Optical resolution describes the ability of an imaging system to resolve detail, in the object that is being imaged.
An imaging system may have many individual components, including one or more lenses, and/or recording and display components. Each of these contributes (given suitable design, and adequate alignment) to the optical resolution of the system; the environment in which the imaging is done often is a further important factor.
Lateral resolution
Resolution depends on the distance between two distinguishable radiating points. The sections below describe the theoretical estimates of resolution, but the real values may differ. The results below are based on mathematical models of
Airy disc
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, ...
s, which assumes an adequate level of contrast. In low-contrast systems, the resolution may be much lower than predicted by the theory outlined below. Real optical systems are complex, and practical difficulties often increase the distance between distinguishable point sources.
The resolution of a system is based on the minimum distance
at which the points can be distinguished as individuals. Several standards are used to determine, quantitatively, whether or not the points can be distinguished. One of the methods specifies that, on the line between the center of one point and the next, the contrast between the maximum and minimum intensity be at least 26% lower than the maximum. This corresponds to the overlap of one Airy disk on the first dark ring in the other. This standard for separation is also known as the
Rayleigh criterion
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. ...
. In symbols, the distance is defined as follows:
where
*
is the minimum distance between resolvable points, in the same units as
is specified
*
is the
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 ...
of light, emission wavelength, in the case of fluorescence,
*
is the index of refraction of the media surrounding the radiating points,
*
is the half angle of the pencil of light that enters the objective, and
*
is the
numerical aperture
This formula is suitable for confocal microscopy, but is also used in traditional microscopy. In
confocal laser-scanned microscopes, the full-width half-maximum (FWHM) of the
point spread function is often used to avoid the difficulty of measuring the Airy disc.
This, combined with the rastered illumination pattern, results in better resolution, but it is still proportional to the Rayleigh-based formula given above.
Also common in the microscopy literature is a formula for resolution that treats the above-mentioned concerns about contrast differently. The resolution predicted by this formula is proportional to the Rayleigh-based formula, differing by about 20%. For estimating theoretical resolution, it may be adequate.
When a condenser is used to illuminate the sample, the shape of the pencil of light emanating from the condenser must also be included.
Molecular Expressions Microscopy Primer: Anatomy of the Microscope - Numerical Aperture and Resolution
/ref>
In a properly configured microscope, .
The above estimates of resolution are specific to the case in which two identical very small samples that radiate incoherently in all directions. Other considerations must be taken into account if the sources radiate at different levels of intensity, are coherent, large, or radiate in non-uniform patterns.
Lens resolution
The ability of 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''), ...
to resolve detail is usually determined by the quality of the lens, but is ultimately limited by 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 ...
. Light coming from a point source
A point source is a single identifiable ''localised'' source of something. A point source has negligible extent, distinguishing it from other source geometries. Sources are called point sources because in mathematical modeling, these sources can ...
in the object diffracts through the lens 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 ...
such that it forms a diffraction pattern in the image, which has a central spot and surrounding bright rings, separated by dark nulls; this pattern is known as an Airy pattern, and the central bright lobe as an Airy disk
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, ...
. The angular radius of the Airy disk (measured from the center to the first null) is given by:
where
*''θ'' is the angular resolution in radians,
*''λ'' is the 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 ...
of light in meters,
*and ''D'' is the diameter
In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord of the circle. Both definitions are also valid for ...
of the lens aperture in meters.
Two adjacent points in the object give rise to two diffraction patterns. If the angular separation of the two points is significantly less than the Airy disk angular radius, then the two points cannot be resolved in the image, but if their angular separation is much greater than this, distinct images of the two points are formed and they can therefore be resolved. Rayleigh defined the somewhat arbitrary "Rayleigh criterion
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. ...
" that two points whose angular separation is equal to the Airy disk radius to first null can be considered to be resolved. It can be seen that the greater the diameter of the lens or its aperture, the greater the resolution. Astronomical telescopes have increasingly large lenses so they can 'see' ever finer detail in the stars.
