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Absorbance measurement in dense media via conventional optical spectroscopy techniques leads to inaccurate results. This is mainly due to multiple scattering phenomena that contribute to the overall light extinction in the interrogated sample. This limitation imposes the use of dilute solutions for absorption spectroscopy. However, depending on the polarity of the solvent used, the absorption spectrum may vary over a given solution. Structured illumination technique offers an alternative to this problem, and provides the ability to calculate in-situ optical properties in dense media. In this paper, we propose two processing methods applied to images acquired by structured laser illumination planar imaging (SLIPI) technique to extract extinction coefficients μ_e of probed solutions: The first is based on the implementation of principal component analysis (PCA) and the second, on the calculation of Mean Value. In practice, two kinds of studies were carried out: one quantitative set of measurements within chlorophyll liquid solutions and a second set with concentrated coffee solutions, with controlled proportion and concentrations for each sample. These two proposed analytical techniques are advantageous because they are very easy to implement and provide a much simpler alternative to the previous one. Both methods offer satisfactory results, similar to those obtained with the original method which is based on 1D Fourier transform.

Matter is mostly made up of structures with various properties that react in various ways to photon interaction. This is the case, for example, of biological tissues whose composition is inhomogeneous and sometimes dense. This, in homogeneity property of the matter, becomes a challenging issue in diagnosis using classical method of optical spectroscopy. It uses the Beer-Lambert law which establishes the proportionality between the concentration of chemical species, the absorptivity and the path length traveled by the light in the media [

In this work, we have developed new data processing techniques applied to the same types of images acquired by SLIPI technique. These analytical methods are based on algorithms edited in our laboratory, based on Principal Component Analysis (PCA) method, and Mean Value (MV) method. Both methods provide satisfactory and interesting results compared to the previous method.

In practice, we have measured firstly the extinction coefficients of several chlorophyll dense solutions, extracted from fresh banana leaves. The use of chlorophyll as a sample would be beneficial in preventing food shortages and protecting vegetation. This could lead to a study of vegetation protection against harmful factors of climate change. Secondly, we applied these proposed methods to dense liquid coffee solutions whose concentrations are very well known and whose mode of preparation is well defined. Note that the results obtained from these three methods, for each sample examined with laser radiation of wavelengths 450 nm and 638 nm, have shown the pertinence of our computational algorithms, because they provide similar results to the existing method. They are also rather fast and provide very similar results to those of the existing method. The evaluated variations between extinction coefficients calculated via the standard method and those that we propose are estimated between 0.00% and 2.13% which appear very weak. Such observations could confirm the relevance of the suggested techniques with a minimal risk of error.

The SLIPI technique was inspired by structured illumination microscopy principle [

where

By registering

The first examined media were chlorophyll solutions. The chlorophyll solutions were exclusively extracted from fresh leaves of five banana trees grown on different sites. These leaves were mashed and infused into alcohol, hence used as a solvent. In order to avoid any unwanted reaction, we proceeded then to the filtering of the obtained solutions, in absence of light. This allowed us to obtain dense solutions of chlorophyll from fresh leaves of each plant noted S_{1}, S_{2}, S_{3}, S_{4} and S_{5}. These solutions were classified according to their level of turbidity: From high-concentrated (S_{1}) to lowest (S_{5}).

The coffee solutions are prepared using instant coffee (from the brand “Nescafé Classic”) made of 100% robust a coffee. An initial solution C_{1} is created by dissolving 6 grams of coffee into 450 ml of water. This dilution results to a concentration equals to 1% from the initial coffee concentration C_{1}. From this solution, 4 solutions have been, once again, prepared to obtain a linear decrease in concentration.

The SLIPI technique used in solving optimization problems in the fuel efficiency, had proven to be capable of multiple scattering suppressing in dense sprays imaging [

distance between them is equal to the sum of these focal lengths. The laser sheet created by a cylindrical lens, and modulated using a 5 lp/mm Ronchi grating is then completely reflected through a plane mirror on the cuvette containing the sample. A 14-bit EM-CCD camera (maximum number of photons 2^{14} − 1 = 16383) located at 90˚ to the propagation direction of the laser light sheet, capture the modulated image generated in the cuvette. The recording of acquired images is provided by a personal computer linked to the camera (see

The standard strategies used in order to process the images acquired by SLIPI set-up and applied to turbid media, is based on single phase scattering detection by means of Fourier transform [

where y is the spatial vector,

For that purpose, one creates two reference signals

Multiplying the column vector

And

Which can be simplified to

And

Three components can be identified by frequency analyzing of

The tilde assignment in these relations indicates the applied frequency filtering. From these,

One can extract the amplitude of the modulation from a modulated image using Equations (6)-(14). The modulated component_{e}, can be done by applying an exponential fit to

The amplitude of the intensity decreases from column P to Q according to the light intensity profile represented. The 1D Fourier transform (FT) applied to the curves P and Q, makes it possible to obtain the reduction in strength of the 1^{st} order peak (modulation frequency). This frequency is then filtering and isolated after applying the lock-in algorithm, which finally reveals the exponential decay (see

