Kubelka-Munk Research Articles

First-order goniospectrophotometric spectral modeling of isotropic and anisotropic colorant mixtures

Color modeling of translucent and opaque media commonly uses two-constant Kubelka-Munk (KM) turbid media theory. KM theory is designed for isotropic color systems that rely on absorption and scatter to produce an overall reflected color. KM theory has previously been considered inadequate to use with interference pigments (IPs) due to their specular reflected, angle-dependent color and anisotropic behavior. If, however, an IP's reflected color is considered to contribute to the background reflectance and not as a colorant in a mixture with a conventional colorant, KM theory can be used. KM theory was successfully implemented to predict the goniospectrophotometric, normalized spectral reflectance of conventional colorants and IP mixtures.

Empirical relationship between Kubelka–Munk and radiative transfer coefficients for extracting optical parameters of tissues in diffusive and nondiffusive regimes

Kubelka–Munk (K-M) theory is a phenomenological light transport theory that provides analytical expressions for reflectance and transmittance of diffusive substrates such as tissues. Many authors have derived relations between coefficients of K-M theory and that of the more fundamental radiative transfer equations. These relations are valid only in diffusive light transport regime where scattering dominates over absorption. They also fail near boundaries where incident beams are not diffusive. By measuring total transmittance and total reflectance of tissue phantoms with varying optical parameters, we have obtained empirical relations between K-M coefficients and the radiative transport coefficients for integrating sphere-based spectrophotometers that use uniform, nondiffusive incident beams. Our empirical relations show that the K-M scattering coefficients depend only on reduced scattering coefficient (μ's), whereas the K-M absorption coefficient depends on both absorption (μa ) and reduced scattering (μs' ) coefficients of radiative transfer theory. We have shown that these empirical relations are valid in both the diffusive and nondiffusive regimes and can predict total reflectance within an error of 10%. They also can be used to solve the inverse problem of obtaining multiple optical parameters such as chromophore concentration and tissue thickness from the measured reflectance spectra with a maximum accuracy of 90% to 95%.

Tunable filter-based multispectral imaging for detection of blood stains on construction material substrates Part 1 Developing blood stain discrimination criteria

In this article, we establish blood stain detection criteria that are less substrate dependent for use in a liquid crystal tunable filter-based multispectral-imaging system. Kubelka-Munk (KM) theory is applied to transform the acquired stains' reflectance spectra into the less substrate dependent spectra. Chosen spectral parameters are extracted from the KM absorbance spectra of several stain samples on several substrates. Blood discrimination criteria based upon those spectral parameters are then established from empirical data, tested, and refined. In our newly invented method, instead of introducing conventional contrast enhancement on the blood stain image, blood stain determination is executed mathematically via Boolean logic, resulting in more discriminative blood stain identification. This proposed approach allows for nondestructive, quick, discriminative, and easy-to-improve presumptive blood stain detection. Experimental results confirm that our blood stain discrimination criteria can be used to locate blood stains on several construction materials with high precision. True positive rates (sensitivity) from 0.60 to 0.95 are achieved depending on blood stain faintness and substrate types. Also, true negative rates (specificity) between 0.55 and 0.96 and identification time of 4-5 min are accomplished, respectively. The established blood stain discrimination criteria will be incorporated in a real blood stain detection system in part 2 of this article, where system design and considerations as well as speed issues are discussed.

Photocatalysis/catalysis by innovative TiN and TiN-Ag surfaces inactivate bacteria under visible light

This study presents the design, preparation, testing and characterization of TiN and TiN-Ag nanoparticulate films leading to photocatalytic and catalytic inactivation of Escherichia coli. When Ti was sputtered in N2 atmosphere, the TiN films unexpectedly revealed semiconductor properties when irradiated under visible light due to the formation of TiO2 showing absorption in the visible spectral region. In TiN-Ag films, Ag enhances the photocatalytic activity of TiN leading to faster bacterial inactivation. Evidence for the presence of TiO2 and TiN in the films is presented by XPS. The TiN layers 50nm thick sputtered by DC for 3min led to complete inactivation of E. coli within 120min. But TiN layers with a thickness >50nm hinder the surface diffusion of charges reducing bacterial inactivation. The rate of TiN deposition was ∼1.4×1015atoms TiN/cm2s. For the TiN-polyester samples under visible light a 3log10 bacterial reduction (99.9%) was observed within 30min while for TiN-Ag samples the same bacterial reduction was attained within ∼15min. The absorption of the TiN-Ag samples in Kubelka–Munk (KM) units was directly proportional to the E. coli inactivation kinetics. TiN-Ag plasmon nanostructures are concurrently formed under low intensity visible light and accelerated bacterial inactivation. This study shows that TiN films have the potential to replace Ag-based disinfection materials leaching Ag into the environment.

