Scattering Coefficient Μs Research Articles

Development of silicone-based phantoms for biomedical optics from 400 to 1550 nm

This work describes the development of silicone-based evaluation phantoms for biomedical optics in the wavelength range from 400 to 1550 nm. The absorption coefficient μa and the reduced scattering coefficient μs′ were determined using an integrating sphere setup. Zirconium dioxide pigments were used as scatterers and carbon black as absorbers. We developed an in-house manufacturing process using a Hauschild SpeedMixer to ensure reproducibility. A set of nine cubic phantoms with three different reduced scattering and absorption coefficients was produced. Prediction of the μa and μs′ was done by using the weighted mass concentrations of the used materials. The average prediction accuracy over all wavelengths and phantoms is 1.0% for the reduced scattering coefficient and 3.5% for the absorption coefficient.

Effect of forchlorfenuron and thidiazuron on kiwifruits’ internal qualities, optical properties and their relationship during growth

Forchlorfenuron (1-(2-chloropyridin-4-yl)-3-phenylurea, CPPU) and thidiazuron (N-Phenyl-N′-1,2,3-thiadiazol-5-ylurea, TDZ) are two widely used plant growth regulators in kiwifruit cultivation. They can promote fruit size, but it is unclear whether they have same effect on internal qualities, optical properties and cell structure of kiwifruit, and whether the kiwifruits treated with CPPU and TDZ can be identified based on optical properties. To answer these questions, the kiwifruits treated with 20 mg/L CPPU and 2 mg/L TDZ solutions were used as samples, and the untreated kiwifruits were used as control to investigate the optical properties (absorption coefficient μa and reduced scattering coefficient μs′), internal qualities (soluble solids content (SSC), firmness and moisture content) and microstructure of pulp tissue during the growth. Moreover, the relationship between the optical properties and internal qualities were analyzed, and the potential for identifying the kiwifruits treated with CPPU and TDZ based on optical properties was evaluated. The results showed that CPPU and TDZ increased the SSC and reduced the firmness of kiwifruits, but had some different effects on the moisture content and cell size. CPPU and TDZ did not influence the change trend of μa and μs′ with wavelength, but affected their values and the relationship with internal qualities. In general, the mean μa of the kiwifruits treated with CPPU and with TDZ was the largest and the smallest at the absorption peaks (980 nm, 1190 nm and 1420 nm), respectively. The linear discriminant analysis modeling results showed that the spectra of μa with μs′ had greater potential in identifying the kiwifruits treated with CPPU/TDZ with accuracy of 75.76 %.

Generic and Model-Based Calibration Method for Spatial Frequency Domain Imaging with Parameterized Frequency and Intensity Correction.

Spatial frequency domain imaging (SFDI) is well established in biology and medicine for non-contact, wide-field imaging of optical properties and 3D topography. Especially for turbid media with displaced, tilted or irregularly shaped surfaces, the reliable quantitative measurement of diffuse reflectance requires efficient calibration and correction methods. In this work, we present the implementation of a generic and hardware independent calibration routine for SFDI setups based on the so-called pinhole camera model for both projection and detection. Using a two-step geometric and intensity calibration, we obtain an imaging model that efficiently and accurately determines 3D topography and diffuse reflectance for subsequently measured samples, taking into account their relative distance and orientation to the camera and projector, as well as the distortions of the optical system. Derived correction procedures for position- and orientation-dependent changes in spatial frequency and intensity allow the determination of the effective scattering coefficient μs' and the absorption coefficient μa when measuring a spherical optical phantom at three different measurement positions and at nine wavelengths with an average error of 5% and 12%, respectively. Model-based calibration allows the characterization of the imaging properties of the entire SFDI system without prior knowledge, enabling the future development of a digital twin for synthetic data generation or more robust evaluation methods.

Real-time monitoring of biomass during Escherichia coli high-cell-density cultivations by in-line photon density wave spectroscopy.

