A Simple Optical Sensor Based Approach for Early ...

A Simple Optical Sensor Based Approach for Early Stage Dry Eye Symptoms Detection Ramona Galatus 1*, Tiberiu Marita2, Andrea Seceleanu3, Nunzio Cennamo4 and Luigi Zeni 4,5 1

Department Basis of Electronics, Optoelectronics and Optical Integrated Components Group, Technical University of Cluj-Napoca, Str. Memorandumului 28, 400114 Cluj-Napoca, Romania;

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E-Mail: [email protected] Department Computer Science, Image Processing and Pattern Recognition Group, Technical University of Cluj-Napoca, Str. Memorandumului 28, 400114 Cluj-Napoca, Romania; E-Mail: [email protected] Ophthalmology Department, Eye Clinic, Varnamo Hospital, 33153 Varnamo, Sweden; E-Mail: [email protected], Tel: +46 722 702 602 Department of Industrial and Information Engineering, Second University of Naples, Via Roma 29, 81031 Aversa, Italy; E-Mails: [email protected] (N.C.); [email protected] (L.Z.) CNR-IREA via Diocleziano 328, 80124 Naples, Italy

* Author to whom correspondence should be addressed; E-Mail: [email protected] ; Tel.: +40-264-401-413; Fax: +40-264 -591-340.

The research is financed by the project “Development and support of multidisciplinary postdoctoral programmes in major technical areas of national strategy of Research-Development-Innovation” 4D-POSTDOC, contract no. POSDRU/89/1.5/S/52603, co-funded by the European Social Fund through Sectoral Operational Programme Human Resources Development 2007-2013 and in part by the EXCEL Project under Contract POSDRU/89/1.5/S/62557. The SPR-sensor development was supported by the project PON01_01525 “MONICA”.

Abstract As a primary research environment for the Dry Eye Symptoms (DES), a simple optical sensor based approach is proposed. The designed test is based on easy to use and cost effective equipment. The eye-blinking evaluation in the first step is based on a low cost imaging solution to evaluate the Symptomatic Tear Break-Up Time (SBUT). This factor is correlated with refractive index changes, using a surface Plasmon resonance (SPR) biosensor, in order to recommend an appropriate choice for artificial tears eye drops to treat the DES or various measures that can be used to avoid the symptoms. A tapered-fiber geometry was proposed for the SPR sensor in order to improve its response sensitivity (S=1 × 103). It can be used for refractive index changes (with resolution=0.0010

RIU) in an extended interval that includes the requested one [1.334-1.336] for real time evaluation of the tear sample. The multimodal sensor system was used to investigate the risk for developing dry eye on a sample consisting of volunteers in the 20 to 50 age group category (i.e. intensive professional computer users). The results of an experimental analysis were also reported. Keywords: dry eye; integrated software application, eye-blink parameter monitoring; plastic multimode optical fiber; low cost Surface Plasmon Resonance (SPR) sensor; fast label-free detection, D-type POF (plastic optical fiber). 1. Introduction Dry Eye Syndrome (DES), also known as keratoconjunctivitis sicca, is a condition associated with changes in the quality and quantity of tears, causing the eyes to feel dry and irritated. It was also shown that symptoms reported by women tend to be higher than that by men. Studies have revealed that the prevalence is higher with women over the age of 50 (about 3 million) [1][2], but it can affect men and women of any age. Dry eye may also be a sign to investigate other possible health issues. Often confused with allergies or other extrinsic cause, dry eye is frequently undiagnosed and can develop into long-term complications if left untreated. Since symptomatic patients are not always easy identified, an early detection test based on easy to use and cost effective equipment is desired for a primarily research environment. The same technique can be used also to monitor the effect of the treatment. Until now, there is no proven cure for dry eye, but there are a variety of treatments that can help sooth its symptoms and avoid increasing the severity of syndrome. The two major classifications of dry eye are aqueous tear-deficient dry eye (ADDE) and evaporative dry eye (EDE) [3], but they are not mutually exclusive. According to this classification, low blink rate is an intrinsic cause associated with EDE. Occupational factors may cause a slow blink rate, representing a risk for dry eye. In the present paper the risk for developing dry eye was investigated on a sample consisting of 30 volunteers in the 20 to 50 age range (i.e. intensive professional computer users). As a first step in the investigation, a Webcam based algorithm is used to estimate the blink rate for the normal reflex processes of blinking in different activity