Estimating total suspended matter concentration in tropical coastal waters of the Berau estuary, Indonesia

This study presents the application of a semi-empirical approach, based on the Kubelka–Munk (K-M) model, to retrieve the total suspended matter (TSM) concentration of water bodies from ocean colour remote sensing. This approach is validated with in situ data sets compiled from the tropical waters of Berau estuary, Indonesia. Compared to a purely empirical approach, the K-M model provides better results in the retrieval of TSM concentration on both data sets (in situ and Medium Resolution Imaging Spectrometer (MERIS)). In this study, the K-M model was calibrated with in situ measurements of remote-sensing reflectance (R rs) and TSM concentration. Next, the inverse K-M model was successfully applied to images taken by the MERIS instrument by generating regional maps of TSM concentration. MERIS top-of-atmosphere radiances were atmospherically corrected using the Moderate Spectral Resolution Atmospheric Transmittance (MODTRAN) radiative transfer model. The best correlation between R rs measured in situ and R rs MERIS was found to be at a wavelength of 620 nm. The TSM concentrations retrieved using the K-M model showed a lower root mean square error (RMSE), a higher coefficient of determination and a smaller relative error than those retrieved by the purely empirical approach.

Optical absorption and scattering of bovine cornea, lens, and retina in the near-infrared region

The optical properties of bovine ocular tissues have been determined at laser wavelengths in the near-infrared (NIR) region. The inverse adding doubling (IAD), Kubelka-Munk (KM), and inverse Monte Carlo (IMC) methods were applied to the measured values of the total diffuse transmission, total diffuse reflection, and collimated transmission to determine the optical absorption and scattering coefficients of the bovine cornea, lens and retina from 750 to 1,000 nm using a CW Ti:sapphire laser. The optical properties obtained from these three methods have been compared and are discussed.

The Kubelka-Munk Diffuse Reflectance Formula Revisited

We use an integral equation approach to finding the Kubelka-Munk (KM) diffuse reflectance formula and extend the result by finding the apparent path length and total intensity distribution inside an infinite, homogeneous, diffusely reflecting medium with isotropic scattering. We then expand the approach to three dimensions to show that the KM formula is correct for total diffuse reflectance when scattering, excitation, and detection are all isotropic. We obtain simple and exact results for the angular distribution of diffuse reflection and for the total diffuse reflectance when the incident light has an isotropic angular distribution, when it strikes at a single angle of elevation, and when it has the steady-state angular distribution. This work includes some results that employ Chandrasekhar's H function, so we also provide a program for the rapid evaluation of H. “[Supplementary material is available for this article. Go to the publisher's online edition of Applied Spectroscopy Reviews for the following free supplemental resource: Program to compute the value of Chandrasekhar's H function]

Validity limits of Kubelka–Munk theory for DRIFT spectra of photodegraded solid wood

The validity of the Kubelka–Munk (K-M) theory was investigated to determine the IR absorption spectra of wood based on diffuse reflection infrared Fourier transform (DRIFT) measurements taken on photodegraded samples. After analysing plenty of DRIFT spectra of wood and examining the shape of the K-M equation, it can be concluded that the measured K-M function can be used as an absorption spectrum if the values of the function are below 14 K-M units. Above this limit, the K-M theory, which was created for poorly absorbing materials, does not give the absorption of wood properly. If a matt aluminium plate is used as a background material and the values are between 14 and 40, absorption changes can be calculated after normalisation of the spectra. This normalising manipulation is only successful if there is an absorption peak close to the examined one which does not change its absorption during the photodegradation.

