Development of a Portable Optomechatronic System to Obtain the Characterization of Transparent Materials and Dielectric Thin Films

Abstract

This paper outlines the design and fabrication of a portable optomechatronic system based on the theta-2theta configuration, which explores various optical characterization techniques for transparent materials and dielectric thin films. These techniques include Brewster angle and Abelès-Brewster angle measurements, critical angle measurements, and the surface plasmon resonance technique. The system consists of a mechanical assembly of rotating stages, a semiconductor laser, a photodiode connected to a data acquisition card, and a user interface for controlling the stepper motor rotation stages. Utilizing a BK7 substrate, the motorized stage achieved a resolution of 0.010. The Brewster angle measured was 56.550, with a refractive index (n) of 1.5137. The relative error obtained was Δn/n = 3.82 × 10⁻⁴, with a sensitivity of 164.27 RIU/degree and an accuracy of 0.37/degree. Furthermore, the discrepancies between theoretical and experimental refractive indices for different prisms at 639 nm ranged from ±7 × 10⁻⁴ to ±73 × 10⁻⁴. After testing various samples, the system demonstrated its capability to perform fast, precise, and non-invasive measurements. Its portability allows for use in diverse environments and applications.

1. Introduction

In recent years, significant efforts have been dedicated to developing optical sensors for characterizing transparent materials and dielectric thin films [1,2,3,4]. This development involves various optical techniques that ensure reliable and accurate measurements [5,6,7,8]. In conjunction with optics, advances in mechatronics have automated existing processes and systems, enhancing their accuracy and efficiency in sample characterization. Additionally, this progress enables multidisciplinary research to improve measurement techniques and engineering applications [9,10,11,12].

Reflectometry using linearly p-polarized light (also known as transverse magnetic or TM light, where the electric field is parallel to the plane of the incident, transmitted, and reflected beam) is a common method for the optical characterization of materials. Whether in bulk or thin film form, this technique is crucial for sensing applications, especially since thin films often act as transducer mediums selectively responding to specific analytes, whether they are gaseous, liquid, or solid. However, this method typically requires expensive and specialized equipment, often used under laboratory conditions, making it time-consuming and dependent on specialized personnel.

The refractive index can be estimated for transparent bulk materials by determining the Brewster angle using a goniophotometer with linearly p-polarized light. In this context, the refractive index of the incident medium must be lower than that of the transmitted medium, such as at an air–glass interface [13,14]. This technique is quick, straightforward, and precise. To find the Brewster angle, which is the angle of minimum reflectance, one needs only a flat surface aligned with the axis of rotation of the Ɵ-2Ɵ system. Once the Brewster angle is determined, the refractive index can be calculated using the formula $n=\tan \left(\theta \right)$.

The measurement of the critical angle has been used to characterize both transparent materials with a real refractive index [15] and absorbent materials with a complex refractive index [16]. This method involves measuring the reflectivity at the interface between two media, where the incident medium has a higher refractive index than the transmitted medium. The critical angle is defined as the angle at which total internal reflection begins. One of the main challenges with this technique is developing an accurate mathematical model for theoretical experimental curve fitting, as it relies on the Fresnel equations and/or Mie theory for colloidal systems. The prism coupling method generates guided modes using either transverse magnetic (TM) or transverse electric (TE) polarized light, while the surface plasmon resonance (SPR) technique exclusively uses p-polarized light [17,18,19]. Even a relatively thick material (a solid analyte) placed on a prism coated with a metal film (such as silver, gold, or aluminum) can produce guided modes and generate surface plasmons when illuminated with p-polarized light. Additionally, the SPR technique allows the use of prisms with various refractive indices, which can help to tune the measurement range and sensitivity of the sensor (dn/dƟ). The surface plasmon resonance technique, particularly in the Kretschmann configuration with a prism, is widely used to characterize liquids [20], solids [21], or gases [22], especially valued for its ability to monitor molecular reactions in real time without requiring labels [23].

