Diffraction-limited
Encyclopedia
Microscope
A microscope is an instrument used to see objects that are too small for the naked eye. The science of investigating small objects using such an instrument is called microscopy...
, telescope
Telescope
A telescope is an instrument that aids in the observation of remote objects by collecting electromagnetic radiation . The first known practical telescopes were invented in the Netherlands at the beginning of the 1600s , using glass lenses...
, or camera
Camera
A camera is a device that records and stores images. These images may be still photographs or moving images such as videos or movies. The term camera comes from the camera obscura , an early mechanism for projecting images...
— can be limited by factors such as imperfections in the lenses or misalignment. However, there is a fundamental maximum to the resolution of any optical system which is due to diffraction
Diffraction
Diffraction refers to various phenomena which occur when a wave encounters an obstacle. Italian scientist Francesco Maria Grimaldi coined the word "diffraction" and was the first to record accurate observations of the phenomenon in 1665...
. An optical system with the ability to produce images with angular resolution
Angular resolution
Angular resolution, or spatial resolution, describes the ability of any image-forming device such as an optical or radio telescope, a microscope, a camera, or an eye, to distinguish small details of an object...
as good as the instrument's theoretical limit is said to be diffraction limited.
The resolution of a given instrument is proportional to the size of its objective, and inversely proportional to the wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
of the light being observed. For telescopes with circular apertures, the size of the smallest feature in an image that is diffraction limited is the size of the Airy disc
Airy disc
In optics, the Airy disk 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....
.
In astronomy
Astronomy
Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...
, a diffraction-limited observation is one that is limited only by the optical power of the instrument used. However, most observations from Earth are seeing
Astronomical seeing
Astronomical seeing refers to the blurring and twinkling of astronomical objects such as stars caused by turbulent mixing in the Earth's atmosphere varying the optical refractive index...
-limited due to atmospheric
Earth's atmosphere
The atmosphere of Earth is a layer of gases surrounding the planet Earth that is retained by Earth's gravity. The atmosphere protects life on Earth by absorbing ultraviolet solar radiation, warming the surface through heat retention , and reducing temperature extremes between day and night...
effects. Optical telescopes on the Earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...
work at a much lower resolution than the diffraction limit because of the distortion introduced by the passage of light through several kilometres of turbulent atmosphere. Some advanced observatories have recently started using adaptive optics
Adaptive optics
Adaptive optics is a technology used to improve the performance of optical systems by reducing the effect of wavefront distortions. It is used in astronomical telescopes and laser communication systems to remove the effects of atmospheric distortion, and in retinal imaging systems to reduce the...
technology, resulting in greater image resolution for faint targets, but it is still difficult to reach the diffraction limit using adaptive optics.
Radiotelescopes are frequently diffraction-limited, because the wavelengths they use (from millimeters to meters) are so long that the atmospheric distortion is negligible. Space-based telescopes (such as Hubble
Hubble Space Telescope
The Hubble Space Telescope is a space telescope that was carried into orbit by a Space Shuttle in 1990 and remains in operation. A 2.4 meter aperture telescope in low Earth orbit, Hubble's four main instruments observe in the near ultraviolet, visible, and near infrared...
, or a number of non-optical telescopes) always work at their diffraction limit, if their design is free of optical aberration.
The Abbe diffraction limit for a microscope
The observation of sub-wavelength structures with microscopes is difficult because of the Abbe diffraction limit. Ernst Abbe found in 1873 that light with wavelength λ, traveling in a medium with refractive index n and converging to a spot with angle
will make a spot with radius
The denominator
is called the numerical apertureNumerical aperture
In optics, the numerical aperture of an optical system is a dimensionless number that characterizes the range of angles over which the system can accept or emit light. By incorporating index of refraction in its definition, NA has the property that it is constant for a beam as it goes from one...
(NA) and can reach about 1.4 in modern optics, hence the Abbe limit is roughly d=λ/2. With green light around 500nm the Abbe limit is 250nm which is large compared to most nanostructures or biological cells which have sizes on the order of 1μm and internal organelles which are much smaller. To increase the resolution, shorter wavelengths can be used such as UV and X-ray microscopes. These techniques offer better resolution but are expensive, suffer from lack of contrast in biological samples and may damage the sample.