Only the very highest quality lenses have diffraction limited resolution, however, and normally the quality of the lens limits its ability to resolve detail. This ability is expressed by the Optical Transfer Function
The optical transfer function (OTF) of an optical system such as a camera, microscope, human eye, or projector specifies how different spatial frequencies are captured or transmitted. It is used by optical engineers to describe how the optics pro ...
which describes the spatial (angular) variation of the light signal as a function of spatial (angular) frequency. When the image is projected onto a flat plane, such as photographic film or a solid state detector, spatial frequency is the preferred domain, but when the image is referred to the lens alone, angular frequency is preferred. OTF may be broken down into the magnitude and phase components as follows:
where
*
*
*and are spatial frequency in the x- and y-plane, respectively.
The OTF accounts for aberration, which the limiting frequency expression above does not. The magnitude is known as the Modulation Transfer Function (MTF) and the phase portion is known as the Phase Transfer Function (PTF).
In imaging systems, the phase component is typically not captured by the sensor. Thus, the important measure with respect to imaging systems is the MTF.
Phase is critically important to adaptive optics
Adaptive optics (AO) is a technology used to improve the performance of optical systems by reducing the effect of incoming wavefront distortions by deforming a mirror in order to compensate for the distortion. It is used in astronomical tele ...
and holographic systems.
Sensor resolution (spatial)
Some optical sensors are designed to detect spatial differences in electromagnetic energy
In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of a ...
. These include photographic film
Photographic film is a strip or sheet of transparent film base coated on one side with a gelatin photographic emulsion, emulsion containing microscopically small light-sensitive silver halide crystals. The sizes and other characteristics of th ...
, solid-state devices ( CCD, CMOS detectors, and infrared detectors like PtSi and InSb
Indium antimonide (InSb) is a crystalline compound made from the elements indium (In) and antimony (Sb). It is a narrow- gap semiconductor material from the III- V group used in infrared detectors, including thermal imaging cameras, FLIR systems, ...
), tube detectors (vidicon
Video camera tubes were devices based on the cathode ray tube that were used in television cameras to capture television images, prior to the introduction of charge-coupled device (CCD) image sensors in the 1980s. Several different types of tubes ...
, plumbicon
Video camera tubes were devices based on the cathode ray tube that were used in television cameras to capture television images, prior to the introduction of charge-coupled device (CCD) image sensors in the 1980s. Several different types of tubes ...
, and photomultiplier A photomultiplier is a device that converts incident photons into an electrical signal.
Kinds of photomultiplier include:
* Photomultiplier tube, a vacuum tube converting incident photons into an electric signal. Photomultiplier tubes (PMTs for sh ...
tubes used in night-vision devices), scanning detectors (mainly used for IR), pyroelectric
Pyroelectricity (from the two Greek words ''pyr'' meaning fire, and electricity) is a property of certain crystals which are naturally electrically polarized and as a result contain large electric fields. Pyroelectricity can be described as the a ...
detectors, and microbolometer
A microbolometer is a specific type of bolometer used as a detector in a thermal camera. Infrared radiation with wavelengths between 7.5–14 μm strikes the detector material, heating it, and thus changing its electrical resistance. This resista ...
detectors. The ability of such a detector to resolve those differences depends mostly on the size of the detecting elements.
Spatial resolution is typically expressed in line pairs per millimeter (lppmm), lines (of resolution, mostly for analog video), contrast vs. cycles/mm, or MTF (the modulus of OTF). The MTF may be found by taking 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 spatial sampling function. Smaller pixels result in wider MTF curves and thus better detection of higher frequency energy.
This is analogous to taking the Fourier transform of a signal sampling
In signal processing, a signal is a function that conveys information about a phenomenon. Any quantity that can vary over space or time can be used as a signal to share messages between observers. The ''IEEE Transactions on Signal Processing'' ...
function; as in that case, the dominant factor is the sampling period, which is analogous to the size of the picture element (pixel
In digital imaging, a pixel (abbreviated px), pel, or picture element is the smallest addressable element in a raster image, or the smallest point in an all points addressable display device.
In most digital display devices, pixels are the smal ...
).
Other factors include pixel noise, pixel cross-talk, substrate penetration, and fill factor.
A common problem among non-technicians is the use of the number of pixels on the detector to describe the resolution. If all sensors were the same size, this would be acceptable. Since they are not, the use of the number of pixels can be misleading. For example, a 2-megapixel
In digital imaging, a pixel (abbreviated px), pel, or picture element is the smallest addressable element in a raster image, or the smallest point in an all points addressable display device.
