2.1.

Preparation of Samples

2.2.

Dynamic Laser Speckle Setup

Figure 1 presents the experimental setup to acquire the speckle patterns generated in time by the illumination of the samples using a linearly polarized He–Ne laser beam (632.8 nm, 30 mW). The beam size of the expanded laser light was 110 mm in diameter, presenting a monitored area of a square edge with 38 mm. The images were acquired by a compact macrolens (SIGMA) with a focal length of 50 mm, numerical aperture of $f/16$ (speckle size was $12.35\mu \mathrm{m}$), connected to an Allied Vision Technologies charge-coupled diode (CCD) camera (AVT Marlin F-145B), pixel size of $4.65\mu \mathrm{m}$.

Fig. 1

Experimental configuration adopted to get the dynamic laser speckle of cells and of drying paint.

2.3.

Methodology to Speckle Patterns Acquisition

In the case of raw cells, at the beginning of each hour, during 8 h, a collection of 120 images (8 bits, $640\times 480\text{pixels}$, and shutter speed $1/125\mathrm{s}$) was acquired at a rate of one frame per second. While in the case of paint drying, at the beginning of each minute, during 10 min, a collection of 96 images was acquired at a rate of 15 frames per second.

2.4.

Image Processing

The speckle patterns were analyzed by graphical and numerical indexes. The graphical index adopted was the generalized differences (GDs)²⁶ addressed by Eq. (1). The outcomes were used to evaluate the level of homogeneity in the map of activity that can be presented in colors, with blue meaning low activity and red meaning high activity (or in gray levels, with dark gray meaning low activity and light gray meaning high activity).

The numerical index adopted was the average value of the differences (AVD)²⁶ presented as

The construction of the THSP using the traditional selection of a line (Fig. 2) and the alternative proposal using random points in the first image (Fig. 3) was done before the adoption of Eq. (2).

Fig. 2

THSP methodology: (a) using the traditional selection of a row in a collection of speckle patterns in time, (b) random points in the first image (ROI) and fixed in the other images in time, and (c) of random points in the SROIs.

Fig. 3

ROI treatment: (a) detail of the data used to construct the THSP using the random points and the selection of pixels in a line within the ROI and (b) detail of the division of subregions within the main ROI (SROI), using random points and a line within each SROI.

3.1.

Analysis of the Distribution of Cells

In Fig. 4, it is possible to see the maps of activity in wells with 200,000 cells dispersed without a defined cluster and without a homogeneous activity of the cells. The outcomes are the GDs of 128 images in time, in nine different hours. In the DGs, the activities address from blue (dark gray), representing the low activity, to red (light gray), representing the high activity of the cells. The inhomogeneity in the maps of activities presents a challenge in the numerical analysis of the biospeckle laser, when usually a line in the ROI within the wells is the source of data. For example, if you choose lines to get the pixels in the center of the wells (ROI), those lines would not always pass in the same area where the cells are expressing their activities. During 8 hours, the number of cells grew without a pattern covering the area of the wells.

Fig. 4

Results of the GDs in the main ROI with cells alive during 8 h.

In Fig. 5, one can see the THSP images related to the cells samples for the traditional and proposed methods.

Fig. 5

THSP images of cells using (a) random points and (b) traditional method.

3.2.

Numerical Analysis Using a Line and Random Points

In Fig. 6, the AVD outcomes of the biospeckle patterns related to the wells are presented using lines of 244 pixels, columns of 250 pixels, and the same number of random points within the ROI. The adoption of lines or columns with close sizes presented significant differences in the traditional method or even when the random points were used. This reinforces the hypothesis that the set of a line of a column to get the desired information from a whole image can be done by chance and, thus, can compromise the results when inhomogeneities occur.

Fig. 6

Evolution of the biospeckle activity measured by the AVD index using (a) lines of 250 and 244 and (b) random points.

Therefore, the outcome of the evolution of the biospeckle activity in the cells during time, using the AVD, is addressed in the same graphic (Fig. 7) in which the difference between them regarding the variance is clear. The random points presented a smaller variance than the traditional method using the line.