states. The results are correlated with a second step investigation of the refractive index changes of the tear sample. The ocular tear film structure is complex and its details are not completely elucidated till now, but some features are well established. The three component layers of the tears are: •

lipid layer (oil) - outermost layer, that are derived mainly from the secretions produced by the meibomian glands; its main role is to stabilize the tear film and prevent evaporation of the aqueous layer. When this layer is not functioning properly, the water layer beneath will evaporate faster than usual and will cause dry eyes symptoms. These symptoms are also common in blepharitis, and some skin disorders.

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aqueous layer (water and salt) – middle layer, produced by the main lachrymal gland and its accessories. If the lachrymal glands do not produce enough water then the oil layer and the mucous layer may touch and cause stringy discharges.

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mucin layer (mucous) – lower layer, immediately adjacent to the corneal epithelium, that is produced by specialized conjunctival cells and ocular surface epithelial cells [4].

Between blinks, the aqueous layer of the tear film evaporates to some extent in all subjects, but very evident for those with dry eye disease. Normally, eyes have a complex balance between lachrymal production, mucin and meibum production. The DES is characterized by a decreased production of one of the three components mentioned above. The osmolarity (the salt content in the tears) is wide-accepted by experts as an indicator of the presence and severity of dry eye [5],[6]. The most prevalent problem deals with the sample size, because dry eye patients generally have less tears (tear flow averaged 0.10 +/- 0.08 microliters/minute in patients with dry eye versus 0.15 +/- 0.12 microliters/minute in patients without dry eye [7]). To test for the consistence of the tear films a low cost Surface Plasmon Resonance (SPR) sensor based on D-type POF (Plastic Optical Fiber) is proposed. It can be used for real time refractive index changes (with a small variation of 0.001 RIU – Refractive Index Unit) evaluation of small volume (less then 0.1 microliter) tear-samples. The average normal refractive index of the tears is 1.336 RIU. Using the SPR sensor, the analysis of the salt concentration and protein concentration, in

two-part time based measurement can be investigated. The light launching condition using input tapered fiber, improve the sensitivity of sensor response. The solution was adopted considering previous literature results with in-sensing taper-profile [8]. Furthermore, in the future, this SPR biosensor technology can be used to detect chemical markers [9] (particularly antigens-antibody interaction [10]) in tear samples, specific for different eye diseases. The sensor has multiple-layer geometry on the sensing area and thus the easy binding of the antibody is facilitated by the upper gold layer. A prospective clinical trial will be considered for the method’s validation. In the last decade, more attention was given to the developments of non-invasive methods for pre-corneal tear film surface analysis, which are well synthesized in [11]. The proposed SPR biosensor is simple to use, is small in size, works on small analyte-sample sizes, is cost effective for specific non-invasive applications and can be integrated into the proposed multimodal sensorial system.

2. Definitions and Samples Preparation 2.1 Eye-blink detection algorithm The eye motion presents high nonlinearity and the eye-tracking technologies are yet too expensive in routine use. The eye-blinking algorithms are mainly used in the vision based state monitoring drivers [12], [13], [14], [15] and human-computer interaction for persons with disabilities for eye typing process [16], [17]. To monitor the volunteers sample of intensive computer users, a WEB-camera based eye-tracking solution (with minimum 30fps) is adopted as a method to quantify the modification of the blinking pattern during computer-interface activities compared with normal activity (used as etalon). According to [18] the mean duration of the half amplitude of the blinking for normal subjects, which during normal activity is 111 ±51 ms, with an average blinking rate of 12 blinks/min (1 blink about – 5 sec). The rate modification is also associated with the neuronal activity. Blink stage depends on amplitude and velocity of eyelid movements which is not a subject of the present paper, but can be consider for the future development. The relative velocity of eyelid movements during blinks can be measured with the alternative method of infrared (IR) reflectance method [18] or using high speed professional cameras instead of an ordinary Webcam.

