Aspherical Lens in Digital Photography is designed to correct the aberrations produced by the usual spherical and optically differs from the spherical shape. Previously we discussed about Chromatic Aberration. If you think about the Photographic Lens Design, it will be apparent that; more complex the lens design is; more complex the spherical and other aberrations will be. Spherical aberration is not in case of lens, but for the mirror of DSLR too. The basic physics is that, due to the increased refraction of light rays like the prism; light rays when they strike a mirror near the edge, it results in an imperfection of the produced image. In case of mirror this is corrected for our eyes by using a bigger sized mirror or by using a specially coated mirror. As Lens is the set of element which will basically determine the quality of image with a given image sensor; Asperical Lens becomes an important element to reduce the errors in Digital Camera / DSLR. Digital camera, except the pro grade full frame DSLR and medium format camera; itself has many additional issues which were not present in traditional film photography. This is why today Aspherical Lens plays a role in Digital Photography.
Basic Optics of Spherical and Asperical Lens
A typical spherical lens theoretically has one Atlantic point; this is named because theoritically at this point there will be no spherical aberration. Mathematically it equals to the result of the radius of the sphere divided by the index of refraction of the lens material. Mostly crown glass is used for Photography Lens; a typical value of refractive index for crown glass is 1.5, which translates to the practical prediction that about 67% of diameter of a typical spherical lens will be aberration free. Focusing becomes less than ideal due to this spherical shape, apart from the aberration. Spherical lens are much easier to produce than aspherical ones, thereby less costly.
So to correct the error; we theoretically have two ways; one is to to use multiple spherical elements or other elements like stop to compensate or eliminate the spherical aberration or to use aspheric lens. When we are saying a Aspheric Lens for DSLR, it is becoming more costly and complex as one optical lens can not usually be used for the lens unit of camera.
The Optics of Aspherical Lens
The form rotationally symmetric aspheric lenses is usually considered as conics; it can be a a part of circle, ellipse, parabola, hyperbola etc. An aspheric lens lens has the surface profile which are not the full portion of a sphere or cylinder, if you think in a 3D world. It has to be remembered that; they must be rotationally symmetrical aspheric lenses, otherwise it will create issues if allowed to rotate in all directions freely.
Various camera and Lens manufacturers has different offerings for different DSLR models. It must to be noted that; size of the sensor matters as there is the crop factor. Technically, Aspherical Lens is more important to correct the issues in Full frame and medium format DSLR cameras.