Autofocus technology significantly enhances the imaging process, enabling rapid target acquisition and improving productivity and efficiency. It plays a crucial role in modern technological development. Currently, autofocus technologies can be categorized into three primary methods: the pre-scan focus map method, the deep learning calculation method, and the real-time reflective focus method. Each has its advantages and limitations. For example, the pre-scan focus map method requires multiple images and offers poor anti-interference capabilities; the deep learning calculation method has a limited focusing range and requires extensive system training; the real-time reflective focus method, although the most widely used, presents several challenges. Achieving real-time, fast, multi-level autofocus with a wide focusing range remains an urgent issue in the industry.

In this paper, we propose a multilayer automatic focusing method based on biaxial axicon mirrors. A collimated laser beam passes through two inverted axicon mirrors with matching angles, resulting in a collimated, parallel annular beam. After being blocked, a semi-annular beam is produced, which propagates through the system. Upon reaching the sample plane via a beam splitter and objective lens, multiple surfaces on the object side reflect the semi-annular beam to the objective lens. The returned beam is then reflected by the beam splitter and imaged onto a CCD or CMOS sensor. Using the conjugate relationship between the object and image, multiple semi-annular spots are formed on the image plane, sharing a common center but without overlapping. The energy center position of each spot correlates with the defocus of the sample, enabling the determination of the defocus amount and direction of different reflective surfaces. Through closed-loop control of a servo motor, fast automatic focusing across multiple levels can be achieved.

Through simulation and experimental setups, a multilayer autofocus system based on a Nikon 20× objective lens is designed, as shown in Figs. 6 and 10. Using Eq. (4), the axial resolution of the system is calculated to be 0.4 μm, as shown in Fig. 8. A comparison between Zemax software simulations and experimental results confirms the theoretical accuracy. By analyzing Eq. (11), the result shown in Fig. 9(a) aligns with Tracepro software simulations, demonstrating that the beam edge obtained with this method is clear and easy to interpret. The system’s achromatic performance and defocusing simulations (Fig. 7) meet the expected outcomes. The experimental setup of the multilayer autofocus system, as shown in Fig. 11(a), is consistent with both theoretical and simulation results.

In this paper, we propose a novel multilayer focusing method based on axicon mirrors, highlighting its advantages in terms of diffraction effects, energy efficiency, and beam selection. We derive the relationship between the aperture and width of the circular beam, the refractive index of the axicon, and the distance between axicon mirrors, providing direct experimental guidance. A method for aperture segmentation and energy superposition is proposed to calculate the resolution of the semi-annular beam. Using Fresnel-Kirchhoff diffraction theory, the specific energy distribution of Gaussian beams after passing through an axicon mirror is derived. Based on this theory, an automatic focusing system using a 20× objective lens is designed and constructed. The annular beam’s aperture is 20 mm, the axicon refractive index is 1.4585, and the distance between the biaxial axicon mirrors is 123 mm. The system achieves a spatial resolution of 0.77 μm and an axial resolution of 0.40 μm, and the focusing accuracy is about 1/4 depth of field of the microscope objective lens. The theory’s validity is verified through both simulations and experiments, demonstrating that the beam quality produced by this method is ideal for applications requiring multilayer autofocus, such as in biomedical and electronic circuit fields.