In this work, we present the development of a portable optomechatronic system with two motorized rotation stages of 0.01 degrees of angular resolution to scan the reflected light from the sample, using light “p” polarized of a diode laser centered at 639 nm. The system and data acquisition are controlled with Arduino through a Labview user interface. The system is used for reflectometry applications, which include critical angle measurement, Brewster angle measurement, Abelès-Brewster, surface plasmon resonance in the prism-based Kretschmann configuration, and scattering surface plasmon resonance. MATLAB (Version 2024, The MathWorks, Inc.) and LabVIEW (Version 2020, National Instruments) algorithms are used to fit experimental and theoretical reflectance curves.

2. Materials and Methods

2.1. Theory: Matrix Method

The matrix method is a mathematical design based on Fresnel equations that facilitates the optical design of thin films due to its simplicity and understanding of the physical phenomena around thin films [24]. Each layer added to the array is represented as a 2 × 2 matrix, making it easy and simple to design and simulate the propagation of an electromagnetic wave on a boundary between two media or a multilayer system. The theoretical reflectance of a thin film or a multilayer system is expressed as “R”:

$$R={\left|r\right|}^2={\left|{\displaystyle \frac{{\eta }_0-Y}{{\eta }_0+Y}}\right|}^2$$

(1)

where

$$Y={\displaystyle \frac{H}{E}}$$

(2)

and

$$\left[\begin{array}{c}E\\ H\end{array}\right]=\prod _{j=1}^k\left[\begin{array}{cc}\mathit{cos}{\delta }_j& {\displaystyle \frac{i\mathit{sin}{\delta }_j}{{\eta }_j}}\\ i{\eta }_j\mathit{sin}{\delta }_j& \mathit{cos}{\delta }_j\end{array}\right]\left[\begin{array}{c}1\\ {\eta }_s\end{array}\right]$$

(3)

where r is the value of the reflection coefficient, n₀ is the refractive index of the incident medium, and Y is the admittance of the multilayer system. H and E represent the amplitude of the tangential magnetic and electric fields, respectively. The optical admittance of the j-th thin film is n_j = n_j/cosθ_j for P polarization. δ_j represents the phase thickness and is given by δ_j = 2δ_jπn_jd_j (cosθ_j)/λ. d_j is the physical thickness, n_j is the refractive index of the thin film, λ is the wavelength, n_s is the refractive index from the substrate or output medium, and θ_j is the angle for the incident medium in the j medium. The electric and magnetic fields are expressed as a column vector; each thin film is a 2 × 2 transfer matrix. The calculation consists of successive multiplications of the column vector by the transfer matrix.

2.1.1. Critical Angle

For a media boundary where the incident medium, n₁, has a higher refractive index than the second medium, n₀, we have, after a certain angle (critical angle), a total internal reflection [25]. The critical angle reflectance curve can be generated from Equation (1) by setting the thickness of any layer to zero, the incident medium, for example, $n_1$ = 1.5149 for glass and $n_0$ = 1 for air for the exit medium (see Figure 1).

2.1.2. Brewster Method

For a boundary of two media where the incident medium has a lower refractive index than the second medium and doing an angular scan in the reflectivity of p-polarized illumination, we will have an angle where the reflectance will be null, which will be the Brewster angle, and it is related to the refractive index of the material, $n=tan \left({\theta }_B\right)$ [26]. The reflectivity curve can be generated with Equation (1) making $n_0<n_1$ and setting the thickness equal to zero for any layer, for example, $n_0$ = 1 and $n_1$ = 1.5149 at λ = 639 nm, for air and BK7 glass, as shown in Figure 2.

2.1.3. The Abelès-Brewster

This technique consists of illuminating a substrate with and without a dielectric film coating with p-polarized laser light. Two curves of the intensity of light reflected by the substrate with and without coating are obtained, and the angle where the curves intersect corresponds to the Brewster angle of the film; the refractive index of the dielectric film can be determined by $n=tan \left({\theta }_B\right)$, Figure 3 [27]. Regardless of the thickness of the dielectric thin film, it always maintains the same Brewster angle value.

2.1.4. Surface Plasmon Resonance

Surface plasmon resonance (SPR) is a phenomenon that occurs when electrons in a metallic thin film are excited and travel in parallel at a metal–dielectric interface with charge density oscillations, where the resonance angle (${\theta }_r$) is related to the dielectric material. The ${\theta }_r$ is detected as a dip in the reflectance curve [28].

