# Multifocal diffractive lens

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For eyeglass lenses, see [Progressive lens](/source/Progressive_lens).

A **multifocal diffractive lens** is a [diffractive optical element](/source/Diffractive_optical_element) (DOE) that allows a single incident [beam](/source/Laser_beam) to be [focused](/source/Focus_(optics)) simultaneously at several positions along the [propagation](/source/Wave_propagation) [axis](/source/Optical_axis).[1]

## Principle of operation

An incident [laser](/source/Laser) beam is deflected by grooved [diffraction pattern](/source/Diffraction_grating) into axial diffraction orders along its [optical axis](/source/Optical_axis). The foci appear around the [far field](/source/Fraunhofer_diffraction) position. With an additional focusing lens, foci from multifocal lens will appear at certain distances from the focal point of the lens.

## Theory

The multifocal spots location is a function of refractive [focal length](/source/Focal_length) *f*Refractive and predetermined diffractive focal length *f*Diffractive The focal spot at the "zero" order refers to the refractive focal length of the lens being used.

The distance between the focal spots can be described by the equation

- \frac {1}{f_m} = \frac {1}{f_\mathrm{Refractive}}+\frac{m}{f_\mathrm{Diffractive}},\ \mathrm{for}\ m = \pm 1, \pm 2, \pm 3...,
- where *fm* is the focal length for the *m*th diffractive order,
- *f*Refractive is the focal length of the refractive lens, and
- *f*Diffractive is the focal length of the diffractive lens.

## Applications

- [Laser cutting](/source/Laser_cutting)
- [Laser drilling](/source/Laser_drilling)
- [Microscopy](/source/Microscopy)
- [Ophthalmology](/source/Ophthalmology): Multifocal [contact lenses](/source/Contact_lens) and [multifocal intraocular lenses](/source/Multifocal_intraocular_lens)[1]

## External links

- [HOLOOR Application note for Multifocal Lenses](http://www.holoor.co.il/Diffractive_optics_Applications/Application-Notes-Multifocal-Lens.htm)
- [Interactive Optical calculator for Multifocal Lenses](http://www.holoor.co.il/Diffractive_Optics_Products/Calculators.htm)
- [Beam Propagation through multifocal lens (Movie)](https://www.youtube.com/watch?v=lWBPzMAUjxs)

## References

1. ["Multifocal diffractive lens generating several fixed foci at different design wavelengths"](https://www.researchgate.net/publication/322694970)

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Adapted from the Wikipedia article [Multifocal diffractive lens](https://en.wikipedia.org/wiki/Multifocal_diffractive_lens) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Multifocal_diffractive_lens?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.