Investigation of near infrared reflectance by tuning the shape of SnO 2 nanoparticles

Different shaped SnO 2 nanoparticles have been prepared via a sol–gel method. We investigate the relationships between morphology, crystal size and reflectance of as-prepared products. In addition, we also demonstrate the different shaped nanoparticles have different crystal sizes, namely 5.9, 7.5, 10.2 nm by XRD. And the calculated results are consistent with the TEM. Furthermore, the UV–vis–NIR results show that the reflectance is tightly related with the crystal size and its morphology. With the enhanced alkaline, the reflectance values decreased to 84% along with the square shaped particle sizes increased to 10.2 nm. According to S ∝ 1/ d, the particle size ( d) decreases, while the scattering coefficient ( S) increases. The absorption of samples in the near-infrared region increased to 0.07 which led to the depth of penetration enhancing caused the reflectance decreased. This matches well with the Kubelka–Munk (KM) theory.

Predicting the spectral reflectance factor of translucent paints using Kubelka‐Munk turbid media theory: Review and evaluation

AbstractThe use of Kubelka‐Munk (K‐M) turbid media theory in predicting the spectral reflectance factor of an opaque specimen from the specimen's constituent optical constants is well established in practice and well described in the literature. For translucent samples, there is a paucity of published results and the approaches are disparate. Accordingly, a review of K‐M theory and its application for predicting the spectral reflectance factor of translucent samples is presented and tested. Four methods for determining the absorption and scattering coefficients with respect to a certain film thickness are described: the black‐white method, the infinite method, the masstone‐tint method, and the two‐region method. The black‐white and infinite methods use the general form of the K‐M equation. The masstone‐tint method can be used for both the general form and the opaque simplification. The two‐region method, combining opaque and translucent approaches, was enhanced in this research and included an opacity calculation to automatically differentiate opaque and translucent spectral regions and a smoothing technique to combine both spectral regions. The two‐region method was tested using a set of acrylic‐emulsion artist paints and glazes spanning a range of opacities from opaque to nearly transparent. The results were reasonable and provided statistically significant improvement compared with the opaque simplification, commonly used in art conservation science and industrial color matching. © 2009 Wiley Periodicals, Inc. Col Res Appl, 34, 417–431, 2009

Optical absorption and scattering of bovine cornea, lens and retina in the visible region

Optical properties of bovine ocular tissues were determined at laser wavelengths in the visible region. The inverse adding doubling (IAD), Kubelka-Munk (KM), and inverse Monte Carlo (IMC) methods were applied to the measured values of the total diffuse transmission, total diffuse reflection, and collimated transmission to determine the optical absorption and scattering coefficients of the bovine cornea, lens and retina at 457.9 nm, 488 nm, and 514.5 nm laser lines from an argon ion laser. The optical properties obtained from these three methods were compared, and their validity is discussed.

In Situ DRIFT Characterization of Organic Matter Composition on Soil Structural Surfaces

The properties of preferential flow path surfaces may affect transport processes in structured soil. Wetting and sorption depends on the organic matter (OM) at the effective outermost surface of flow paths, which is largely unknown locally with respect to OM composition and distribution. The objectives are to adapt Diffuse Reflectance infrared Fourier Transform (DRIFT) spectral analysis for the in situ characterization of coated crack surfaces and linings of earthworm burrow walls. The Kubelka‐Munk (KM) transformed DRIFT spectra are used to analyze OM composition in terms of the ratio between CH‐ (Band A) and C=O groups (Band B). The A/B ratio indicates a relation between hydrophobic and hydrophilic groups in OM. Disturbed soil samples are arranged (i) in standard cup (CUP) and (ii) larger box (BOX) devices; intact aggregate and burrow surfaces are prepared from clods with cracks and earthworm burrows. The disturbed samples with relatively homogeneous surfaces are used to compare data obtained from CUP with those from the BOX device. The A/B ratios are determined in a stepwise mapping‐type procedure and compared with pictures of the surfaces for inferring a spatial distribution of OM composition along transects. The DRIFT mapping results indicate negligibly small texture effects for the finer‐textural subsoil samples for which the applicability of KM is not restricted. For intact surfaces like soil aggregates, cracks, and earthworm burrow walls, the A/B ratios are relatively higher near a root residue and relatively lower near a quartz grain. The millimeter‐scale variability of OM composition obtained here by an in situ analysis of A/B ratios at structural surfaces seems promising for determination of locally distributed OM properties. The DRIFT mapping may improve understanding the development of soil structural properties, from which descriptions of preferential flow and transport may benefit.

