In spherical plus lenses, peripheral rays are more strongly refracted than rays near the optical axis. This aberration is known as spherical aberration.
If the surface of the plus lens is "folded open" in the peripheral areas so that the surface structure deviates from the spherical shape (aspherical surface), all rays coming from the distance meet again at one point. The aberration is corrected.
In the peripheral zones of eyeglass lenses, the interplay of spherical aberration with the viewing eye leads to a deviation from the specified dioptric power (spherical error). This spherical error is perceived as blurring by the eyeglass wearer.
If an object point lying outside the optical axis is imaged by a lens with a spherical power, astigmatism results due to the oblique incidence of the light bundle. A dot is no longer imaged as a dot, but as two image lines.
This aberration, known as astigmatic error, primarily influences the image quality of eyeglass lenses. When the wearer looks at an angle through the lens, there is a deviation (astigmatic error) from the specified dioptric power which he perceives as blur. The higher the dioptric power of the lens, the more pronounced this error becomes.
In the design of aspherical and atoriodal surfaces, oblique astigmatism can be minimized by deviating deliberately from the spherical shape.
In ca. 1804 the English physician Wollaston discovered that visual acuity decreases when an eyeglass wearer looked through the periphery of the biconvex lenses used at that time, and that meniscus-shaped lenses provided a sharper image. After this discovery, repeated attempts were made to improve the imaging properties of lenses. The first attempts to design meniscus-shaped lenses with reduced peripheral blurring were undertaken by the ophthalmologists Ostwald and Tscherning. However, the results were of no practical significance, as they were computed only for very small viewing angles and for lenses with a theoretical center thickness of zero.
Although optimal imaging properties were achieved with the first point focal lenses, the pronounced curvature of the lenses proved to be a major cosmetic drawback, especially for high prescriptions in the plus range.
To make lenses more attractive, so-called periscopic lenses were introduced, in which one surface was almost flat. This also made the lens flatter overall, but considerable aberrations were experienced in the peripheral zones. In higher dioptric powers in particular, these aberrations led to blurred vision.
The solution – a good appearance and good vision with a single lens – came in the form of the asphere and the atorus. In 1986 Carl Zeiss was the first manufacturer – and still is the only manufacturer – to offer a single vision lens with an atoroidal front surface: the Hypal lens. This modern surface design permits outstanding image quality over a wide field of view and, at the same time, flat, cosmetically attractive lenses.
Every rotationally symmetrical surface which deviates from a spherical shape is termed as an aspheric surface (asphere). The radius of curvature of such a surface changes continuously from the vertex to the periphery.
In ZEISS single vision lenses, the asphere is generated on the front surface of the lens. The computer calculates the ideal front surface design for every dioptric power.
The asphere is used for lenses with a spherical and astigmatic power. In lenses with a spherical power the blur occurring in the peripheral zones is optimally corrected with an asphere. However, in lenses with an astigmatic power the asphere can only be optimized for one principal meridian.
If the rotationally symmetrical asphere is optimized for the stronger principal meridian of a lens with an astigmatic power, astigmatic error remains in the other principal meridian. In lenses with a low astigmatic power this error is negligibly small, but in plus lenses with a high cylinder it becomes so noticeable that correction for both principal meridians is recommended. ZEISS has solved this problem with the development of the "atorus".
A non-rotationally symmetrical surface with unequal curvatures in principal meridians perpendicular to each other, of which at least one curvature is not circular in shape, is known as an atoroidal surface, or atorus for short.
In single vision lenses, the atorus – like the asphere – is generated on the front surface of the lens. The atorus is used for eyeglass lenses with an astigmatic power, with the front surface of the lens deviating to different degrees from a spherical shape in each meridian.
The surface design of the atorus is specially adapted to each dioptric power so that the optimal correction is always obtained for both principal meridians. The atoroidal surface design – a ZEISS exclusive – therefore permits outstanding correction of aberrations for single vision lenses with an astigmatic power.
Progressive lenses by ZEISS are the ultimate in high technology. Thanks to the aspheric design of the distance zone of the progressive surface, the correction of aberrations is directly incorporated in the progressive lens design. The front surface of a ZEISS progressive lens is both the progressive surface (asymmetrical free-form surface) and a correcting asphere. This design is used in the progressive lenses Gradal HS and Gradal Top.
In single vision lenses with an astigmatic power, the correction of aberrations can be achieved by the atorus on the front surface. For progressive lenses, however, the development of an atoroidal Rx surface (back surface) was necessary for this purpose.
In the past:
No aspheric progressive lens design was available
The computation and production of an atoroidal Rx surface are extremely complex. ZEISS has succeeded in developing and implementing a special technique for this purpose. Every atoroidal Rx surface is exactly computed giving due consideration to sphere, cylinder, axis and addition. This means that outstanding imaging properties are also achieved for a progressive lens with an astigmatic power.
With an aspheric progressive surface and an atoroidal Rx surface, it is possible to take both image quality and cosmetic aspects of the lens into account to a very high degree.
Aspheric progressive lens design and atoroidal Rx surface