Focus (optics)

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Eye focusing ideally collects all light rays from a point on an object into a corresponding point on the retina. Focusing on retina.svg
Eye focusing ideally collects all light rays from a point on an object into a corresponding point on the retina.
A demonstration of camera focus on different distances, showing a bamboo rooftop FocusDemonstration-BambooRooftop.jpg
A demonstration of camera focus on different distances, showing a bamboo rooftop
Text on a page that is partially in focus, but mostly not in varying degrees DOF-ShallowDepthofField.jpg
Text on a page that is partially in focus, but mostly not in varying degrees

In geometrical optics, a focus, also called an image point, is a point where light rays originating from a point on the object converge. [1] Although the focus is conceptually a point, physically the focus has a spatial extent, called the blur circle. This non-ideal focusing may be caused by aberrations of the imaging optics. Even in the absence of aberrations, the smallest possible blur circle is the Airy disc caused by diffraction from the optical system's aperture; the diffraction is the ultimate limit in the light focus ability of any optical system. Aberrations tend to worsen as the aperture diameter increases, while the Airy circle is smallest for large apertures.

An image, or image point or region, is in focus if light from object points is converged almost as much as possible in the image, and out of focus if light is not well converged. The border between these is sometimes defined using a "circle of confusion" criterion.

A principal focus or focal point is a special focus:

Diverging (negative) lenses and convex mirrors do not focus a collimated beam to a point. Instead, the focus is the point from which the light appears to be emanating, after it travels through the lens or reflects from the mirror. A convex parabolic mirror will reflect a beam of collimated light to make it appear as if it were radiating from the focal point, or conversely, reflect rays directed toward the focus as a collimated beam. A convex elliptical mirror will reflect light directed towards one focus as if it were radiating from the other focus, both of which are behind the mirror. A convex hyperbolic mirror will reflect rays emanating from the focal point in front of the mirror as if they were emanating from the focal point behind the mirror. Conversely, it can focus rays directed at the focal point that is behind the mirror towards the focal point that is in front of the mirror as in a Cassegrain telescope.

See also

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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), usually arranged along a common axis. Lenses are made from materials such as glass or plastic and are ground, polished, or molded to the required shape. A lens can focus light to form an image, unlike a prism, which refracts light without focusing. Devices that similarly focus or disperse waves and radiation other than visible light are also called "lenses", such as microwave lenses, electron lenses, acoustic lenses, or explosive lenses.

<span class="mw-page-title-main">Optics</span> Branch of physics that studies light

Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviolet, and infrared light. Light is a type of electromagnetic radiation, and other forms of electromagnetic radiation such as X-rays, microwaves, and radio waves exhibit similar properties.

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 focal length indicates that the system diverges light. A system with a shorter focal length bends the rays more sharply, bringing them to a focus in a shorter distance or diverging them more quickly. For the special case of a thin lens in air, a positive focal length is the distance over which initially collimated (parallel) rays are brought to a focus, or alternatively a negative focal length indicates how far in front of the lens a point source must be located to form a collimated beam. For more general optical systems, the focal length has no intuitive meaning; it is simply the inverse of the system's optical power.

<span class="mw-page-title-main">Circle of confusion</span> Blurry region in optics

In optics, a circle of confusion (CoC) is an optical spot caused by a cone of light rays from a lens not coming to a perfect focus when imaging a point source. It is also known as disk of confusion, circle of indistinctness, blur circle, or blur spot.

<span class="mw-page-title-main">Parabolic reflector</span> Reflector that has the shape of a paraboloid

A parabolicreflector is a reflective surface used to collect or project energy such as light, sound, or radio waves. Its shape is part of a circular paraboloid, that is, the surface generated by a parabola revolving around its axis. The parabolic reflector transforms an incoming plane wave travelling along the axis into a spherical wave converging toward the focus. Conversely, a spherical wave generated by a point source placed in the focus is reflected into a plane wave propagating as a collimated beam along the axis.

<span class="mw-page-title-main">Angular resolution</span> Ability of any image-forming device to distinguish small details of an object

Angular 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, thereby making it a major determinant of image resolution. It is used in optics applied to light waves, in antenna theory applied to radio waves, and in acoustics applied to sound waves. The colloquial use of the term "resolution" sometimes causes confusion; when an optical system is said to have a high resolution or high angular resolution, it means that the perceived distance, or actual angular distance, between resolved neighboring objects is small. The value that quantifies this property, θ, which is given by the Rayleigh criterion, is low for a system with a high resolution. The closely related term spatial resolution refers to the precision of a measurement with respect to space, which is directly connected to angular resolution in imaging instruments. The Rayleigh criterion shows that the minimum angular spread that can be resolved by an image-forming system is limited by diffraction to the ratio of the wavelength of the waves to the aperture width. For this reason, high-resolution imaging systems such as astronomical telescopes, long distance telephoto camera lenses and radio telescopes have large apertures.