The model-based approaches presented in [17], for eye blink detection was found to be an appropriate starting point for the proposed solution. However, only the final blink detection stage based on pattern matching between the open eye pattern and the current view of the eye [17].[39] was used to get the correlation score for eye blink detection. The eye segmentation process [17] based on basic image processing functions (image differencing, morphological operations, labeling,) was replaced with a much more robust approach. The steps of the proposed eye-blink detection algorithm are presented in Figure 1.

Figure 1. Flow-chart of the proposed eye-blink detection algorithm

1) The algorithm monitors the existence of a face in the image detected using the OpenCV [20] implementation of the Viola & Jones [21] face detection algorithm (which assures real time capabilities). The algorithm can be used in order to detect also any other facial component as the eyes, mouth or nose using the appropriate Haar cascade classifier model trained for these objects [22]. 2) Once the face is detected in the first image, the eyes’ positions are inferred considering the eye as an object and applying the Viola & Jones detection algorithm on these objects. Furthermore, the detected eye positions are validated by applying a variant of the Cumulative Distribution Function (CDF) algorithm [40] for pupil detection to increase the robustness of the eye position detection. This ensures the invariance of the algorithm to small head rotations (up to 15 degrees roll angle) and scaling (Viola & Jones method and subsequent approaches as [39] cannot infer the head rotations). The right eye template is extracted from the first valid frame in which the face/eye was detected (assuming the user has the eyes open in the first frame). 3) The approach presented in [39] lacks the face tracking step, and therefore cannot compensate false negative situation encountered with the Viola & Jones detector. Therefore the face is tracked using the OpenCV [20] implementation of the CAMSHIFT object tracking algorithm [23], which provides further invariance to the position and orientation of the face object. When the tracking of the face object is lost the algorithm is reinitialized (1). 4) A ROI (Region Of Interest) containing the right eye is extracted around the current right eye position (detected in the same way as mentioned in step 2) rather than using anthropomorphic features of the face as in [32], [39]. The ROI is slightly bigger (≈ 1.5 … 2 times then the eye template) in order to accommodate the usage of the template matching algorithm in the next step (5). Compute the normalized correlation function [16] obtained by matching the eye template against the current ROI. For the matching procedure the OpenCV matchTemplate function was used with the maximum value of the correlation function ranging between 0 and 1. This value is used as the correlation score for the eye blink pattern analysis (Figure 2). The eye blink event can be inferred from the correlation score by thresholding the plot of the correlation score with an arbitrary threshold value (experimentally set at about 0.7 to 0.8). The exact reference moment of the blink can be computed by taking the mid interval of the time range when the correlation plot is below the threshold

(Fig. 3). The accuracy of this value is dependent on the image acquisition frame rate (30 fps for our experiments) but is not an issue for the current application. Using a higher frame rate camera some further in depth analyses of the eye blink pattern could be used in the future.

1 0.95 0.9 Correlation score

0.85 0.8 0.75 0.7 0.65 0.6 0.55 0 1 2 4 5 6 7 8 9 11 12 13 14 15 16 18 19 20 21 22 23 25 26 27 28 29 30 32 33 34 35 36 37 39 40 41 42 43 44 46 47 48 49 50 51 53 54 55 56 57 58

0.5 Time [s]

Figure 2. The plot of the correlation scores for normal blinking behavior (≈ 12 blinks/min).

