Angular resolution in the context of M87*

The angular diameter, angular width, angular size, apparent diameter, or apparent size is an angular separation (in units of angle) describing how large a sphere or circle appears from a given point of view. In the vision sciences, it is called the visual angle, and in optics, it is the angular aperture (of a lens). The angular diameter can alternatively be thought of as the angular displacement through which an eye or camera must rotate to look from one side of an apparent circle to the opposite side.

A person can resolve with their naked eyes diameters down to about 1 arcminute (approximately 0.017° or 0.0003 radians). This corresponds to 0.3 m at a 1 km distance, or to perceiving Venus as a disk under optimal conditions.

The Very Large Telescope (VLT) is an astronomical facility operated since 1998 by the European Southern Observatory, located on Cerro Paranal in the Atacama Desert of northern Chile. It consists of four individual telescopes, each equipped with a primary mirror that measures 8.2 metres (27 ft) in diameter. These optical telescopes, named Antu, Kueyen, Melipal, and Yepun (all words for astronomical objects in the Mapuche language), are generally used separately but can be combined to achieve a very high angular resolution. The VLT array is also complemented by four movable Auxiliary Telescopes (ATs) with 1.8-metre (5.9 ft) apertures.

The VLT is capable of observing both visible and infrared wavelengths. Each individual telescope can detect objects that are roughly four billion times fainter than what can be seen with the naked eye. When all the telescopes are combined, the facility can achieve an angular resolution of approximately 0.002 arcsecond. In single telescope mode, the angular resolution is about 0.05 arcseconds.

In astronomy, seeing is the degradation of the image of an astronomical object due to turbulence in the atmosphere of Earth that may become visible as blurring, twinkling or variable distortion. The origin of this effect is rapidly changing variations of the optical refractive index along the light path from the object to the detector.Seeing is a major limitation to the angular resolution in astronomical observations with telescopes that would otherwise be limited through diffraction by the size of the telescope aperture.Today, many large scientific ground-based optical telescopes include adaptive optics to overcome seeing.

The strength of seeing is often characterized by the angular diameter of the long-exposure image of a star (seeing disk) or by the Fried parameter r₀. The diameter of the seeing disk is the full width at half maximum of its optical intensity. An exposure time of several tens of milliseconds can be considered long in this context. The Fried parameter describes the size of an imaginary telescope aperture for which the diffraction limited angular resolution is equal to the resolution limited by seeing. Both the size of the seeing disc and the Fried parameter depend on the optical wavelength, but it is common to specify them for 500 nanometers.A seeing disk smaller than 0.4 arcseconds or a Fried parameter larger than 30 centimeters can be considered excellent seeing. The best conditions are typically found at high-altitude observatories on small islands, such as those at Mauna Kea or La Palma.

The Chandra X-ray Observatory (CXO), previously known as the Advanced X-ray Astrophysics Facility (AXAF), is a Flagship-class space telescope launched aboard the Space Shuttle Columbia during STS-93 by NASA on July 23, 1999. Chandra is sensitive to X-ray sources 100 times fainter than any previous X-ray telescope, enabled by the high angular resolution of its mirrors. Since the Earth's atmosphere absorbs the vast majority of X-rays, they are not detectable from Earth-based telescopes; therefore space-based telescopes are required to make these observations. Chandra is an Earth satellite in a 64-hour orbit, and its mission is ongoing as of 2025. Chandra is one of the Great Observatories, along with the Hubble Space Telescope, Compton Gamma Ray Observatory (1991–2000), and the Spitzer Space Telescope (2003–2020). The telescope is named after the Nobel Prize-winning Indian-American astrophysicist Subrahmanyan Chandrasekhar. Its mission is similar to that of ESA's XMM-Newton spacecraft, also launched in 1999 but the two telescopes have different design foci, as Chandra has a much higher angular resolution and XMM-Newton higher spectroscopy throughput.