Fig. 7

Evolution of the biospeckle activity measured by the AVD index using line with size of 244 and 244 random points in an ROI using a square inscribed in a circle, named main ROI.

Using Table 1, it is possible to see the values of the standard deviations (SDs) related to the graphics presented in Fig. 7. The SDs of the proposed method using the random points are smaller than the traditional method with the line, in accordance with the whiskers in the variance graphics (Fig. 7). The reduction of the variance, if compared to the traditional method, proves the viability of the random method of selection proposed to build the THSP and thus to analyze the assay of cells.

Table 1

Outcomes of AVD related to cells inside the main ROI using a line and random points to build a THSP. The outcomes are represented by the mean values of AVD and their SD with the respective percentages regarding the mean value.

3.3.

Influence of the Number of Points in the Time History of the Speckle Pattern Construction

In Table 2, the mean values of AVD index and the random points in the main ROI to construct the THSP are increased. All the values of AVD index were done, and the mean values were obtained with the respective SDs representing their evolution with respect to the number of random points.

Table 2

Results of the AVD of the cells in all times representing the SD with respect to the number of points.

The stabilization of the SD can be better seen in Table 2, particularly after 20,000 random points. This means that the number of points is relevant for reducing the variation of the AVD values but with a saturation after one third of the total points are chosen. In this case, the main ROI has $244\times 250\text{pixels}$, and thus the number of possible points is 61,000.

3.4.

Analysis in Subregion of Interests

An alternative way to use the random points to build the THSP was the division of the main ROI in SROIs, as presented in Fig. 8, where the GD applied in the separated SROI presented different maps of activity, which proved the inhomogeneity of the sample.²⁸

Fig. 8

Results of the GDs in cells alive within the nine SROI.

In Fig. 9, the differences observed were tested using the numerical approach (AVD), using the line and random points to construct the THSP before the AVD outcome.

Fig. 9

Average of the variations of the AVD of illuminated cells with the construction of the THSP, using one line and random points.

In Table 3, the values of the SD, representing the average of the nine SROI, are presented, and they are higher than the case of the main ROI (Table 1), particularly when the random points were used. The tendency of the random selection of points to reduce the variability was reinforced in the small SROI, despite the increase of the SD. Additionally, that increase was expected since the reduction of points (to 80 pixels) reduced the ability of the proposed technique to provide a dilution of the outliers.

Table 3

Outcomes of the mean values of the AVD related to cells inside the nine SROI using a line and random points to build a THSP. The outcomes are represented by the mean values of AVD and their SDs.

In Figs. 10 and 11, the comparison of the results of Tables 1 and 3 is presented. The comparison of the results of the AVD using the main ROI and the nine SROIs presents the higher SDs in the approach using SROIs than the main ROI when the random points were used. The comparison can be also seen when the THSP is constructed using a line in the middle of the ROI (Fig. 11).

Fig. 10

Variations of the AVD when the THSP was constructed using random points selected in the main ROI or in the nine SROIs.

Fig. 11

Variations of the AVD when the THSP was constructed using a line of points in the main ROI or in the nine SROIs.

Thus, when one has samples with a level of inhomogeneity, the adoption of random points to build the THSP is the best option, and it will be better if the ROI is large enough to cover the observed sample. This method can be efficient for bacterial activity rather than the graphical methods used to monitor activities regarding the inhomogeneity of the sample.²⁷

3.5.

Analysis in a Homogenous Sample—Drying Paint

The adoption of a sample with high homogeneity than the cells was tested using the two distinct ways to build the THSP. The drying paint is usually considered homogeneous, and in Fig. 12, it is possible to see the maps of activity after the GD processing, where the magnitudes of the levels of activity in the drying paint are closer than the levels in the case of cells assay.

Fig. 12

Results of the GDs in the main ROI with drying paint.

In Fig. 13, one can see the THSP images related to the drying paint samples, related to the traditional and proposed method.

Fig. 13

THSP images of paint drying using (a) random points and (b) traditional method.

The results of the adoption of the two ways to construct the THSP are presented in Fig. 14, where it is possible to see the small differences between the mean values and the variances, proving the limited efficiency of the random points to construct the THSP and to reduce the influence of nonhomogeneous areas in the monitored samples.

