With the continuous improvement of processing technology, research on insect compound eyes has made great progress [
22,
23]. By using an uneven surface in a compound eye, the problem of inaccuracy in each sub-eye is effectively solved. The Zemax ray tracing of a single-surface complex eye model is shown in
Figure 1. According to the trace results, the incident ray corresponding to each sub-eye can be focused on a light detection target surface. However, due to the spherical structure of the surface of the microlenses at all levels, a large spherical aberration exists in the compound eye, which affects the overall imaging effects and has a great impact on target tracking and multi-target positioning in later uses of the compound eye [
24]. Therefore, we performed aspheric optimization of the microlenses at all levels to improve the overall imaging quality of the compound eye.
2.1. Structural Design of the Variable Focal Length Artificial Compound Eye
The overall structure of the curved compound eye for zoom, as shown in
Figure 2a, divides the curved surface into three equal parts, each with an angle of 120° and a corresponding “focal length” that is different. For the red, yellow, and green parts of the design, as depicted in
Figure 2a, the focal lengths of the central small eye are 2.227 mm, 1.927 mm, and 2.527 mm, respectively. In this way, zooming can be achieved within a certain range to enhance the imaging performance of the artificial compound eye.
The microlens array on the curved substrate ultimately needs to be imaged on a planar photodetector array, which results in different distances from the center of microlenses that are at different locations on the substrate to the photodetection array. According to the geometric imaging principle, the effective focal length of the microlens is equal to the distance from the center of the microlens to the photodetection array, so only microlenses at the same position in each region have the same size. Apart from a central lens in the red area of the structure, the microlens arrays in the three areas have the same relative positions and numbers of lenses (
Figure 2a).
The design parameters of the variable-focus surface compound eye structure are shown in
Table 1.
The distance from the optical center of the central eye to the target surface of the photodetector is taken as a design reference, and the distance from the center of each microlens to the photodetection array is the effective focal length of each sub-eye [
12,
13]. Taking the sub-eye array in the red area (
Figure 2a) as an example, as shown in
Figure 2b, the sub-eyes are divided into five levels according to their deflection angle relative to the central sub-eye. The sub-eyes in each level also have the same distance from the target surface of the photodetector. Therefore, the focal length and radius of curvature are also the same for all sub-eyes in a level.
According to the geometric relationship between the radius of curvature of the lens and the deflection angle of the sub-eyes, the effective focal length of the sub-eyes in each level can be calculated. The distance
λn from the inner surface of the substrate corresponding to the center of the
nth (
n ≤ 5) sub-eye to the photodetector target surface is
R—curved base radius; θ—suborbital deflection angle; λ1–5—the distance between the sub-eye and the optical detection array.
The effective focal length of the sub-eyes at all levels can be obtained from the thin lens manufacturing equation
where
fn is the effective focal length of the
nth sub-eye,
rn is the radius of curvature of the
nth sub-eye,
R is the radius of the curved surface base, and
ni is the refractive index of the material selected for making the compound eye. According to Equation (2), the initial values of the effective radii of the sub-eyes in the red region can be obtained, as shown in
Table 2.
According to the obtained initial parameters of each sub-eye, a parametric model of curved compound eye is established in Zemax, and ray tracing is performed to study the imaging performance of the sub-eyes of each level. By analyzing the ray tracing results of the first-degree sub-eye,
Figure 3a, it can be seen that although the sub-eye can be imaged, the image does not converge to a single point. From the ray fan,
Figure 3b, it is found that there is a large spherical aberration in the initial structure, and the ray aberration is 5.4 μm. From the dot plot,
Figure 3c, it is seen that the radius of the Airy diffraction spot is 4.035 μm, which is relatively decentralized, and affects the imaging capability of the microlens.
In order to obtain the best imaging quality, aspherical optimization of the sub-eye structure is required. We establish a target optimization function in terms of the effective focal length (EFFL), spherical aberration (SPHA), and modulation transfer function (MIFT), setting optimization target values and weights for each. Then, to optimize the sub-eye’s spherical aberration, we determine the radius of curvature for each level that obtains the best imaging quality.
After optimization, the surface of the sub-eye becomes an aspherical structure, as shown in
Figure 4. According to the Zemax ray tracing results,
Figure 4a, the light is well focused to a point by the aspherical sub-eye, and no divergence of light occurs. At the same time, the analysis of the aspherical surface of the fan shows that the spherical aberration of the lens is greatly changed, and the aberration of the sub-areas are reduced to about 2.98 μm, as shown in
Figure 4b. Observing the aspherical eyelet spot diagram,
Figure 4c, the dispersion of the Airy diffraction spot has a root mean square radius of 1.448 μm and is relatively concentrated, which is beneficial to improving the imaging quality of the sub-eye lens.
The subocular surface is changed from a spherical surface to an aspheric surface, and the spherical aberration at each level of the sub-eye is reduced to one-hundredth of the initial structure. However, the non-spherical sub-eye structure puts forward higher requirements on the processing level of the compound mold for the later curved surface.
Table 3 shows the ball differences before and after optimization of the red zone subocular lens.
Table 4 shows the various dimensions of the optimized aspherical microlens in the red region. After the model is derived from Zemax, it is assembled to a corresponding position on the curved surface to form a three-focal-length microlens array.