In most digital display devices, pixels are the sm ...
camera of 20-micrometre-square pixels will have worse resolution than a 1-megapixel camera with 8-micrometre pixels, all else being equal.
For resolution measurement, film manufacturers typically publish a plot of Response (%) vs. Spatial Frequency (cycles per millimeter). The plot is derived experimentally. Solid state sensor and camera manufacturers normally publish specifications from which the user may derive a theoretical MTF according to the procedure outlined below. A few may also publish MTF curves, while others (especially intensifier manufacturers) will publish the response (%) at the Nyquist frequency
In signal processing, the Nyquist frequency (or folding frequency), named after Harry Nyquist, is a characteristic of a sampler, which converts a continuous function or signal into a discrete sequence. In units of cycles per second ( Hz), it ...
, or, alternatively, publish the frequency at which the response is 50%.
To find a theoretical MTF curve for a sensor, it is necessary to know three characteristics of the sensor: the active sensing area, the area comprising the sensing area and the interconnection and support structures ("real estate"), and the total number of those areas (the pixel count). The total pixel count is almost always given. Sometimes the overall sensor dimensions are given, from which the real estate area can be calculated. Whether the real estate area is given or derived, if the active pixel area is not given, it may be derived from the real estate area and the fill factor, where fill factor is the ratio of the active area to the dedicated real estate area.
where
* the active area of the pixel has dimensions ''a''×''b''
* the pixel real estate has dimensions ''c''×''d''
In Gaskill's notation, the sensing area is a 2D comb(''x'', ''y'') function of the distance between pixels (the ''pitch''), convolved with a 2D rect(''x'', ''y'') function of the active area of the pixel, bounded by a 2D rect(''x'', ''y'') function of the overall sensor dimension. The Fourier transform of this is a function governed by the distance between pixels, convolved with a function governed by the number of pixels, and multiplied by the function corresponding to the active area. That last function serves as an overall envelope to the MTF function; so long as the number of pixels is much greater than one, then the active area size dominates the MTF.
Sampling function:
where the sensor has ''M''×''N'' pixels
Sensor resolution (temporal)
An imaging system running at 24 frames per second is essentially a discrete sampling system that samples a 2D area. The same limitations described by Nyquist apply to this system as to any signal sampling system.
All sensors have a characteristic time response. Film is limited at both the short resolution and the long resolution extremes by reciprocity breakdown. These are typically held to be anything longer than 1 second and shorter than 1/10,000 second. Furthermore, film requires a mechanical system to advance it through the exposure mechanism, or a moving optical system to expose it. These limit the speed at which successive frames may be exposed.
CCD and CMOS are the modern preferences for video sensors. CCD is speed-limited by the rate at which the charge can be moved from one site to another. CMOS has the advantage of having individually addressable cells, and this has led to its advantage in the high speed photography
High-speed photography is the science of taking pictures of very fast phenomena. In 1948, the Society of Motion Picture and Television Engineers (SMPTE) defined high-speed photography as any set of photographs captured by a camera capable of 69 ...
industry.
Vidicons, Plumbicons, and image intensifiers have specific applications. The speed at which they can be sampled depends upon the decay rate of the phosphor used. For example, the P46 phosphor has a decay time of less than 2 microseconds, while the P43 decay time is on the order of 2-3 milliseconds. The P43 is therefore unusable at frame rates above 1000 frames per second (frame/s). See for links to phosphor information.
Pyroelectric detectors respond to changes in temperature. Therefore, a static scene will not be detected, so they require choppers
Chopper may refer to:
Arts and entertainment
* ''Chopper'' (comics), a horror comic book mini-series
* ''Chopper'' (film), a 2000 Australian film by and about Mark "Chopper" Read
* Chopper (''Judge Dredd''), a character in British comics anth ...
. They also have a decay time, so the pyroelectric system temporal response will be a bandpass, while the other detectors discussed will be a lowpass.
