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A spatial filter is an optical device which uses the principles of Fourier optics to alter the structure of a beam of light or other
electromagnetic radiation In physics, electromagnetic radiation (EMR) is a self-propagating wave of the electromagnetic field that carries momentum and radiant energy through space. It encompasses a broad spectrum, classified by frequency or its inverse, wavelength ...
, typically
coherent Coherence is, in general, a state or situation in which all the parts or ideas fit together well so that they form a united whole. More specifically, coherence, coherency, or coherent may refer to the following: Physics * Coherence (physics ...
laser A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word ''laser'' originated as an acronym for light amplification by stimulated emission of radi ...
light Light, visible light, or visible radiation is electromagnetic radiation that can be visual perception, perceived by the human eye. Visible light spans the visible spectrum and is usually defined as having wavelengths in the range of 400– ...
. Spatial filtering is commonly used to "clean up" the output of lasers, removing aberrations in the beam due to imperfect, dirty, or damaged optics, or due to variations in the laser
gain medium The active laser medium (also called a gain medium or lasing medium) is the source of optical gain within a laser. The gain results from the stimulated emission of photons through electronic or molecular transitions to a lower energy state from ...
itself. This filtering can be applied to transmit a pure
transverse mode A transverse mode of electromagnetic radiation is a particular electromagnetic field pattern of the radiation in the plane perpendicular (i.e., transverse) to the radiation's propagation direction. Transverse modes occur in radio waves and micr ...
from a multimode laser while blocking other modes emitted from the
optical resonator An optical cavity, resonating cavity or optical resonator is an arrangement of mirrors or other optical elements that confines light waves similarly to how a cavity resonator confines microwaves. Optical cavities are a major component of lasers, ...
. The term "filtering" indicates that the desirable structural features of the original source pass through the filter, while the undesirable features are blocked. An apparatus which follows the filter effectively sees a higher-quality but lower-powered image of the source, instead of the actual source directly. An example of the use of spatial filter can be seen in advanced setup of micro-Raman spectroscopy. In spatial filtering, a
lens A lens is a transmissive optical device that focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a compound lens consists of several simple lenses (''elements'') ...
is used to
focus Focus (: foci or focuses) may refer to: Arts * Focus or Focus Festival, former name of the Adelaide Fringe arts festival in East Australia Film *Focus (2001 film), ''Focus'' (2001 film), a 2001 film based on the Arthur Miller novel *Focus (2015 ...
the beam. Because of
diffraction Diffraction is the deviation of waves from straight-line propagation without any change in their energy due to an obstacle or through an aperture. The diffracting object or aperture effectively becomes a secondary source of the Wave propagation ...
, a beam that is not a perfect
plane wave In physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of ...
will not focus to a single spot, but rather will produce a pattern of light and dark regions in the
focal plane In Gaussian optics, the cardinal points consist of three pairs of points located on the optical axis of a rotationally symmetric, focal, optical system. These are the '' focal points'', the principal points, and the nodal points; there are two ...
. For example, an imperfect beam might form a bright spot surrounded by a series of concentric rings, as shown in the figure to the right. It can be shown that this two-dimensional pattern is the two-dimensional
Fourier transform In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input then outputs another function that describes the extent to which various frequencies are present in the original function. The output of the tr ...
of the initial beam's transverse
intensity Intensity may refer to: In colloquial use * Strength (disambiguation) *Amplitude * Level (disambiguation) * Magnitude (disambiguation) In physical sciences Physics *Intensity (physics), power per unit area (W/m2) *Field strength of electric, m ...
distribution. In this context, the focal plane is often called the ''transform plane''. Light in the very center of the transform pattern corresponds to a perfect, wide plane wave. Other light corresponds to "structure" in the beam, with light further from the central spot corresponding to structure with higher ''
spatial frequency In mathematics, physics, and engineering, spatial frequency is a characteristic of any structure that is periodic across position in space. The spatial frequency is a measure of how often sinusoidal components (as determined by the Fourier tra ...