The plasmon resonance curve can be simulated from Equation (1) by making several considerations: (a) The illumination must be p-polarization, (b) the refractive index of the prism must be higher than the refractive index of the material adjacent to the metal film (analyte), (c) the interface between the metal film and the dielectric material must have opposite dielectric constants [21]; for example, ε = n² for glass is (1.5149)², and for gold is $\epsilon =N^2={(n-ik)}^2=(n^2-k^2)+i2nk={\epsilon }_r+{\epsilon }_i$, where $N$ is the complex refractive index, k is the extinction coefficient, and ε_r and ε_i are the real and imaginary parts of the dielectric constant of the metal film. SPR curves with F5 and BK7 prisms with gold coatings (50 nm thick) simulated with air and distilled water are shown in Figure 4a. And SPR curves with SK16 and SF6 prisms with gold coatings (50 nm thick) simulated with air and distilled water are shown in Figure 4b to show the detection range and resolution for each prism.

2.1.5. Surface Plasmon Resonance and Scattering

When plastic particles are added to the dielectric medium, the phenomenon of Rayleigh scattering (the wavelength of the beam is greater than the diameter of the particles) or Mie scattering (the wavelength of the beam is smaller than the diameter of the particles) occurs, where the light is re-emitted in different directions when it hits each particle. In studies carried out on scattering, the concentrations, diameters of the particles, and/or the effective refractive index ($n_{eff}$) of the sample were determined:

Tuoriniemi et al. [29] calculated the effective refractive index ($n_{eff}$) using coherent scattering theory (CST) as a function of the filling fraction ($f=c_p/V_p$) and the particle diameter ($d_{part}$). The $n_{eff}$ followed a unique curve for each $d_{part}$ ($V_p=(4/3)\mathsf{\pi }{\left[\right(d_{part}/2]}^3$), as a function of the number concentration ($c_p$) of the polystyrene (PS) particle, so it was possible to simultaneously determine both the $d_{part}$ and the number concentration ($c_p$) by fitting the CST to the $n_{eff}$ values measured by SPR for a series of colloid dilutions. The effective refractive index was calculated with the next formula:

$$\begin{gathered} n_{eff}= \\ {n_m\left[1+{\displaystyle \frac{4\pi i{c}_p}{k_s^3}}S\left(0\right)+{\displaystyle \frac{4{\pi }^2{c}_p^2}{k_s^6{\cos }^2\left({\theta }_m\right)}}\left[{S_{\pi -2{\theta }_m}}^2\left(d_{part},n_{part},k_s\right)-{{S_0}^2\left(d_{part},n_{part},k_s\right)}^2\right]\right]}^{1/2} \end{gathered}$$

(4)

where $n_m$ is the refractive index of the medium, $k_s=(2\pi /\lambda )·n_m$ is the wave vector in the sample, λ is the wavelength of the coherent light, ${\theta }_m$ $(\pi /2+\left|\alpha \right|i)$ is the propagation angle in the sample (calculated from ${\theta }_r$ by sequentially applying Snell’s law at the interfaces), $n_{part}$ is the refractive index of the particle, and $S\left(0\right)$ and $S_{\pi -2{\theta }_m}$ are the scattering elements calculated with Mie theory [30] for p-polarized light using the Mätzler (2002a), MATLAB (1992, The MathWorks, Inc.) code package [31].

Figure 5 shows the scattering simulation for a NK7 prism with gold film (N = 0.1736 – 3.4930i) and a distilled water sample (n = 1.3314) containing polystyrene (PS, n = 1.5870) particles at different concentrations (0%, 5%, 10%, 15%, 20%, 25%), at a wavelength of 639 nm.

