# Optoelectronic Instrumentation and Measurement Strategies for Optical Chemical (Bio)Sensing
## 4 Design of Applications
### Fiber Optic pH Sensor Based on Fluorescent Radiometric Intensity Measurement
#### 4.1.2 Measurement Technique  
As was explained in Section 3.2, the measurement of luminescence intensity is a simple technique, although its accuracy is compromised by variations in the excitation light, optical path, and concentration of the luminophore; therefore, ratiometric measurements are preferable in comparison to absolute-intensity-based measurements. In this way, many of the possible sources of error can be eliminated. During the optical sensor characterization, two types of characteristics were obtained: the emission spectra of the sensing phase as a function of pH and the reflectance spectra of the sensing phase as a function of pH. From these characteristics, a novel ratiometric intensity measurement technique was proposed based on the ratio between the fluorescent emission intensity and the reflected light intensity reaching the two photodetectors [48], with both signals being proportional to the perturbation that was to be eliminated.  
The light that reaches the optoelectronic sensor is that reflected by the chemical sensor (\(I_{\text{R}}\)) and the one that corresponds to its fluorescent emission (\(I_{\text{F}}\)). The first of these has two components, specular reflection (\(I_{\text{SR}}\)) and diffused reflection (\(I_{\text{DR}}\)), both with the same wavelength as the incident signal but with a substantial difference: the specular reflectance does not depend on the pH because it does not interact with the sensor and only depends on the angle of incidence. The diffuse reflectance, on the other hand, does interact with the sensor and depends on the dispersion and absorption coefficients of the analyte, after which a pH function will result. Diffuse reflectance does not involve a process with loss of energy, so its wavelength remains the same as that of incident light but is reissued isotopically. The relationship between the intensity of the fluorescent emission (\(I_{\text{F}}\)) and the intensity of reflected light (\(I_{\text{R}}\)) that reaches the two photodetectors is:  
\[R_{\text{t1}}=\frac{I_{\text{F}}}{I_{\text{R}}} \tag{12}\]  
The fluorescent emission of the sensor phase reached by the photodetector can be expressed as:  
\[I_{\text{F}}=k_{1}I_{\text{ex}}[\text{Ind}] \tag{13}\]  
where \(k_{1}\) is the proportionality constant, \(I_{\text{ex}}\) is the intensity of the excitation light reaching the detection phase, and \([\text{Ind}]\) is the concentration of the fluorescent indicator. On the other  
Figure 14: (**a**) Excitation and emission spectra of the sensing phase as a function of pH. (**b**) Reflectance spectra of the sensing phase as a function of pH.  
hand, the total light reflected by the sensor phase is the sum of the specular reflected light and the diffused reflected light:  
\[I_{\text{R}}=I_{\text{SR}}+I_{\text{DR}} \tag{14}\]  
The specular reflectance is independent of pH, due to the absence of any interaction with the sensor phase. This is a fraction of the reflected excitation light following [PERSON]'s laws, so it only depends on the incident angle:  
\[I_{\text{SR}}=k_{2}I_{\text{ex}} \tag{15}\]  
where \(k_{2}\) is the proportionality constant. The diffuse reflectance depends on pH through the concentration of the fluorescent form of the indicator:  
\[I_{\text{RD}}=-k_{3}I_{\text{ex}}[\text{Ind}] \tag{16}\]  
where \(k_{3}\) is the negative proportionality constant, since the diffuse reflectance is inversely proportional to the pH (Figure 2); therefore, Expression (14) is:  
\[I_{\text{R}}=-k_{2}I_{\text{ex}}-k_{3}I_{\text{ex}}[\text{Ind}] \tag{17}\]  
and Expression (12) is:  
\[R_{\text{t1}}=\frac{k_{1}I_{\text{ex}}[\text{Ind}]}{k_{2}I_{\text{ex}}-k_{3}I _{\text{ex}}[\text{Ind}]}=\frac{k_{1}[\text{Ind}]}{k_{2}-k_{3}[\text{Ind}]} \tag{18}\]  
As such, this ratiometric method is at least theoretically independent of drifts in excitation light. The main drawback of this method is the need to separate the two emissions, so it is a selective optical filtering method.