An efficient monitoring and control strategy is the basis for a reliable production process. Conventional optical density (OD) measurements involve superpositions of light absorption and scattering, and the results are only given in arbitrary units. In contrast, photon density wave (PDW) spectroscopy is a dilution-free method that allows independent quantification of both effects with defined units. For the first time, PDW spectroscopy was evaluated as a novel optical process analytical technology tool for real-time monitoring of biomass formation in Escherichia coli high-cell-density fed-batch cultivations. Inline PDW measurements were compared to a commercially available inline turbidity probe and with offline measurements of OD and cell dry weight (CDW). An accurate correlation of the reduced PDW scattering coefficient µs ' with CDW was observed in the range of 5-69 g L-1 (R2 = 0.98). The growth rates calculated based on µs ' were comparable to the rates determined with all reference methods. Furthermore, quantification of the reduced PDW scattering coefficient µs ' as a function of the absorption coefficient µa allowed direct detection of unintended process trends caused by overfeeding and subsequent acetate accumulation. Inline PDW spectroscopy can contribute to more robust bioprocess monitoring and consequently improved process performance.

Determination of scattering coefficient and scattering anisotropy factor of tissue-mimicking phantoms using line-field confocal optical coherence tomography (LC-OCT)

Line-field Confocal Optical Coherence Tomography (LC-OCT) is an imaging modality based on a combination of time-domain optical coherence tomography and reflectance confocal microscopy. LC-OCT provides three-dimensional images of semi-transparent samples with a spatial resolution of ∼1 μm. The technique is primarily applied to in vivo skin imaging. The image contrast in LC-OCT arises from the backscattering of incident light by the sample microstructures, which is determined by the optical scattering properties of the sample, characterized by the scattering coefficient μs and the scattering anisotropy factor g. In biological tissues, the scattering properties are determined by the organization, structure and refractive indexes of the sample. The measurement of these properties using LC-OCT would therefore allow a quantitative characterization of tissues in vivo. We present a method for extracting the two scattering properties μs and g of tissue-mimicking phantoms from 3D LC-OCT images. The method provides the mean values of μs and g over a lateral field of view of 1.2 mm × 0.5 mm (x × y). It can be applied to monolayered and bilayered samples, where it allows extraction of μs and g of each layer. Our approach is based on a calibration using a phantom with known optical scattering properties and on the application of a theoretical model to the intensity depth profiles acquired by LC-OCT. It was experimentally tested against integrating spheres and collimated transmission measurements for a set of monolayered and bilayered scattering phantoms.

Optical characterization of liquid phantoms in 500–1000 nm using an improved single integrating sphere system

This paper reports on optical characterization (absorption coefficient μa and reduced scattering coefficient μs′) of liquid phantoms in the wavelength range of 500–1000 nm using an improved single integrating sphere system. 54 liquid optical phantoms (18 pure absorption, pure scattering and mixed samples each) with known optical properties were first prepared. The overall performance of a laboratory-established single integrating sphere system was then evaluated, and the results indicated that the system has perfect stability, repeatability, and accuracy in optical property measurement. After that, effect of cuvette size (i.e., optical path and wall thickness) on optical property measurement was investigated. The experimental results showed that the discrepancies of the measured optical properties for the pure absorption and scattering phantoms held by different cuvettes with varying optical paths and wall thicknesses were within 8.76 %. Finally, the effect of different concentrations of absorber and scatterer on optical property determination of mixed liquid phantoms were explored. It was found the measured optical properties of the mixed liquid phantoms had a considerable difference from those of the pure absorption and pure scattering phantoms. We guessed that the addition of the absorber (scatterer) would dilute the concentration level of scatterer (absorber), and also brought about interaction between the two particles, and thus resulting in an offset for the measured optical properties. Future work needs to test our conjecture from the micro level, like monitoring the dynamic change of the absorption and scattering particle distribution and interaction, when optically characterizing the mixed liquid phantoms.

Exploitation of inline photon density wave spectroscopy for titania particle syntheses

AbstractIn this work, inline (or in‐situ) monitoring of titania particle formation with photon density wave spectroscopy is shown to provide helpful information for process optimization for higher particle yields. Titania particles have been synthesized by the controlled hydrolysis of tetraethyl orthotitanate. Without calibration or dilution, photon density wave spectroscopy provides access to dispersions' reduced scattering coefficient μs'. Hence, information can be obtained inline about processes that are otherwise challenging for established particle characterization methods. Photon density wave spectroscopy results suggest that the titania particles disintegrate over time after their formation. Consistent with that hypothesis, a decreasing particle yield with reaction time has been observed. The disintegration can be hindered by adding a sufficient amount of hexadecylamine, such that the particle yield after 24 h can be increased by 44% for the given syntheses.

