Effect of static scatterers in laser speckle contrast imaging: an experimental study on correlation and contrast

Laser speckle contrast imaging (LSCI) is a non-invasive microvascular blood flow assessment technique with good temporal and spatial resolution. Most LSCI systems, including commercial devices, can perform only qualitative blood flow evaluation, which is a major limitation of this technique. There are several factors that prevent the utilization of LSCI as a quantitative technique. Among these factors, we can highlight the effect of static scatterers. The goal of this work was to study the influence of differences in static and dynamic scatterer concentration on laser speckle correlation and contrast. In order to achieve this, a laser speckle prototype was developed and tested using an optical phantom with various concentrations of static and dynamic scatterers. It was found that the laser speckle correlation could be used to estimate the relative concentration of static/dynamic scatterers within a sample. Moreover, the speckle correlation proved to be independent of the dynamic scatterer velocity, which is a fundamental characteristic to be used in contrast correction.


Introduction
Laser speckle contrast imaging (LSCI) is a widely used tool for blood perfusion assessment, with established results in many medical fields (Briers et al 2013, Humeau-Heurtier et al 2013, Senarathna et al 2013. This technique makes it possible to produce two-dimensional perfusion maps of large areas, with good temporal and spatial resolution, at a reasonable cost (Richards et al 2013). Along with its non-invasive characteristic, it plays an important role in microcirculation assessment.
LSCI is often used in highly vascularized tissues, like cerebral and retinal tissues, because they contain low concentrations of static scatterers which increases the signal-to-noise ratio (SNR) (Parthasarathy et al 2010a, Basak et al 2014. However, LSCI is also used in low vascularized tissues, like the forearm (Mahé et al 2012), containing high concentrations of static scatterers. Scatterers of this type influence the blood flow evaluation, and should be taken into account when a laser speckle contrast analysis is performed.
In spite of LSCI's large range of applications (Kazmi et al 2015b), this technique continues to be a major field of investigation in biomedical imaging (Kazmi et al 2015c, Braga and González-Peña 2016, Khaksari and Kirkpatrick 2016a, Kirby et al 2016, Nadort et al 2016 due to its known limitations. The major limitations of LSCI are related to its maximum assessment depth-which is low-along with the lack of quantitative blood perfusion values . Traditional laser speckle imaging is a very superficial assessment technique, in which 95% of the interactions occur up to a tissue depth of 700 μm (Davis et al 2014). Diffuse laser speckle contrast (Bi et al 2013) and laser speckle tomography techniques have recently been developed , Huang et al 2015 in order to improve LSCI assessment depth.
The development of a quantitative LSCI method is extremely important for clinical studies (Boas and Dunn 2010). Quantitative results are mandatory for meaningful inter-patient studies, and for the comparison of studies performed under different conditions, or in different institutions. In the quest for quantitative laser speckle imaging, many variations of the original technique have been explored. These methods are mainly based on the use of multi-exposure times (Parthasarathy et al 2010b), based on calibration with other devices (Nadort et al 2013), Effect of static scatterers in laser speckle contrast imaging: an experimental study on correlation and contrast or based on diffuse correlation spectroscopy , Huang et al 2015. Despite all these efforts, a fully quantitative laser speckle method, with the ability to correctly determine blood perfusion in units of moving blood volume per volume of tissue per second (e.g. ml/ml/s), is still the main challenge of LSCI research (Kirby et al 2016).
LSCI is often performed in a qualitative rather than quantitative way, because speckle signals are influenced by many factors difficult to characterize. Among these factors, we can highlight the scatterers' size, the blood vessel calibre (Kazmi et al 2015a), the incident light intensity (Kirby et al 2016), the coherence and polarization of the light (Thompson et al 2011), the speckle size (Ramirez-San-Juan et al 2013), the velocity distribution theor etical models , and the presence of static scatterers (Parthasarathy et al 2008). An intensive study of each of these factors is necessary, in order to have a precise knowledge of its influence on the laser speckle contrast signal.
Many works (Parthasarathy et al 2008, Mazhar et al 2011, Dunn 2012, Ramirez-San-Juan et al 2014, Kazmi et al 2015b, Khaksari and Kirkpatrick 2016a have discussed and dealt with the effect of static scatterers in LSCI. Almost all of these studies were focused only on the effect of different concentrations of static scatterers in the spatial or temporal contrast values. The present work introduces an in-depth study on the effect of the static and dynamic scatterers, in both laser speckle contrast and correlation signals, with a special focus on the determination of the intensity autocorrelation for a large time delay between laser speckle patterns.

