A supercontinuum laser based double integrating sphere setup in combination with an unscattered transmittance measurement setup was developed and carefully validated for optical characterization of turbid samples in the 500-2250 nm wavelength range. A set of 57 liquid optical phantoms, covering a wide range of absorption and scattering properties, were prepared and measured at two sample thicknesses. The estimated bulk optical properties matched well for both thicknesses, and with theory and literature, without significant crosstalk between absorption and scattering. Equations were derived for the bulk scattering properties μs, μs’ and g of Intralipid® 20% which can be used to calculate the bulk scattering properties of intralipid-dilutions in the 500-2250 nm range.
© 2013 Optical Society of America
Bulk optical properties (BOP): bulk absorption coefficient µa, bulk scattering coefficient µs, reduced scattering coefficient µs’, and scattering phase function p(θ) or the derived anisotropy factor g, determine the propagation of light through biological tissues and other turbid media, and have therefore been the subject of research for many years . In medical diagnostics, therapy and surgery, knowledge about tissue’s BOP is essential for the correct prediction of photon distribution. Moreover, insight in a tissue’s BOP is crucial for the interpretation and quantification of diagnostic data, along with the estimation of the irradiance efficiency in photodynamic therapy and laser treatment [1,2]. In spectroscopic applications, for example quality analysis in the food industry, µa gives insight into the chemical composition of the analyzed product, while µs and g provide information on the microstructure and texture [3,4]. Moreover, the range of the sample’s BOP can be used as an input for light propagation models, derived from the radiative transfer equation, in order to foresee and interpret the signals collected by an optical and/or spectroscopic sensor for samples with varying BOP. Consequently, this information can be consulted in the optimization of the sensor design for a specific sample type .
The BOP of turbid media cannot be measured directly, but have to be estimated. Typically, measurements in the time domain, frequency domain or continuous wave domain are combined with inverse light propagation models, in order to retrieve the BOP . If in vitro characterization of a thin (mm-range) homogeneous sample slab is feasible, the total reflectance and transmittance can be measured with integrating spheres. These measurements, whether or not combined with an unscattered transmittance measurement, are generally accepted as the ‘golden standard’ method to estimate BOP from [1,2,4,5,7,8].
Bulk optical properties cannot be estimated directly from integrating sphere and unscattered transmittance measurements. Light propagation models describe the forward relation between optical properties and optical measurements, but cannot be easily inverted . Forward simulation of total reflectance and transmittance values for a large set of bulk optical properties with Monte Carlo (MC) simulations or adding doubling (AD) can result in an accurate lookup-table. Nonetheless, the full procedure will have to be repeated if the setup is slightly modified, or if changes happen to the sample dimensions or sample refractive index. Accordingly, iterative procedures have been developed, starting from an initial guess for the BOP and updating these until the difference between simulated and measured values for total reflectance and transmittance are within the range of tolerance [9–11]. MC simulations are very flexible and, therefore, result in an accurate estimation, but are also computationally very intensive . AD still allows high flexibility, while the calculation time is only a small fraction compared to that for MC [9–11].
Since µa in the Vis and short-wave NIR (780-1100 nm) is relatively low for most biological media, the total reflectance and transmittance in integrating sphere measurements is sufficiently high. Moreover, the ratio of the two can be optimized (on average ideally equal) by varying the sample thickness, resulting in accurate estimations of the BOP. For many applications, including medicine, this is the wavelength range of interest, noticeable by the large number of publications on BOP in this range . However, for spectroscopic applications, the NIR range (> 1100 nm) is more valuable because of the presence of many important molecular overtone and combination vibrations [7,12]. Since water is a strong absorber in this region, and often the dominant sample component, total reflectance and transmittance can be very low and a high power illumination is necessary to obtain a sufficiently high signal to noise ratio on the detectors . High-power laser diodes are suitable for this purpose , but as these are monochromatic, a different laser diode would be needed for every wavelength at which the BOP should be determined. On the other hand, the divergence of a high-power halogen light bulb makes it challenging to minimize the stray light and the size of the illumination spot on the sample . The latter is important to minimize the light losses at the lateral sides of the sample and cuvette/glass plates in integrating sphere measurements . Those light losses are not captured by the reflectance, nor the transmittance sphere and are, therefore, interpreted by the models as absorbed light, resulting in an overestimation of µa . Although most models correct for this phenomenon, it is advised to reduce its portion. An often used rule of thumb suggests to make the beam spot as small as possible and maximize the sample’s aspect ratio: sample diameter and sample sphere-port at least 10 times larger than the sample thickness. The sample port diameter is limited because its area should cover less than 10 percent of the total sphere area to maintain the properties of a ‘perfect integrating sphere’ and, additionally, a smaller sphere (area) results in a higher detector signal [9,16]. Another disadvantage of sample illumination with a high-power halogen light source in a post-dispersive setup is the risk of heating and dehydrating the sample.