Method for tissue clearing: temporal tissue optical clearing.

Light absorption and scattering in biological tissue are significant variables in optical imaging technologies and regulating them enhances optical imaging quality. Optical clearing methods can decrease light scattering and improve optical imaging quality to some extent but owing to their limited efficacy and the potential influence of optical clearing agents on tissue functioning, complementing approaches must be investigated. In this paper, a new strategy of optical clearing proposed as time-dependent or temporal tissue optical clearing (TTOC) is described. The absorption and scattering in light interaction with tissue are regulated in the TTOC technique by altering the pulse width. Here, the dependence of optical properties of matter on the pulse width in a gelatin-based phantom was investigated experimentally. Then, a semi-classical model was introduced to computationally study of Ultra-short laser/matter interaction. After studying phantom, the absorption and scattering probabilities in the interaction of the pulse with modeled human skin tissue were investigated using the proposed model for pulse widths ranging from 1µs to 10fs. The propagation of the pulse through the skin tissue was simulated using the Monte Carlo technique by computing the pulse width-dependent optical properties (absorption coefficient µa, scattering coefficient µs, and anisotropy factor g). Finally, the penetration depth of light into the tissue and reflectance for different pulse widths was found.

Optical properties of different kiwifruit cultivars (Actinidia deliciosa and Actinidia chinensis) and their correlation with internal quality

It has been reported that fruit cultivars could be detected by using near-infrared spectroscopy. Therefore, it is doubted that the optical properties (OPs) have differences among different fruit cultivars. However, it is not clear the difference in OPs and whether there is a difference in the relationship between OPs and internal quality. To answer these questions, four kiwifruit cultivars in two species, i.e., ‘Hayward’ and ‘Xuxiang’ of Actinidia deliciosa and ‘Huayou’ and ‘Hongyang’ of Actinidia chinensis, were selected as representative samples to obtain OPs (absorption coefficient μa and reduced scattering coefficient μs') of pulp and peel in storage and 950–1650 nm using an integrating sphere system. Then the relationship between the OPs and internal quality (soluble solids content (SSC), moisture content, and firmness) and microstructure were analyzed. Moreover, the optical parameter with greater potential in classifying kiwifruit cultivars was investigated. The results showed that the changes in μa and μs' with time differed among the four cultivars. Significant differences in the values of μa and μs' were noted among the four cultivars at some given times. For a given species, the investigated two cultivars had an obvious difference in OPs. Below about 1400 nm, the pulp’s μa of ‘Hayward’, ‘Huayou’, and ‘Hongyang’ was positively correlated with SSC and negatively related to moisture content and firmness, and the correlation coefficients changed little with wavelength. However, the correlation coefficients changed greatly for ‘Xuxiang’. Kiwifruit cultivars affect OPs and their relationship with the internal quality. The modeling results of the linear discriminant analysis showed that the μa had greater potential than μs' in identifying kiwifruit cultivars. The study provides useful information for identifying fruit cultivars and internal quality by using near-infrared spectroscopy technology.

Improved Process Control by Using the Effective Scattering Coefficients to Determine the Fat Content in Homogenized Cow-Based Milk with Multivariate Data Modeling

Commercially available homogenized cow- and plant-based milks were investigated by optical spectroscopy in the range of 400–1360 nm. Absorbance spectra, the effective scattering coefficient μs′, and the spectral absorption coefficient μa were recorded for 23 milk varieties and analyzed by multivariate data analysis. Cow- and plant-based milks were compared and discriminated using principal component analysis combined with a quadratic discriminant analysis. Furthermore, it was possible to discriminate the origin of plant-based milk by μa and the fat content in cow-based milk by μs′. Partial least squares regression models were developed to determine the fat content in cow-based milk. The model for μs′ proved to be the most efficient for this task with R2 = 0.98 and RMSEP = 0.19 g/100 mL for the external validation. Thus, optical spectroscopy together with multivariate data analysis is suitable for routine laboratory analysis or quality monitoring in the dairy production.

