical properties based on random frog selected hyperspectral data,” Postharvest Biology and Technology, vol. 106, pp. 1–10, 2015, doi: 10.1016/j.postharvbio.2015.03.014.
[31]A. Siedliska, P. Baranowski et al., “Detection of pits in fresh and frozen cherries using a hyperspectral system in transmittance mode,” Journal of Food Engineering, vol. 215, pp. 61–71, 2017, doi: 10.1016/j.jfoodeng.2017.07.028.
[32]Y. Xia, S. Fan et al., “Multi-factor fusion models for soluble solid content detection in pear (Pyrus bretschneideri ‘Ya’) using Vis/NIR online half-transmittance technique,” Infrared Physics & Technology, vol. 110, p. 103443, 2020, doi: 10.1016/j.infrared.2020.103443.
[33]T. Stegmaier, M. Linke et al., “Bionics in textiles: flexible and translucent thermal insulations for solar thermal applications,” Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 367, no. 1894, pp. 1749–1758, 2009, doi: 10.1098/rsta.2009.0019.
[34]M. Dowson, D. Harrison et al., “Improving the thermal performance of single-glazed windows using translucent granular aerogel,” International Journal of Sustainable Engineering, vol. 4, no. 3, pp. 266–280, 2011, doi: 10.1080/19397038.2011.558931.
[35]B. Huang, Y. Wang et al., “Fabrication and energy efficiency of translucent concrete panel for building envelope,” Energy, vol. 248, p. 123635, 2022, doi: 10.1016/j.energy.2022.123635.
[36]R. W. Fleming and H. H. Bülthoff, “Low-level image cues in the perception of translucent materials,” ACM Transactions on Applied Perception, vol. 2, no. 3, pp. 346–382, 2005, doi: 10.1145/1077399.1077409.
[37]D. Yu, S. Wenbin et al., “Measurements of the characteristics of transparent material using digital holography,” Advances in Materials Science and Engineering, vol. 2013, pp. 1–7, 2013, doi: 10.1155/2013/598737.
[38]D. Hirsch, E. C. Graff et al., “Influence of common transparent materials on the accuracy of image-based velocimetry,” Measurement Science and Technology, vol. 26, no. 8, p. 087002, 2015, doi: 10.1088/0957-0233/26/8/087002.
[39]S. Busato and A. Perevedentsev, “A simple imaging-based technique for quantifying haze and transmittance of materials,” Polymer Engineering & Science, vol. 58, no. 3, pp. 345–352, 2018, doi: 10.1002/pen.24580
[40]S. Busato, D. Kremer et al., “Imaging‐based metrics drawn from visual perception of haze and clarity of materials. I. method, analysis, and distance‐dependent transparency,” Macromolecular Materials and Engineering, vol. 306, no. 5, p. 2100045, 2021, doi: 10.1002/mame.202100045.
[41]D. Rebhan, M. Rosenberger et al., “Principle investigations on polarization image sensors,” in Photonics and Education in Measurement Science 2019, B. Zagar, P. Mazurek, M. Rosenberger, and P.-G. Dittrich, Eds., Jena, Germany: SPIE, 2019, p. 58. doi: 10.1117/12.2533590.
[42]S. H. Baek, D. S. Jeon et al., “Simultaneous acquisition of polarimetric SVBRDF and normals,” ACM Transactions on Graphics, vol. 37, no. 6, pp. 1–15, 2018, doi: 10.1145/3272127.3275018.
[43]A. Kalra, V. Taamazyan et al., “Deep polarization cues for transparent object segmentation,” in 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Seattle, WA, USA: IEEE, 2020, pp. 8599–8608. doi: 10.1109/CVPR42600.2020.00863.
[44]H. Mei, B. Dong et al., “Glass segmentation using intensity and spectral polarization cues,” in 2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), New Orleans, LA, USA: IEEE, 2022, pp. 12612–12621. doi: 10.1109/CVPR52688.2022.01229.
[45]L. Yu, A. Kosuge et al., “An anomaly detection system for transparent objects using polarized-image fusion technique,” in 2022 IEEE Sensors Applications Symposium (SAS), Sundsvall, Sweden: IEEE, 2022, pp. 1–6. doi: 10.1109/SAS54819.2022.9881251.
[46]R. Sun, T. Liao et al., “Polarization dehazing method based on separating and iterative optimizing airlight from the frequency domain for different concentrations of haze,” Applied Optics, vol. 61, no. 35, p. 10362, 2022, doi: 10.1364/AO.475021.
[47]X. F. H. DALSA TELEDYNE, “Polarization-based imaging: basics and benefits.” https://www.photonics.com/Articles/Polarization-Based_Imaging_Basics_and_Benefits/a60734 (accessed Jun. 26, 2023).
[48]F. Meriaudeau, M. Ferraton et al., “Polarization imaging for industrial inspection,” Presented at the Electronic Imaging 2008, p. 681308. doi: 10.1117/12.767915.
[49]V. Cheung, S. Westland et al., “A comparative study of the characterisation of colour cameras by means of neural networks and polynomial transforms,” Coloration Technology, vol. 120, no. 1, pp. 19–25, 2004, doi: 10.1111/j.1478-4408.2004.tb00201.x.
[50]C. Gómez-Polo, M. P. Muñoz et al., “Comparison of the CIELab and CIEDE2000 color difference formulas,” The Journal of Prosthetic Dentistry, vol. 115, no. 1, pp. 65–70, 2016, doi: 10.1016/j.prosdent.2015.07.001.
[51]G. Ginesu, F. Massidda et al., “A multi-factors approach for image quality assessment based on a human visual system model,” Signal Processing: Image Communication, vol. 21, pp. 316–333, 2006, doi: 10.1016/j.image.2005.11.005.
[52]Y. Yang, J. Ming et al., “Color image quality assessment based on CIEDE2000,” Advances in Multimedia, vol. 2012, pp. 1–6, 2012, doi: 10.1155/2012/273723.
[53]H. Cheng, J. Chu et al., “Turbid underwater polarization patterns considering multiple mie scattering of suspended particles,” Photogrammetric Engineering & Remote Sensing, vol. 86, no. 12, pp. 737–743, 2020, doi: 10.14358/PERS.86.12.737.
[54]M. J. Stephen and G. Cwilich, “Rayleigh scattering and weak localization: Effects of polarization,” Physical Review B, vol. 34, no. 11, pp. 7564–7572, 1986, doi: 10.1103/PhysRevB.34.7564.
[55]S. N. Jha, Ed., Nondestructive Evaluation of Food Quality: Theory and Practice. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. doi: 10.1007/978-3-642-15796-7.
[56]Y. Yi, B. Tao et al., “Residual stresses in glass after molding and its influence on optical properties,” Procedia Engineering, vol. 19, pp. 402–406, 2011, doi: 10.1016/j.proeng.2011.11.132.
[57]D. Rinaldi, P. P. Natali et al., “The refraction indices and brewster law in stressed isotropic materials and cubic crystals,” Crystals, vol. 11, no. 9, pp. 1104, 2021, doi: 10.3390/cryst11091104.