A method for determining the complex refractive index dispersion of absorbing materials without thickness information

Abstract

The complex refractive index dispersion (CRID) of absorbing materials is very important in many fields, especially in printing industry and medical research. However, due to their strong absorbing, CRID determination is still a challenge. In this study, without diluting treatment or the thickness information, a method is proposed to calculate the CRID of absorbing materials, based merely on the reflectance and transmittance spectra measurements. The method separates the CRID into absorbing part and transparent part based on Kramers-Kronig relations, and it also uses the common Cauchy dispersion formula and Fresnel reflection formula. The CRID of methyl-red-doped poly (methyl methacrylate) (MR-PMMA) (3% mass fraction) and hemoglobin (Hb) solutions (320 g/L) are determined over the spectral range from 400 nm to 750 nm, and the result shows good stability and consistency of the method.

References

[1] Sydoruk O, Zhernovaya O, Tuchin V, et al. . Refractive index of solutions of human hemoglobin from the near-infrared to the ultraviolet range: Kramers-Kronig analysis. Journal of biomedical optics, 2012, 17(11): 115002. Bibcode: , J]

[2] Mazarevica G, Freivalds T, Jurka A. Properties of erythrocyte light refraction in diabetic patients. Journal of biomedical optics, 2002, 7(2): 244-247. Bibcode: , J]

[3] Elblbesy M. The refractive index of human blood measured at the visible spectral region by single-fiber reflectance spectroscopy. AIMS biophysics, 2021, 8(1): 57-65. J]

[4] Gienger J, Gro H, Neukammer J, et al. . Determining the refractive index of human hemoglobin solutions by Kramers-Kronig relations with an improved absorption model. Applied optics, 2016, 55(31): 8951-8961. Bibcode: , J]

[5] Khan R, Gul B, Khan S, et al. . Refractive index of biological tissues: review, measurement techniques, and applications. Photodiagnosis and photodynamic therapy, 2021, 33: 102192. J]

[6] Lazareva E N, Tuchin V V. Blood refractive index modelling in the visible and near infrared spectral regions. Journal of biomedical photonics & engineering, 2018, 4(1): 35-41. J]

[7] Simonot L, Girardeau T, Hebert M. Bronzing effect: predicting the color shine of printed surfaces by estimating the refractive index of the inks. Journal of the optical society of America A, 2023, 40(7): 1443-1450. Bibcode: , J]

[8] Ge S S, Hu Z X, Duan L C, et al. . A method of measuring refractive index of spectacle lens based on frequency domain OCT. Journal of optoelectronics·laser, 2023, 34(4): 429-433 [J]

[9] Niskanen I, Räty J, Peiponen K E. Complex refractive index of turbid liquids. Optics letter, 2007, 32(7): 862-864. Bibcode: , J]

[10] Arosa Y, Lago E L, De La Fuente R. Refractive index measurements in absorbing media with white light spectral interferometry. Optics express, 2018, 26(6): 7578-7586. Bibcode: , J]

[11] Zhang X N, Qiu J, Zhao J M, et al. . Complex refractive indices measurements of polymers in infrared bands. Journal of quantitative spectroscopy and radiative transfer, 2020, 252: 107063. J]

[12] Friebel M, Meinke M. Determination of the complex refractive index of highly concentrated hemoglobin solutions using transmittance and reflectance measurements. Journal of biomedical optics, 2005, 10(6): 064019. Bibcode: , J]

[13] Atchison D A, Smith G. Chromatic dispersions of the ocular media of human eyes. Journal of the optical society of America A, 2005, 22(1): 29-37. Bibcode: , J]

[14] Wang J, Deng Z C, Wang X W, et al. . Measurement of the refractive index of hemoglobin solutions for a continuous spectral region. Biomedical optics express, 2015, 6(7): 2536. J]

[15] Deng Z C, Wang J, Hu Z X, et al. . Study on the relation between the refractive index of fresh muscle tissue and its water content from 400 to 750 nm. Journal of modern optics, 2018, 65(4): 451-455. Bibcode: , J]

[16] Schott North America, Inc. Advanced optics. Optical glass: data sheets[EB/OL]. (2014-2-2) [2022-12-21]. https://mss-p-009-delivery.stylelabs.cloud/api/public/content/56f885e7281e469b8d1ded0c593600d6?v=5e72c5c3&download=true.

[17] Born M, Wolf E. Basic properties of the electromagnetic field. Principles of optics: electromagnetic theory of propagation, interference, and diffraction of light, 2013 Cambridge Cambridge University Press 38-49 [M]

[18] Nelder J A, Mead R. A simplex method for function minimization. Computer journal, 1965, 7(4): 308-313, J]

[19] Deng Z C, Wang J, Ye Q, et al. . A method for measuring the continuous dispersion spectrum of nonlinear refraction coefficients of materials. Optics & laser technology, 2018, 98: 252-256. Bibcode: , J]

[20] Zhernovaya O, Sydoruk O, Tuchin V, et al. . The refractive index of human hemoglobin in the visible range. Physics in medicine and biology, 2011, 56(13): 4013-4021. Bibcode: , J]

[21] Deng Z C, Wang J, Ye Q, et al. . Determination of continuous complex refractive index dispersion of biotissue based on internal reflection. Journal of biomedical optics, 2016, 21(1): 015003. Bibcode: , J]