Structural and optical properties of AlN/Si system

Aluminum nitride (AlN) is a wide band gap III–V semiconductor material which is often used for optical applications. Thin films of aluminum nitride were deposited by ion beam sputtering in an Ar–N 2 atmosphere on Si (1 0 0). For film preparation, the N 2 flow was kept at 5 sccm and the ratio of N 2 and Ar was 4:1. The films have been characterized by Grazing Incidence X-ray Diffraction (GIXRD), X-ray Reflectometry (XRR), Atomic Force Microscopy (AFM) and optical spectroscopy. GIXRD shows that the structure of the as-deposited sample of AlN is hexagonal. It is observed that neither the ion-beam-induced dissociation of the nitride film nor the enhanced nitrogen diffusion across the interface takes place after Au ion irradiation. XRR was used to determine the thickness of the films. The reflectance of the irradiated films increases in the range 200–280 nm. UV–vis spectra were taken in Kubelka Munk (KM) units for as-deposited and irradiated samples. The band gap was calculated for both types of samples, which shows that the band gap of irradiated films of aluminum nitride decreases due to the increase in metal content at the surface. AFM confirms that the roughness of aluminum nitride increases by irradiation.

Relationship between the Kubelka-Munk scattering and radiative transfer coefficients

The relationship between the Kubelka-Munk (K-M) and the transport scattering coefficient is obtained through a semi-empirical approach. This approach gives the same result as that given by Gate [Appl. Opt.13, 236 (1974)] when the incident beam is diffuse. This result and those given by Star et al. [Phys. Med. Biol.33, 437 (1988)] and Brinkworth [Appl. Opt.11, 1434 (1972)] are compared with the exact solution of the radiative transfer equation over a large range of optical properties. It is found that the latter expressions, which include an absorption component, do not give accurate results over the range considered. Using the semi-empirical approach, the relationship between the K-M and the transport scattering coefficient is derived for the case where the incident light is collimated. It is shown that although the K-M equation is derived based on diffuse incident light, it can also represent very well the reflectance from a slab of infinite thickness when the incident light is collimated. However, in this case the relationship between the coefficients has to include a function that is dependent on the anisotropy factor. Analysis indicates that the K-M transform achieves the objective of obtaining a measure that gives the ratio of absorption to scattering effects for both diffuse and collimated incident beams over a large range of optical properties.

Kubelka-Munk Model for Imperfectly Diffuse Light Distribution in Paper

Perfectly diffuse light is a fundamental assumption in the Kubelka-Munk (KM) model. This assumption is, however, seldom fulfilled by real media. In this work, we build a bridge between a weakly absorbing medium with an imperfectly diffuse light distribution and the corresponding KM model relying on a perfectly diffuse light distribution. We multiply the apparent K and S phenomenal coefficients deduced from a learning set medium by a scaling factor expressing the ratio of light diffuseness between the target medium and the learning set medium. For the target medium, thanks to this diffuseness scaling factor, theoretically predicted reflection and transmission spectra agree with the corresponding measured spectra. The illumination geometry, the optical properties and the thickness of the medium have an impact on the light diffuseness and therefore on the proposed diffuseness scaling factor.

Evaluating Single- and Two-Constant Kubelka-Munk Turbid Media Theory for Instrumental-Based Inpainting

Instrumental-based color matching using non-destructive reflection spectrophotometry can be used as an aid in pigment selection for inpainting. This is useful when metamerism is of concern, particularly in modern art where the number of colorants available to artists and conservators is quite large. Simplified methods have been developed for art conservation where a single tint of each pigment mixed with white is required to define a pigment's optical properties based on the single-constant form of Kubelka-Munk (K-M) turbid media theory. Theoretically, this simplification can lead to errors in pigment selection for dark colors and colors not containing a white pigment. Instead, the two-constant form of K-M theory can be used where the model assumptions more closely match the optics of inpainting materials. The two methods were compared using four acrylic emulsion paints with a range of pigment absorption and scattering properties. It was found that the simplified method was inadequate for paints with appreciable and spectrally selective scattering, and as a consequence, pigment selection may result in a greater number of pigments than actually required. It was also found that only two samples per pigment were required to implement the two-constant technique: the mass tone and a tint.