2.2. Materials and Description of the Methods

Optomechatronics is a discipline that integrates optical components and technology into mechatronic systems. It is important to find the right communication devices and protocols to integrate a system that is able to synchronize and provide a response with the best precision and resolution possible, without sacrificing size and cost. The prototype (Figure 6) consists of a laser diode (mod. LPM690-30C, Newport Corporation, Irvine, California, USA) with a wavelength of 639 nm at 30 mW (Figure 6a), a linear polarizer, a sample mount (transparent optical samples such as prisms, flat substrates, and dielectric thin films), a silicon photodiode (mod. S1226-8BK, Hamamatsu Photonics K.K., Hamamatsu City, Japan) with a spectral response range of 320 to 1000 nm and a maximum sensitivity wavelength of 720 nm, two rotation stages with stepper motors (mod. 8MR180-2, STANDA, Vilnius, Lithuania) with a rotation range of 360 degrees with a full step resolution of 0.01 degrees, and a sheet metal cabinet with the power and control electronics. The stepper motors are controlled by an Adafruit Motor Shield for Arduino board that allows for control of up to 2 stepper motors. In addition, the Arduino board is used for data acquisition through an analog input, providing 10 bits of resolution. The optomechatronic design uses a control system with a graphical user interface in LabVIEW. For this stage, the LabVIEW 2020 [32] programs from National Instruments were used with the VISA serial communication library to establish communication with the Arduino Mega 2560 data acquisition card [33].

The laser diode module is the light source that will pass through the sample before reaching the photodiode for acquiring real-time light intensity values as digital data, which are then subjected to analysis and visualization with the help of programming. The laser diode intensity is controlled with a user-defined PWM (pulse width modulation) digital signal through a user interface containing a wide variety of controls and indicators. Specifically, the laser light intensity is controlled from 0–100%, where 0% = 0 VDC and 100% = 5 VDC. The PWM digital signal corresponds to a square pulse width modulation, so a circuit is added to smooth these square waves into more stable signals that help the photodiode to more accurately determine the intensity of the light provided by the laser.

The photodiode captures the reflected light from the sample (prism or substrate) illuminated by the diode laser and converts this incident light into a flow of electric current, which can be measured to give a reading of the intensity of the incident light. However, for the signal to be detected, it is necessary to design a circuit with a signal amplification stage from 0 to 12 volts.

The Arduino card acquires the data from the photodiode in real time and displays them on the user interface. The display of the light intensity in real time allows for observing the changes that occur throughout the manipulation of the system. Although the manufacturing of the enclosure containing the photodiode greatly decreases the amount of spurious light perceived by the photodiode, placing the system in a laboratory with controlled lighting will always provide better measurements and results than operating in uncontrolled lighting conditions and with reflections from the floor, walls, and other surfaces. The control program can retain and use these data to be analyzed and processed. The main function of the Arduino board is to acquire, control, and process the system’s data. The board is powered by a USB connection to the computer. Its digital and analog pins are used to control the intensity of the laser light, acquire data from the photodiode, and monitor when the limit switches on each motor are pressed, indicating the 0° position.

The rotary stages are controlled digitally, using a bipolar stepper motor (included). Stepper motors operating in the bipolar scheme require changing the direction of the current flow through their coils in an appropriate sequence to cause constant rotational motion. Typically, the current handled by the coils is very high for the values handled by the data acquisition and control cards, so it is necessary to include an H bridge [34] per coil. The stepper motors are controlled with the help of the Adafruit Motor Shield v2.3 card [35], which contains the H bridges necessary to control up to two stepper motors. This card, as its name indicates, is placed on the Arduino Mega 2560 card as if it were a shield. The Motor Shield v2.3 card is powered with the same voltage provided by the Arduino card. In the same way, the motors connected to its terminals can be powered with this voltage; however, it has the option of an external power supply with up to 12 VDC to give sufficient power to the motors.

The main components of the system and the operation are shown in the diagram in Figure 7. The computer controls the Arduino, which in turn reads and writes data from electronic components such as the light source, motors, and photodiode sensor. The intensity of the light source is variable; the light passes through a linear polarizer and the sample, whose reflection is detected by the photodiode. The photodiode detects the light intensity in real time, and this is recorded in Arduino and displayed in the user interface in normalized reflectance units. The stepper motors move the sample and the photodiode; their position, speed, step type, and other parameters are defined by the user interface on the computer to carry out their digital control.