<span class="mw-page-title-main">Optical telescope</span> Telescope for observations with visible light

An optical telescope is a telescope that gathers and focuses light mainly from the visible part of the electromagnetic spectrum, to create a magnified image for direct visual inspection, to make a photograph, or to collect data through electronic image sensors.

<span class="mw-page-title-main">Reflecting telescope</span> Telescopes which utilize curved mirrors to form an image

A reflecting telescope is a telescope that uses a single or a combination of curved mirrors that reflect light and form an image. The reflecting telescope was invented in the 17th century by Isaac Newton as an alternative to the refracting telescope which, at that time, was a design that suffered from severe chromatic aberration. Although reflecting telescopes produce other types of optical aberrations, it is a design that allows for very large diameter objectives. Almost all of the major telescopes used in astronomy research are reflectors. Many variant forms are in use and some employ extra optical elements to improve image quality or place the image in a mechanically advantageous position. Since reflecting telescopes use mirrors, the design is sometimes referred to as a catoptric telescope.

Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light. Because light is an electromagnetic wave, other forms of electromagnetic radiation such as X-rays, microwaves, and radio waves exhibit similar properties.

<span class="mw-page-title-main">Diffraction-limited system</span> Optical system with resolution performance at the instruments theoretical limit

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.

<span class="mw-page-title-main">Newtonian telescope</span> Type of reflecting telescope

The Newtonian telescope, also called the Newtonian reflector or just a Newtonian, is a type of reflecting telescope invented by the English scientist Sir Isaac Newton, using a concave primary mirror and a flat diagonal secondary mirror. Newton's first reflecting telescope was completed in 1668 and is the earliest known functional reflecting telescope. The Newtonian telescope's simple design has made it very popular with amateur telescope makers.

<span class="mw-page-title-main">Airy disk</span> Diffraction pattern in optics

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. The Airy disk is of importance in physics, optics, and astronomy.

<span class="mw-page-title-main">Cassegrain reflector</span> Combination of concave and convex mirrors

The Cassegrain reflector is a combination of a primary concave mirror and a secondary convex mirror, often used in optical telescopes and radio antennas, the main characteristic being that the optical path folds back onto itself, relative to the optical system's primary mirror entrance aperture. This design puts the focal point at a convenient location behind the primary mirror and the convex secondary adds a telephoto effect creating a much longer focal length in a mechanically short system.

<span class="mw-page-title-main">Spatial filter</span>

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, typically coherent laser light. 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 itself. This filtering can be applied to transmit a pure transverse mode from a multimode laser while blocking other modes emitted from the optical resonator. 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.

X-ray optics is the branch of optics that manipulates X-rays instead of visible light. It deals with focusing and other ways of manipulating the X-ray beams for research techniques such as X-ray diffraction, X-ray crystallography, X-ray fluorescence, small-angle X-ray scattering, X-ray microscopy, X-ray phase-contrast imaging, and X-ray astronomy.

Autocollimation is an optical setup where a collimated beam leaves an optical system and is reflected back into the same system by a plane mirror.

<span class="mw-page-title-main">Curved mirror</span> Mirror with a curved reflecting surface

A curved mirror is a mirror with a curved reflecting surface. The surface may be either convex or concave. Most curved mirrors have surfaces that are shaped like part of a sphere, but other shapes are sometimes used in optical devices. The most common non-spherical type are parabolic reflectors, found in optical devices such as reflecting telescopes that need to image distant objects, since spherical mirror systems, like spherical lenses, suffer from spherical aberration. Distorting mirrors are used for entertainment. They have convex and concave regions that produce deliberately distorted images. They also provide highly magnified or highly diminished (smaller) images when the object is placed at certain distances.

<span class="mw-page-title-main">Vergence (optics)</span> Angle between converging or diverging light rays

In optics, vergence is the angle formed by rays of light that are not perfectly parallel to one another. Rays that move closer to the optical axis as they propagate are said to be converging, while rays that move away from the axis are diverging. These imaginary rays are always perpendicular to the wavefront of the light, thus the vergence of the light is directly related to the radii of curvature of the wavefronts. A convex lens or concave mirror will cause parallel rays to focus, converging toward a point. Beyond that focal point, the rays diverge. Conversely, a concave lens or convex mirror will cause parallel rays to diverge.

<span class="mw-page-title-main">Ball lens</span> Spherical lens

A ball lens is an optical lens in the shape of a sphere. Formally, it is a bi-convex spherical lens with the same radius of curvature on both sides, and diameter equal to twice the radius of curvature. The same optical laws may be applied to analyze its imaging characteristics as for other lenses.

References

  1. "Standard Microscopy Terminology". University of Minnesota Characterization Facility website. Archived from the original on 2008-03-02. Retrieved 2006-04-21.