''. A pattern with very fine details will produce light very far from the transform plane's central spot. In the example above, the large central spot and rings of light surrounding it are due to the structure resulting when the beam passed through a circular
aperture In optics, the aperture of an optical system (including a system consisting of a single lens) is the hole or opening that primarily limits light propagated through the system. More specifically, the entrance pupil as the front side image o ...
. The spot is enlarged because the beam is limited by the aperture to a finite size, and the rings relate to the sharp edges of the beam created by the edges of the aperture. This pattern is called an
Airy pattern In optics, the Airy disk (or Airy disc) and Airy pattern are descriptions of the best-focus (optics), focused Point source#Light, spot of light that a perfect lens (optics), lens with a circular aperture can make, limited by the diffraction of ...
, after its discoverer
George Airy Sir George Biddell Airy (; 27 July 18012 January 1892) was an English mathematician and astronomer, as well as the Lucasian Professor of Mathematics from 1826 to 1828 and the seventh Astronomer Royal from 1835 to 1881. His many achievements inc ...
. By altering the distribution of light in the transform plane and using another lens to reform the collimated beam, the structure of the beam can be altered. The most common way of doing this is to place an aperture in the beam that allows the desired light to pass, while blocking light that corresponds to undesired structure in the beam. In particular, a small circular aperture or "
pinhole A hole is an opening in or through a particular medium, usually a solid body. Holes occur through natural and artificial processes, and may be useful for various purposes, or may represent a problem needing to be addressed in many fields of e ...
" that passes only the central bright spot can remove nearly all fine structure from the beam, producing a smooth transverse intensity profile, which may be almost a perfect
gaussian beam In optics, a Gaussian beam is an idealized beam of electromagnetic radiation whose amplitude envelope in the transverse plane is given by a Gaussian function; this also implies a Gaussian intensity (irradiance) profile. This fundamental (or ...
. With good optics and a very small pinhole, one could even approximate a plane wave. In practice, the diameter of the aperture is chosen based on the
focal length The focal length of an Optics, optical system is a measure of how strongly the system converges or diverges light; it is the Multiplicative inverse, inverse of the system's optical power. A positive focal length indicates that a system Converge ...
of the lens, the diameter and quality of the input beam, and its
wavelength In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats. In other words, it is the distance between consecutive corresponding points of the same ''phase (waves ...
(longer wavelengths require larger apertures). If the hole is too small, the beam quality is greatly improved but the power is greatly reduced. If the hole is too large, the beam quality may not be improved as much as desired. The size of aperture that can be used also depends on the size and quality of the optics. To use a very small pinhole, one must use a focusing lens with a low
f-number An f-number is a measure of the light-gathering ability of an optical system such as a camera lens. It is calculated by dividing the system's focal length by the diameter of the entrance pupil ("clear aperture").Smith, Warren ''Modern Optical ...
, and ideally the lens should not add significant aberrations to the beam. The design of such a lens becomes increasingly more difficult as the f-number decreases. In practice, the most commonly used configuration is to use a microscope objective lens for focusing the beam, and an aperture made by punching a small, precise, hole in a piece of thick metal foil. Such assemblies are available commercially.


Spherical waves

By omitting the second lens that reforms the collimated beam, the filter aperture closely approximates an intense point source, which produces light that approximates a
spherical A sphere (from Ancient Greek, Greek , ) is a surface (mathematics), surface analogous to the circle, a curve. In solid geometry, a sphere is the Locus (mathematics), set of points that are all at the same distance from a given point in three ...
wavefront. A smaller aperture implements a closer approximation of a point source, which in turn produces a more nearly spherical wavefront.


See also

*
Köhler illumination Köhler illumination is a method of specimen illumination used for transmitted and reflected light (trans- and epi-illuminated) optical microscopy. Köhler illumination acts to generate an even illumination of the sample and ensures that an image ...
, which applies spatial filtering to incoherent light for microscopy *
Pinhole camera A pinhole camera is a simple camera without a lens but with a tiny aperture (the so-called ''Pinhole (optics), pinhole'')—effectively a light-proof box with a small hole in one side. Light from a scene passes through the aperture and projects a ...


References

{{DEFAULTSORT:Spatial Filter Optical components Physical optics Laser science es:Filtro óptico#Filtro espacial