Figure 8 shows the alignment process performed to prepare the sample for angular scanning and measuring its angle of minimum reflectance. The sample is positioned at 0° (Figure 8A) with its flat face perpendicular to the light source, and the reflection of the sample is aligned with the light source. A second alignment is performed by rotating the sample 90 degrees (Figure 8B) and verifying that the flat face is parallel to the light beam. The sample is moved so that the light beam impinges on the flat face without passing through the sample. After proper alignment, the sample is moved to 30° (Figure 8C), and the position of the photodiode is adjusted based on the reflection of the sample.

The National Instruments LabVIEW graphical programming environment [36] was chosen to develop the control of the electronic components, mathematical analysis, acquisition, real-time data display, and the main user interface of the presented project. Due to its extensive library content, LabVIEW offers us different tools, such as the VISA serial communication to have reliable communication links with the Arduino Mega 2560 data acquisition card [33] and the Adafruit Motor Shield v2.3 motor controller.

Figure 9 shows the user interface with the program enabled and a real-time measurement being performed; the data are being saved, and the current position of both motors is updated in real time. This interface facilitates the user’s interaction with the system, and it can control and visualize the performance of the system components. On the left side, the controls can be seen, and the indicators necessary to operate the system. On the right side are the measurement tools, analysis of results, as well as important information for its correct operation. The “Graphics” tab has the light intensity controller of the laser diode to avoid saturation of the photodetector, which has an indicator that works in real time.

3. Results

The complete system has the main objective of characterizing transparent optical samples (prisms and flat substrates) as well as dielectric thin films. To verify the system, the following were performed: (a) A critical angle measurement on a BK7 prism was realized; (b) Brewster angle measurements were performed on four prisms: FK5 (n = 1.4858), BK7 (n = 1.5149), SK16 (n = 1.6180), and SF6 (n = 1.7981) [37] at λ = 639 nm; (c) measurements on substrates of BK7 with MgF₂ dielectric thin film (n = 1.3769) were performed using the Abelès-Brewster technique; (d) SPR measurements with a BK7 prism/Au(50 nm)/air and BK7 prism/Cr(3 nm)/Au(50 nm)/air, and a sensogram of an immobilization of lacasses on a BK7prism/Cr/Au were performed; and (e) SPR measurements of FK5prism/Ag(50 nm)/colloidal suspension of water/0.1 µm and 1 µm were performed.

3.1. Critical Angle Measurement

The measurement of the critical angle is a very simple technique since it only requires a glass prism, for example, BK7, where a beam of light is made to hit the prism/sample interface. From the curve generated with angular scanning, the critical angle is obtained, and employing Snell’s law, the real refractive index of the sample is estimated, although some works have used this technique to calculate the complex refractive index [38,39]. Figure 10 shows the reflectometric curve of a BK7 prism, obtaining the critical angle of 41.3140. Applying Snell’s law (n₁ sin θ₁ = n₂ sin θ₂), but θ₂ is 90 degrees, so the refractive index of the prism would be n₁ = 1/sin(θ₂) = 1/sin (41. 3140) = 1.5147.

3.2. Brewster Angle Measurement

If we consider the reflectance concerning the angle of a thin film on a glass substrate, we have that the angle of minimum reflectance would be the Brewster angle, ${\theta }_B$, of the substrate, we can determine the refractive index of the bulk material by applying equation $n=tan\left({\theta }_B\right)$.

Once the measurements of the four prisms were carried out, the analysis was performed using the Brewster angle analysis tab, which can be found within the same program used to operate the system. In this tab, the samples can be quickly characterized, and it can be determined whether the measurement was correct or if there is an error involved.

Figure 11 shows a summary of the reflectance graphs obtained for the FK5, BK7, SF6, and SK16 prisms. It can be seen that the glass with the lowest minimum angle and therefore the lowest refractive index is FK5, followed by BK7, SK16, and SF6 with the highest refractive index among this group.

Table 1. Refractive index estimation of different prisms based on the measurement of the Brewster angle. Difference ($n_t-n_c$) between theoretical ($n_t$) and calculated ($n_c$) refractive index for different prisms at the wavelength of 639 nm.