If objects within the scene are in motion relative to the imaging system, the resulting motion blur
Motion blur is the apparent streaking of moving objects in a photograph or a sequence of frames, such as a film or animation. It results when the image being recorded changes during the recording of a single exposure, due to rapid movement or lo ...
will result in lower spatial resolution. Short integration times will minimize the blur, but integration times are limited by sensor sensitivity. Furthermore, motion between frames in motion pictures will impact digital movie compression schemes (e.g. MPEG-1, MPEG-2). Finally, there are sampling schemes that require real or apparent motion inside the camera (scanning mirrors, rolling shutters) that may result in incorrect rendering of image motion. Therefore, sensor sensitivity and other time-related factors will have a direct impact on spatial resolution.
Analog bandwidth effect on resolution
The spatial resolution of digital systems (e.g. HDTV
High-definition television (HD or HDTV) describes a television system which provides a substantially higher image resolution than the previous generation of technologies. The term has been used since 1936; in more recent times, it refers to the g ...
and VGA
Video Graphics Array (VGA) is a video display controller and accompanying de facto graphics standard, first introduced with the IBM PS/2 line of computers in 1987, which became ubiquitous in the PC industry within three years. The term can no ...
) are fixed independently of the analog bandwidth because each pixel is digitized, transmitted, and stored as a discrete value. Digital cameras, recorders, and displays must be selected so that the resolution is identical from camera to display. However, in analog systems, the resolution of the camera, recorder, cabling, amplifiers, transmitters, receivers, and display may all be independent and the overall system resolution is governed by the bandwidth of the lowest performing component.
In analog systems, each horizontal line is transmitted as a high-frequency analog signal. Each picture element (pixel) is therefore converted to an analog electrical value (voltage), and changes in values between pixels therefore become changes in voltage. The transmission standards require that the sampling be done in a fixed time (outlined below), so more pixels per line becomes a requirement for more voltage changes per unit time, i.e. higher frequency. Since such signals are typically band-limited by cables, amplifiers, recorders, transmitters, and receivers, the band-limitation on the analog signal acts as an effective low-pass filter
A low-pass filter is a filter that passes signals with a frequency lower than a selected cutoff frequency and attenuates signals with frequencies higher than the cutoff frequency. The exact frequency response of the filter depends on the filter des ...
on the spatial resolution. The difference in resolutions between VHS (240 discernible lines per scanline), Betamax
Betamax (also known as Beta, as in its logo) is a consumer-level analog recording and cassette format of magnetic tape for video, commonly known as a video cassette recorder. It was developed by Sony and was released in Japan on May 10, 1975, ...
(280 lines), and the newer ED Beta format (500 lines) is explained primarily by the difference in the recording bandwidth.
In the NTSC
The first American standard for analog television broadcast was developed by National Television System Committee (NTSC)National Television System Committee (1951–1953), Report and Reports of Panel No. 11, 11-A, 12–19, with Some supplement ...
transmission standard, each field contains 262.5 lines, and 59.94 fields are transmitted every second. Each line must therefore take 63 microseconds, 10.7 of which are for reset to the next line. Thus, the retrace rate is 15.734 kHz. For the picture to appear to have approximately the same horizontal and vertical resolution (see Kell factor
The Kell factor, named after RCA engineer Raymond D. Kell, is a parameter used to limit the bandwidth of a sampled image signal to avoid the appearance of beat frequency patterns when displaying the image in a discrete display device, usually t ...
), it should be able to display 228 cycles per line, requiring a bandwidth of 4.28 MHz. If the line (sensor) width is known, this may be converted directly into cycles per millimeter, the unit of spatial resolution.
B/G/I/K television system signals (usually used with PAL
Phase Alternating Line (PAL) is a colour encoding system for analogue television. It was one of three major analogue colour television standards, the others being NTSC and SECAM. In most countries it was broadcast at 625 lines, 50 fields (25 ...
colour encoding) transmit frames less often (50 Hz), but the frame contains more lines and is wider, so bandwidth requirements are similar.
Note that a "discernible line" forms one half of a cycle (a cycle requires a dark and a light line), so "228 cycles" and "456 lines" are equivalent measures.
System resolution
There are two methods by which to determine "system resolution" (in the sense that omits the eye, or other final reception of the optical information). The first is to perform a series of two-dimensional convolution
In mathematics (in particular, functional analysis), convolution is a operation (mathematics), mathematical operation on two function (mathematics), functions ( and ) that produces a third function (f*g) that expresses how the shape of one is ...
s, first with the image and the lens, and then, with that procedure's result and a sensor (and so on through all of the components of the system). Not only is this computationally expensive, but normally it also requires repetition of the process, for each additional object that is to be imaged.