A pre-dispersive setup consisting of a broadband supercontinuum laser in combination with a monochromator, or an acousto-optic tunable filter, could combine high power illumination with the flexibility for selecting the proper wavelength and bandwidth. Moreover, this type of light source enables a high power (mW/nm) pre-dispersive sample illumination with a small spot size (easiness to focus), but without the risk of heating and dehydrating the sample . A supercontinuum laser beam is generally formed by severe spectral broadening of the original pump beam through nonlinear processes. In the last decade, the development of supercontinuum laser sources has emerged and they became widely commercially available, finding applications in a diverse range of optics fields, including optical coherence tomography, fluorescence imaging, broadband and time-of-flight spectroscopy among many others .
In principle, only a single integrating sphere is necessary to measure both total reflectance and total transmittance sequentially by repositioning the sphere or the sample and light source [1,4,14]. However, the repositioning might disturb the alignment, producing erroneous measurements. In the case of heterogeneous samples, different sample parts might be illuminated and measured in the sequential measurements, resulting in a possibly meaningless estimation of the BOP. Moreover, sample degradation and dehydration might happen during the measurement, because of the prolonged measurement time and the extra time needed for realignment and recalibration in between both measurements . When two integrating spheres are placed with respectively the exit and entry port towards the front and back of the sample slab, it becomes possible to simultaneously measure the reflectance and transmittance of the sample [7,8,19]. Such double integrating spheres (DIS) measurements are essential if the sample undergoes some external stimulation, such as heat, pressure, or a chemical change during the measurement (at a single wavelength) . However, the reflectance and transmittance spectra acquired from the DIS setup have to be corrected for the exchange of light through the sample between the two spheres .
Since the sphere multiplier factor, which is in a direct relation to the detector signal, increases rapidly with increasing sphere wall reflectivity, the latter needs to be maximized . Spectralon® coating generally has the highest reflectivity in the full Vis and NIR range. However, the coating thickness needs to be 7 mm or more to ensure these properties. At the sample ports, where the spheres touch the sample, this thickness causes an irregular transition between the sample and the inner sphere wall, resulting in an imperfect collection of the total reflectance and/or transmittance. From the thin film coatings, which are especially designed for reflectance and transmittance integrating spheres, Infragold® has the highest reflectivity properties over the entire NIR range . However, the low reflectivity of Infragold® in the Vis is limiting the signal in that wavelength range. Yet, in many applications, the sample’s total reflectance and transmittance in the Vis is rather high and the low reflectivity of Infragold® in that wavelength range is not causing problems. Accurate measurement of the sphere wall reflectivity is, however, very important in order to calculate the exact total reflectance and transmittance .
Accurate measurement of the unscattered transmittance allows for the estimation of the bulk extinction coefficient (µt). When combined with DIS measurements, all the BOP (µa, µs and g) can be derived without any assumptions . However, for many samples, a correct measurement of the unscattered transmittance is complicated since strongly forward scattered photons can hardly be distinguished from the unscattered ones. As the real unscattered transmittance decreases, the collected scattered photons are becoming more significant, resulting in an overestimation of the unscattered transmittance and an underestimation of the derived µt. In order to reduce the number of collected scattered photons, the sample thickness and the collection angle of the detector should be minimized. The latter can be achieved by minimizing the sensitive detector area using slits, and/or by increasing the distance between sample and detector [6,9,22–25]. The minimum slit size is, however, limited in order to maintain sufficient signal, while the maximum sample-detector distance is depending on the available space for the setup. For thick sample slabs with a high µs and g, it is more likely to capture scattered photons in the unscattered transmittance measurement and, therefore, the spectra need to be inspected thoroughly [6,9,22–25]. Ideally, the µt spectra, derived from the unscattered transmittance through the Beer-Lambert law, and by taking into account the effect of specular reflectance at each boundary, should be identical for different thicknesses of the same turbid sample. However, the thicker the sample, the lower the allowed µs and/or g will be in order to limit the contribution of scattered photons to the unscattered transmittance. As a result, the thicker version of the same turbid sample will always result in a lower µt. If the difference is significant, the unscattered transmittance and µt for the thick sample is far from correct. An underestimation of µt will automatically result in an underestimation of both µs and g. Therefore, measurement of the same sample for different sample thicknesses is a good technique to verify the reliability of the unscattered transmittance. On the other hand, if the sample is not placed perfectly perpendicular to the incident light beam, refraction of the unscattered light inside the sample (and cuvette) might happen and only a portion will be captured by the detector, causing an underestimation of the real unscattered transmittance . For these reasons it is advised to measure the unscattered transmittance in a configuration that is optimized for this measurement, apart from the integrating sphere(s) [9,15].