Obtaining higher resolution
There are techniques for producing images that appear to have higher resolution than allowed by simple use of diffraction-limited optics. Although these techniques improve some aspect of resolution, they generally come at an enormous increase in cost and complexity. Usually the technique is only appropriate for a small subset of imaging problems, with several general approaches outlined below.Extending numerical aperture
For a given numerical apertureNumerical aperture
In optics, the numerical aperture of an optical system is a dimensionless number that characterizes the range of angles over which the system can accept or emit light. By incorporating index of refraction in its definition, NA has the property that it is constant for a beam as it goes from one...
(NA), the resolution of microscopy
Microscopy
Microscopy is the technical field of using microscopes to view samples and objects that cannot be seen with the unaided eye...
for flat objects under coherent illumination can be improved using interferometric microscopy
Interferometric microscopy
Interferometric microscopy or Imaging interferometric microscopy is the concept of microscopy whichis related to holography, synthetic-aperture imaging, and off-axis-dark-field illumination techniques....
. Using the partial images from a holographic recording of the distribution of the complex optical field, the large aperture image can be reconstructed numerically. Another technique, 4 PI Microscopy
4Pi Microscope
A 4Pi Microscope is a laser scanning fluorescence microscope with an improved axial resolution. The typical value of 500-700 nm can be improved to 100-150 nm which corresponds to an almost spherical focal spot with 5-7 times less volume than that of standard confocal microscopy.-Working...
uses two opposing objectives to double the effective numerical aperture, effectively halving the diffraction limit.
Among sub-diffraction limited techniques, structured illumination holds the distinction of being one of the only methods that can work with simple reflectance without the need for special dyes or fluorescence and at very long working distances. In this method, multiple spatially modulated illumination patterns are used to double the effective numerical aperture. In principle, the technique can be used at any range and on any target provided that illumination can be controlled. Additionally, if exogenous contrast agents are used, the technique can also achieve >2 fold increase in resolution.
Near-field techniques
The diffraction limit is only valid in the far field. Various near-fieldNear and far field
The near field and far field and the transition zone are regions of the electromagnetic radiation field that emanates from a transmitting antenna, or as a result of radiation scattering off an object...
techniques that operate less than 1 wavelength of light away from the image plane can obtain substantially higher resolution. These techniques exploit the fact that the evanescent field
Evanescent wave
An evanescent wave is a nearfield standing wave with an intensity that exhibits exponential decay with distance from the boundary at which the wave was formed. Evanescent waves are a general property of wave-equations, and can in principle occur in any context to which a wave-equation applies...
contains information beyond the diffraction limit which can be used to construct very high resolution images, in principle beating the diffraction limit by a factor proportional to how far into the near field an imaging system extends. Techniques such as total internal reflectance microscopy
Total internal reflection fluorescence microscope
A total internal reflection fluorescence microscope is a type of microscope with which a thin region of a specimen, usually less than 200 nm, can be observed.-Background:...
and metamaterials-based superlens
Superlens
A superlens, super lens or perfect lens is a lens which uses metamaterials to go beyond the diffraction limit. The diffraction limit is an inherent limitation in conventional optical devices or lenses. In 2000, a type of lens was proposed, consisting of a metamaterial that compensates for wave...
can image with resolution better than the diffraction limit by locating the objective lens extremely close (typically hundreds of nanometers) to the object. However, because these techniques cannot image beyond 1 wavelength, they cannot be used to image into objects thicker than 1 wavelength which limits their applicability.
Far-field techniques
Far-field imaging techniques are most desirable for imaging objects that are large compared to the illumination wavelength but that contain fine structure. This includes nearly all biological applications in which cells span multiple wavelengths but contain structure down to molecular scales. In recent years several techniques have shown that sub-diffraction limited imaging is possible over macroscopic distances. These techniques usually exploit optical nonlinearityNonlinear optics
Nonlinear optics is the branch of optics that describes the behavior of light in nonlinear media, that is, media in which the dielectric polarization P responds nonlinearly to the electric field E of the light...
in a material's reflected light to generate resolution beyond the diffraction limit.
Among these techniques, the STED Microscope has been one of the most successful. In STED, multiple laser beams are used to first excite, and then quench fluorescent dyes. The nonlinear response to illumination caused by the quenching process in which adding more light causes the image to become less bright generates sub-diffraction limited information about the location of dye molecules, allowing resolution far beyond the diffraction limit provided high illumination intensities are used.