Figure 3. A detailed view of the plot from Figure 2 in a 45 ms interval. Exact eye blink moment can be estimated as the mid interval of the time range when the correlation plot is below the threshold. 2.2 Optical Sensor Design A laboratory SPR biosensor [25] developed at the Department of Industrial and Information Engineering, Second University of Naples, Italy, was used in this study. The characteristics of the plastic optical fiber are: •

PMMA (PolyMethylMethAcrylate) core of 980 µm and a fluorinated polymer cladding of 20 µm;

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Numerical aperture (NA) is 0.46 with the refractive indexes of the materials are about 1.49 for the PMMA[26] core and 1.41 for the fluorinated polymer cladding, in the visible range of interest.

The fiber has a locally removed cladding along its half circumference. POF is composed of soft materials and a simple-controlled procedure of side-polishing with a polishing machine and polishing papers (8 µm to 1 µm) was adopted. Since the dimensions of the samples can be easily controlled, POF is preferred to the glass multimode fiber. Ordinary fibers are no longer cylindrically symmetrical after side-polished, called also D-type fiber. The state of linearly polarized light oriented parallel to a polished surface is the TE mode (Transverse Electric, i.e. no electric field in the direction of propagation). Its orthogonal state is the TM mode (Transverse Magnetic, i.e. no magnetic field in the direction of propagation) that has a contribution to plasmonic effect. The core was exposed with spin-coating procedure to a 1.5 µm buffer of Microposit S1813 photoresist. The dispersion curve is described in [27] (the average refractive index 1.61 is larger than previous removed cladding). The gold film, 40 nm thin, was added by using a sputtering machine (Bal-Tec SCD 500). The sensing region obtained has about L=10 mm in length. In order to include the sensor in a laboratory setup, the fiber ends are prepared to get the optimal performance. At the input fiber, a tapered profile is constructed in a way to improve the sensor’s response (Figure 4.b). The incident rays enter parallel with propagation axis (Oz axis) due to a collimating lens. Using a fiber optic cutting block at 90 degrees and an angled-polishing puck, an input angle α (about 76 degrees) is obtained that is close related, under Snell’s Law and transfer matrix formalism (Appendix), with the maximum resonance angle φr((λi) (with an average value of 83 degrees) of the input spectrum range (λi). The incident angle range at the sensing area is restricted to the interval with maximum contribution to the plasmonic effect. The design is found to be better than the 90 degrees-cut of the fiber-end sensor in terms of optimal sensitivity and SNR (signal-to-noise ratio). The four-layer D-type sensing region consists of core, buffer layer, gold layer and sensed medium. As reference for data normalization, the spectrum-acquisition with no analytes (air) is considered. For theoretical design, the transfer matrix formalism described in Appendix, was used in order to obtain a SPR geometry suitable for refractive index changes of the sample (around 1.336 RIU).

Figure 4. SPR geometry based on POF. (a). 3D view of D-type SPR sensor (b). tapered fiber in longitudinal section The plasmon is a quantum of plasma oscillation [28]. Collective oscillations of electrons (plasmons) can appear at the surface of certain metals under light irradiation, forming surface plasmons. In SPR (surface plasmon resonance) model analysis, a p-polarized light (or TM - transverse magnetic) causes the excitation of electron density oscillations (SPW- surface plasmon wave) at the metal-dielectric interface. When the energy as well as the momentum of both, the incident light and SPW, match, a resonance occurs. At the resonance conditions, the propagation constant of the generated evanescent wave (as a result of Attenuated Total Reflection - ATR) of the incident light at an angle θincident through a light coupling device (in this case optical fiber) of refractive index ncore, is equal to that of the SPW:

K plasmon

KATR=Kplasmon.

