As one of the important means of optical imaging in vivo, two-photon microscopes are widely used in biomedical related research fields, such as brain neuroscience, neurodegenerative diseases, embryonic development, and especially in cerebral cortex imaging. The shape of the mammalian brain is irregular and the contour is like a curved surface, but most microscopes are plane field of view. Therefore, the two-photon fluorescence imaging of the mammalian brain will cause uneven imaging depth of the field center and field edge, and with the expansion of the imaging field of view, it will become more and more obvious, thus affecting the imaging quality. In order to solve the problems of small field of view and mismatch between field of view and curvature of brain contour when traditional two-photon microscope is used for two-photon fluorescence imaging of cerebral cortexes, an optical design scheme of two-photon microscope objective lens with large field of view and curved field of view is proposed.

According to Seidel aberration theory, the major aberrations in the optical system, including spherical aberration, coma and astigmatism, are completely corrected and the field curvature is retained. The field curvature at this time is called Petzval field curvature. The curvature radius of the mouse brain contour is matched by controlling the value of Petzval field curvature. A set of solutions for solving the initial structure of coaxial three-mirror system is derived. On the basis of the coaxial system, the aperture occlusion in the optical system is eliminated by means of an off-axis field of view. By introducing free-form surface to the primary mirror, the secondary mirror and the third mirror, and using 15 term xy polynomials to characterize the free-form surface shape of the system, an off-axis three-mirror imaging system using free-form surface is further optimized.

Based on Seidel aberration theory, a set of corrected initial solutions of the basic aberration is derived. In the absence of astigmatism, the Petzval field curvature is increased to match the radius of curvature of the mouse brain contour. A set of solutions for the initial structure of coaxial three-mirror system with bending field of view is derived (Table 2). The numerical aperture NA is 0.15, the radius of curvature of the field of view reaches 6 mm, the field of view angle reaches 9°×18°, and the size of the field of view is up to 3.5 mm (Fig. 6), which demonstrates that the optical performance of the optimized system is good (Figs. 7-9). By reasonably controlling the system structure parameters in the initial structure selection and taking advantage of the structural advantages of the off-axis reflective optical system, a design scheme for the joint use of dual objective lenses without physical interference (Fig. 10) is obtained, which is conducive to further improving the size of the imaging field of view.

In order to solve the problems of small field of view and uneven imaging of the center and the edge of the field of view in two-photon imaging of mouse cerebral cortexes by conventional two-photon microscopy, a design method of two-photon microscope objective lens with large field of view and curved field of view is proposed. Based on Seidel aberration theory, a set of initial solutions of coaxial three-mirror system with corrected basic aberration is obtained. In the absence of astigmatism, the Petzval field curvature is increased to match the radius of curvature of the mouse brain contour. The designed system has a numerical aperture of 0.15, a radius of curvature of the field of view of 6 mm, and a field of view angle of 9°×18°. Taking advantage of off-axis reflective optical system, an innovative design scheme for the joint use of the dual objective lens system without physical interference is realized, which provides a design basis for the simultaneous two-photon fluorescence imaging of the left and right cerebral cortexes of mice, and increases the size of the imaging field of view. The 15 term xy polynomials are introduced to characterize the free-form surface shape of the system, and the system aberration is well corrected. The average aberration of the system in the full field of view is 0.014λ, which can meet the needs of high-resolution brain neural network imaging in large field of view. This method has reference value for the design of two-photon microscope with large field of view and curved field of view. In addition, the proposed method can also be applied to other scenes that require the radius of curvature of the field of view