Second Quantum of Lens Design

Anamorphic lenses have different effective focal length (EFL) in the horizontal and vertical section planes, which are also the only planes of symmetry. Thus this lens type is not rotationally symmetric.
The EFL in the horizontal section is shorter than the EFL in the vertical plane and since the sensors are also larger horizontally, the lens will have a larger horizontal field of view.
The anamorphic factor is the ratio of the efl in the vertical section to the EFL in the horizontal section. Common values are between 1.3 and 2.
So, the power distribution inside the lens has to be different in the two sections. To achieve this, asymmetric lens elements have to be used. These are lens elements having different optical powers in two perpendicular sections. These lenses have at least one non- rotationally symmetric surface. The simplest surface shape used is the cylindrical surface.
Inside the above lens design, the asymmetric lens elements are hatched in blue. 
The anamorphic lens was first created to have a widescreen projection in the theatres, by compressing the image on the common film material and enlarging the image by the same factor during projection.
This type of image formation has a side effect that was ignored at that time but which has brought these lenses to a renaissance nowadays: a very specific kind of bokeh called anamorphic bokeh.
This anamorphic effect is opening new spaces of creativity for designing the Character of the lens.