In response to a decrease in NASA funding in 2024 by the US Congress, Chandra is threatened with an early cancellation despite having more than a decade of operation left. The cancellation has been referred to as a potential "extinction-level" event for X-ray astronomy in the US. A group of astronomers have put together a public outreach project to try to get enough American citizens to persuade the US Congress to provide enough funding to avoid early termination of the observatory.

Magnification is the process of enlarging the apparent size, not physical size, of something. This enlargement is quantified by a size ratio called optical magnification. When this number is less than one, it refers to a reduction in size, sometimes called de-magnification.

Typically, magnification is related to scaling up visuals or images to be able to see more detail, increasing resolution, using microscope, printing techniques, or digital processing. In all cases, the magnification of the image does not change the perspective of the image.

An electron microscope is a microscope that uses a beam of electrons as a source of illumination. It uses electron optics that are analogous to the glass lenses of an optical light microscope to control the electron beam, for instance focusing it to produce magnified images or electron diffraction patterns. As the wavelength of an electron can be up to 100,000 times smaller than that of visible light, electron microscopes have a much higher resolution of about 0.1 nm, which compares to about 200 nm for light microscopes. Electron microscope may refer to:

• Transmission electron microscope (TEM) where swift electrons go through a thin sample
• Scanning transmission electron microscope (STEM) which is similar to TEM with a scanned electron probe
• Scanning electron microscope (SEM) which is similar to STEM, but with thick samples
• Electron microprobe similar to a SEM, but more for chemical analysis
• Low-energy electron microscope (LEEM), used to image surfaces
• Photoemission electron microscope (PEEM) which is similar to LEEM using electrons emitted from surfaces by photons

Additional details can be found in the above links. This article contains some general information mainly about transmission and scanning electron microscopes.

The Event Horizon Telescope (EHT) is a telescope array consisting of a global network of radio telescopes. The EHT project combines data from several very-long-baseline interferometry (VLBI) stations around Earth, which form a combined array with an angular resolution sufficient to observe objects the size of a supermassive black hole's event horizon. The project's observational targets include the two black holes with the largest angular diameter as observed from Earth: the black hole at the center of the supergiant elliptical galaxy Messier 87, and Sagittarius A*, at the center of the Milky Way.

The Event Horizon Telescope project is an international collaboration that was launched in 2009 after a long period of theoretical and technical developments. On the theory side, work on the photon orbit and first simulations of what a black hole would look like progressed to predictions of VLBI imaging for the Galactic Center black hole, Sgr A*. Technical advances in radio observing moved from the first detection of Sgr A*, through VLBI at progressively shorter wavelengths, ultimately leading to detection of horizon scale structure in both Sgr A* and M87. The collaboration now comprises over 300 members, and 60 institutions, working in over 20 countries and regions.

Radio astronomy is a subfield of astronomy that studies celestial objects using radio waves. It started in 1933, when Karl Jansky at Bell Telephone Laboratories reported radiation coming from the Milky Way. Subsequent observations have identified a number of different sources of radio emission. These include stars and galaxies, as well as entirely new classes of objects, such as radio galaxies, quasars, pulsars, and masers. The discovery of the cosmic microwave background radiation, regarded as evidence for the Big Bang theory, was made through radio astronomy.

Radio astronomy is conducted using large radio antennas referred to as radio telescopes, that are either used alone, or with multiple linked telescopes utilizing the techniques of radio interferometry and aperture synthesis. The use of interferometry allows radio astronomy to achieve high angular resolution, as the resolving power of an interferometer is set by the distance between its components, rather than the size of its components.

In light microscopy, oil immersion is a technique used to increase the resolving power of a microscope. This is achieved by immersing both the objective lens and the specimen in a transparent oil of high refractive index, thereby increasing the numerical aperture of the objective lens.

Without oil, light waves reflect off the slide specimen through the glass cover slip, through the air, and into the microscope lens (see the colored figure to the right). Unless a wave comes out at a 90-degree angle, it bends when it hits a new substance, the amount of bend depending on the angle. This distorts the image. Air has a very different index of refraction from glass, making for a larger bend compared to oil, which has an index more similar to glass. Specially manufactured oil can have nearly exactly the same refractive index as glass, making an oil-immersed lens nearly as effective as having glass entirely around the sample (which would be impractical).