The main objective of this study was to develop and thoroughly validate a setup that enables very accurate measurements of the diffuse reflectance, total transmittance and unscattered transmittance in the 500 to 2250 nm wavelength range for the optical characterization of strongly scattering and absorbing samples. First, a thorough description is given about the developed setup, the validation set of liquid optical phantoms, the measurement procedure and the BOP estimation procedure. Secondly, the optical properties estimation procedure is validated by comparing the bulk optical properties estimated for the liquid optical phantoms based on measurement at two different thicknesses. A second validation consists in the comparison of the estimated optical properties with those found in literature. Finally, equations are derived which describe the scattering properties of pure Intralipid® 20% (IL), an often used scattering agent, in the 500-2250 nm wavelength range in the absence of dependent scattering.
2. Materials and methods
The elaborated setup for accurate measurement of diffuse reflectance (MR), total transmittance (MT) and unscattered transmittance (MU) of turbid sample slabs in the 500-2250 nm wavelength range is schematically illustrated in Fig. 1. It consists of a flexible high-power light source which produces a pre-dispersed narrow collimated light beam and allows for fast and automated wavelength and waveband selection, two integrating spheres with detectors and an unscattered transmittance measurement path. This setup is validated on a set of 57 liquid optical phantoms, designed to cover a wide range of absorption and scattering properties.
2.1 High-power pre-dispersive light source
A supercontinuum laser (SC450-4, Fianium Ltd., Southampton, UK) with 4 Watt total output power and spectral broadening over the range 450-2400 nm is used as a light source. The white laser light is focused (F/3.9) into a high-precision Czerny-Turner monochromator (Oriel Cornerstone 260 ¼ m, Newport, Irvine, USA) with a lens (f = 30 mm). All lenses in the entire setup, are 1 inch diameter uncoated plano-convex N-BK7 lenses (LA*, Thorlabs Inc., New Jersey, USA), suitable for the full Vis-NIR spectral range. The monochromator is equipped with a built-in shutter and two high-efficiency gratings to cover the entire Vis-NIR range: one for the 450-1400 nm range (model 74164) and one for the 900-2800 nm range (model 74169). In combination with the 1 mm output slit width, the bandwidth for the two gratings is respectively 3.1 and 6.2 nm. The wavelength for switching between the two gratings is set at 1050 nm.
The pre-dispersed beam leaving the exit port of the monochromator is collimated by a lens (f = 30 mm) and projected onto a long-pass filter which blocks the higher order diffracted light from the grating. The long-pass filter in the light path can be automatically changed with a motorized filter wheel (model 74010, Newport, Irvine, US). For wavelengths below 650, 1100, 2000 and 2500 nm, a long-pass filter with a cut-on wavelength of respectively 400, 600, 1050 and 1300 nm (FEL*, Thorlabs Inc., New Jersey, USA) is brought into the light path. Behind the filter wheel, the light beam is split by a beam splitter in a sample path (90% reflected) and a reference path (10% transmitted) to enable for laser stability monitoring. The light beam of the reference path is again split (50% reflected, 50% transmitted) by a beam splitter to be focused by a lens (f = 30 mm) on respectively a one-stage Peltier-cooled extended-InGaAS detector to monitor the stability for wavelengths above 1050 nm, and a Si detector (respectively PDA10DT-EC and PDA100A, Thorlabs Inc., New Jersey, USA) for wavelengths below 1050 nm. Both beam splitters (respectively type 4-9101 and 4-0101, Optometrics, Massachusetts, USA) are of the “polka dot” type, having a splitting ratio which is constant over the entire Vis-NIR range and independent of the polarization ratio and illumination angle. The light beam of the sample path is sent to a motorized flip mirror (MFF001/M and ME1-P01, Thorlabs Inc., New Jersey, USA) to reflect the light towards the DIS measurement path, or pass the light to the unscattered transmittance measurement path.
2.2 Double integrating sphere measurement path
In the DIS measurement path, the light beam is focused by a lens (f = 200 mm) on the center of the sample located in the sample holder. The sample holder is positioned between two Infragold® coated 6 inch diameter integrating spheres (RT-060-IG, Labsphere Inc., North Sutton, USA). The spheres and the sample holder are all mounted on a rail (System rail SYS 90, OWIS GmbH, Germany) to simplify and maintain good alignment. The sphere ports touching the sample are 1 inch diameter, while the entrance port of the reflectance sphere and all detector ports of both spheres are ½ inch in diameter. In order to ensure the detection of diffuse light only, all detector ports are masked from the sample ports and locations of first impact on the sphere wall by internal baffles. Each sphere is equipped with two detectors similar to those used in the reference path: a one-stage Peltier-cooled extended-InGaAs detector (PDA10DT-EC Thorlabs Inc., New Jersey, USA) for the range from 1050 nm to 2250 nm, and a Si detector (PDA100A, Thorlabs Inc., New Jersey, USA) for the 500-1050 nm range. Because of the sphere geometry, the sample is illuminated under an angle of 9°. This makes it possible to measure both diffuse and total reflectance by respectively including or excluding the specular reflected light. The specular light can be excluded by installing a 1 inch diameter light trap (LT-100, Labsphere Inc., North Sutton, USA). A custom-made aluminum sample holder fits very precisely on the sample ports of the spheres, such that the sample (cuvette surface) is in line with the sphere wall. The sample holder is insulated and its temperature can be controlled (10-80 ± 0.2°C) by pumping water from a temperature controlled water bath through the hollow sample holder body surrounding the sample. To quantify the optical power focused on the sample for full laser power (4 W) and 1 mm output slit size of the monochromator, the optical power was measured from 400 until 2500 nm in steps of 50 nm with a power meter (PM200) in combination with a photodiode power sensor (700-1800nm; S132C) and a thermal power sensor (190-25.000 nm; S302C, All Thorlabs Inc., New Jersey, USA). The acquired power spectrum is illustrated in Fig. 2.
