Multifocal contact lenses or multifocal intraocular lenses are widely used ophthalmic devices. Traditionally, they are intended for the partial correction of presbyopia in the adult population and, more recently, they are also used with the aim of trying to slow down the progression of myopia in boys and girls.
The main characteristic of these designs is that they provide different optical power to different parts of the lens, thus focusing each part at a different distance.

Now, a study published in the journal Applied Optics has published a new mathematical procedure that allows the unique design of multifocal lenses without discontinuities, among other improvements.

Current status of progressive lenses

Until now, the conventional procedure to design the different curvatures of the lens after calculating the powers that are needed does not generate smooth transitions between the different parts of the lens and also restricts the number of possible designs.

The abrupt transitions of multifocal designs are a critical, and often overlooked, problem in manufacturing due to the fact that acute angles cannot be manufactured by either diamond turning or injection molding.

These abrupt transitions can also introduce unwanted optical effects, such as ghosting or light scattering.

An alternative is to smooth these discontinuities in manufacturing. However, this strategy prevents evaluating the optical effect of the transition zones at the design stage, without controlling their final contribution to the lens.

The study

One of the main motivations of this article has been to analyze the multifocal wavefronts that allow the design of lenses with also smooth transitions that have undoubted advantages over those that are not.
In this study, a mathematical procedure has been developed to uniquely construct multifocal wavefronts called umbilical line.
This family of surfaces has been inspired by the first prototypes of progressive lenses used in glasses, which have a specific segment that connects the center of the lens with its edge.
In the article, the researcher provides several examples of multifocal wavefronts belonging to this family, including a smooth variant of the so-called “light sword element”.
The shape of the representation of the mean curvature of the umbilical-line multifocal wavefronts implies that any wavefront of this type is smooth and, consequently, suitable to be obtained through conventional manufacturing techniques.

Traditionally, progressive multifocal lenses have been restricted to contain only axially symmetric surfaces (a line or axis of symmetry can be drawn on them).
However, in recent times, designs that also include power variation along the angular coordinate have been shown to provide some significant benefits. For example, it is better against variations in the pupil during adaptations (the pupil changes with different light intensity, and also when focusing with the eyes on a nearby object).

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