An astronomical interferometer or telescope array is a set of separate telescopes, mirror segments, or radio telescope antennas that work together as a single telescope to provide higher resolution images of astronomical objects such as stars, nebulas and galaxies by means of interferometry. The advantage of this technique is that it can theoretically produce images with the angular resolution of a huge telescope with an aperture equal to the separation, called baseline, between the component telescopes. The main drawback is that it does not collect as much light as the complete instrument's mirror. Thus it is mainly useful for fine resolution of more luminous astronomical objects, such as close binary stars. Another drawback is that the maximum angular size of a detectable emission source is limited by the minimum gap between detectors in the collector array.

Interferometry is most widely used in radio astronomy, in which signals from separate radio telescopes are combined. A mathematical signal processing technique called aperture synthesis is used to combine the separate signals to create high-resolution images. In Very Long Baseline Interferometry (VLBI) radio telescopes separated by thousands of kilometers are combined to form a radio interferometer with a resolution which would be given by a hypothetical single dish with an aperture thousands of kilometers in diameter. At the shorter wavelengths used in infrared astronomy and optical astronomy it is more difficult to combine the light from separate telescopes, because the light must be kept coherent within a fraction of a wavelength over long optical paths, requiring very precise optics. Practical infrared and optical astronomical interferometers have only recently been developed, and are at the cutting edge of astronomical research. At optical wavelengths, aperture synthesis allows the atmospheric seeing resolution limit to be overcome, allowing the angular resolution to reach the diffraction limit of the optics.

In optics, any optical instrument or system – a microscope, telescope, or camera – has a principal limit to its resolution due to the physics of diffraction. An optical instrument is said to be diffraction-limited if it has reached this limit of resolution performance. Other factors may affect an optical system's performance, such as lens imperfections or aberrations, but these are caused by errors in the manufacture or calculation of a lens, whereas the diffraction limit is the maximum resolution possible for a theoretically perfect, or ideal, optical system.

The diffraction-limited angular resolution, in radians, of an instrument is proportional to the wavelength of the light being observed, and inversely proportional to the diameter of its objective's entrance aperture. For telescopes with circular apertures, the size of the smallest feature in an image that is diffraction limited is the size of the Airy disk. As one decreases the size of the aperture of a telescopic lens, diffraction proportionately increases. At small apertures, such as f/22, most modern lenses are limited only by diffraction and not by aberrations or other imperfections in the construction.

The Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) is a Japanese remote sensing instrument onboard the Terra satellite launched by NASA in 1999. It has been collecting data since February 2000.

ASTER provides high-resolution images of Earth in 14 different bands of the electromagnetic spectrum, ranging from visible to thermal infrared light. The resolution of images ranges between 15 and 90 meters. ASTER data is used to create detailed maps of surface temperature of land, emissivity, reflectance, and elevation.

A balloon-borne telescope is a type of airborne telescope, a sub-orbital astronomical telescope that is suspended below one or more stratospheric balloons, allowing it to be lifted above the lower, dense part of the Earth's atmosphere. This has the advantage of improving the resolution limit of the telescope at a much lower cost than for a space telescope. It also allows observation of frequency bands that are blocked by the atmosphere.

Aperture synthesis or synthesis imaging is a type of interferometry that mixes signals from a collection of telescopes to produce images having the same angular resolution as an instrument the size of the entire collection. At each separation and orientation, the lobe-pattern of the interferometer produces an output which is one component of the Fourier transform of the spatial distribution of the brightness of the observed object. The image (or "map") of the source is produced from these measurements. Astronomical interferometers are commonly used for high-resolution optical, infrared, submillimetre and radio astronomy observations. For example, the Event Horizon Telescope project derived the first image of a black hole using aperture synthesis.