a "double aspheric" lens is just a lens with some combination of asphericity on the front surface and atoricity on the back surface. The back surface will only be atoric in prescriptions with cylinder power. Overall, the optical and mechanical differences between a "double aspheric" lens design and a conventional single aspheric surface will depend upon the design choices and level of sophistication of either lens design.
Obviously, a lens with an atoric surface will provide better control of peripheral optical aberrations in lenses with cylinder power. For lenses with sphere power only, the optical differences between a "double aspheric" lens design and a single aspheric surface are negligible.
You can improve cosmetics if you judiciously control the distribution of asphericity between the front and back surfaces, which would be more likely with a "double aspheric" lens design. Plus lenses will be thinner with aspheric front surfaces, for instance, whereas minus lenses will be thinner with aspheric back surfaces. Not every "double aspheric" lens design does this though.
For the wearer, this results in lenses that look better and perform better since the world they see is closer to natural size. In addition, the lenses provide a larger clear field-of-vision through the window of the lens frame, since magnification of objects seen through the lens has been neutralized. However, modern aspheric semi-finished lens blanks are rotationally symmetrical—that is, within a base curve, there is only one amount of asphericity and it is the same in all meridians for all prescriptions for which the lens blank is intended. Therefore, prescriptions with cylinder corrections (for astigmatism) have only
one meridian corrected by the asphericity.
For patients with astigmatism, the resulting areas of clear vision are improved most significantly in the sphere power meridian of the prescription. The cylinder meridian would not have the correct asphericity due to the difference in power and the field of clear vision in that meridian would be reduced when compared to the other meridian. If the ability to aspherize the power in the cylinder meridian was also possible, then the field of clear vision in both meridians would be further improved and you would be able to offer the same
quality of vision to the full range of single-vision wearers, including those with high prescriptions. This is, in fact, the case for lenses called double aspheric.
All so-called "double Aspheric" lenses are actually atoric on the back surface. The vast majority of prescription combinations will contain cylinder power, which will necessitate a toric back surface. Any asphericity applied to the back surface will therefore result in atoricity. In the handful of SKUs that have only sphere power, a rotationally symmetrical surface will be applied to the back of the lens, resulting in an "aspheric" back surface, which is practically speaking just a "special case" of atoricity.
These lenses have two different amounts of asphericity on the same surface, located 90 degrees apart. Only a few manufacturers cast finished lenses with
an atoric back surface (different asphericity in each meridian) and these have been typically limited to 1.67 high-index lenses. Another option is to free-form
the back surface of the lens with the correct asphericity for each power, but this approach is as yet very limited in availability.