Optical Design of a Large-Angle Spectral Confocal Sensor for Liquid Surface Tension Measurement

The surface tension of a liquid droplet can be determined by fitting its actual profiles using the Young-Laplace equation, effectively reducing the measurement of surface tension to an accurate determination of the droplet's profiles. Spectral confocal sensors are high-precision, interference-resistant, non-contact measurement systems for droplet surface profiling, employing a light source together with a dispersive objective lens and a spectrometer to acquire depth-dependent spectral information. The accuracy and stability of surface tension measurements can be effectively enhanced by spectral confocal sensors measuring the droplet surface profile. Although existing spectral confocal sensors have significantly improved measurement range and accuracy, their angular measurement performance remains limited, and deviations may arise at droplet edges with large inclinations or pronounced surface profile variations. This study presents the optical design of a large-angle spectral confocal sensor. By theoretically analyzing the conditions for generating linear axial dispersion in the dispersive objective lens, a front-end dispersive objective lens was designed by combining positive and negative lenses. Based on a Czerny-Turner (C-T) configuration, the back-end spectrometer was designed under the astigmatism-free condition, taking into account both central and edge wavelength effects. Zemax was employed for simulation optimization and tolerance analysis of each optical module. The results show that the designed system achieves an axial dispersion of 1.5 mm over the 430-700 nm wavelength range, with a maximum allowable object angle of ±40° and a theoretical resolution of 3 μm. The proposed spectral confocal sensor maintains high measurement accuracy over a wide angular range, facilitating precise measurement of droplet surface tension at large inclination angles.