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

## TL;DR

A new optical system was designed to measure liquid surface tension accurately even at large angles.

## Contribution

The design of a large-angle spectral confocal sensor with ±40° measurement field and 1.5 mm axial dispersion is novel.

## Key findings

- The system achieves 1.5 mm axial dispersion over 430–700 nm wavelength range.
- It maintains high accuracy for droplet surface tension measurement at large inclination angles.
- The design includes a dispersion objective lens and a Czerny–Turner spectrometer meeting astigmatism-free conditions.

## Abstract

What are the main findings?
This study designed a large-angle spectral confocal sensor optical system with 1.5 mm axial dispersion across the 430–700 nm wavelength range and a ±40° wide-angle measurement field, providing optical support for high-precision acquisition of surfaces with large inclination angles.A front-end/back-end optical structure was constructed, comprising a dispersion objective lens and a Czerny–Turner (C-T) spectrometer meeting the astigmatism-free condition. The system design and optimization were completed, with its engineering feasibility verified through tolerance analysis.

This study designed a large-angle spectral confocal sensor optical system with 1.5 mm axial dispersion across the 430–700 nm wavelength range and a ±40° wide-angle measurement field, providing optical support for high-precision acquisition of surfaces with large inclination angles.

A front-end/back-end optical structure was constructed, comprising a dispersion objective lens and a Czerny–Turner (C-T) spectrometer meeting the astigmatism-free condition. The system design and optimization were completed, with its engineering feasibility verified through tolerance analysis.

What are the implications of the main findings?
The proposed spectral confocal sensor optical system has been developed to enable accurate extraction of droplet surface profiles under high-inclination conditions and, combined with the Young–Laplace equation, enables high-precision determination of droplet surface tension.The system retains high measurement accuracy over a wide range of angles, providing robust technical support for the precise characterization of high-inclination surfaces and offering a reference framework for the systematic design of large-angle spectral confocal sensors.

The proposed spectral confocal sensor optical system has been developed to enable accurate extraction of droplet surface profiles under high-inclination conditions and, combined with the Young–Laplace equation, enables high-precision determination of droplet surface tension.

The system retains high measurement accuracy over a wide range of angles, providing robust technical support for the precise characterization of high-inclination surfaces and offering a reference framework for the systematic design of large-angle spectral confocal sensors.

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.