2.3 Unscattered transmittance measurement path
In the unscattered transmittance measurement path, a 7.5 mm round slit is placed immediately before and after the sample, while a third similar slit is placed 1.5 m behind the sample. All three slits are optically aligned. This design ensures a collection angle of only 5 mrad to minimize the number of scattered photons captured. The sample is placed in a temperature controlled sample holder (cfr. DIS measurement path) located perpendicular to the incident collimated light beam. Behind the third slit, a motorized flip mirror (MFF001/M and ME1-P01, Thorlabs Inc., New Jersey, USA) is located that can reflect or pass the light either towards the Si detector (PDA100A, Thorlabs Inc., New Jersey, USA) or the extended-InGaAs detector (PDA10DT-EC Thorlabs Inc., New Jersey, USA).
All components (laser, monochromator, filter wheel, flip mirrors and detectors) of the setup are automatically controlled or read by a data acquisition card (NI PCI-6251) and the measurement procedure is programmed in LabView 8.5 (both National Instruments Corporation, Texas, USA).
2.4 Liquid optical phantoms
A set of 57 (8x7 + 1) liquid optical phantoms was designed and prepared to cover a wide range of absorption and scattering properties [Fig. 3]. Methylene Blue (M9140, Sigma-Aldrich, Missouri, USA), Intralipid® 20% (batch 10FH1726, expiring date 07/2014, Fresenius Kabi, Germany) and water were respectively used as absorbing, scattering and dilution agent and mixed in different ratios. IL is originally developed for intravenous feeding and contains 20% (w/w) soybean oil (SBO), emulsified (1.2% w/w egg lecithin) in water. Taking into account the density of the different components, this results in a volume concentration of 22.7% scattering particles in pure IL [22,25,29,30]. As IL is an emulsion of fat in water, with mainly fat globules smaller than 500 nm diameter, the globules act as spherical scattering particles. Because the diameter of most fat globules is smaller than the wavelength of the considered Vis and NIR electromagnetic radiation, the scattering is maximal for the smallest wavelengths and decreases with increasing wavelength. In biomedical optics, IL is often used to mimic scattering by biological tissues [6,22,25–30]. Since the batch-to-batch variability in scattering properties of IL is very small and IL is highly stable over time and at different temperatures, it is very suitable for calibration and comparison of different setups developed for optical characterization [26,27,31]. MB was chosen as absorber since it has a sharp absorption peak in the 500-750 nm range where the absorption by water and IL is minimal .
A MB stock solution of 400 µM was prepared and different volumes were pipetted to create different absorption levels for the optical phantoms [cfr. rows in Fig. 3]. For increasing row number in Fig. 3, respectively 0, 1, 2, 4, 8, 16, 32 and 36 ml MB stock solution was used. To create different scattering levels, an increasing amount of IL was added with increasing column letter in Fig. 3. In total, 7 scattering levels were created corresponding to 1, 2, 4, 8, 16, 32 and 64 ml IL. Eventually, water was added to obtain 100 ml for all phantoms and phantoms were carefully shaken. Following this, the phantoms with increasing row number have MB concentrations of respectively 0, 4, 8, 16, 32, 64, 128 and 136 µM, while increasing column letter [Fig. 3] corresponds to a concentration of respectively 0.227, 0.454, 0.908, 1.816, 3.632, 7.264 and 14.528% (v/v) scattering particles. Additionally, pure IL was also added to the set of phantoms to measure. The set of 56 liquid optical phantoms together with IL will further be referred to as ‘phantoms’.
2.5 Measurement of liquid phantoms
All liquid phantoms were freshly prepared and measured at room temperature (22 ± 0.5°C) for two sample thicknesses: 0.55 and 1.1 mm. Measurement of the same sample at two thicknesses should result in the same estimated BOP values. Therefore, it is an interesting technique to evaluate the measurement setup and the BOP estimation routine . Moreover, it is a better technique than varying the concentration, since for a dilution series, scattering and absorption are connected, especially in the NIR, and the effect of dependent scattering has to be taken into account [6,9,22,25].
