Instituto de Óptica “Daza de Valdés”

Multifocal wavefronts with prescribed caustics in axially symmetric optical systems

25 May, 2022 | Ciencias de la imagen-en

New theoretical study to design multifocal lenses

The design of a lens is not something trivial, since it involves expensive computational calculations that involve the use of computers since the 60s of the last century.
Since then, the successive scientific-technological advances in this field have allowed the current designs of multifocal lenses.

These multifocal lenses provide distributions of light that are not concentrated around a single point (monofocality), but around certain places or over a large region.

Multifocal and/or extended depth of focus optical beams and designs are on the rise in optics thanks to the development of techniques that allow the control of light beams (for example, thanks to spatial light modulators), controlling the shape what is called a wave front.
The diversity of applications of these technologies is high, they not only serve as ophthalmic corrections for presbyopia but also have application in data storage, microscopy, computational photography, optical micromanipulation (optical tweezers) or non-diffractive beams in atomic and non linear optics.

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But what is a wavefront?

A wave front is defined as the locus that unites all the points that, at a given instant, are in the same state of vibration, that is, they have the same phase.
On the water surface successive wave fronts form concentric circles.

The design of the wavefront consists of, first, looking for the one that, when emerging from the optical system, provides the desired multifocal and/or extended depth of focus properties.

This can be done through theoretical and computational simulations, experiments, or both.
Once the optimal wavefront has been found, the next step is to design a lens or optical system that will receive an incoming wavefront and exit that optimal wavefront.


What are the caustic surfaces of a wavefront?

Within ray optics theory, caustics are associated with spatial locations where two or more rays intersect, giving those locations a higher concentration of light.

These concentrations of light, especially sunlight, can burn. The word caustic comes from the Greek καυστός, to burn, via the Latin, causticus, burning. A common situation where caustics can be observed is when light shines through a drinking glass. The glass casts a shadow, but it also produces a curved region of bright light.

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Although in most direct focusing applications it is mandatory to use wave optics theory, for accurate simulation of beam propagation or evaluation of optical performance of a lens, the method developed in this work offers an approach to, at least characterize some basic properties or explore possible design solutions. From all this arises the analysis of caustics as a natural tool to explore the multifocal properties of wavefronts.

The general objective of this work is to offer a theoretical framework to predict the existence or not of wavefronts with prescribed multifocal properties. Additionally, the fundamentals of a methodology to design multifocal solutions given some caustic constraints have been described.

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