The other method is to transform each of the components of the system into the spatial frequency domain, and then to multiply the 2-D results. A system response may be determined without reference to an object. Although this method is considerably more difficult to comprehend conceptually, it becomes easier to use computationally, especially when different design iterations or imaged objects are to be tested.
The transformation to be used is the Fourier transform.
Ocular resolution
The human eye
The human eye is a sensory organ, part of the sensory nervous system, that reacts to visible light and allows humans to use visual information for various purposes including seeing things, keeping balance, and maintaining circadian rhythm.
...
is a limiting feature of many systems, when the goal of the system is to present data to humans for processing.
For example, in a security or air traffic control function, the display and work station must be constructed so that average humans can detect problems and direct corrective measures. Other examples are when a human is using eyes to carry out a critical task such as flying (piloting by visual reference), driving a vehicle, and so forth.
The best visual acuity
Visual acuity (VA) commonly refers to the clarity of vision, but technically rates an examinee's ability to recognize small details with precision. Visual acuity is dependent on optical and neural factors, i.e. (1) the sharpness of the retinal ...
of the human eye at its optical centre (the fovea) is less than 1 arc minute per line pair, reducing rapidly away from the fovea.
The human brain
A brain is an organ that serves as the center of the nervous system in all vertebrate and most invertebrate animals. It is located in the head, usually close to the sensory organs for senses such as vision. It is the most complex organ in a v ...
requires more than just a line pair to understand what the eye is imaging. Johnson's criteria defines the number of line pairs of ocular resolution, or sensor resolution, needed to recognize or identify an item.
Atmospheric resolution
Systems looking through long atmospheric paths may be limited by turbulence
In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to a laminar flow, which occurs when a fluid flows in parallel layers, with no disruption between ...
. A key measure of the quality of atmospheric turbulence is the seeing diameter, also known as Fried's seeing diameter. A path which is temporally coherent is known as an ''isoplanatic'' patch.
Large apertures may suffer from aperture averaging, the result of several paths being integrated into one image.
Turbulence scales with wavelength at approximately a 6/5 power. Thus, seeing is better at infrared wavelengths than at visible wavelengths.
Short exposures suffer from turbulence less than longer exposures due to the "inner" and "outer" scale turbulence; short is considered to be much less than 10 ms for visible imaging (typically, anything less than 2 ms). Inner scale turbulence arises due to the eddies in the turbulent flow, while outer scale turbulence arises from large air mass flow. These masses typically move slowly, and so are reduced by decreasing the integration period.
A system limited only by the quality of the optics is said to be diffraction-limited
The resolution of an optical imaging system a microscope, telescope, or camera can be limited by factors such as imperfections in the lenses or misalignment. However, there is a principal limit to the resolution of any optical system, due to t ...
. However, since atmospheric turbulence is normally the limiting factor for visible systems looking through long atmospheric paths, most systems are turbulence-limited. Corrections can be made by using adaptive optics
Adaptive optics (AO) is a technology used to improve the performance of optical systems by reducing the effect of incoming wavefront distortions by deforming a mirror in order to compensate for the distortion. It is used in astronomical tele ...
or post-processing techniques.
where
* is the spatial frequency
* is the wavelength
*''f'' is the focal length
*''D'' is the aperture diameter
*''b'' is a constant (1 for far-field propagation)
*and is Fried's seeing diameter
Measuring optical resolution
A variety of measurement systems are available, and use may depend upon the system being tested.
Typical test charts for Contrast Transfer Function
The contrast transfer function (CTF) mathematically describes how aberrations in a transmission electron microscope (TEM) modify the image of a sample.Spence, John C. H. (1988 2nd ed) ''Experimental high-resolution electron microscopy'' (Oxford U. ...
(CTF) consist of repeated bar patterns (see Discussion below). The limiting resolution is measured by determining the smallest group of bars, both vertically and horizontally, for which the correct number of bars can be seen. By calculating the contrast between the black and white areas at several different frequencies, however, points of the CTF can be determined with the contrast equation.
where
* is the normalized value of the maximum (for example, the voltage or grey value of the white area)
* is the normalized value of the minimum (for example, the voltage or grey value of the black area)
When the system can no longer resolve the bars, the black and white areas have the same value, so Contrast = 0. At very low spatial frequencies, ''C''max = 1 and ''C''min = 0 so Modulation = 1. Some modulation may be seen above the limiting resolution; these may be aliased and phase-reversed.