(1)

KATR= K 0 ncore sin θ incident

(2)

2   ε metal nsen sin g 1/ 2 = Re  K 0 ( ) ; 2 ε metal + nsen   sin g

(3)

K

with the following notation:

0

=

2π

λ

(4)

ε metal - real part of the metal dielectric constant, n sen sin g - refractive index of the sensing layer. In a general transmission function the fiber-optic properties, launching conditions and ray direction influence the incident angle to the sensing region and, as a consequence, the transmittance curve (T(λ)). The power at the fiber’s output at a specific wavelength can be approximated by integrating the product of the whole light reflectance with the angular power distribution corresponding to the light source used (Eq 5). The uniform light propagation along fiber length is assumed and TE and TM polarization components equally distributed (skew ray does not have a definite polarization),.Also both Rs, Rp (reflection coefficients for TE and TM polarization) were considered:

Pout ( λ , n sen sin g ) =

θ2 1 θ2 N N ( ∫ R p P0 ( λ ,θ , n sen sin g )d θ + ∫ R s P0 ( λ ,θ , n sen sin g )d θ ) θ θ 1 2 1

N=

L D tan(θ )

(5)

(6)

where N is the number of reflections within the sensitive area, that is calculated as a function of L (the length of the sensitive area), D (the diameter of the fiber) and the angle interval restricted around resonant angle range [θ1 ,θ 2 ] ⊆ [θ critical,90] . The power distribution arriving at the end-face of the fiber can be expressed as in Eq. 7.

P0 dθα

2 ncore sin θ cosθ dθ 2 (1 − ncore cos 2 θ ) 2

(7)

The considered model has good real data results even if it does not take into account scattering from possible roughness of the layer, diffraction or dispersion and mode coupling phenomena because of the small sensing fiber path [29]. In a light intensity absorption-based fiber optic SPR sensor, normalized

transmitted power (T(λ)) is determined relatively to the transmitted power obtained for the blank (air) medium (Pref(λ)).

T (λ ) =

Pout (λ ) Pref (λ )

(8)

The sensor sensitivity can be expressed by computing the ratio between consecutive shift in resonance wavelength related to unit change in refractive index. The theoretical values are discussed for different parameter geometries in order to optimize the sensor manufacture.

S (nsen sin g ) =

δλresonance  nm  δnsen sin g  RIU 

(9)

The sensitivity value can be approximated with the variation of minimum transmitted power, T(λ), that corresponds to resonance wavelength, related to the unit change in refractive index. The resolution or signal-to-noise ratio (SNR) of the SPR sensor is inversely proportional to the full width at half maximum of the SPR response curve. The narrower the width of the transmitted power, T(λ) curve, the higher the obtained detection accuracy is. With the input angle, under Snell’s Law, a restricted incidence angle interval around θ resonance = 830 was obtained for a higher detection accuracy.

 δλ  SNR (nsen sin g ) =  resonance   δλFWHM  nsen sin g

(10)

2.3. Experimental Setup The experimental setup was arranged to measure the in-fiber spectrum, following the intensity method (Fig 5). It is composed by a broad-band halogen lamp source, with λ=400~1300nm with narrow spot (Ocean Optics : Model no. HL-2000-LL)that enters into a collimating lens connected to illuminate the α-input angle of D-type optical sensor system A spectrum analyzer, with a detection range from 200 nm to 850 nm

(Ocean Optics “USB2000+UV-VIS”, FWHM=1.5nm) was used. The spectrometer is connected to a PC, and the Ocean Optics dedicated software is used to achieve and save the data, in order to analyze different experimental conditions. The calibrating specimens were measured with the Abbé refractometer as reference.

Halogen lamp

SMA905+Adaptor connector

Sensing region

L Adjustable

PC Spectrometer

collimating lens with SMA905 connector

USB interface

Figure 5. Experimental setup for SPR based on POF. The tear samples extracted from patients have small volume (of the orders of ~200 nanoliter). Generally the patients that exhibit dry-eye symptoms have fewer tears. This makes handling samples more difficult. A glass micropipette with L-shape 1.5mm capillary is used to perform the extraction of the tears from volunteers in such a way to avoid irritation and excess tear productions which can modify the results. The physician places the micropipette near the lower lid and with soft touching, the tear is collected into recipient. A micro-dispensed system that uses precise air pressure to force an exact amount of fluid out is used to accurately place the tear-sample fluid on the SPR sensing surface. This surface is larger than the area that can be covered by the volume of the tear, and more than one tear (coming from the same eye) can be placed at one time. Two-part time readings are followed, in just few seconds interval, to avoid rapid evaporation of the analyte. The tear sample is a sum of water, salt and protein as principal components.

