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:<math>\frac{P Q_e t}{\sqrt{P Q_e t}} = \sqrt{P Q_e t}</math>.
Apart from the quantum efficiency it depends on the incident photon flux and the exposure time, which is equivalent to the [[Exposure (photography)|exposure]] and the sensor area; since the exposure is the integration time multiplied with the image plane [[illuminance]], and illuminance is the [[luminous flux]] per unit area. Thus for equal exposures, the signal to noise ratios of two different size sensors of equal quantum efficiency and pixel count will (for a given final image size) be in proportion to the square root of the sensor area (or the linear scale factor of the sensor). If the exposure is constrained by the need to achieve some required [[depth of field]] (with the same shutter speed) then the exposures will be in inverse relation to the sensor area, producing the interesting result that if depth of field is a constraint, image shot noise is not dependent on sensor area. For identical f-number lenses the signal to noise ratio increases as square root of the pixel area, or linearly with pixel pitch. As typical f-numbers for lenses for cell phones and DSLR are in the same range {{f/|1.5
===Read noise===
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===Dynamic range===
Dynamic range is the ratio of the largest and smallest recordable signal, the smallest being typically defined by the 'noise floor'. In the image sensor literature, the noise floor is taken as the readout noise, so <math> DR = Q_\text{max} / \sigma_\text{readout}</math><ref>{{cite
== Sensor size and diffraction ==
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In considering the effect of sensor size, and its effect on the final image, the different magnification required to obtain the same size image for viewing must be accounted for, resulting in an additional scale factor of <math>1/{C}</math> where <math>{C}</math> is the relative crop factor, making the overall scale factor <math>1 / (N C)</math>. Considering the three cases above:
For the 'same picture' conditions, same angle of view, subject distance and depth of field, then the
In both the 'same photometric exposure' and 'same lens' conditions, the
== Sensor format and lens size ==
It might be expected that lenses appropriate for a range of sensor sizes could be produced by simply scaling the same designs in proportion to the crop factor.<ref>{{cite journal|last=Ozaktas|first=Haldun M|author2=Urey, Hakan|author3=Lohmann, Adolf W.|title=Scaling of diffractive and refractive lenses for optical computing and interconnections|journal=Applied Optics|year=1994|volume=33|issue=17|pages=3782–3789|doi=10.1364/AO.33.003782|pmid=20885771|bibcode=1994ApOpt..33.3782O|hdl=11693/13640|s2cid=1384331 |hdl-access=free}}</ref> Such an exercise would in theory produce a lens with the same
In summary, as sensor size reduces, the accompanying lens designs will change, often quite radically, to take advantage of manufacturing techniques made available due to the reduced size. The functionality of such lenses can also take advantage of these, with extreme zoom ranges becoming possible. These lenses are often very large in relation to sensor size, but with a small sensor can be fitted into a compact package.
Small body means small lens and means small sensor, so to keep [[smartphone]]s slim and light, the smartphone manufacturers use a tiny sensor usually less than the 1/2.3" used in most [[bridge camera]]s. At one time only [[Nokia 808 PureView]] used a 1/1.2" sensor, almost
== Active area of the sensor ==
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== Sensor size and shading effects ==
Semiconductor image sensors can suffer from shading effects at large apertures and at the periphery of the image field, due to the geometry of the light cone projected from the exit pupil of the lens to a point, or pixel, on the sensor surface. The effects are discussed in detail by Catrysse and Wandell.<ref name=Catrysse>{{cite book|last=Catrysse |first=Peter B. |author2=Wandell, Brian A. |editor-first1=Nitin |editor-first2=Jeffrey M. |editor-first3=Ricardo J. |editor-last1=Sampat |editor-last2=Dicarlo |editor-last3=Motta |title=Digital Photography |chapter=Roadmap for CMOS image sensors: Moore meets Planck and Sommerfeld |volume=5678 |issue=1 |pages=1 |doi=10.1117/12.592483 |year=2005 |chapter-url=http://www.imageval.com/public/Papers/EI%205678-01%20Peter%20Catrysse.pdf |access-date=29 January 2012 |url-status=dead |archive-url=https://web.archive.org/web/20150113004959/http://www.imageval.com/public/Papers/EI%205678-01%20Peter%20Catrysse.pdf |archive-date=13 January 2015 |bibcode=2005SPIE.5678....1C |citeseerx=10.1.1.80.1320 |s2cid=7068027 }}</ref>
In the context of this discussion the most important result from the above is that to ensure a full transfer of light energy between two coupled optical systems such as the lens' exit pupil to a pixel's photoreceptor the [[Etendue|geometrical extent]] (also known as etendue or light throughput) of the objective lens / pixel system must be smaller than or equal to the geometrical extent of the microlens / photoreceptor system. The geometrical extent of the objective lens / pixel system is given by
where {{math|
where {{math|''w''<sub>photoreceptor</sub>}} is the width of the photoreceptor and {{math|(''f''/#)<sub>microlens</sub>}} is the f-number of the microlens.