Extraction of the anisotropy factor and refractive index of biological tissue in the near-infrared region from diffusion approximation in the spatial frequency domain

In order to characterize biological tissue or to model light propagation in tissue medium it is necessary to define four key optical parameters, namely, absorption coefficient μa, reduced scattering coefficient μs’, anisotropy factor g (or scattering phase function), and refractive index n. Successful derivation of these valuable parameters can provide comprehensive information regarding the condition of tissue during disease pathogenesis and therapy and help to build accurate light propagation simulator. Usually, absorption and reduced scattering coefficients are investigated while the other two are assuming to be constant factors (g≈ 0.9, n≈ 1.4) across the near-infrared region. In order to quantify the g and n spectrum of a sample, we propose the use of spatial frequency domain (SFD). In SFD, periodic illumination patterns (structured illumination) at different spatial frequencies and wavelengths are serially projected onto the sample surface. Then, the collected diffusely reflected light is analyzed via the diffusion equation (or Monte Carlo simulation) in SFD to separately recover the sample’s absorption and scattering properties over a wide field of view. This work aimed to use the solution of the diffusion equation (DE) developed for the diffuse reflectance in SFD to estimate the wavelength-dependent variability of the g and n parameters of various turbid samples in the near-infrared spectral region. Since the solution of DE contains four unknown parameters, we use four different spatial frequencies to extract these four components; four equations at four different frequencies with four unknown parameters are solved at each of the four discrete wavelengths used. During data processing of n, its wavelength-dependence was fitted using the dispersion model of Sellmeier. While there are several approaches to retrieving information about g and n, the work in SFD offers an easier and more straightforward framework and grants expanded capability to this domain by enlarging its measurement range.

Frequency shifting model for diffuse optical tomography

The Diffuse Optical Tomography (DOT) imaging modality is an interesting research field for researchers since it has uncertainties in the solution space. DOT imaging modality is an unsolved scientific problem. Inverse problem solution and image reconstruction have never been of their best quality. Reconstructed images have low spatial resolution. The scattering nature of low-energized diffusive light is the obscuring effect for DOT modality. DOT has 3 functional sub-branches which are Continuous Wave, Time-Resolved, and Frequency-Domain. In this work, one new approach to Frequency Domain Diffuse Optical Tomography (FDDOT) biomedical optic imaging modality is presented to the readers. Frequency shifting data were added to the forward model problem which has source-detector couplings and several imaging voxels. 100 MHz center core light modulation frequency was selected as modulation frequency. 169 source-detector matches were used on back-reflected imaging geometry. Absorption coefficient µa was selected 0.1 cm−1. Scattering coefficient µs was selected 100 cm−1. 1-µm x, y, z cartesian grid coordinates were used in each direction for imaging tissue-like simulation media. A total of 100 frequency shifts were added to the forward model problem which has 5 Hz frequency step. 2 inclusion objects were embedded inside the imaging simulation phantom to be reconstructed. Their optical absorption coefficient µa = 0.7 cm−1. Two inclusion images were successfully reconstructed with the low contrast to noise ratio (CNR) and position error. The frequency shifting technique is first applied for FDDOT here in this work. This technique increased the total number of equations in the forward model problem; hence it is helping to solve the inverse problem more accurately. In this work, the positive effect of using frequency shifting methodology was observed. Differentiation of 2 embedded inclusions was completed and illustrated in this work. Two different scenarios were compared with each other. In the first scenario, only 100 MHz center core frequency was used for one source-detector match. In the second scenario, 100 additional shifted frequencies over 100 MHz center core frequency were added. It was seen that the second scenario which has more frequency shifts is superior to the general concept FDDOT methodology. This work shows that the frequency shift technique might be used for future FDDOT devices.

Experimental validation of a recently developed model for single-fiber reflectance spectroscopy.

.Significance: We recently developed a model for the reflectance measured with (multi-diameter) single-fiber reflectance (SFR) spectroscopy as a function of the reduced scattering coefficient , the absorption coefficient , and the phase function parameter . We validated this model with simulations.Aim: We validate our model experimentally. To prevent overfitting, we investigate the wavelength-dependence of and propose a parametrization with only three parameters. We also investigate whether this parametrization enables measurements with a single fiber, as opposed to multiple fibers used in multi-diameter SFR (MDSFR).Approach: We validate our model on 16 phantoms with two concentrations of Intralipid-20% ( and at 500 nm) and eight concentrations of Evans Blue ( to at 605 nm). We parametrize as .Results: Average errors were 7% for , 11% for , and 16% with the parametrization of ; and 7%, 17%, and 16%, respectively, without. The parametrization of improved the fit speed 25 times (94 s to ). Average errors for only one fiber were 50%, 33%, and 186%, respectively.Conclusions: Our recently developed model provides accurate results for MDSFR measurements but not for a single fiber. The parametrization prevents overfitting and speeds up the fit.