3. Results and Discussion 3.1. Eye blink detection rate assessment as a clue for dry-eye detection The dry eye test can be also assessed manually using the Symptomatic Tear Break-Up Time (SBUT) method presented in [30]. The steps of this procedure are

described below: •

Blink 2 times, then stare straight ahead

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Avoid blinking for as long as possible

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Note the time on a stop-watch clock when you begin to feel eye discomfort (burning, grittiness, dryness, etc.)

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The SBUT is the amount of time (in seconds) that passes between your last complete blink and the moment you experience eye discomfort.

1 0.95 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55 0.5

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If the SBUT time is 5 seconds or less, dry eye symptom can be present, because the tear film on the eyes is breaking up too quickly, leaving the surface of the eyes unprotected.

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Figure 6. A typical test scenario for a person that doesn’t exhibit dry eye symptom (SBUT>> 5 s).

Time [s]

Figure 7. A typical test scenario for a person that may have dry eye symptom (SBUT < 5s).

As an alternative to the manual test, using the proposed automated Webcam based eye blink detection method, the test can be used on-line to monitor dry eye symptom, especially for persons prone to it (professional computer users etc.). In Figure 6 and Figure 7 the eye blinking pattern in the form of the correlation score provided by the Webcam based method for some SBUT test scenarios are shown. Figure 6 shows a typical test scenario for a person that doesn’t exhibit dry eye symptom (SBUT >> 5 s), while Figure 7 shows a typical test scenario for a person that may have dry eye symptom (SBUT < 5 s).

3.2. SPR contribution for borderline dry eye detection The sensor was tested on different salt concentration solution (%NaCl) with refractive index that was measured with Abbé refractometer as reference. The correspondence for refractive index of protein standards was considered from [31]. The sensitivity of the sensor was calculated as the response shift in resonance wavelength in the range of interest, per unit change in the refractive index of the sensing region (S=1 x103[nm/RIU]). The sensor’s response accuracy is FWHM/∆n=1.5 x103 [nm/RIU], and signal-to-noise ratio, SNR=0.67. Using the SPR sensor, the analysis of the salt concentration and protein concentration, in two-part time based measurement can be investigated. The first reading step (osmolarity) was performed after a few milliseconds because salt migrates more quickly to the surface of the sensing area than the other components of the tear sample. The proteins, which are more voluminous, reach a bit later the sensing surface and, as a consequence, the refractive index should increase. Thus, a second reading can be done to estimate the protein concentration. After the last reading, the surface is cleaned with a pure water solution and dried. The tear sample has a lower refractive index (RI) in dry eye symptoms (has higher-water-content). The higher the protein concentration, the higher the refractive index of the sample (at the extreme condition, for example, the protein pure solution has 1.55 refractive index [33] ). For normal eye, the RI of tears varies from 1.33698±0.00110. In our sample, the RI varies from 1.3350 to 1.3375 (Figure 8 and Figure 9), depending of the blinking ratio. The SPR sensor response is linear (Figure 10)

2

Normalized Transmitted Light Intensity

1.8

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0.8

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650 Wavelengths[nm]

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Figure 8. Experimentally obtained SPR transmission spectra for different refractive index values of the sample medium, normalized with the air spectrum 1.3

Normalized Transmitted Light Intensity

1.25 1.2 1.15 Reference Teoretical (T) 1.334 Experimental(E) 1.334 T 1.335 E 1.335 T 1.3361 E 1.3361 T 1.3369 E 1.3369 T 1.3371 E 1.3371 T 1.3375 E 1.3375 T 1.338 E 1.338