Prism	${\mathit{n}}_{\mathit{t}}$ [37]	${\mathit{n}}_{\mathit{c}}=\mathbf{tan}\left({\mathit{\theta }}_{\mathit{B}}\right)$ ± 3.82 × 10−4	Difference
FK5	1.4858	tan 56.07° = 1.4865	±7 × 10−4
BK7	1.5149	tan 56.55° = 1.5137	±12 × 10−4
SK16	1.6180	tan 58.21° = 1.6135	±45 × 10−4
SF6	1.7981	tan 60.82° = 1.7908	±73 × 10−4

shows the prisms used in the experiment, the theoretical and calculated refractive indices, as well as the difference of each measurement. It is important to mention that the optomechatronic system is semi-automatic, since the alignment stage is manual and the theta-2theta movement is automatic. Each motorized rotation stage has a resolution of 0.01 degrees. Therefore, the automation of the alignment is a pending point of this optomechatronic system to improve the measurements. Considering that the minimum value for the angle measurement is ΔƟ = 0.010, this value affects the refractive index in Δn (Δn = tg(ƟB + ΔƟ) − n). This ΔƟ = 0.010 is considered the absolute error. Considering the measurement for the BK7 substrate, the resolution of the motorized stage of 0.010, a Brewster angle of 56.550, and n = 1.5137, then the relative error was Δn/n = 3.82 × 10⁻⁴. The sensitivity (dn/dƟ) is about 164.27 RIU/degree, and the accuracy was (DA = 1/ΔƟ × 0.5) 0.37/degree [40]. The main features of the previous and proposed systems are shown in

Table 2. Main features of the previous and proposed systems.

	Previous System [41]	Proposed System
Light source	He-Ne laser (polarized). The intensity output is controlled by a neutral attenuator.	Diode laser (a linear polarizer must be used). The intensity output is controlled by a frontal panel program.
Motorized rotation stages	Resolution of 0.0002 degrees with integrated motor controller (motorized rotation stage Newport model FCR100)	Resolution is 0.01 degrees. Motor controller with the Arduino board (Motorized Rotation Stage, STANDA, model 8MR-180)
All system	Non-portable	Portable

.

3.3. Abelès-Brewster Technique

This is probably the simplest of all methods for measuring the refractive index of a film. No difficult calculations are required, and the measurement is independent of knowledge of the refractive index of the substrate and the thickness of the film. It is therefore of no consequence if the substrate is itself covered by a film or is optically inhomogeneous at the surface. No absolute intensity measurements are required if only the refractive index required. The film must, however, be isotropic and homogeneous [27]. Figure 12 shows the Abeles-Brewster technique with the intersection point at ${\theta }_B=53.95°$ (tan ${\theta }_B=1.3739$).

3.4. Surface Plasmon Resonance with Angular Interrogation and Sensorgram

The most common glass used in SPR is BK7 because it can be used with a cover glass coated with a thin metallic film and adhered to the prism by its flat face utilizing an index-matching oil with the same refractive index as the prism glass and the cover glass. Figure 13a shows an experimental SPR curve of a BK7 prism coated with a 50 nm thick gold film on a flat surface. This system is adequately used with angular interrogation to estimate the refractive index of substances attached to the metal film, but when it is desired to monitor molecular reactions, the SPR system is used at a fixed position, which is half the slope of the SPR curve (sensorgram), and a film of chromium or titanium dioxide is adhered to the gold film between the prism and the gold because the gold film has poor adhesion to the glass (see Figure 13b).

In the case of sensing with angular interrogation, the angular sensitivity is 172⁰/RIU, using a prism BK7 as a coupling system, a Cr/Au thin film, and at λ = 639 nm of a polarized diode laser source. In biosensing applications, changes in the refractive index are usually caused by the accumulation of mass (i.e., proteins) on the surface of the sensor. The SPR curve of the immobilization of laccases in water is used to determine the fixed angle (the angle at which the middle of the steepest falling slope of the SPR curve is located: FWHM-L) to realize the sensogram in real time (Figure 14). At this experimental fixed angle (${\theta }_{\mathrm{F}\mathrm{W}\mathrm{H}\mathrm{M}-\mathrm{L}}=69.5993°$), each biochemical reaction will be shown in the SPR system as a change in the intensity of the light reflected through the prism and arriving in the photodetector.