Monte Carlo simulation driven time resolved photon fluence analysis

In this study, time resolved (TR) Monte Carlo (MC) simulation program code was run to generate photon fluencies with increasing time steps. TR MC simulation was performed for ten time series from 4 ps to 52 ps. Generated photon fluencies were transferred to the image analysis programming platform. Imaging device geometry was created for test purpose in image reconstruction programming platform environment. Forward model weight matrix functions were calculated during each time period for 38 sources, and 38 detectors according to the back-reflected imaging geometry. A homogenous phantom, which simulated tissue, was chosen. Depending on the homogeneous tissue optical properties, such as tissue absorption coefficient μa, and tissue scattering coefficient μs, photons emitted from the laser source positions; migrated differently inside the imaging tissue. Photons migrate inside the tissue by some multiplication factor of ps depending on the tissue type for each 100-micrometer vertical distance. Superficial photons come photodetector point fast, depend on the source-detector neighborhood distances and tissue optical properties, respectively. Time resolved diffuse optic tomography (TRDOT) imaging systems are an emerging biomedical optic imaging modality due to progressive electronic technologies are helping to build the systems faster and cheap. As such, emerging microelectronic technology is giving important access to design and implement compact laser sources and photodetector units. Vertical cavity surface emitting light (VCSEL) as laser source and single photon avalanche diode (SPAD) arrays as photodetector units are becoming in common use as important hardware tools for designers and researchers in this field. TR diffuse photon analysis should be done routinely for better understanding of TRDOT devices. Hence, MC simulation driven TR photon fluence analysis was done for such a purpose in this study.

Measurement of absorption and reduced scattering coefficients in Asian human epidermis, dermis, and subcutaneous fat tissues in the 400- to 1100-nm wavelength range for optical penetration depth and energy deposition analysis.

.Significance: In laser therapy and diagnosis of skin diseases, the irradiated light distribution, which is determined by the absorption coefficient and reduced scattering coefficient of the epidermis, dermis, and subcutaneous fat, affects the treatment outcome and diagnosis accuracy. Although values for and have been reported, detailed analysis for Asian skin tissues is still lacking.Aim: We present and measurements of Asian skin tissues in the 400- to 1100-nm wavelength range for evaluating optical penetration depth and energy deposition.Approach: The measurements with Asian human skin samples are performed employing a double integrating sphere spectrometric system and an inverse Monte Carlo technique. Using the measured parameters, the optical penetration depth and energy deposition are quantitatively analyzed.Results: The of the epidermis layer varies among different ethnic groups, while the of the other layers and the of all of the layers exhibit almost no differences. The analysis reveals that the optical penetration depth and the energy deposition affect the photodynamic therapy treatment depth and the heat production in skin tissue, respectively.Conclusions: The experimentally measured values of and for Asian skin tissues are presented, and the light behavior in Asian skin tissues is analyzed using a layered tissue model.

Dependency of the optical scattering properties of human milk on casein content and common sample preparation methods.

.Significance. Quantifying human milk composition is important for daily nutritional management in neonatal intensive cares worldwide. Photonic solutions based on visible light can potentially aid in this analysis, as energy content of human milk depends largely on fat content, and the optical scattering properties of human milk predominantly depend on the size and concentration of fat globules. However, it is expected that human milk scattering changes upon homogenization, routinely done before analysis, which may affect fat globule size.Aim. The first aim of this study was to investigate how the most common homogenization methods (gently inverting by hand, vortexing, and sonication) affect the optical properties of human milk. The second aim was to estimate the scattering contribution of casein micelles, the second most dominant scatterers in human milk.Approach. We combined diffuse reflectance spectroscopy with spectroscopic optical coherence tomography to measure the scattering coefficient , reduced scattering coefficient , and anisotropy between 450 and 600 nm.Results. Sonication induced the strongest changes in , , and compared to the gently inverted samples (203%, 202%, and 7%, respectively, at 550 nm), but also vortexing changed with 20%. Although casein micelles only showed a modest contribution to and at 550 nm (7% and 1%, respectively), their contribution to was 29%.Conclusions. The scattering properties of human milk strongly depend on the homogenization method that is employed, and gentle inversion should be the preferred method. The contribution of casein micelles was relatively small for and but considerably larger for .