The liquid phantoms were measured inside a custom-made cuvette consisting of two parallel 1.1 mm thick glass plates (Borofloat33, Schott, Germany) separated by a spacer (respectively 0.55 and 1.1 mm thickness). The cuvette fits very precisely in the sample holder of both the DIS and unscattered transmittance measurement path. Two times a day, the setup was calibrated (dark and white calibration) according to the procedure described by Prahl . The dark current of each detector was measured with the built-in shutter of the monochromator closed. A calibrated 99% Spectralon® reflectance standard (SRS-99-010, Labsphere Inc., North Sutton, USA) was installed on the sample port of the reflectance sphere to perform the white calibration. For the white calibration measurement in the unscattered transmittance measurement path, a neutral density filter (optical density 1, 2 or 3; all Qioptiq Limited, Luxembourg), whose transmittance matched the closest to the MU of the particular sample, was selected and precisely located inside the sample holder. No significant detector drift was noticed in the dark and white calibrations from measurements within a day.
For all measurements the reflectance sphere was equipped with the light trap to only capture the diffuse reflected light. First, the sample was measured from 500 to 2250 nm with an interval step of 5 nm in the DIS measurement path, followed by measurement in the unscattered transmittance path. A single measurement (DIS or unscattered transmittance) takes ± 300 seconds for 351 wavelengths. All different phantoms and both thicknesses were measured randomly with laser power at maximum and the monochromator slit size at 1 mm. The cuvette was cleaned and dried thoroughly before loading the next sample.
2.6 Estimation of bulk optical properties
The inverse adding doubling (IAD) program developed and optimized by Prahl [9,10] was consulted for the estimation of the BOP values from MR, MT and MU measurements. Apart from the three measurements (MR, MT and MU), a few other setup and sample related parameters have to be uploaded for the inverse estimation: The sphere wall efficiency was estimated according to the procedure described by the manufacturer [9,16], while the reflectance standard was calibrated by the manufacturer for the full wavelength range. The exact transmittance of the neutral density filters was measured in the unscattered transmittance measurement path and compared to an empty path. The diameter of the light spot on the sample between the two integrating spheres was measured over the full wavelength range by replacing the sample with a black iris diaphragm, and measuring the minimum iris opening (2.5 mm at 500 nm and 5 mm at 2250 nm) for which the transmittance signal was not significantly reduced compared to an open iris. The wavelength-dependent real refractive index of the cuvette windows was provided by the manufacturer (Schott, Germany) for the full wavelength range, while the real refractive index (n) of the sample was calculated based on the volume concentration of scattering particles or lipid (Φp) in the sample as: nsample = nwater + 0.14Φp [25,29]. The wavelength-dependent real refractive index of water at room temperature was adopted from Hale and Querry . The effect of MB on the sample’s refractive index was neglected because of the low concentrations. The absorption-efficiency of the light trap was determined by reflectance measurements on a specular reflectance standard (STAN-SSH, Ocean Optics Inc., Dunedin, USA) for all wavelengths.
A Matlab (version 7.10, The Mathworks Inc., Massachusetts, USA) routine was developed to calculate MR, MT and MU from the sample measurements, taking into account the calibration and reference measurements. Hence, the developed code sends the data, together with the other information about the sample and setup, to the IAD routine, and extracts and plots the estimated BOP values.
3. Results and discussion
3.1 Liquid phantom spectra
The acquired diffuse reflectance spectra (MR) for the phantoms with minimum (A*) and maximum scattering (G*) for thickness 0.55 mm (a) and 1.1 mm (b) are illustrated in Fig. 4. The spectra of the other phantoms had a similar shape and are situated in between these extremes. Overall, higher scattering results in higher MR values and absorption peaks can be noticed as dips in the MR values. Clear absorption peaks of water at 970, 1200, 1450 and 1950 nm  and of MB around 665 nm  can be observed. Increasing MB concentrations for a fixed scattering level (same color) can be noticed from the decreasing MR values between 500 and 750 nm. A larger sample thickness results in a noticeable higher MR when absorption is low. This effect is, however, reduced in the regions of high absorption by MB (665 nm) and water (> 1400 nm), especially for the highly scattering phantoms.
The MT spectra for phantoms A* and G* are shown in Fig. 5. Compared to MR, an opposite effect can be noticed, with a decreasing MT for increasing scattering. Similar to MR, the dips in the MT spectra correspond to the absorption peaks of water and MB. Increasing the sample thickness results in an overall decrease of MT with a stronger effect at regions of high absorption. For high concentrations of lipid (G*), even a small lipid absorption peak can be noticed as an extra dip around 1210 and 1720 nm .
As can be seen from Fig. 6 the effect of scattering and absorption on the unscattered transmittance spectra (MU) is more pronounced than for the MT spectra. In the NIR, for the phantom with the lowest scattering (A*), MU is almost equal to MT because the effect of scattering is negligible here. As expected, a logarithmic decay in MU can be noticed with increasing sample thickness.