Background
In order to explain the influence of differences in static scatterer concentration on LSCI, a short mathematical analysis is required. The autocorrelation function of the laser speckle patterns is often the starting point for the analysis of LSCI, because the dynamic laser speckle information is encoded in time. Hence, the function that relates the field autocorrelation with the intensity autocorrelation (Siegert relation) can be defined as where g 2 (τ ) is the intensity autocorrelation function, g 1 (τ ) is the field autocorrelation function, and β is a normalization constant that accounts for system imperfections, particularly for the speckles' spatial averaging Yodh 1997, Briers et al 2013). It should be noted that the Siegert relation is only valid if the light electric field is a random Gaussian variable (Lemieux and Durian 1999). Since this relation has been applied in the past for both ordered flow (Parthasarathy et al 2008, Nadort et al 2013 and Brownian motion Webster 1996, Dunn et al 2001), we conclude that it can be applied in our experimental conditions. A good overview of the two statistical models mainly used for ordered flow (Gaussian) and Brownian motion (Lorentzian) can be found in . The original LSCI theory described by Fercher and Briers (1981) has been improved over the years in order to account for many of the factors that affect laser speckle imaging . Among these modifications, the correction factor ρ has been included in the field autocorrelation function as a way to estimate the fraction of static scatterers present in the sample. The ρ value can be defined as (Zakharov et al 2009) where I s represents the average light intensity scattered by the static scatterers, and I d that scattered by dynamic scatterers. The inclusion of this new factor results in the separation of the field autocorrelation function into two parts, one for the dynamic scatterers (g 1d (τ )) and the other for the static scatterers ( g 1s (τ )) (Boas and Dunn 2010): Static scatterers are expected to produce a constant speckle signal over time, making the static autocorrelation function independent of τ. Moreover, since the static scatterers contribution is always the same within the temporal region of interest, the correlation between consecutive patterns is equal to 1 (g 1s (τ ) = 1) (Boas and Yodh 1997). Thus, by replacing g 1 (τ ) in equation (1) we obtain When the time difference (τ) between two speckle patterns is much larger than the scatterers' decorrelation time (τ = ∆t τ c ), the dynamic autocorrelation function becomes insignificant (g 1d (∆t) ≈ 0). This is equivalent to saying that, in this specific condition, the correlation between two patterns is only dependent on the amount of light scattered by static and dynamic scatterers, yielding Zakharov et al (2009) g 2 (∆t) = 1 + β ρ 2 .
Zakharov et al (2009) proposed a practical method to estimate ρ using only laser speckle imaging data. Their method starts from the definition of intensity autocorrelation (Fercher and Briers 1981), and substitutes its denominator by the multiplication of the images' spatial average because the they are completely decorrelated: where A and B are two consecutive laser speckle images, ° corresponds to the Hadamard product (elementwise multiplication) and . . . s represents the spatial averaging. This method is only valid when the two speckle images have a temporal gap much greater than the expected decorrelation time. This requirement impedes the use of this method in high speed laser speckle imaging systems like those proposed in Dragojević (2015) and Sun et al (2015). The use of laser speckle correlation as described in equation (7) raises an important theoretical question. This metric is not normalized to the actual image, in contrast to the standard correlation coefficient, which is normalized to the image average. This fact leads to changes in speckle correlation, computed using this method, not only when the image morphology changes but also when the image average changes (for further reference please see the conclusions of Vaz (2016)). This issue turns out to have a strong effect when multiple exposure times are used, if the average light intensity does not remain constant.
The increase of I s produces an increase in the decorrelation time (contrast increase) of the speckle pattern (Parthasarathy et al 2008, Ramirez-San-Juan et al 2014. On the contrary, an increase of the dynamic scattered light leads to a decrease of the decorrelation time, resulting in a lower contrast image. In fact, it is the relation between the light scattered from dynamic and static scatterers that defines the ρ value. This is the basic idea behind the use of correlation to estimate the amount of light reflected by the static/dynamic scatterers. By rearranging the previous equations, we find that ρ can be computed as and that g 2 (∆t), expressed in terms of scattered light, is equivalent to (9) Figure 1 presents the theoretical relations between the variables involved in this study. The first subfigure, figure 1(a), shows that, at ρ close to 0, the correlation increases slowly with the increase of ρ. On the contrary, for higher ρ values, the correlation changes rapidly for short increases of ρ. This function has been plotted using equation (6) and considering β ≈ 0.6 (see results). Figure 1(b) shows that the evolution of g 2 (∆t) is approximately linear after an initial low sensitivity zone where the increase of static scattered light does not produce an increase of the correlation. This analysis is only valid when I s and I d are two independent variables-i.e. when changes in I s do not produce any variation in I d , and vice versa. The x-axis units are expressed in number of times of dynamic scattered light (× I d ), resulting in I s = 0.5 for I d = 2 I s .
