<p>Dye leakage and the nonlinear relationship between absorbance and pH affect the pH measurement precision of absorption-based optic sensors and limit their application. Based on the preparation of a transparent sol–gel thin film with a phenol red indicator, this work assumed that the absorbancies had an exponential relationship to the concentrations of the indicator, and the multi-wavelength equation for the pH was derived as follows:
where <i>n</i> is the exponential coefficient, <i>e</i><sub>1</sub>, <i>e</i><sub>2</sub>, and <i>e</i><sub>3</sub> are the extinction coefficient ratios, and <i>R</i> is the ratio of the absorbancies. The calculation parameters for an immobilized phenol red film were p<i>K</i><sub>a</sub> = 8.577, <i>e</i><sub>1</sub> = 0.0191, <i>e</i><sub>2</sub> = 1.530, <i>e</i><sub>3</sub> = 0.2992, and <i>n</i> = 0.6322, while those for an immobilized phenol red/Triton X-100 film were p<i>K</i><sub>a</sub> = 8.612, <i>e</i><sub>1</sub> = 0.0507, <i>e</i><sub>2</sub> = 1.501, <i>e</i><sub>3</sub> = 0.3687, and <i>n</i> = 0.3931. The correspondence between the calculated p<i>K</i><sub>a</sub> and the p<i>K</i><sub>a</sub> from the calibration curve verifies the equation. The calculation parameters remain stable as the indicator content is increased, but change with an increase in the Triton X-100 content. Using the equation, the calculated pH shows stable behavior over a long duration regardless of dye leakage, and the calculated precision is 0.0053. The method provides drift-free and precise water pH measurements for <i>R</i> that is not dependent on the total concentration of the indicator, and can be applied to online monitoring.</p
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