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Phase Corrector Plates

Definition: transparent plates for modifying the phase profile of light

Alternative term: phase plates

More specific terms: spherical aberration compensation plates, Schmidt corrector plates

German: Phasenkorrekturplatten

Category: general optics

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Phase corrector plates (or phase plates) are transparent plates which are used for modifying the phase profile of light sent through them – for example, for compensating wavefront deformations in the form of spherical aberrations in an optical system. (Further applications are discussed below.) Typically, the spatial variation of the optical phase changes is relatively smooth and slow, e.g. on a length scale of millimeters – unlike the situation in transmission gratings where diffraction at much smaller structures is utilized.

Particularly for cases where the purpose is the compensation of spherical aberrations, the phase change profile is radially symmetric, i.e., depends only on a radial coordinate r, the distance from some center location. Frequently, the specified phase change of a plate is determined by a polynomial function of that radial coordinate, particularly with terms of 4th, 6th and 8th order. However, there are also phase plates with more complicated (possibly not radially symmetric) and even pseudo-random profiles for certain applications.

In many cases, anti-reflection coatings are applied to both surfaces of a phase corrector plate in order to minimize reflection losses and potentially disturbing effects of parasitic reflected beams. A low absorption coefficient of the used material is also desirable, particularly for application with high-power laser beams, where significant absorption would introduce a transverse temperature profile which would modify the refractive index profile and thus the obtain phase changes.

Working Principles

There are two fundamentally different operation principles on which a phase corrector plate can be based:

  • One or both surfaces of the plate can have a tailored surface relief, which implies a spatially variable path length through the plate material (e.g. an optical glass). As the refractive index of that material is substantially higher than that of air, even small surface features lead to substantial phase changes.
  • Other phase corrector plates utilize a variation of the refractive index in the medium, while having flat (and typically parallel) surfaces.

The same distinction is made for optical lenses: these can either have curved (convex or concave) surfaces or an internal refractive index variation; in the latter case one has a gradient-index lens. Indeed, phase corrector plates are sometimes called aspheric lenses due to their similarity. However, the basic function of a lens is focusing or defocusing light, while phase correctors, as their names says, are used for introducing other kinds of phase changes.

There are also designs involving more than one type of optical material. For example, one may produce a suitable surface profile on a plate with a certain material and cover that with another material having a slightly different refractive index and a flat top surface. Due to the small index contrast, the obtained phase profile is much less dependent on the details of the surface profile. One thus requires a profile with larger elevations, which is easier to produce with sufficient accuracy.

Applications of Phase Corrector Plates

Phase corrector plates can be used for various purposes; some examples:

  • An important application area is the compensation of optical aberrations in imaging systems: spherical aberrations, coma and others. For example, a specific solution for certain optical telescopes is the Schmidt corrector plate. A special and somewhat unusual case is the application to human vision [5].
  • Similarly, aberrations often need to be corrected when very tightly focusing a laser beam. This is particularly the case when a beam has experienced wavefront distortions, e.g. when passing an optical amplifier.
  • Pseudo-random phase plates can be used for testing adaptive optics systems.

For successful application of a phase corrector plate, that optical element can in principle be inserted at different positions in the beam path. For example, it may be placed before or after an optical amplifier for compensating its aberrations. However, its phase change profile needs to be optimized for the particular position, because phase distortions may evolve substantially during beam propagation.

Fabrication of Phase Corrector Plates

Various techniques are available for fabricating phase corrector plates which are based on a surface relief. For example, one may apply diamond turning, as is also used in other areas of optical fabrication, particularly when freeform elements need to be made. Other options are etching techniques and photolithography.

Other techniques are applied for generating refractive index variations within plates. For example, one may apply methods of holography for automatically obtaining the required phase profiles for compensating the optical aberrations of certain optical elements [1].

Alternative Solutions

For the compensation of phase aberrations, the use of phase corrector plate is often not the only solution:

  • A more flexible, but also more complex and expensive solution is to use a spatial light modulator – effectively, to build an adaptive optical system. The advantage is essentially that the phase correction profile can be optimized during operation.
  • In many cases, aberrations can also be compensated with a proper combination of ordinary optical elements, such that at least certain aberrations from different elements more or less cancel each other. Tailored phase corrector plates, however, give more freedom to compensate multiple types of aberrations at the same time.
  • Sometimes, one can use a meniscus corrector – a meniscus lens which does not provide a focusing function but introduces spherical aberrations tailored to compensate such aberrations from another optical element.
  • Sometimes, the aberration correction can be integrated into another optical element. For example, one can use aspherical lenses, possibly even with a freeform surface, instead of an ordinary lens combined with a phase corrector plate. The advantages of that approach are a simpler setup and that one avoids two additional optical surfaces introducing additional propagation losses.

Suppliers

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Bibliography

[1]J. Upatnieks, A. Vander Lugt and E. Leith, “Correction of lens aberrations by means of holograms”, Appl. Opt. 5 (4), 589 (1966), doi:10.1364/AO.5.000589
[2]E. Everhart, “Making corrector plates by Schmidt's vacuum method”, Appl. Opt. 5 85), 713 (1966), doi:10.1364/AO.5.000713
[3]R. N. Wilson, “Corrector systems for Cassegrain telescopes”, Appl. Opt. 7 (2), 253 (1968), doi:10.1364/AO.7.000253
[4]D. T. Moore, “Catadioptric system with a gradient-index corrector plate”, J. Opt. Soc. Am. 67 (9), 1143 (1977), doi:10.1364/JOSA.67.001143
[5]A. Y. Yi and T. W. Raasch, “Design and fabrication of a freeform phaseplate for high-order ocular aberration correction”, Appl. Opt. 44 (32), 6869 (2005), doi:10.1364/AO.44.006869
[6]Y. Lumer et al., “Use of phase corrector plates to increase the power of radially polarized oscillators”, J. Opt. Soc. Am. B 27 (7), 1337 (2010), doi:10.1364/JOSAB.27.001337

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See also: optical phase
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