Our study is focused on the determination of the autocorrelation function in very specific conditions. All the experiments have been conducted in order to approximate the computed intensity correlation to equation (6) by using large inter-frame and exposure times. This is equivalent to saying that the g 2 (∆t) values presented in this work correspond to the autocorrelation function asymptote. This fact contrasts with, for example, quasi-elastic light scattering and diffuse wave spectroscopy Kirkpatrick 2008, Kirkpatrick et al 2008), in which the exposure times are very short, and the autocorrelation function profile can be computed with much higher precision.
A laser speckle imaging prototype and an experimental bench test have been developed in order to confirm the relation of equation (9) (figure 1(b)), and to study the effect of I s and I d on spatial laser speckle contrast.

Experimental bench
A customized laser speckle device was used to perform this experiment (figure 2). This device uses a coherent light source (BioRay, Coherent Inc.), with an optical power of 40 mW, with a light wavelength of 640 nm, and with an elliptical beam (2.4 × 1.4 mm). The light source was mounted in a cage system and coupled with a vertical polarizer and with a beam expander which was used to control the final beam size. A 45° reflecting mirror was used to direct the laser beam towards the sample.
A digital video camera (Pixelink B-741U), connected to a C-mount lens with a fixed focal length of 50 mm (Edmund 67715), was used to record the speckle patterns. An orthogonal polarizer was attached to the camera lens, in order to remove the light directly reflected from the air-sample interface-which contains no valuable information (Basak et al 2012).
The camera was programmed with a frame rate of 20 frames per second (fps), a fixed resolution of 320 × 240 pixels and an exposure time of 6 ms. This exposure time was selected because it corresponds to the same as the one used in commercial devices (Perimed PeriCam PSI). The frame rate ensures an inter-frame time of approximately 44 ms. A long inter-frame time is an essential feature of the system since the time difference between two consecutive frames (∆t) must be larger than the scatterers decorrelation time (τ c ), which varies from micro seconds to a few milliseconds (Parthasarathy et al 2008, Thompson andAndrews 2008).
The optimum system aperture ( f /#) was selected so as to match a speckle size (d) of at least two pixels per speckle for each dimension, in order to fulfill the Nyquist theorem . The theoretical equation d = 1.2(1 + M)λf /# was used to estimate the laser speckle diameter. The system magnification was experimentally computed using an optical resolution target (USAF 1951 1X), and corresponds to M = 0.2. Since the camera pixel size is 6.7 × 6.7 µm, the minimum system aperture result is 14.5. An aperture of f/16 was selected because the camera lens only admits discrete values of f /#.

Phantom
An optical phantom, composed of two distinct parts, has been developed. The bottom part consists of a small longitudinal channel, into which a fluid can be inserted. The top part consists of a doped silicone layer used to simulate various concentrations of static scatterers.
The bottom part has been constructed in acrylic glass, and encloses a channel, with length of 40 mm and a depth of 0.5 mm, with two holes in its ends (inlet and outlet). The channel width is variable, being narrow at  (6)) using β ≈ 0.6; (b) light reflected by static scatterers and correlation (equation (9)). The units of (b) x-axes (× I d ) correspond to the number of times of dynamic scattered light intensity. Phys. Med. Biol. 63 (2018) 015024 (12pp) the edges (2 mm) and wider at the central segment (5 mm). Figure 3(a) depicts the phantom acrylic channel, in which the width variations are clearly visible. All the experiments were performed in the central part of the channel, i.e. where its width is 5 mm.