Depletion-Induced Flocculation of Concentrated Emulsions Probed by Photon Density Wave Spectroscopy.

Stable, creaming-free oil in water emulsions with high volume fractions of oil (ϕ = 0.05-0.40, density matched to water) and polysorbate 80 as an emulsifier were characterized without dilution by Photon Density Wave spectroscopy measuring light absorption and scattering behavior, the latter serving as the basis for droplet size distribution analysis. The emulsion with ϕ = 0.10 was used to investigate flocculation processes induced by xanthan as a semi-flexible linear nonabsorbing polymer. Different time regimes in the development of the reduced scattering coefficient μs' could be identified. First, a rapid, temperature-dependent change in μs' during the depletion process was observed. Second, the further decrease of μs' follows a power law in analogy to a spinodal demixing behavior, as described by the Cahn-Hilliard theory.

Determination of the optical properties of cholesteatoma in the spectral range of 250 to 800 nm.

Cholesteatoma of the ear can lead to life-threatening complications and its only treatment is surgery. The smallest remnants of cholesteatoma can lead to recurrence of this disease. Therefore, the optical properties of this tissue are of high importance to identify and remove all cholesteatoma during therapy. In this paper, we determine the absorption coefficient µ a and scattering coefficient µ s ' of cholesteatoma and bone samples in the wavelength range of 250 nm to 800 nm obtained during five surgeries. These values are determined by high precision integrating sphere measurements in combination with an optimized inverse Monte Carlo simulation (iMCS). To conserve the optical behavior of living tissues, the optical spectroscopy measurements are performed immediately after tissue removal and preparation. It is shown that in the near-UV and visible spectrum clear differences exist between cholesteatoma and bone tissue. While µ a is decreasing homogeneously for cholesteatoma, it retains at the high level for bone in the region of 350 nm to 580 nm. Further, the results for the cholesteatoma measurements correspond to published healthy epidermis data. These differences in the optical parameters reveal the future possibility to detect and identify, automatically or semi-automatically, cholesteatoma tissue for active treatment decisions during image-guided surgery leading to a better surgical outcome.

Determination of material optical properties from diffusive reflection light intensity profiles at multiple distances

Optical absorption and scattering properties are often estimated from the diffusive reflection light intensity at only one distance from the material surface, which often encounters accuracy and convergence issues. In this work, a method was proposed to determine optical properties by using diffusive reflection light intensity profiles at multiple distances, which enhanced data richness as a result of the intensity profiles are linearly independent. In this method, five features of light intensity profiles (contrast, correlation, energy, homogeneity, and second moment) were used to reduce the data dimensions. To demonstrate the effectiveness of the proposed method, Monte Carlo (MC) simulations were used to generate diffusive reflection light intensity profiles with noise at different distances for various combinations of four optical properties (absorption coefficient μa, scattering coefficient μs, isotropic coefficient g, and refractive index n). The five profile feature vectors were used as inputs and the four optical parameters were used as outputs to train and test a backpropagation (BP) neural network. The influences of noise levels and the number of diffusive light intensity profiles on parameter estimation accuracy were investigated. The four optical parameters estimated by the BP network were compared with the results estimated by the traditional least squares method, which shows that the proposed method can estimate the optical properties with higher accuracy and better convergence.

Spectral determination of μa, μs and g from single and multiple scattering signals with one optically thick sample

Development of robust and easy-to-implement methods for quantitative turbidity characterization by inherent properties of absorption and scattering can have wide applications. We report a new method for multiparameter characterization of turbid samples with three photodiodes based on the radiative transfer (RT) theory. Instead of acquiring collimated transmittance by spatial filtering and scattered light signals by integrating spheres, the method determines RT parameters from forward transmittance dominated by light of single scattering and non-hemispherical diffuse reflectance and transmittance dominated by light of multiple scattering. A Monte Carlo based inverse algorithm has been developed to rapidly obtain absorption coefficient μa, scattering coefficient μs and anisotropy factor g at multiple wavelengths. The method has been validated with different sphere suspensions against the Mie theory. RT parameters for suspensions of spheres of 0.966 µm and 11 µm in nominal diameter values has been determined in a spectral region of 460–1000 nm and the uniqueness of the inverse solutions has been proved at selected wavelengths.