Fig. 14

Variations of the AVD when the THSP was constructed using a line of points in the main ROI and using random points in drying paint.

At this point, it is relevant to discuss the results involving the random points. The criteria for choosing random points instead of a simple line of points in the ROI are based on the study of nonuniform quantization of a signal.^29–31 Thus, to quantize efficiently an information from a signal source (in this case, an ROI information from the pixels with intensity light values varying in time), the digitalized regions (codebook) should be based on the probability density function of the information in the ROI.

In Fig. 15, the black dots represent the selection of analyzed points in an ROI and gray dots represent the interested information to be measured. In Fig. 15(a), a set of randomly selected points with a nonuniform quantization of information was used, while using a uniform probability distribution to choose the points. In Fig. 15(b), an example of uniform quantization in which the points analyzed (black points) are regularly distributed is shown. In Fig. 15(c), the classic case with a selection of points in a line is presented. Finally, in Fig. 15(d), a set of randomly selected points in a nonuniform quantization of information with the particularity that the probability density function of the spatial distribution of information is known, so the probability density function of chosen points is influenced by it is presented.

Fig. 15

Alternatives to analyze the biospeckle data using (a) points (codebook) selected randomly (uniform distribution) in the ROI, (b) points selected uniformly in the ROI, (c) points selected conforming a line, and (d) points selected randomly (any known distribution).

Analyzing the case in Fig. 15(c), it is easy to see that the chosen points (black) are far from the points with the interested information (gray); even if we select a different line, digitalized regions where the distance between selected and desired points will be bigger will exist, and consequently the result of processing this information will not be representative. By other side, the case presented in Fig. 15(d) has a proximity between the chosen points and the desired points; thus, these values are representatives. In this method, we need to have the information about the probability density function of the spatial distribution of the information, which is not always easy to obtain, but it is possible to make an approximation assuming that the information is distributed fulfilling a Gaussian distribution around a central point in a desired area. The alternative presented in Fig. 15(a) is the best option when the probability density function of the spatial distribution is not known (such as the case of cells monitoring) because the chosen points (black) have a good proximity to the desired points (gray) and the selection of points varies between repetitions.

In this work, we presented the alternatives shown in Figs. 15(a) and 15(c). The alternative presented in Fig. 15(d) is the Gaussian distribution around a desired point, and it is useful in cases where we would like to know the activity addressed by the biospeckle laser in a well-defined area. In Sec. 3.6, one can see the case of Gaussian distribution applied in a seed and in a tissue with cancer cells.

3.6.

Alternative to Collect the Random Points—Gaussian Distribution

An alternative way to select points to construct a THSP using a random distribution around a central point (pixel) is presented in Fig. 16, where the spatial probability distribution of the selected points (dots) around the chosen central pixel is defined by a Gaussian distribution, for example, if we define $x$ and $y$ as two aleatory coordinates of a random point, with probability density functions $f(X)$ and $f(Y)$ of the variables $X$ and $Y$, respectively. In the below equation, one can have a probability density function

Fig. 16

Coffee seed with the endosperm selected by the random points in a Gaussian distribution expressed by the dots.

In the case of Fig. 16, 200 points were chosen with a ${\sigma }_X={\sigma }_Y=25$ around the central pixel $({\mu }_X,{\mu }_Y)=(300,200)$. Thus, with the points selected in Fig. 16, the THSP presented in Fig. 17 was formed, where it is expressed as a matrix of 200 lines and 128 columns, representing both the quantity of points and analyzed images, respectively.

Fig. 17

THSP of 200 points selected in the coffee seed using random points.

Finally, in Fig. 18, a Gaussian distribution in a sample where we can see that the interest region is in a specific point of the image, in this case, the normal tissue aside an area of cancer tissue is presented.

Fig. 18

Cancer cells aside normal tissue where the random points were collected in a Gaussian distribution expressed by the circles.

In Fig. 19, one can see the THSP image related to the tissue sample for the proposed method to illustrate the Gaussian distribution of the random points selected.

Fig. 19

THSP of 100 points selected in the tissue using random points.