A set of six different silicone layers have been made, with a constant thickness of approximately 1.3 mm and different static scatterer concentrations ([S s ]). These layers are composed of a bulk substance (Sylgard ® 184 silicone elastomer) doped with particles of TiO 2 (Sigma-Aldrich titanium (IV) oxide, 1% Mn doped, nanopowder, particle size <100 nm). The titanium dioxide particles act as static dispersers because they are trapped in the silicone matrix. These materials were chosen because they have been used in other biomedical studies (Bisaillon et al 2008, de Bruin et al 2010, Tchvialeva et al 2011, Nadort et al 2016. Table 1 presents the scatterer concentration of each layer, ranging from 0 to 2 mg of TiO 2 per millilitre of elastomer. Figure 3(b) shows the optical phantom mounted in a 3D printed support. The injection and collection of fluid was performed using two micropipette tips. The injected fluid consists of semi-skimmed milk with a particle concentration (lipids + proteins + carbohydrates) of 99 mg ml −1 and particle sizes ranging from 0.1 μm to 2 μm. The use of milk has a number of advantages over the use of blood; specifically, it does not sediment, it is much easier to handle, and presents a behavior similar to intralipid solutions (Waterworth et al 1995, Cubeddu et al 1997. This fluid has also been used in several optical based studies (Wojtkiewicz et al 2009, Figueiras et al 2010, Figueiras 2012, and in some LSCI works (Winchester andChou 2004, Thompson andAndrews 2010). The work from Thompson and Andrews (2010) applied a multi-exposure LSCI to milk, with results similar to those found in red blood cells.
Various concentrations of fluid were used, in order to specify the concentration of dynamic scatterers in the sample ([S d ]). The milk was diluted with water in 1:1(50%) and 3:1 (75%) milk:water volume proportions. Additionally, milk was used without dilution (100%) and with the addition of extra static scatterers (200%)-the latter being achieved by adding powdered milk to the semi-skimmed milk (0.1 g ml −1 ).
The milk was pumped into the phantom using a motorized syringe pump, Razel ® scientific instruments model R-99, with several inflows. The applied flows had been previously simulated using multiphysics software, in order to determine the corresponding channel core velocity. The flows used here (table 2) were selected in order to ensure a phantom core speed in the physiological range (Reece et al 2013). A detailed description of this simulation can be found in Vaz (2016

Signal processing details
The β constant had been determined before the use of the phantom, since it is a characteristic value of the developed prototype, and does not depend on the sample. Practically, this constant corresponds to the highest The channel device below the static scatterers membrane, the micropipette injection system, and the support structure. A black paperboard was used in order to present secondary light reflections. contrast that the system can achieve. It was computed by using a white paper sheet as sample (Thompson et al 2011). The laser speckle contrast was computed in a 5 × 5 pixel region, and β taken as equal to its mean. This process led to a normalization constant of β = 0.596. The same sample (white paper sheet) was used to experimentally determine the minimum speckle size. First, the central line of the 2D-power spectral density (PSD) was computed. After that, a Gaussian curve was fitted to this data, and its full width at half maximum (FWHM) taken as the minimum speckle size (Kirkpatrick et al 2007). The minimum speckle size determined with the PSD was 2.44 pixels per speckle.
All the combinations of fluid flow, milk concentration and static scatterer layer were analyzed, resulting in 120 video sequences, each of 600 frames (30 s). All the acquisitions were segmented to be limited to the wider channel segment. The speckle correlation has been computed in regions of 5 × 5 pixels, in the same way as laser speckle contrast (see below). For each acquisition, 599 correlation maps (I g2 ) have been computed, and the mean (Ī g2 ) associated with each acquisition.
The modified Tompkins-τ algorithm has been used to exclude the outliers from each data-set, using a twotailed distribution with a 95% confidence interval. According to this algorithm, the exclusion criterion can be computed as (Dieck et al 2005, Anbarasi et al 2011 where n is the number of samples, and t α/2 is the critical value of a Student's t-distribution of n − 2 samples, with a degree of confidence α. With the remaining points, the mean ( g 2 ) and standard deviation (δg 2 ) of the correlation have been computed for each configuration. An outlier removal algorithm was applied in order to remove possible areas where the phantoms could present imperfections, such as clusters of scatterers or cracks in the channel. Finally, the speckle contrast has also been computed using the spatial algorithm (s-K)  because it is still the most used in LSCI. The methods used to post-process the contrast maps were the same used for correlation (mean contrast map and outliers removal). The computation element corresponds to 5 × 5 pixels.

