SPECTROPHOTOMETRIC SYSTEM FOR MEASURINGTHE CHARACTERISTICS OF LIGHT SCATTERED BY BIOLOGICALTISSUES AND HUMORAL MEDIA

V. V. Barun,* V. P. Dick, and A. P. Ivanov UDC 535.36:53.082.53

The structure, assembly, and physical capabilities of a spectrophotometric system intended for studying biotis-sues and humoral fluids are described. It can be used to investigate all the characteristics of scattered lightat wavelengths of 400–1000 nm that are of interest for various problems in biomedical optics. Examples ofthese problems include noninvasive diagnostics of the structural and biophysical parameters of human skintissue, analysis of the hemoglobin composition, sizes and degree of aggregation of erythrocytes, and evaluat-ing the depth of penetration of light into biotissue. Pilot experiments on measuring the characteristics of scat-tered light are conducted in order to select an optimum operating mode for the system, estimate its errors,and develop ways of minimizing these errors.

Keywords: light, scattering, biological tissue, humoral fluid, spectrum, diffuse reflection coefficient.

Introduction. Spectral methods are widely used in practice for determining the composition, as well as thestructural and optical characteristics of various media. The use of these methods for noninvasive diagnostics of bio-logical tissues is, however, not yet widely used, despite such obvious advantages compared to the other methods, suchas a painless interaction with light, convenience in data acquisition, and the absence of costly and consumable mate-rials. These and other advantages of optical diagnostics have not yet been made use of for a number of reasons. Onereason is the lack of commercially available equipment for measuring the characteristics of light scattered by biotis-sues in vivo. For this, laboratory installations based on standard instruments are used, such as spectrophotometer orspectrometers that have been modified to deal with a particular problem. The measured spectral energy characteristicsare usually coefficients of diffuse and directed reflection and transmission of light [1–6], as well as the angular struc-ture of the reflected or transmitted light [7, 8]. The basis of the detection system in this case is an integrating sphereand (or) a goniometer. As a result, the apparatus become cumbersome and is not suitable for experimenting with "liv-ing" biotissues. Thus, the experiments are typically done on specially prepared samples under in vitro conditions or inmodel media. A somewhat paradoxical situation has developed: many methods have been developed and tested for re-covering diagnostically important parameters of biotissues (see below) based on these measured characteristics of light,but it is difficult to use them in practice because of a lack of corresponding experimental means. We note anothergroup of devices based on fiber optics and intended mainly for measuring the radial dependences of backscatteredlight [9–11]. These devices are compact, do not have the above mentioned disadvantages, and are actually used inmedical practice. They employ different (compared to the first group of methods) algorithms for data processing andtechniques for solving biomedical inverse problems. A comparison of these two types of measurement schemes and adiscussion of their advantages and disadvantages lie beyond the scope of this article, so we do not dwell of fiber opticdevices in the following.

Another reason for the insufficiently widespread use of spectrophotometric devices in medical practice is thatthe known and standard spectroscopic methods of measuring and processing the data are based on using the Bouger–Lambert–Beer law, so they can only be used for optically transparent or weakly scattering media. Biological tissues,of course, are highly turbid objects, and multiple light scattering will occur even in a geometrically thin object. This

B. I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, 68 Nezavisimosti Ave., Minsk,220072, Belarus; e-mail: barun@dragon.bas-net.by; Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 79, No. 2,pp. 299–308, March–April, 2012. Original article submitted May 5, 2011.

0021-9037/12/7902-0279 ©2012 Springer Science+Business Media, Inc. 279

Journal of Applied Spectroscopy, Vol. 79, No. 2, May, 2012 (Russian Original Vol. 79, No. 2, March–April, 2012)

∗To whom correspondence should be addressed.

makes it much more difficult to extract useful information from the measured optical signal and requires the creationof special algorithms and computer programs for solving the inverse problem. A number of such algorithms are knownin the literature, including the Monte-Carlo numerical inversion method [5, 6, 9], analytic approaches [3, 12] based onengineering approximations to the theory of radiative transfer [13], and empirical [9–11] methods constructed by ap-proximation of experimental data.

