As science and technology develop by leaps and bounds, requirements for the comprehensive performance of optical systems are getting higher. Optical systems are developing towards lightweight, simple structure, excellent optical performance, and low manufacturing cost. Due to its good optical properties, thermal stability, and flat field characteristics, the diffractive optical element is applied to the achromatic field. It can not only increase the degree of freedom of optical design but also break through many limitations of traditional optical systems. It has incomparable advantages in improving the image quality and reducing the volume and weight of the system, whereas its dispersion characteristics limit the application in the wide band. In this paper, a combination of multiple-order diffractive elements (MODs), refractive elements (ROEs), and diffractive Fresnel elements (DFLs) is proposed to realize the achromatism of the system, which greatly enhances the practicability of diffractive lenses under the wide band. In the field of wide band, the achromatic and apochromatic refractive-diffractive hybrid optical system can be realized. After analyzing and comparing surface shapes, the results which can optimize the imaging quality of the optical system are obtained. The proposed design can promote the application of the refractive-diffractive hybrid optical system in the field of achromatic and be conducive to the application of multiple-order diffractive element combination system in the field of achromatic.

This paper analyzes the optical system composed of multiple-order diffractive elements, refractive elements, and diffractive Fresnel elements. Under the guidance of scalar diffraction theory, the combined optical system is mathematically expressed based on the Seidel third-order aberration theory. Firstly, according to the achromatic and apochromatic characteristics of the system, the focal power of the system is expressed, and the expression relationship is obtained. Then, according to the third-order aberration theory of the thin lens, the third-order aberration coefficients of the three elements after gluing are obtained, and the conjugate parameters and bending parameters of the system are expressed by the definition and relational expression of the conjugate angle of the thin lens. By the given specific parameters, an achromatic and apochromatic system based on the proposed design concept is obtained, and the spherical aberration and coma aberration of the system are corrected. A better surface is selected after the three optical elements and comparing their different surface morphologies are analyzed. The achromatic and imaging quality of the three elements are compared mainly from the three modes of planar, spherical, and aspheric surfaces.

Through the mathematical derivation of the system, the Seidel aberration coefficients of the spherical aberration and coma of the system are set to zero respectively. Via the given parameters, a three-element glued optical system with corrected spherical aberration and achromatic and apochromatic aberration is obtained (Fig. 3). Then, the system is placed under the base surface of planar, spherical, and aspheric surface respectively, and some of its parameters are controlled to be the same (Table 1). By changing its aspheric coefficient and radian coefficient (Table 2), a comparative analysis is carried out under the optical system with a focal length f=20 mm, a field of view of 3.5°, an F number of 4, and a working band of 400-700 nm in the visible light band. It is concluded that the system has a better quality under spherical and aspheric surfaces (Fig. 5), smaller axial aberration, and a more obvious achromatic effect (Fig. 6), which is markedly better than under the plane surface. The modulation transfer function and the encircled energy of the spherical and aspheric surfaces are compared. It is concluded that when the system is an aspheric surface, the modulation transfer function of the system is 0.6683, which is much higher than that of the system with the spherical surface (0.3653), and the encircled energy is also higher (Fig. 7). Therefore, the three-element combined system is more suitable for achromatic requirements and has a better imaging quality when the aspheric surface is used.

In this paper, the optical system composed of MOD, ROE, and DFL is analyzed based on the third-order aberration theory of Seidel. In the given working band of 400-700 nm, the expression and calculation of the system bending parameters, conjugate parameters, and lens curvature are utilized to simultaneously correct the spherical aberration and coma aberration of the three-element glued refractive-diffractive hybrid achromatic system. The surface shape of the system is analyzed, and the achromatic situation and the imaging quality of the system with the planar, spherical, and aspheric surfaces are compared. It is found that the imaging quality of the system is better, the diffraction energy is more, and the achromatic effect is more obvious when the system is aspherical. The imaging optical system with spherical, aspheric, or free-form surface has a higher design freedom and a stronger aberration correction ability than that with the traditional planar surface. It also undertakes more tasks of balancing aberrations in the system and is easier to achieve the design goal of miniaturization and lightweight of the system. The designed system designed has small size, lightweight, and simple structure, which has broad application prospects in the field of space optics.