The chromatic confocal displacement sensor forms a spectral dispersion of polychromatic light along the axial direction of the dispersion lens. When an object is within the effective dispersion range, its axial position can be determined by analyzing the wavelength of the reflected light. This sensor offers high detection accuracy, fast detection speed, and good stability, making it a crucial tool for the semiconductor industry, material science, biology, medical detection, and diagnostics. The dispersion lens is an important component of the chromatic confocal displacement sensor. The axial detection ability of the sensor is determined by its dispersion range and numerical aperture. This study found that a relatively small object or image numerical aperture of the dispersion lens results in a long overall length that hinders its miniaturization. In this study, we aim to develop a dispersion lens with a large numerical aperture and small volume to enhance the measurement accuracy and range of the chromatic confocal displacement sensor.

This paper presents the working principle of the chromatic confocal displacement sensor, then examines the factors affecting its main performance indicators, such as axial measurement range, linearity, and axial resolution. The axial measurement range of the sensor is determined by the axial chromatic aberration of the dispersion lens, and a combination of at least two glasses is required for optimal linearity. The control variable method is used to analyze the influence of image numerical aperture, working wavelength, and dispersion range on the axial resolution. Subsequently, the study investigates the factors affecting the shortening ratio in the reverse telephoto structure. Finally, the optical design structure is processed and modified based on experiments conducted to validate the accuracy of the theoretical analysis.

The dispersion lens, designed using the reverse telephoto structure, has a shorter axial length and a larger image numerical aperture. The axial optical length is 135 mm, and the image numerical aperture is 0.48. With the same lens parameters, the axial length of the dispersion lens is about 35% shorter compared with that of the standard dispersion lens. The axial dispersion of the lens is 3.5 mm. While extending the axial dispersion can increase the measurement range, it also weakens the optical energy and reduces instrument signal-to-noise ratio. Increasing the image square numerical aperture of the dispersion lens improves the measurement signal-to-noise ratio but also increases head aberration, and affects linearity and dispersion range. Therefore, it is necessary to balance the design index of the dispersion lens. The image quality detection and performance evaluation experiments conducted on the adjusted dispersion lens show a maximum measurement standard deviation of 0.05 μm, a maximum average absolute error of 0.04 μm, and the actual axial resolution is better than 0.5 μm. The maximum measurement angle for the measured object is approximately 28.5°, confirming the accuracy of the theoretical analysis.

In this study, a compact long-axial dispersive spectral confocal lens with chromatic dispersion is designed by using the reverse telephoto structure. The design reduces the axial length of the lens by about 35% compared with conventional finite-range conjugate dispersion lens with the same performance parameters. A length reduction ratio formula is provided, which serves as a guide for designing chromatic confocal lenses with small object numerical aperture and large image numerical apertures. In application, the goals of the spectral confocal lens include expanding the dispersion range, increasing the numerical aperture of the image, and maintaining the near-linear dispersion performance. However, these three parameters are also related to energy utilization of the measurement system, volume, and the complexity of the lens. Increasing the numerical aperture of the image will improve the measurement signal-to-noise ratio but will increase the image aberration of the lens head, and the linearity and dispersion range will also be affected. The axial resolution of a dispersion lens is positively correlated with the image numerical aperture and the axial dispersion range, but the large numerical aperture and the long-axial dispersion range constraint the lens design and need to be balanced. The lens has an image square numerical aperture of 0.48 and can measure angles upto 28.5° inclined surface. To further improve the image square numerical aperture of the lens, it is necessary to increase the number of lens. As aspheric processing technology matures, aspheric correction of spherical aberration becomes an option for large numerical aperture lenses. Using optical fiber with smaller core diameter and spectrometer with higher resolution can further improve the axial resolution of the measurement system. The spectral confocal dispersion lens design in this study is advantageous for miniaturization displacement or three dimensional measuring instruments. Fewer lenses and glass types are conducive to commercial adoption and application.