The purpose of this paper is to develop a compact and easily transported system which combines the conven-ience of in vivo measurement of various spectral characteristics of scattered light, with the possibility of combinedstudy of singly and multiply scattered light by biotissues and humoral media, and provides the experimental results inabsolute units that allow the use of analytic methods (similar to those in [3, 12]) for solving the inverse problem ofrecovering the structural and biophysical parameters of the medium. Data on these parameters of tissue and bloodmake it possible to detect a range of pathologies of the skin surface and blood in terms of a deviation of measuredparameters from normal values [14], to analyze the depth of penetration of light into tissue during light therapy [14],including photodynamic therapy, and to estimate the thermal regime for biotissue during cryothermy or laser hyper-thermy of the surface of the skin.

The Measurement System. The instrument is built on a modular principle. This ensures operational flexibil-ity of the system, with simple assembly and disassembly, and small size. The basic components are individual unitsproduced by the firm OceanOptics. The components common to the different variants include a light source based onan HL-2000-Li halogen lamp, a USB4000-VIS-NIR spectrometer (receiver), and a personal computer. In addition, thesystem includes a number of common auxiliary units and attachments, including SPECTRASUITE software, QP4000-2-VIS-BX receiver and transmitter fiber optics, a type 74-ACR collimator, and a type WS-1 optical etalon (referencestandard). Interchangeable modules, some of which are manufactured by OceanOptics and some of which have beendeveloped and manufactured at the Stepanov Institute of Physics, are additionally used in measuring various charac-teristics of scattered light.

Figure 1 is a structural diagram of the system as configured for measuring the spectral coefficients of diffusereflection. Light from the source 1 is incident on a transmitting fiber optic cable 2 and propagates out of it in theform of a diverging beam with a full aperture angle of ~25o. A collimator 3 forms a parallel beam of diameter ≈3mm. When necessary, an interference filter 4 is installed to select a required wavelength of light. The light then entersan ISP-80-8-R integrating sphere 5. A calibrating optical etalon is first placed in the measurement port of the integrat-ing sphere, and then a sample 6 of biotissue or humoral fluid is placed there. The optical etalon for the entire wave-length range of 360–1000 nm has a certified reflectivity close to unity. The light reflected by the objects passesthrough a fiber optic cable 7 and on to a photodetector 8 that measures the spectrum of the optical signal (400–1000 nm) and, after calibration, the coefficient of diffuse reflection from the biotissue, which is passed on to the com-puter 9. The detector in the spectrometer is a CCD strip. A computer program represents the experimental data in aformat compatible with the computer. The measured signal from the photodetector 8 is delivered to a USB port 10 ofthe computer 9, where it is finally processed. The data is transmitted every 5 ms through the USB port 10 (by theprogram). The operating system is Windows 98/2000/XP.

The system can operate in the following measurement modes: (1) diffuse reflection coefficients of biotissues,such as skin or samples of humoral fluids, using an integrating sphere with the test sample or a cuvette with humoralfluid placed in its receiver aperture; (2) diffuse transmission coefficients of samples of humoral fluid using an integrat-ing sphere with a cuvette for measuring multiple scattering of light; (3) directed transmission coefficients (attenuationindices) of a sample of humoral fluid in a cell for measuring the intensity of singly scattered light; and, (4) indica-trices for reflection of light by biological objects using a goniometer. The goniometer at the receiver aperture ismounted on the test sample or, if convenient, the sample is placed on the goniometer. The sample is illuminated nor-mal to its surface and the light is detected at a given angle. This angle can be varied discretely over 15–75o relativeto the sample normal. The receiver and illuminator channels are interchangeable. It is possible to install thin-film po-larizers in the receiver and illuminator channels to study the scattering of polarized light.

The principle behind the measurement of the reflection coefficients of biological objects is standard [2] andcan be understood from Fig. 1. The coefficients of diffuse transmission for samples of humoral fluids are measuredanalogously, but the cuvette with the samples is installed at the input to the integrating sphere. A beam of white lightfrom the source passes through the transmitting fiber and collimator, is incident on the cuvette, and is scattered by the

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test fluid. The resulting diffuse light enters the integrating sphere and passes out of it, through a second collimator andreceiver fiber, and on to the receiver-spectrometer. The spectrometer records the scattered light spectrum and (aftercalibration) the optical diffuse transmission coefficients of the humoral fluid.

For measuring the transmission of direct light in vitro (for samples of humoral media or thin sections of bi-otissue), a beam of white light from the source passes through the transmitting fiber and collimator and then entersand passes through the cuvette with the test fluid. It then passes through a second collimator into a receiver fiber andonward to the spectrometer. The spectrometer detects the spectral intensity of the light that has been attenuated by thefluid and, after calibration with respect to a standard cuvette, transfers values of the transmission coefficient at differ-ent wavelengths to the computer. The two collimators provide the required divergence of the incident and detectedlight, so that the accuracy of measuring the transmission coefficient can be increased.