3.2 Estimated bulk optical properties
The three measurements (MR, MT and MU) for each phantom were used as inputs for the IAD routine to estimate the BOP values at every wavelength. In Fig. 7, the estimated µa values in the range of the absorption peak of MB (500-750 nm) are plotted for all the liquid phantoms, measured at a thickness of 0.55 (a) and 1.1 mm (b). The µa spectra for phantoms with the same MB concentration (absorption level) are grouped and the average is plotted together with the standard deviation (error bars). A clear increase in µa can be noticed with increasing MB concentration. The peaks in µa around 615 and 665 nm are caused respectively by MB dimers and monomers. With increasing MB concentration the equilibrium between monomers and dimers shifts in favor of the dimers . As a result of this, the peak around 615 nm becomes more significant. Sample thickness has no noticeable effect on the estimated µa spectra, proving the accuracy of the measurement setup and estimation routine. For the thicker samples, however, the standard deviation within a group is significantly higher, especially for the higher µa values. This can be explained by the fact that the measured MT and MU spectra are significantly decreasing with increasing thickness at the absorption bands, resulting in a lower signal to noise ratio. This confirms that optimizing the sample thickness is important for reducing the uncertainty on the estimated BOP values .
Because MB has no absorption peaks in the NIR and an increasing IL concentration results in a decrease in absorption by water due to the water displacement effect, the µa spectra in the NIR range [Fig. 8] are grouped for fixed IL concentration (scattering level). It should be noted that no error bars have been indicated for the IL group since it only contains one sample (pure IL). The effect of water displacement can be clearly observed at the water absorption bands around 1450 and 1950 nm in the µa spectra. Exactly the same effect and comparable µa spectra can be seen for both sample thicknesses [Figs. 8(a) and (b)]. However, because of the extremely low MR, MT and MU values around 1950 nm, no accurate BOP estimations could be established in this region. Therefore, these were removed from the figures. For the thicker (1.1 mm) samples, MT and MU in that wavelength region were even lower and consequently less accurate. Therefore, a larger part of the BOP spectra had to be removed [Fig. 8(b)]. The estimated µa spectra in the NIR for the phantoms with highest water concentrations (> 99% v/v; phantoms A* – C*) are nearly identical to the µa spectrum of water as reported in literature . For phantoms with high IL concentrations (phantoms G* and IL), a small additional fat absorption peak can be noticed around 1210 and 1720 nm .
In Fig. 9(a) the estimated µa values at 665 nm (mean and standard deviation) for both thicknesses are plotted against the corresponding MB concentration. A clear linear relation can be fitted to the data for MB concentrations below 70µM (R2 = 0.996). Above this concentration the fraction of MB dimers increases drastically, reducing the fraction of monomers that absorb around 665 nm . The slope of the fitted line is 0.1071 cm−1µM−1, which is very close to the theoretical molar absorption coefficient of MB monomers at 664 nm of 0.095 cm−1µM−1 .
In Fig. 9(b), the effect of water displacement is illustrated by plotting the µa at 1450 nm against the volume concentration of water. A nearly linear increase (R2 = 0.975) of µa at 1450 nm can be noticed with increasing volume concentration of water. At high water concentrations, the variability in µa at 1450 nm is, however, high. The most plausible explanation for this is the low MR, MT and/or MU at this wavelength [Figs. 4-6], especially for low scattering and 1.1 mm sample thickness, resulting in less accurate measurements and BOP estimations.
The estimated reduced scattering coefficient (µs’) values, corresponding to µs(1-g), are plotted in Fig. 10 for both sample thicknesses. Almost identical µs’ spectra could be expected for fixed scattering levels and were, therefore, grouped together. An exponential decay of µs’ with increasing wavelength can be observed for all phantoms and a similar trend is found in literature [25,26,30,31]. Phantoms with higher IL concentrations resulted in higher µs’ spectra. However, the effect seems to diminish for increasing IL concentration and increasing wavelength. This observation could be attributed to the effect of dependent scattering, which occurs when the concentration of scattering particles is high enough such that individual scattering events are influencing each other [6,22,25]. Typically, the scattering is more ‘dependent’ if the wavelength increases compared to the scattering particle diameter [6,35]. The standard deviation on the estimated µs’ values, indicated by the error bars, was extremely small and almost no absorption signature could be observed. This highlights the quality of the measurements and BOP estimations obtained with the elaborated DIS setup based on a supercontinuum laser. Moreover, the BOP values estimated from the measurements at both sample thicknesses show a very good agreement. It can also be concluded that the MB concentration had no influence on the scattering, as the standard deviation of the µs’ spectra in the MB absorption region (500-750 nm) was not higher compared to other wavelengths.