When using other methods, including the interferogram, sinusoid, and the edge in the ISO 12233 target, it is possible to compute the entire MTF curve. The response to the edge is similar to a step response
The step response of a system in a given initial state consists of the time evolution of its outputs when its control inputs are Heaviside step functions. In electronic engineering and control theory, step response is the time behaviour of the out ...
, and the Fourier Transform of the first difference of the step response yields the MTF.
Interferogram
An interferogram created between two coherent light sources may be used for at least two resolution-related purposes. The first is to determine the quality of a lens system (see LUPI), and the second is to project a pattern onto a sensor (especially photographic film) to measure resolution.
NBS 1010a/ ISO #2 target
This 5 bar resolution test chart is often used for evaluation of microfilm systems and scanners. It is convenient for a 1:1 range (typically covering 1-18 cycles/mm) and is marked directly in cycles/mm. Details can be found in ISO-3334.
USAF 1951 target
The USAF 1951 resolution test target consists of a pattern of 3 bar targets. Often found covering a range of 0.25 to 228 cycles/mm. Each group consists of six elements. The group is designated by a group number (-2, -1, 0, 1, 2, etc.) which is the power to which 2 should be raised to obtain the spatial frequency of the first element (e.g., group ''-2'' is 0.25 line pairs per millimeter). Each element is the 6th root of 2 smaller than the preceding element in the group (e.g. element 1 is 2^0, element 2 is 2^(-1/6), element 3 is 2(-1/3), etc.). By reading off the group and element number of the first element which cannot be resolved, the limiting resolution may be determined by inspection. The complex numbering system and use of a look-up chart can be avoided by use of an improved but not standardized layout chart, which labels the bars and spaces directly in cycles/mm using OCR-A extended font.
NBS 1952 target
The NBS 1952 target is a 3 bar pattern (long bars). The spatial frequency is printed alongside each triple bar set, so the limiting resolution may be determined by inspection. This frequency is normally only as marked after the chart has been reduced in size (typically 25 times). The original application called for placing the chart at a distance 26 times the focal length of the imaging lens used. The bars above and to the left are in sequence, separated by approximately the square root of two (12, 17, 24, etc.), while the bars below and to the left have the same separation but a different starting point (14, 20, 28, etc.)
EIA 1956 video resolution target
The EIA 1956 resolution chart
The EIA 1956 Resolution Chart (until 1975 called RETMA Resolution Chart 1956) is a test card originally designed in 1956 to be used with black and white analogue TV systems, based on the previous (and very similar) RMA 1946 Resolution Chart. It ...
was specifically designed to be used with television systems. The gradually expanding lines near the center are marked with periodic indications of the corresponding spatial frequency. The limiting resolution may be determined by inspection. The most important measure is the limiting horizontal resolution, since the vertical resolution is typically determined by the applicable video standard (I/B/G/K/NTSC/NTSC-J).
IEEE Std 208-1995 target
The IEEE 208-1995 resolution target is similar to the EIA target. Resolution is measured in horizontal and vertical TV lines.
ISO 12233 target
The ISO 12233 target was developed for digital camera applications, since modern digital camera spatial resolution may exceed the limitations of the older targets. It includes several knife-edge targets for the purpose of computing MTF by 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, ...
. They are offset from the vertical by 5 degrees so that the edges will be sampled in many different phases, which allow estimation of the spatial frequency response beyond the Nyquist frequency
In signal processing, the Nyquist frequency (or folding frequency), named after Harry Nyquist, is a characteristic of a sampler, which converts a continuous function or signal into a discrete sequence. In units of cycles per second ( Hz), it ...
of the sampling.
Random test patterns
The idea is analogous to the use of a white noise
In signal processing, white noise is a random signal having equal intensity at different frequencies, giving it a constant power spectral density. The term is used, with this or similar meanings, in many scientific and technical disciplines, ...
pattern in acoustics to determine system frequency response.
