A spatial filter is an optical device which uses the principles of
Fourier optics Fourier optics is the study of classical optics using Fourier transforms (FTs), in which the waveform being considered is regarded as made up of a combination, or '' superposition'', of plane waves. It has some parallels to the Huygens–Fresnel pr ...
to alter the structure of a beam of light or other
electromagnetic radiation
In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic field, electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, inf ...
, typically
coherent
Coherence, coherency, or coherent may refer to the following:
Physics
* Coherence (physics), an ideal property of waves that enables stationary (i.e. temporally and spatially constant) interference
* Coherence (units of measurement), a deri ...
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" is an acronym for "light amplification by stimulated emission of radiation". The fir ...
light
Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 tera ...
. 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 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 a ...
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 microwav ...
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 forms a cavity resonator for light waves. Optical cavities are a major component of lasers, surrounding the gain medium and provi ...
.
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 which 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, or its plural form foci may refer to:
Arts
* Focus or Focus Festival, former name of the Adelaide Fringe arts festival in South Australia Film
*''Focus'', a 1962 TV film starring James Whitmore
* ''Focus'' (2001 film), a 2001 film based ...
the beam. Because of
diffraction
Diffraction is defined as the interference or bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture. The diffracting object or aperture effectively becomes a s ...
, a beam that is not a perfect
plane wave
In physics, a plane wave is a special case of wave or field: a physical quantity whose value, at any moment, is constant through any plane that is perpendicular to a fixed direction in space.
For any position \vec x in space and any time t, th ...
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. For ''ideal'' ...
. 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
A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, ...
of the initial beam's transverse
intensity 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, an aperture is a hole or an opening through which light travels. More specifically, the aperture and focal length of an optical system determine the cone angle of a bundle of rays that come to a focus in the image plane.
An opt ...
. 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- focused spot of light that a perfect lens with a circular aperture can make, limited by the diffraction of light. The Airy disk is of importance in physics, ...
, after its discoverer
George Airy
Sir George Biddell Airy (; 27 July 18012 January 1892) was an English mathematician and astronomer, and the seventh Astronomer Royal from 1835 to 1881. His many achievements include work on planetary orbits, measuring the mean density of the E ...
.
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 en ...
" 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 a beam of electromagnetic radiation with high monochromaticity whose amplitude envelope in the transverse plane is given by a Gaussian function; this also implies a Gaussian intensity (irradiance) profile. This ...
. 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 optical system is a measure of how strongly the system converges or diverges light; it is the inverse of the system's optical power. A positive focal length indicates that a system converges light, while a negative foca ...
of the lens, the diameter and quality of the input beam, and its
wavelength
In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats.
It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...
(longer wavelengths require larger apertures). If the hole is too small, the beam quality is greatly improved but the
power
Power most often refers to:
* Power (physics), meaning "rate of doing work"
** Engine power, the power put out by an engine
** Electric power
* Power (social and political), the ability to influence people or events
** Abusive power
Power may a ...
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
In optics, the f-number of an optical system such as a camera lens is the ratio of the system's focal length to the diameter of the entrance pupil ("clear aperture").Smith, Warren ''Modern Optical Engineering'', 4th Ed., 2007 McGraw-Hill ...
, 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
In optical engineering, the objective is the optical element that gathers light from the object being observed and focuses the light rays to produce a real image. Objectives can be a single lens or mirror, or combinations of several optical elem ...
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 () is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. A sphere is the set of points that are all at the same distance from a given point in three-dimensional space.. That given point is the ce ...
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 o ...
, 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'')—effectively a light-proof box with a small hole in one side. Light from a scene passes through the aperture and projects an inverted image o ...
References
{{DEFAULTSORT:Spatial Filter
Optical components
Physical optics
Laser science
es:Filtro óptico#Filtro espacial