The µt spectra, calculated from the MU measurements, are illustrated in Fig. 11 for 0 µM MB phantoms at 4 different scattering levels and both sample thicknesses. Because of the low scattering [Fig. 10], the µt spectra for both thicknesses of phantom B1 overlap very well over the entire wavelength range. However, as the scattering increases, the estimated µt spectra for both sample thicknesses start to diverge [gray-highlighted zone in Fig. 11]. For phantom C1 both curves diverge below 600 nm, while in the case of phantoms E1 and IL this divergence is even more severe and extends up to 800 nm and even 1200 nm, respectively. When both curves diverge, the estimated µt value for 1.1 mm sample thickness can be considered the most erroneous as these Mu measurement enclose the most scattered photons . Therefore, the wavelength regions for which the estimated µt value for 1.1 mm sample thickness was more than 2% smaller, compared to the µt for 0.55 mm thickness of the same sample, were excluded from the BOP estimations. In Fig. 11, the estimated µt values for 1.1 mm thickness seem to stabilize at a constant value in the wavelength region where they diverge from those estimated for 0.55 mm thickness, while the latter keep increasing with decreasing wavelength. This can most likely be attributed to an increasing contribution of the scattered photons to the acquired Mu signal. For the E1 and IL phantoms such a stabilization at a constant value can also be noticed in the µt spectra estimated from the Mu measurements at 0.55 mm thickness, but at considerably shorter wavelengths compared to the 1.1 mm thickness. As this effect can, most likely, also be contributed to an increasing contribution of scattered photons to the Mu signal, the wavelength regions where this occurs [Fig. 11, gray-highlighted] have also been excluded from the BOP estimation.
In the wavelength regions where the MU data was excluded from the BOP estimations, an estimate of g was provided to the IAD routine  in order to obtain an estimation for µa and µs’ in respectively Figs. 7-9 and 10. This estimate of g was derived from the linear relation with wavelength, valid from 400 to 1100 nm, found in literature . However, without a reliable value for MU, and consequently µt, it is not possible to extract µs from µt, and g from µs’ . For the phantoms and wavelengths for which a reliable MU could be measured [Fig. 11, not gray-highlighted], an estimation for µs and g has been performed which is plotted in respectively Figs. 12 and 13. However, no accurate estimations could be established for both µs [Fig. 12] and g [Fig. 13] in the region around 1970 nm because of the very high absorption by water [Fig. 8], especially for the phantoms with high water concentration.
Similar trends can be observed in the µs spectra [Fig. 12] as were observed in the µs’ spectra [Fig. 10]. In Fig. 12 the µs spectra have been bundled for fixed scattering levels and the average and standard deviation within a group have been plotted. The µs spectra follow an exponential decay with increasing wavelength, which is in agreement with the observations of other researchers [25,29]. Higher µs values can be related to higher IL concentrations. However, due to, most likely, the attribution of dependent scattering, this effect reduces with increasing IL concentration and increasing wavelength [22,25,35]. The estimated µs spectra are expected to be very reliable since the standard deviations within a group for a fixed scattering level are small and the estimations for the two sample thicknesses are consistent. Again, there is no increase in the standard deviation on the estimated µs values in the 500-750 nm regions, which indicates that the MB concentration and thus the µa value had no significant influence on the estimated µs values.
The anisotropy factor g is the only BOP which only influences two of the three measurements on a sample: MR and MT, while µa and µs have an impact on MR, MT and MU . Consequently, the estimation of g is less stable, and more prone to measurement inaccuracies, compared to the estimation of µa and µs. This can be perceived by the relatively large standard deviations within a scattering level group [Fig. 13]. Moreover, in the regions of low MR, MT and/or MU signals due to high absorbance, the variability is increased, especially for the 1.1 mm sample thickness. For the phantoms with low scattering level (A* and B*), no accurate estimations for g >1050 nm could be established. Therefore, no values are plotted in this range. Similar spectral behavior of g can be observed between two sample thicknesses [Fig. 13(a) versus (b)]. A linear decrease of g with increasing wavelength can be noticed in the Vis and short-wave NIR range, which is in agreement with the findings of other researchers [25,29]. However, to our knowledge, there are no reports on the values of g for wavelengths above 1100 nm. From our measurements, it can be concluded that g follows a non-linear decay for higher wavelengths. In the scenario of independent scattering, g is depending only on the size, shape and material properties of the scattering particle and the material properties of the host medium, and not on the number of scattering particles . Since only the number of scattering particles is varied between different scattering levels of the phantoms, one would expect the same g spectra for all phantoms. However, g seems to decrease with increasing IL concentration. This phenomenon was already observed at a single wavelength (633 nm) by Zaccanti et al.  and was attributed to the effect of dependent scattering [6,22,35]. In our study, the effect of dependent scattering on g becomes insignificant if the volume concentration of the IL scattering particles is below 2% (phantoms A* – D*). However, further research is needed to fully understand the effect of dependent scattering on the BOP .