Monotonically increasing sinusoid patterns
The interferogram used to measure film resolution can be synthesized on personal computers and used to generate a pattern for measuring optical resolution. See especially Kodak MTF curves.
Multiburst
A multiburst signal is an electronic waveform used to test analog transmission, recording, and display systems. The test pattern consists of several short periods of specific frequencies. The contrast of each may be measured by inspection and recorded, giving a plot of attenuation vs. frequency. The NTSC3.58 multiburst pattern consists of 500 kHz, 1 MHz, 2 MHz, 3 MHz, and 3.58 MHz blocks. 3.58 MHz is important because it is the chrominance
Chrominance (''chroma'' or ''C'' for short) is the signal used in video systems to convey the color information of the picture (see YUV color model), separately from the accompanying luma signal (or Y' for short). Chrominance is usually represente ...
frequency for NTSC video.
Discussion
Using a bar target that the resulting measure is the contrast transfer function
The contrast transfer function (CTF) mathematically describes how aberrations in a transmission electron microscope (TEM) modify the image of a sample.Spence, John C. H. (1988 2nd ed) ''Experimental high-resolution electron microscopy'' (Oxford U. ...
(CTF) and not the MTF. The difference arises from the subharmonics of the square waves and can be easily computed.
See also
* Angular resolution
* Display resolution
The display resolution or display modes of a digital television, computer monitor or display device is the number of distinct pixels in each dimension that can be displayed. It can be an ambiguous term especially as the displayed resolution is ...
* Image resolution
Image resolution is the detail an image holds. The term applies to digital images, film images, and other types of images. "Higher resolution" means more image detail.
Image resolution can be measured in various ways. Resolution quantifies how ...
, in computing
* Minimum resolvable contrast Minimum resolvable contrast (MRC) is a subjective measure of a visible spectrum sensor’s or camera's sensitivity and ability to resolve data. A snapshot image of a series of three bar targets of selected spatial frequencies and various contrast c ...
* Siemens star
A Siemens star, or spoke target, is a device used to test the resolution of optical instruments, printers, and displays. It consists of a pattern of bright "spokes" on a dark background that radiate from a common center and become wider as they ...
, a pattern used for resolution testing
* Spatial resolution
In physics and geosciences, the term spatial resolution refers to distance between independent measurements, or the physical dimension that represents a pixel of the image. While in some instruments, like cameras and telescopes, spatial resolut ...
* Superlens A superlens, or super lens, is a lens which uses metamaterials to go beyond the diffraction limit. For example, in 1995, Guerra combined a transparent grating having 50nm lines and spaces (the "metamaterial") with a conventional microscope immersio ...
* Superresolution
References
* Gaskill, Jack D. (1978), ''Linear Systems, Fourier Transforms, and Optics'', Wiley-Interscience.
* Goodman, Joseph W. (2004), ''Introduction to Fourier Optics (Third Edition)'', Roberts & Company Publishers.
* Fried, David L. (1966), "Optical resolution through a randomly inhomogeneous medium for very long and very short exposures.", J. Opt. Soc. Amer. 56:1372-9
* Robin, Michael, and Poulin, Michael (2000), ''Digital Television Fundamentals (2nd edition)'', McGraw-Hill Professional.
* Smith, Warren J. (2000), ''Modern Optical Engineering (Third Edition)'', McGraw-Hill Professional.
* Accetta, J. S. and Shumaker, D. L. (1993), ''The Infrared and Electro-optical Systems Handbook'', SPIE/ERIM.
* Roggemann, Michael and Welsh, Byron (1996), ''Imaging Through Turbulence'', CRC Press. {{ISBN, 0-8493-3787-9
* Tatarski, V. I. (1961), ''Wave Propagation in a Turbulent Medium'', McGraw-Hill, NY
External links
Norman Koren's
website - includes several downloadable test patterns
* UC Santa Cruz Prof. Claire Max's lectures and notes fro
Astronomy 289C
Adaptive Optics
* George Ou's re-creation of th
EIA 1956 chart
from a high-resolution scan
Do Sensors “Outresolve” Lenses?
- on lens and sensor resolution interaction
Resolution
Resolution(s) may refer to:
Common meanings
* Resolution (debate), the statement which is debated in policy debate
* Resolution (law), a written motion adopted by a deliberative body
* New Year's resolution, a commitment that an individual mak ...