A specific feature of the procedure for determination of optical properties of turbid biological tissues and media in calculation for noninvasive medical spectrophotometry

In contemporary medical engineering industry, oneof the key problems of development of methods, apparatuses, and devices for optical spectroscopy of biologicaltissues is the compilation of effective computation algorithms providing maximal accuracy and reliability ofdetermination of initial optical properties of the object ofinterest from experimental data [14, 18]. Optical properties of biological tissues can be determined from radiationfluxes measured experimentally by solving inverse problems of scattering [11], which employ different methodsof description of radiation propagation medium. In turbidlightscattering biological media (most biological mediaare turbid [22]), numerical models of transition theoryand lightscattering in turbid media should be used [8,20]. The models have a limited number of solutions.Therefore, approximate solutions are often used for practical purposes in photometry of turbid media. For example, flux Kubelka–Munk (KM) approaches are widelyused in the practice of noninvasive spectrophotometry,because they are simple and illustrative. Moreover, theKM models allow the final calculation equations to bederived in explicit analytical form [8, 12, 17, 18, 2124].In terms of transition theory and KM models, internaloptical properties of turbid media are completely characterized by linear optical extinction and scattering coefficients. The linear optical extinction and scattering coefficients are determined coefficients of differential equations describing the model. In optics, the KM models are purely photometricand phenomenological models based on heuristic principles providing separation of radiation field into discreterectangular fluxes. The principles also support the validity of linear equation of energy balance for each flux inmedium element [2, 48, 24]. In the simplest case, twoonedimensional flux KM models are considered. Suchmodel represents onedimensional radiation propagationmedium with two oppositely directed fluxes

Image-Based Color Ink Diffusion Rendering

This paper proposes an image-based painterly rendering algorithm for automatically synthesizing an image with color ink diffusion. We suggest a mathematical model with a physical base to simulate the phenomenon of color colloidal ink diffusing into absorbent paper. Our algorithm contains three main parts: a feature extraction phase, a Kubelka-Munk (KM) color mixing phase, and a color ink diffusion synthesis phase. In the feature extraction phase, the information of the reference image is simplified by luminance division and color segmentation. In the color mixing phase, the KM theory is employed to approximate the result when one pigment is painted upon another pigment layer. Then, in the color ink diffusion synthesis phase, the physically-based model that we propose is employed to simulate the result of color ink diffusion in absorbent paper using a texture synthesis technique. Our image-based ink diffusing rendering (IBCIDR) algorithm eliminates the drawback of conventional Chinese ink simulations, which are limited to the black ink domain, and our approach demonstrates that, without using any strokes, a color image can be automatically converted to the diffused ink style with a visually pleasing appearance.

Qualifying the arguments used in the derivation of the revised Kubelka-Munk theory: reply

The fundamental assumptions made in the revised Kubelka-Munk (KM) model of light propagation in scattering and absorptive media, recently proposed [J. Opt. Soc. Am. A21, 1942 (2004); 22, 866 (2005)], are critically reviewed and analyzed. The authors argue that the model, now questioned by Edström [J. Opt. Soc. Am. A24, 548 (2007)] is well founded on physical grounds and consistent with the original KM model, which has been the cornerstone of light propagation studies and utilized for more than half a century.

Quantitative monomolecular coverage of barium glass by the silane coupling agent γ-methacryloxypropyltrimethoxysilane

To study the monomolecular coverage of the silane coupling agent gamma-methacryloxypropyltrimethoxysilane (gamma-MPS) on the barium glass filler surface. Kubelka-Munk (K-M) function values of the isolated OH-groups on the barium glass filler surface, which were based on the change of gamma-MPS concentrations, were measured using the quantitative analysis of the diffuse reflectance infrared Fourier transform (DRIFT) spectroscopy. When all of the isolated OH-groups on the filler surface disappeared (where the K-M function values was zero), the monomolecular coverage of the gamma-MPS molecules on the filler surface was indicated by the linear regression analysis. The relationship tallied with negative linear correlation between the K-M function values of the isolated OH-groups on the barium glass surface and the concentrations of gamma-MPS. Each gamma-MPS molecule occupied 0.21 nm(2) when the monomolecular coverage was formed on the barium glass surface. The result of this study indicated the optimal amount of silane coupling agent on silanated barium glass filler during the production of resin composite.