The analysis methods we are proposing are applied to the images captured by the CCD camera, produced from the convolution of the diffracting pattern by the system’s transfer function. These analysis techniques are based on algorithms developed using Matlab R2014a; and globally aim at filtering the light intensity crossing the solution, in order to evaluate and extract noises. We make the assumption that the light passing through the studied media is composed of two components: The multiple scattered photons which are uncorrelated along the optical path and then regarded as noises, and the single scattered light possessing the distinguishing characteristics imposed by the spatial modulation. These codes based on a signal processing have a principle stipulating that the sum of intensities measured on each line of the diffraction pattern, plus the sum of the noises must be equal to an intensity that will tend to the incident flux

where

In the Mean Value Method, we made the average of illuminated lines intensities in the modulation before tracing the total decrease of luminous flow. Therefore, the hypothesis that emanates from this approach is that, when we make the average line by line, the mean value of the intensity obtained will tend towards

In the Principal Component Analysis (PCA) method, we extract the correlations between lines. This method consists of applying principal component analysis on each line. Therefore, the same assumption:

^{rst} line), ^{nd} line), …, ^{th} line, assuming I_{n} on each n line does not vary, as shown in

Thus, by extracting the correlations existing between the lines, the first principal component that we will obtain, must correspond to

Let us develop now mathematical descriptions which underlie the suggested techniques.

On each enlightened line L, the incident light will undergo an exponential decay according to the following equation.

where

Let assume that the line pixel is composed of the single scattered photon

So let write that:

For all N lines of the diffraction pattern, one can write:

As N increase,

A pre-processing of the raw data consists in extracting the correlations existing between the illuminated lines in the captured image by the CCD. This makes it possible to improve the contrast of the image containing the information on the optical properties of the sampled medium. This technique makes it possible to make the diffracted lines of the grating in the raw image (

Applying Principal Component Analysis (CPA), we obtain the matrix of eigenvalues to target the area of interest containing mainly the information. This

area corresponds to the more intense intensity part (red parts in

By decomposition into singular values, one succeeds in extracting the principal components, above the red line (

All these components then made it possible to reconstitute the matrix making it possible to select the main zone of interest, where the information on the extinction coefficients is more perceived.

In order to understand how the radiation inside the liquid solution could vary, we plotted the histogram of the recorded image (

The histogram clearly shows an exponential decay of the light intensity in the probed sample. This exponential decrease is due to the extinction of light flow, caused both the absorption and diffusion according to the following expressions [

And

where

Then we plot curves corresponding to the exponential decay of the light intensity crossing the sample after filtering using Mean Value and PCA methods. The extinction coefficients of each solution probed with wavelengths of 450 nm and 638 nm can be calculated. These extinction coefficients values are extracted by finding the best exponential fit which can be relatively well superimposed to experimental one, as shown in

Then, we look for the convergence of the proposed methods to the standard method.

For each probed sample at 450 nm and 638 nm, the data processing by each of the three techniques of analysis made it possible to plot the various spectra and to calculate the extinction coefficients. Figures 10-13 show the respective curves resulting from the exponential decay of the light crossing each solution and plotted via each method. The various extinction coefficients values are also calculated using each of the three methods. Those are posted in legend.

For the all examined samples, we calculated and extracted the various extinction coefficients values. All these values are recapitulated in each illustration. Note that chlorophyll solutions extinction coefficients calculated at 450 nm by the Fourier transform method are all nearly identical to those obtained with the two other proposed methods. The same remark is also made with wavelength 638 nm for these samples. The extinction coefficients of coffee solutions ob-

tained by each method are also nearly identical at 400 nm on the one hand and at 600 nm on the other hand.

The values of optical properties calculated via the three different approaches made it possible to trace the graphs of variability of each method according to the examined solutions concentrations. By making the differences between the extinction coefficients values obtained with the proposed methods and those of the standard method for each given sample

And

where _{ }

Same work was also made for the extinction coefficients obtained with coffee solutions at 450 nm and at 638 nm using the three techniques.

Note that the extinction coefficients values obtained for each type of solutions via the two proposed techniques are approximately equal to those of standard technic. However, there are small variations in these values. These are between 0.6% and 2.1% for the PCA method at 450 nm and between 0.1% and 1.2% for the wavelength of 638 nm. Similarly with the Mean Value method, there are small fluctuations (slight differences) of the calculated coefficients compared to those calculated with the standard method. These small variations are estimated between 0.1% and 2.3% at 450 nm and between 0.0% and 0.13% for 638 nm radiation.

This leads to assert that these two methods that we are proposing offer similar results to the standard one.

The objective of this study was to provide SLIPI technique with alternative data processing methods to calculate the extinction coefficients and also optical depths of dense solutions. The objectives of this work have been achieved by the use of chlorophyll and coffee solutions at different concentration levels, and they lead satisfactory results. Note that our proposed data processing algorithms, which is based on PCA and Mean Value, made it possible to calculate extinction coefficients

The authors wish to thank the International Science Program (ISP) of Uppsala University for equipment and financial support as well as the Lund Laser Center (LLC). The authors would like to thank Assoc. Prof. Edouard Berrocal for usedull discussions and valuable guidance.

Koffi, T., Regnima, G.-O., Bosson, J., Bagui, O., Edoé, M. and Zoueu1, J.T. (2017) Structured Imagery Processing Strategies for Spectroscopic Measurement in Dense Solutions. Open Journal of Applied Sciences, 7, 262-281. https://doi.org/10.4236/ojapps.2017.76022