Correlation g 2 (∆t)
For each configuration used in this experiment, the correlation function g 2 (∆t) has been computed as mean ± standard deviation (discrete points). These data have been plotted as function of static scatterer concentration. In this paper, only a reduced data-set is shown, for concision. The results are presented only for flows #1 (0 cm 3 h −1 ), #2 (1.5 cm 3 h −1 ), #4 (7 cm 3 h −1 ), and #5 (14 cm 3 h −1 ). The complete data-set can be found in Vaz (2016). Figure 4 presents a graphical analysis of the results obtained for the correlation function g 2 (∆t) where each subfigure represents a different flow and, consequently, a different core velocity. The increase of the static scatterer concentration should produce an increase of the correlation in a range between 1 g 2 (∆t) 1 + β. However, this full range is only achieved for a variation of ρ from 0 to 1-which, in experimental conditions, is never achieved.
Both theoretical equation and experimental data show different sensitivities to ρ changes (theory) and to [S s ] (experimental data) changes. More specifically, they have low sensitivity for lower ρ and lower [S s ], and high sensitivity for higher ρ and higher [S s ]. However, the data shows that our apparatus lacks sufficient sensitivity to detect variations in [S s ] below 1 mg ml −1 . Only for higher concentrations does g 2 (∆t) start to increase with the increase of static scatterer concentration. Another important remark that can be extracted from these data is that, for exclusively dynamic scatterers ([S s ] = 0), the experimental correlation never reaches the unitary value ( g 2 (∆t) = 1). This is equivalent to saying that even using a transparent silicone membrane ([S s ] = 0), there is mutual information between consecutive frames leading to a value of I s > 0. This evidence supports the fact that theoretical g 2 (∆t) values are much lower than those computed experimentally, finishing at g 2 (∆t) = 1.00 in the theory, while in the experiment they remain around 1.01. This is due to experimental imperfections like internal reflections of the microchannel. The milk concentration also has an important effect on the minimum detected correlation value, because higher milk concentrations show lower minimum correlation values. Some conclusions can also be extracted regarding the effect of increasing [S d ]. The increase of the milk concentration corresponds to an increase of the dynamic scatterer concentration ([S d ] )-and, therefore, to an increase of I d . From figure 4 it can be seen that the correlation for 50% milk is in most cases higher than that for 75% milk, and the correlation for 200% milk is lower than that for the other concentrations. These data show a gradual downward shift, which is a consequence of the theoretically horizontal stretch caused by the increase of I d . Moreover, this increase has the effect of stretching the x-axis, because the correlation is sensitive to the ratio between static and dynamic scattered light. Graphically, this corresponds to a delay in the correlation function onset or, in other words, the correlation starts to increase at higher values of [S s ]. The error bars correspond to the standard deviation of the correlation for each case. Since an adaptive algorithm has been used to remove the outliers, these standard deviations have been computed with a different number of points. The minimum number of points for each acquisition was 3165, and the maximum 6803. The correlation values computed from samples with higher [S d ] show smaller error bars, which indicates a more precise result. In other words, the presence of a large amount of dynamic scatterers increases the laser speckle signal-to-noise ratio.
Despite the non-equivalence between the scatterer concentration (used in the experiment) and the average reflected light (detailed by the theory), these data have been fitted to the model described by equation (9). The fitting equation was forced to intersect the y-axis at value 1.00 in spite of the experimental issues revealed by our system (the minimum computed correlation being approximately 1.01). The [S s ] was taken as the I s , and corresponds to the independent variable of the fitting model. The [S d ] was taken as the I d , and corresponds to the fitting parameter. The fitting output has been plotted as the solid line in figure 4.  presents an increase with the increase of milk concentration. The flow changes also produce a variation in the fitted [S d ], but a clear tendency has not been observed.
Regarding the evolution of the correlation as function of the fluid flow (figure 5), an important result can be observed. The increase of the dynamic scatterer velocity results in decorrelation of the image (blurring), which is the same effect caused by a decrease of ρ. This statement could lead us to believe that speckle correlation will be affected by changes in the scatterers' velocity. However, figure 5 shows evidence that changes in the fluid flow do not produce significant variations in g 2 (∆t).
The same evidence as that we have found in our study has also been concluded in recent works on optical microangiography (Choi et al 2016b) and optical coherence tomography (Choi et al 2016a). These works also found that, at long time interval measurements, the field autocorrelation between measurements is independent of the particle velocity, but still responds to changes in particle concentration.
