In-depth Analysis of the Spherical Aberration Problem of Spherical Lenses
Spherical Aberration Phenomenon in Monochromatic Aberration
When a beam of light parallel to the optical axis is incident on a thin lens, under the paraxial approximation, all the light rays seem to converge at the same point on the optical axis, that is, the focus, and the distance f from this point to the lens represents the focal length of the lens. However, in practical applications, the incidence of the light beam is not always limited to the paraxial region. Therefore, the light rays from different aperture regions of the lens will eventually focus at different positions on the optical axis, forming a circular diffuse spot on the image plane. For example, the light rays that are usually incident on the edge of the lens will have a focal point closer to the lens than the focal point of the paraxial light rays. Similarly, for a concave lens, after the light rays that are farther from the axis pass through the lens, the convergence point of their reverse extension lines will also be closer to the lens.
The point Fp where the parallel paraxial light rays focus on the optical axis is called the paraxial focus, while the point Fe where the parallel marginal light rays focus is called the marginal focus. The difference in distance between these two foci is called spherical aberration or spherical aberration. According to the positional relationship between the paraxial image point and the paraxial image plane, spherical aberration can be divided into longitudinal spherical aberration and lateral spherical aberration.
Figure 1.1 (a) Spherical aberration of a converging lens; (b) Spherical aberration of a diverging lens
In an optical system, the spherical aberration of a lens is an issue that cannot be ignored. When light passes through a lens, due to the curvature of the lens itself, light at different positions will focus at different positions, thus forming a circular diffuse spot on the image plane. This focus shift phenomenon caused by the curvature of the lens is reflected in both converging lenses and diverging lenses.
Methods to Reduce Spherical Aberration
Since the calculation formula of spherical aberration is relatively complicated, we only discuss its results here. For a thin lens with a specific focal length, its shape factor q is defined as:
Wherein, R1 and R2 represent the radius of curvature of the two surfaces of the lens respectively. By adjusting the value of the shape factor q, we can control the spherical aberration, and this adjustment method is called lens matching adjustment. For example, when q=+1, R2 tends to infinity, and the lens appears as a plano-convex lens with the convex surface facing the incident light; when q=-1, the lens is a plane. In fact, the size of the spherical aberration of the lens mainly depends on the distribution of the deflection angles of its two refractive surfaces. After calculation, we found that when q≈+0.7, the lens can obtain the minimum spherical aberration, and at the same time, the deflection angles of the light on the two refractive surfaces of the lens are also equal.
In the adjustment of the optical performance of the lens, the deflection angle δ is a key parameter. By adjusting the lens’s curvature, that is, changing the value of the shape factor q, we can effectively control the size of the deflection angle δ, and then optimize the spherical aberration of the lens. This adjustment method is not only applicable to plano-convex lenses, but also to other types of lenses, such as concave lenses and convex lenses.
When the deflection angle satisfies 1=δ2, the spherical aberration of the lens is minimized. In addition, by reasonably configuring two lenses with specific intervals, the spherical aberration of the optical system can also be effectively reduced. According to the equal deflection angle criterion, θ1 and θ2 are set as the deflection angles of the light after passing through the two lenses, then the minimum spherical aberration will correspond to: Under the condition of satisfying 1=θ2, we can deduce that when the spacing t of the two lens combination is equal to their focal length difference, the spherical aberration of the optical system will be minimized. It is particularly worth mentioning that at this time, the achromatic condition and the minimum spherical aberration condition are met at the same time.
Figure 2.2 shows that when two lenses are combined, their spacing should be set to the difference between their focal lengths to achieve the best optical performance. However, in practical applications, due to the inevitable diffraction effect, even if the optical system has no aberration, the image point will still present a diffuse spot. In order to control this effect, an aperture is often used in experiments to limit the paraxial area, but the choice of the aperture diameter needs to be weighed: a diameter that is too small will increase the diffraction effect, and the imaging effect is usually best when the aperture f/D≈5.6 is selected. At the same time, aberrations will affect the image quality under large apertures, and diffraction will also lead to a decrease in image quality under small apertures. Therefore, in order to reduce spherical aberration, we can adjust the shape factor q or use a combined lens method. In addition, a combination of positive and negative lenses that meet the Abbe sine condition, as well as methods such as Qiming lenses, can also effectively reduce spherical aberration, but this article will not go into details.
The key to reducing spherical aberration is to optimize the shape of the lens. By using the best shape lens, we can carefully optimize the radius of curvature of each surface of the lens to minimize spherical error. In addition, the design concept of the achromatic doublet lens is to effectively correct the dispersion phenomenon by gluing lenses with positive and negative dispersion.
In addition, our store also provides lenses of various sizes and working bands to meet the needs of different scientific research projects. At the same time, we also provide customized services to manufacture lenses according to the specific requirements of customers.
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Hanzhong Brisun Optics Co., Ltd. Is the high precision optical element manufacturer provides customized production of Various optical lenses, including spherical lens, cylindrical lens, optical window, mirror, prism, filter, metal base mirror and other high-precision optical elements. The base materials include various optical glass, fused quartz, calcium fluoride (CaF2), zinc selenide (ZnSe), germanium (GE), silicon (SI), sapphire, metal and other materials. And provide antireflective film, high reflection film, spectroscopic film, metal film and other optical coatings.
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