The apparatus described above (without an integrating sphere and cuvette chambers) is used for measuring thereflection indicatrix of biological objects. An optical etalon is used to obtain data in absolute units.

Estimating the Error of the System for Measuring Reflection Coefficients. The validity of any measure-ment is determined by random and systematic errors. Here we discuss the experimental determination of these errorswith primary attention devoted to measurements of the diffuse reflection coefficient.

Effect of detector system noise. The spectral range over which the measured signal is averaged can bechanged by the program. Since the wavelength dependences of the reflection coefficient are smooth, an average spec-tral interval of 10 nm (which corresponds to averaging up to 25 pixels from the CCD array) was chosen for analyzingthe noise. Gray paper with a reflection coefficient of ~20% was chosen as the material for this study. The noise wasanalyzed as the exposure time t for the detected signal and the number of runs were varied. The noise is highest inthe UV and near IR. Figure 2 shows the results of an analysis of the errors in determining the reflection coefficientsat λ = 400 and 1000 nm. The errors were determined in the standard way from the spread in the results of a largenumber of measurements. Figure 3 shows the reflection coefficients of the paper over a wide range of wavelengthsfrom four runs with t = 4 s. It is clear that over a large part of the visible and near IR regions the errors owing tothe noise are <1%. Given that the measurement process for skin should not be prolonged for physiological and otherreasons, it is appropriate to make the measurements with exposure times of no more than 4 s and in four runs.

Effect of luminescence and scattering of light in the spectrometer. The instrument is intended for measuringthe reflection coefficient R(λ) of biological objects. However, a biological object can luminesce when exposed to lightand light can be scattered on the dispersion elements of the spectrometer, itself. As a result, the detector not only re-ceives light reflected by the biological object, but also luminescence and scattered light at different wavelengths. Thisleads to an incorrect determination of R(λ). To estimate these errors we measured the reflection coefficient R using an

Fig. 1. Conceptual diagram of the system: (1) light source, (2) transmitting op-tical fiber cable, (3) collimator, (4) interference filter, (5) integrating sphere,(6) sample of biotissue or humoral fluid, (7) fiber optic receiver cable, (8)photodetector system, (9) personal computer, (10) USB port.

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instrument with and without different filters in the illuminator. Filters were used to cut off the short wavelength regionof the illuminator spectrum, which could cause the skin to luminesce, as well as filters that cutoff only small segmentsof the spectrum. In all these cases, the detected reflection coefficient was essentially unchanged, which means that thelevels of luminescence and scattered light in the apparatus are negligible.

Effect of the distance between the surface of the integrating sphere and a biological object. There is alwaysa gap between the surface being studied (the etalon, skin), which is mounted at the measurement aperture of the inte-grating sphere, and the inner surface of the sphere that limits the acceptance angle of the integrating sphere and af-fects the amount of light entering the sphere. This causes errors in measuring the reflection coefficient. It is wrong todetermine these indirectly by pressing onto tissue in vivo, since this disrupts the blood content, which also changes thereflectivity. Thus, we have estimated these errors by changing the gap between the surface of the sphere and samplesof soft paper with spectrally neutral reflection coefficients of different absolute values. The variation in these reflec-tivities corresponds to the characteristic reflection coefficients of skin in different regions of the spectrum. Thisshowed experimentally that when the gap is reduced, the reflection coefficient R increases by 1–3% owing to an in-crease in the acceptance angle.

Accounting for the background light flux incident on the walls of the integrating sphere. It was mentionedabove that the full divergence angle of the light in the illuminator channel after passing through the fiber optic cableis ≈25o. However, there is a slight amount of light even outside this angle. After the collimator this light strikes thewalls of the integrating sphere and affects the measurement result. The effect of this factor was estimated by the fol-lowing experiment: a stop was positioned on the photodetector to block the light flux. The dark current was deter-

Fig. 2. Relative error (δ) in measurements of the diffuse reflection coefficientat wavelengths of 400 (1, 3) and 1000 nm (2, 4) as a function of the numberof averaging runs (n) for signal exposure times t = 4 (1, 2) and 9 s (3, 4).

Fig. 3. Reflection spectrum of a gray etalon for four runs and t = 4 s.