1.1 1.05 1 0.95 0.9 0.85 0.8

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660 Wavelength [nm]

680

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Figure 9. Comparison of simulated results (theoretical - T) and experimental results (E), in the wavelengths’ range of interest with different refractive index values (that are shown in legend)

Resonance wavelength [nm]

637 636

y = 1041x - 756.64 R2 = 0.9922

635 634 633 632 631 630

1.332 1.333 1.334 1.335 1.336 1.337 1.338 1.339 Refractive index [RIU]

Figure 10. Linear response of the SPR sensor Based on the results, the physician can recommend therapies that work for each individual. They can prescribe an appropriate choice for artificial tears eye drops to treat dry eyes or various measures that can be used to preserve proper tear composition and reduce the risk factor of the computer-display usage in daily life. Physicians can quantitatively monitor disease severity and can intervene timely in a timely fashion through early symptoms detection.

4. Conclusions and Future Work The multimodal sensor system was experimentally tested for primary investigation of the dry-eye symptom on a sample consisting of volunteers of intensive professional’s computer users. The approach uses a two-step integrated technique: eye blinking rate analysis using an automated algorithm based on ordinary Webcams and refractive index changes monitoring of tear sample using sensors based on SPR in plastic optical fiber (with a buffer layer between fiber core and gold film). The proposed low cost SPR devices are based on the excitation of surface plasmons at the interface between the tested medium and a thin gold layer deposited on a photoresist buffer that is spin coated on the D-type dedicated sensing area of the POF core. The incident rays enter parallel with the propagation axis (Oz axis) due to a collimating lens. The tapered fiber-end restricts the guided rays to an incident angle range, at the sensing region, close related with resonant angles of the wavelengths (that have maximum contribution to the plasmonic effect). The taper solution exhibits a sensitivity enhancement compared with traditional 90-degree fiber-end. The observed transmitted spectra is normalized relative to the transmitted spectrum when the outer medium is air. The results of the multimodal sensor system can be used by

physicians to detect suspected dry eye symptoms and to establish a treatment correlated with tear sample components. A larger population study will be considered in the future, correlated with the classic tests [34], [35]. In the literature [36],[37] seven protein markers are mentioned which are used for dry eye in Lab-diagnostic. For the future work, the protein marker tests on low cost SPR proposed sensor will be considered, involving immobilization of specific antibodies on its sensing surface, in order to improve the facility of the multimodal sensor system.

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z analyt

εN dN εk

ε1

dk d1

core

Eincident

θincident KATM

Figure 11. Multilayer system with p-wave (TM-transversal magnetic) incident at the boundary surface between fiber core and sandwich-layers structure

[M] is the characteristic matrix of the layered system:

 M 1,1 [M ] =   M 2,1

 M 1, 2  N −1   cos ς k  =  M 2, 2  ∏ k =1    − iξ k sin ς k

− i sin ς k    ξk    cos ς k  

(11)

where ξ s , pk is the optical admittance defined as a function of polarization state and

ς k , the phase factor of the k-layer.

2 ς k = K 0 nk cosθ k ( y k − yk −1 ) = K 0 d k (ε k − ncore sin 2 θ incident )

ξ ( s , pk)=

2 (ε k − ncore sin 2 θ incident )

(12)

(13)

ε sk

The reflection coefficient (reflectance) of the p-polarized light is given by:

R p =| rp | = 2

( M 11p + M 12p ξ Np)ξ po−( M 21p + M 22p ξ Np)ξ Np

2

(14)

( M 11p + M 12p ξ Np)ξ po+( M 21p + M 22p ξ Np)ξ Np

and for the s-polarized light is given by:

Rs =| rs | = 2

( M 11s + M 12s ξ Ns)ξ os−( M 21s + M 22s ξ Ns)ξ Ns

( M 11s + M 12s ξ Ns)ξ os+( M 21s + M 22s ξ Ns)ξ Ns

2

(15)