In this study, the immobilization process of laccases was based on the methodology of previous works [23]: First, the surface of the chip was functionalized with the alkanethiols MHDA: MUD (250 µM in ethanol), so the groups are available for binding with enzymes. Then, an activation was performed by using EDC/NHS crosslinkers (0.05 M/0.2 M) mixed in a MES buffer at a concentration of 0.01 M and a pH of 5.0. During the activation reaction, esters of carbodiimide were generated, which served as binding sites for the enzyme by forming an amide bond with the amino acids of its structure. In the same study, it was demonstrated that SPR biosensors can achieve high sensitivity and reliability: the authors obtained a limit of detection of 11.7 µg mL⁻¹, a sensitivity of 0.0021 units of reflectance per ng mL⁻¹, a linear response range for the antigen from 39.1 to 122 µg mL⁻¹, and the response was stable for 10 cycles [23].

3.5. SPR and Scattering Measurements

To estimate the effective refractive index of a colloidal suspension of distilled water with polystyrene particles of 0.1 and 1 microns, SPR measurements and scattering theory were made. Figure 15 shows the results of an experiment using a FK5 prism (n = 1.4858) with a ~50 nm thick silver film (N = 0.054801–4.3241i) and a water sample (n = 1.3314) with polystyrene (n = 1.5870) particles with a diameter of 100 nm, at a wavelength of 639 nm. Initially, with the known values, we use the matrix equation (Equation (3)) to obtain the reflectance (Equation (1)) and the resonance angle ${\theta }_r$ = 70.3570°. Equation (2) is then used to obtain $n_{sample}$ = 1.3313 and determine the error = $n_{water}-n_{sample}$ = 0.0001 RIU. The experimental reflectances of the water and the water with PS are then adjusted to the theoretical reflectance to determine the angle of reflectance of the water sample with PS and calculate the $n_{sample}$ (Equation (5)) and see its corresponding percentage (Equation (4)). As can be seen in Figure 15b, there is a linear correlation between the filling fraction and the calculated n_eff.

$$n_{sample}=\sqrt{{\displaystyle \frac{{n_{\mathit{prism}}^2\sin }^2\left({\theta }_r\right)·\left(n_{Au}^2-k_{Au}^2\right)}{\left(n_{Au}^2-k_{Au}^2\right)-n_{prism}^2{\sin }^2\left({\theta }_r\right)}}}$$

(5)

The experimental reflectance result for a distilled water sample with polystyrene particles of 0.1 and 1 micron in diameter (Figure 16) has a resonance angle of ${\theta }_{r\left(0.1\mu \right)}$ = 71.42° and ${\theta }_{r\left(1\mathsf{\mu }\mathrm{m}\right)}$ = 71.56°, very close to the reference sample (distilled water). Therefore, to the result calculated in Equation (5), for this experimental sample, the error is added as an adjustment, giving the following as a result: $n_{sample}$ = 1.3391 + 0.0001 (Adjustment) = 1.3392 and $n_{sample}$ = 1.3401 + 0.0001 (Adjustment) = 1.3402, respectively.

4. Conclusions

The system allows the characterization of bulk and thin film dielectric materials as well as molecular reactions in real time using reflectometry techniques, simply and reliably. Being portable (200 mm × 450 mm × 220 mm, 13 kg), the system can be used in different environments and applications, such as the characterization of materials, monitoring of pollutants, food and pharmaceutical industries, in the field, or in laboratories with limited space. This tool could facilitate the research and development of transparent materials and thin films by providing accessibility and efficiency in obtaining relevant optical information. The system is fast performing, accurate, and carries out non-invasive measurements of the optical properties of thin dielectric films, transparent materials (FS, FK5, BK7, SK16, SF6), and biosensing processes.

The mechatronic development of the system has wide applications in related subjects. The integration of mechanics, electronics, and programming in an optimized way contributed greatly to the quality and accuracy of the results obtained in the known characterized samples. It is intended to enable the system for surface plasmon resonance measurement to characterize broader samples such as liquids, solids, or gases, with applications in chemistry and medicine.