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mined in this way and could be compensated. Then the stop was removed and direct light from the source emergedfrom the integrating sphere through the measurement aperture and was absorbed by a black dump. The detector, nev-ertheless, recorded a signal. This signal is created by direct light incident on the walls of the integrating sphere fromthe background light originating from the optical fiber outside the 25o divergence angle. The signals with and withoutthe etalon in the measurement aperture were measured. We denote the signals created by the light reflected from thestandard and the background illumination of the walls of the integrating sphere by Wref and Wbg, respectively. The de-tector signal is proportional to Wref + Wbg when the etalon is in the measurement aperture of the integrating sphereand to Wbg without the etalon. According to test-ticket data from the manufacturer (OceanOptics) the reflection coef-ficients of the walls of the integrating sphere and of the etalon are approximately the same. Then the fraction of lightincident on the integrating sphere walls is α = Wbg/(Wref + Wbg). The measurements showed that over wavelengths of400–1000 nm, α ranges from 0.017 to 0.030. This means that the measured reflection coefficient Rmeas differs fromthe true R. A correction can be made in two ways. First, measure the spectral value of α. In fact, since the reflectioncoefficient of the etalon is roughly constant over the entire interval 400–1000 nm, the reflectivity of the etalon is ap-proximately constant and equal to 0.99, i.e., R = 1.01W0/Wref, where W0 is the signal from a biological object. ThenRmeas = (W0 + Wbg)/(Wref + Wbg) = (0.99R + Wbg)/(Wref + Wbg) = 0.99R(1 – α) + α. Thus,

R = 1.01 (Rmeas − α)

1 − α . (1)

Second, it is possible to compensate at the photodetector, experimentally, for both the dark current and the backgroundlight on the integrating sphere walls.

Effect of spreading of the illuminator spot in the biotissue volume. When light is incident on a skin surface,it both penetrates into the depth of the tissue and is scattered (spreads out) in the radial direction. The characteristicsize of the smeared out beam [16] may be larger than the diameter of the measurement aperture of the integratingsphere, so that part of the reflected light does not enter the sphere and the measured reflection coefficient will be low.We carried out the following experiment to estimate this factor. The measurement aperture of the integrating spherefor mounting the test sample has an 10-mm-diam opening. Diaphragms of slightly smaller size were introduced intothe opening. In experiments with the etalon, limiting the opening does not cause a change in the signal over the entirespectral interval. This means that the spreading out of the light in the etalon beyond a 10-mm-diam circle is negli-gible. Thus, with the etalon the integrating sphere collects all the reflected light flux, which is essentially equal to theincident flux. The signal from skin at short wavelengths <500 nm also did not change when different diaphragms wereinserted. However, in the red region, an increase in the diameter of the diaphragm was accompanied by an increasein the detected signal. This indicates that the characteristic size of the smeared out light beam emerging from the sur-face of skin and incident on the measurement aperture is greater than the diameter of the latter.

The fraction of the luminous flux picked up by the integrating sphere was estimated by means of theoreticalcalculations. We shall not discuss the computational method in detail here, but only outline the calculations. An ana-lytic expression has been obtained previously in the diffusion approximation to the theory of radiative transfer [13] forthe spreading function of a point that gives the brightness of the surface of a single layer medium simulating the der-mis of the skin [17] irradiated by a point unidirectional source and detected by a point receiver over an angle of 180o.We took the other layers of skin (corneous and epidermis) into account as an additional interface with known coeffi-cients of reflection and transmission [18]. Then the convolution of the backscattered and transmitted signals over theillumination and detection areas was determined analytically. This yielded the actual reflection coefficient and thatmeasured with the instrument, and, therefore, their ratio γ. Given the variations in the properties of skin (different con-centrations of melanin and capillaries) over the limits typical of normal skin [14], this ratio ranges over 1.09–1.10,1.06–1.08, and 1.01–1.02, respectively, at wavelengths of 800, 700, and 600 nm. At shorter wavelengths, γ = 1, as ob-served experimentally. This is related to the higher optical absorption and scattering indices of tissue at short wave-lengths, so the volume in which all the scattering processes take place is reduced. Thus, the reflectivity measured atlonger wavelengths has to be multiplied by γ. Hence, the true reflection coefficient is not to be found using Eq. (1),but by using the formula

R = 1.01γ (Rmeas − α)

1 − α . (2)