IL dilutions are intensively used in biomedical optics to serve as tissue phantoms for calibration and validation of measurement setups in the Vis and short-wave NIR [25,27]. The absorption and scattering properties of such phantoms can be designed by respectively adding an absorber or by dilution, to match the biological tissue’s BOP very closely [1,2,4,13,14,25,29]. However, for wavelengths above 1000 nm, both µs, even for pure IL, and g are much lower compared to the reported values for most biological tissues in that wavelength range [1,5,8,14,37]. An emulsion with larger scattering particles at a lower volume concentration, like for instance raw milk, would result in µs and g spectra which are more comparable to the BOP of biological tissues over the full Vis and NIR wavelength range . The disadvantage of such emulsions would, however, be that these are typically not standardized and much less stable .
In order to compare the BOP values obtained in this study with those reported by other researchers, all spectra were linearly scaled to the case of pure IL with a volume concentration for the scattering particles (Φp) of 22.7% [Fig. 14]. In most studies, IL dilutions were measured for Φp < 2% in order to prevent dependent scattering [25,29]. Therefore, only the spectra of phantoms A* – D* (Φp < 2%) for both thicknesses were used in the comparison. µs and µs’ spectra were scaled by dividing with the actual Φp and multiplying with 0.227 (Φp for pure IL), following the linear relation between scattering and Φp for the case of independent scattering. Referring to the previous paragraph, no scaling was performed on the g spectra. The scattering properties obtained from measurements on two thicknesses (0.55 and 1.1 mm) for each sample agreed very well [Fig. 14] and were, therefore, kept together in the fitting procedure. Following the findings by Michels et al.  and van Staveren et al. , respectively a three- and two-parameter exponential function was successfully fitted (least-squares) to the scaled µs and µs’ data (R2 = 0.992 and 0.989 respectively). For µs’, a good agreement [Fig. 14] was found between the fit for the obtained data and the results reported by Michels et al.  and van Staveren et al. . However, the fit for µs’ by Wen et al.  was significantly lower. The lower values reported by Wen et al.  can most likely be explained by the effect of dependent scattering as they used a concentration of 5% (w/w) scattering particles. The fitted equation for µs was very similar to the one acquired by van Staveren et al. , but resulted in somewhat higher values compared to the µs spectrum reported by Michels et al. . For g, a linear function with both the slope and intercept multiplied with a similar logistic function [Eq. (1)] was consulted in order to accurately (R2 = 0.991) describe the linear relation with wavelength (in nm) in the Vis and short-wave NIR, together with the non-linear behavior above 1300 nm. Again, a good match was found with the linear fit from van Staveren et al. . However, compared to the values reported by Michels et al. , which were measured with a goniometer, the estimated g values were slightly higher.
The fitted equations shown in Fig. 14 and Eq. (1) give a very accurate empirical description of the bulk scattering parameters for pure IL (Φp = 22.7%) in the Vis and NIR wavelength range, for the case of independent scattering. Unfortunately, dependent scattering is dominant in the Vis-NIR for pure IL and, therefore, these equations can only be utilized for IL dilutions with volume concentrations Φp below 2%, especially for longer wavelengths.
A measurement setup combining a high power supercontinuum laser with a monochromator and integrating spheres was designed and developed for accurate measurement of diffuse reflectance, total transmittance and unscattered transmittance of strongly scattering and absorbing sample slabs in the 500-2250 nm wavelength range. The performance of this setup was evaluated and validated on a set of liquid optical phantoms covering a wide range of absorption and scattering properties. The phantoms were measured for two different thicknesses and the bulk optical properties were estimated with an inverse adding doubling routine. The estimated bulk optical properties for both sample thicknesses correspond very well with each other and with values found in literature. The variability on the estimated bulk optical properties was very low for groups for which the same optical properties were expected. Moreover, the separation of the absorption and scattering information was successful as no cross-over of information could be noticed. This demonstrates the high potential of this setup for the optical characterization of very turbid media, such as biological tissues, in the full Vis-NIR range. Additionally, more insights were obtained on the wavelength-dependent effect of dependent scattering on the estimation of the bulk scattering properties of intralipid-dilutions. Finally, equations were fitted to the bulk scattering properties from 500 until 2250 nm for Intralipid® 20% in the case of independent scattering. These equations can be consulted in future research for calculating the bulk scattering properties of intralipid-dilutions in the Vis and NIR range.
Ben Aernouts is funded as a Ph. D. fellowship of the Research Foundation - Flanders (FWO). Rodrigo Watté is a PhD student funded by the Agency for Innovation by Science and Technology in Flanders (IWT). Eduardo Zamora-Rojas was a visiting PhD student at KU Leuven with financial support of the Spanish Ministry of Education as a fellow of the Program “Training of University Teachers”. Mizuki Tsuta was a visiting postdoc at KU Leuven with a mobility grant from the Japanese Science Foundation (JSPS). The authors gratefully acknowledge IWT-Flanders for the financial support through the GlucoSens project (SB-090053). The authors would also like to thank Prof. Scott Prahl (Oregon Institute of Technology, Oregon, USA) for fruitful discussions and sharing his inverse adding doubling code.
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