In the course of this work, one major issue of the use of g 2 (∆t) has been identified: the speckle correlation is dependent not only on the image morphology, but also on the image mean intensity. In this experiment, both the exposure time and laser optical power of all the acquisitions were fixed (6 ms and 40 mW). However, the inclusion of different concentrations of scatterers produces slight variations in the image mean intensity. We believe that, in our experiment, this variation does not affect the values of g 2 (∆t). This should be considered as a study limitation.

Contrast
The contrast results have been plotted as function of the static scatterers concentration. Figure 6 presents the results of the s-K for the milk concentrations of 50%, 75%, 100% and 200%. By analysing this figure, it can be seen that in most cases, the contrast values for a given concentration of static and dynamic scatterers decrease with the increase of fluid flow, confirming LSCI theory. This situation occurs for almost all the presented cases. The only exceptions are the milk 50% [S s ] = 2 mg ml −1 , milk 75% [S s ] = 2 mg ml −1 , milk 100% [S s ] = 0 mg ml −1 and milk 200% [S s ] = 0.25 mg ml −1 .
The contrast value flow dependence is more visible when a milk concentration of 200% is used, due to the reduction of the data error bars. As occurs in the correlation case, this data-set presents higher SNR. It has also been confirmed that the static scatterers concentration has a strong impact in the spatial contrast values. The increment of static scatterers produces an increase of the spatial contrast, which is an effect that can mask fluid    the faster movement; however, this does not occur, due to the [S s ] changes. This example confirms the need to estimate the amount of static scatterers presented in the sample, because the variation of [S s ] leads to erroneous τ c determination. Figure 7 presents the s-K results for a specific fluid flow. In this figure, it can be seen that the variation of [S d ] also influences the contrast values. However this effect is visible only for low concentrations of static scatterers ([S s ] 0.5 mg ml −1 ).

Conclusion
This study has been conducted in order to analyze the influence of differences in concentration of static and dynamic scatterers on both laser speckle correlation and spatial contrast. Taking advantage of a controlled environment, it has been concluded that both [S s ] and [S d ] influence the speckle correlation and contrast. Moreover, evidence that the laser speckle correlation is independent of the fluid velocity was also identified in these experimental conditions-which is a major requirement for the use of speckle correlation in scatterer estimation.
In future studies, it could be interesting to work on the relation between the scatterer concentration (S) and the mean light intensity that reaches the detector I . An experiment where the dynamic scatterers are removed from the sample and the [S s ] is progressively increased can be used to determine a specific relation between these two variables. The same process could be repeated for [S d ] and I d , to obtain another independent relation between these two variables. Finally, these two relations should be tested using a variety of scatterer concentrations, in order to determine whether they persist in these conditions. Moreover, Li and Wang (2017) have studied a different mathematical method of separating the laser speckle signal originating from dynamic and static scatterers. Their method is based on eigen-decomposition filtering, in a technique similar to principal component analysis. The signal components with large eigenvalues are correlated with the signal produced by the static scatterer component. By removing these components, the LSCI signal can be filtered so as to enhance the dynamic scattering signal. Mathematical methods like this should also be considered for future work, in order to improve LSI.
In our study, the analysis of g 2 (∆t) reveals that the speckle correlation is sensitive to variations in both the dynamic and static scatterer concentrations. However, the g 2 (∆t) sensitivity to [S s ] and [S d ] is not constant, and depends on their effective concentrations. On one hand, the correlation sensitivity to [S d ] is higher for low concentrations of static scatterers, i.e. for low values of ρ. On the other hand, the correlation sensitivity to [S s ] is higher for high concentrations of static scatterers (high values of ρ).
The effect of fluid flow changes in the speckle correlation is illustrated in figure 5. These data show that the laser speckle correlation is not influenced by variations in the fluid flow. This key conclusion is of extreme importance in the validation of g 2 (∆t) as a way to estimate the ρ value of the sample. Without this independence, it would be impossible to use the speckle correlation to compute ρ, since g 2 (∆t) would vary with blood flow variations.
Concluding, this work has demonstrated that the spatial speckle contrast is affected by both the static and dynamic scatterers concentrations apart from the fluid velocity. This fact proves the need to use a correction system in order to make the contrast measurements independent from the static scatterer concentration. The speckle correlation could be an important metric to correct for this effect.
As well as the spatial-contrast algorithm, the temporal and spatio-temporal contrast algorithms have been computed using this data-set. This deserves further work dedicated to comparison between LSCI algorithms.