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Spectra of the Diffuse Reflection Coefficient. Many measurements were made of the spectral coefficients ofdiffuse reflection for people of different sexes and ages in different parts of the body. Almost 100 measurements weremade. Figure 4 illustrates some of the results. It is clear that the reflection spectra differ substantially. These curvesindicate ranges of variation in R at different wavelengths that might have a very wide variety of causes. It is not ap-propriate to go into detail here. For λ = 400–575 nm, R = 0.12–0.40. For λ = 575–610 nm there is a sharp rise inthe reflectivity. Within the range from 675–725 nm there is a maximum of R = 0.30–0.48 which is followed by asmooth decrease in R. The spectral variation in the curves is determined [9, 19, 20] by the absorption and scatteringspectra of the optically active constituents of skin tissue. The reflection spectra obtained here are consistent with pub-lished data [9, 20–22].

Apparatus for Measuring the Angular Distribution of Light Reflected by Skin. In the preceding we havediscussed devices for measuring integral characteristics of scattered light — the coefficients of diffuse reflection andtransmission. More complete information (although more difficult to interpret) on the properties of a medium is con-tained in the angular dependences of the light emerging from the surface of skin. If measurements of this kind mustbe made in absolute units (e.g., to determine the brightness coefficients [13]), then it is necessary to use an etalon andto know its characteristics. Figure 5a shows the normalized brightness indicatrices of reflected light from an etalon atdifferent λ. The light was incident along the normal to the surface. The plot was normalized to an angle of ϕ = 15o

with respect to the normal. Each indicatrix is the result of averaging many measurements. It can be seen that with in-creasing angles of observation the brightness decreases for all λ. This means that the reflection from the etalon doesnot obey Lambert’s law, according to which the brightness should remain constant. The reflection indicatrix has aweak wavelength dependence (curves 1–5).

For a theoretical estimate of the indicatrix we note that the etalon essentially absorbs no light, since its re-flectivity is close to unity in this spectral region. According to the asymptotic approximation in the theory of radiativetransfer [13], in this case, for a semi-infinite layer of scattering medium, the brightness coefficient for reflected lightnormalized to an observation angle of ϕ = 15o is given by the simple equation

ρ (ϕ) = 0.404 1 + 4 cos ϕ1 + cos ϕ

, (3)

shown in Fig. 5a (curve 6). As Eq. (3) shows, ρ(ϕ) is independent of wavelength. In addition, ρ(ϕ) for large anglesϕ is considerably smaller [2, 13] than the measurement results. A possible reason for the difference between the theo-retical and experimental results is that Eq. (3) was derived for an infinite scattering medium. The etalon is a denselypacked powder of dispersed particles. This leads to fundamentally different conditions for the passage of light throughits boundary. It changes direction and intensity owing to the jump in the refractive index and the surface roughness.Including the effect of these factors on the angular dependence ρ(ϕ) lies beyond the scope of this article.

Fig. 4. Spectra of the diffuse optical reflection coefficient of the skin of dif-ferent people.

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Figure 5b shows normalized distributions of skin brightness averaged over different sections of the humanarm. The reflection indicatrices become less diffuse at shorter wavelengths. This is related to the increased absorptionof melanin in the epidermis at shorter λ [19, 23] and stronger attenuation of inclined rays compared to rays incidentalong the normal.

Determining the Diffuse Reflection Coefficients from Indicatrices. With angular measurements of the lightreflected from scattering surfaces it is possible to calculate their reflectivities by integration. In fact, for normal inci-dence of light on skin, if we neglect the azimuthal structure of its surface, the flux reflected from the skin is Fref =

2π∫ 0

π ⁄ 2

Iref(ϕ) sin ϕdϕ, where Iref(ϕ) is the intensity of the light reflected from the skin at angle ϕ. The flux reflected

from an etalon is Fet = 2π∫ 0

π ⁄ 2

Iet(ϕ) sin ϕdϕ, where Iet(ϕ) is the intensity of the light reflected from the etalon. Since the

etalon is essentially nonabsorbing and fully reflects the light falling on it, the reflection coefficient of skin is given by

R = Fref

Fet =

∫ 0

π ⁄ 2

Iref (ϕ) sin ϕdϕ

∫ 0

π ⁄ 2

Iet (ϕ) sin ϕdϕ

. (4)

In order to compare the experimental data obtained in the mode where the reflection coefficients and angulardependences are determined, we have made measurements with an integrating sphere and indicatrix meter for differentpeople. The dashed curve in Fig. 6 shows the spectrum of the diffuse reflection coefficient without a correction forspreading of the light beam. An increasing discrepancy between the values of R can be seen as λ increases. Here thereflection coefficients obtained using the integrating sphere are smaller than those obtained with the indicatrix meter.Note that the device for measuring the angular structure of the scattered light was specially developed for experimentswith biological objects. In particular, the diameter of the measurement aperture was made to be substantially largerthan in the integrating sphere in order to eliminate the effect of beam spreading on the experimental data. This againproves that the reflection coefficient measured with the integrating sphere is lower in the red part of the spectrum.

Based on the experiments described here we can propose the following simple method for measuring the re-flection coefficient. As Eq. (4) implies, in order to determine the fluxes reflected from surfaces it is necessary to takeintegrals of I(ϕ) sin ϕ and Iet(ϕ) sin ϕ. In accordance with the theorem of the mean, we replace the numerator and

Fig. 5. Normalized indicatrices of the brightness of light reflected from an eta-lon (a) and from human skin (b) at λ = 900 (1), 800 (2), 700 (3), 600 (4),and 500 nm (5); curve 6 was calculated using Eq. (3).

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denominator in Eq. (4) by values of the functions in the integrands calculated for fixed angles ϕref and ϕet, respec-tively, which can, in general, be different. We note that these functions in the integrands go to zero for ϕ = 0 and π/2,and, therefore, have a maximum for 0 < ϕ < π/2. Therefore, there are two angles ϕref and ϕet each for the numeratorand denominator for which this substitution can be made. Finally, Eq. (4) takes the form

R = I (ϕrefi) sin ϕrefi

Iet (ϕeti) sin ϕeti

, i = 1, 2 . (5)

The indices i in the numerator and denominator can be the same or different; that is, four variants of Eq. (5) can beused.

Based on repeated measurements on the etalon and on several people at different wavelengths, the angleswere found (Table 1) at which the intensity of the light can be observed to determine the spectral reflection coeffi-cient. For the etalon, these angles are 21 and 71o with a mean square error of ±1o, independently of λ. The spread issomewhat greater among different people, and the angles, themselves, increase slightly with increasing λ. Thus, theseexperiments suggest a way of simplifying and cheapening the measurements. For example, in order to determine thediffuse reflection coefficient in absolute units it is not necessary to use an expensive integrating sphere or indicatrixmeter. It is enough to make a device for measuring the intensity of light from biological tissues and a standard at anangle of 21 or 71o, determine the corresponding signals in relative units, and perform the calculations using Eq. (5).

Fig. 6. Spectra of the diffuse reflection coefficient (a) measured using an indi-catrix meter (smooth curve) and a photometric sphere (dashed curve), and oftheir ratio β (b).

TABLE 1. The Angles ϕet and ϕrefi for Different Wavelengths λ

Surface ϕ, degλ, nm

450 500 600 700 800

Etalonϕet1 21 21 21 21 21

ϕet2 71 71 71 71 71

Test subject 1ϕref1 24 23 22 22 21

ϕref2 75 75 73 72 71

Test subject 2ϕref1 23 23 22 21 20

ϕref2 73 73 72 71 70

Test subject 3ϕref1 25 24 23 22 22

ϕref2 75 75 74 73 72

Test subject 4ϕref1 25 25 25 23 22

ϕref2 75 75 74 73 73

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The choice of one or another fixed angle of observation may be dictated by considerations of convenience or simplic-ity of construction.

Conclusion. A set of instrumentation has been created for measuring the spectral (400–1000 nm) coefficientsof diffuse reflection and transmission of biological tissues and humoral media, the coefficients of directed transmissionfor samples of humoral fluid, and the angular distribution of light reflected from the surface of skin. These charac-teristics of scattered light will place methods for solving various problems in biomedical optics at the disposal of re-searchers. For example, with the method and algorithm of [12], the reflection spectra can be used to determine thevolume concentration of capillaries and the degree of oxygenation of blood in the dermis, and the concentration ofmelanin and the thickness of the epidermis. It is also possible to measure the degree of oxygenation and the hemo-globin composition of blood, and the size and degree of aggregation of erythrocytes [24].

This work was supported by State Committee for Science and Technology of Belarus and the Foundation forBasic Research of the Republic of Belarus (project No. F09GKNT-004).

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