<math display="block"> {(f/\#)}_\mathrm{microlens} \le {(f/\#)}_\mathrm{objective} \times \mathit{ff}\,.</math>
Thus if shading is to be avoided the f-number of the microlens must be smaller than the f-number of the taking lens by at least a factor equal to the linear fill factor of the pixel. The f-number of the microlens is determined ultimately by the width of the pixel and its height above the silicon, which determines its focal length. In turn, this is determined by the height of the metallisation layers, also known as the 'stack height'. For a given stack height, the f-number of the microlenses will increase as pixel size reduces, and thus the objective lens f-number at which shading occurs will tend to increase.
▲:<math> G_\mathrm{pixel} \simeq \frac{w_\mathrm{photoreceptor}}{2{(f/\#)}_\mathrm{microlens}} </math>,
In order to maintain pixel counts smaller sensors will tend to have smaller pixels, while at the same time smaller objective lens f-numbers are required to maximise the amount of light projected on the sensor. To combat the effect discussed above, smaller format pixels include engineering design features to allow the reduction in f-number of their microlenses. These may include simplified pixel designs which require less metallisation, 'light pipes' built within the pixel to bring its apparent surface closer to the microlens and '[[Back-illuminated sensor|back side illumination]]' in which the wafer is thinned to expose the rear of the photodetectors and the microlens layer is placed directly on that surface, rather than the front side with its wiring layers.
▲where {{math|<var>w<sub>photoreceptor</sub></var>}} is the width of the photoreceptor and {{math|<var>(f/#)<sub>microlens</sub></var>}} is the f-number of the microlens.
▲:<math> G_\mathrm{pixel} \ge G_\mathrm{objective}</math>, therefore <math> \frac{w_\mathrm{photoreceptor}}{{(f/\#)}_\mathrm{microlens}} \ge \frac{w_\mathrm{pixel}}{{(f/\#)}_\mathrm{objective}}</math>
▲:<math> {(f/\#)}_\mathrm{microlens} \le {(f/\#)}_\mathrm{objective} \times \mathit{ff}</math>
▲Thus if shading is to be avoided the f-number of the microlens must be smaller than the f-number of the taking lens by at least a factor equal to the linear fill factor of the pixel. The f-number of the microlens is determined ultimately by the width of the pixel and its height above the silicon, which determines its focal length. In turn, this is determined by the height of the metallisation layers, also known as the 'stack height'. For a given stack height, the f-number of the microlenses will increase as pixel size reduces, and thus the objective lens f-number at which shading occurs will tend to increase. This effect has been observed in practice, as recorded in the DxOmark article 'F-stop blues'<ref>{{cite web|last=DxOmark|title=F-stop blues|url=http://www.dxomark.com/index.php/Publications/DxOMark-Insights/F-stop-blues|work=DxOMark Insights|access-date=29 January 2012}}</ref>
▲In order to maintain pixel counts smaller sensors will tend to have smaller pixels, while at the same time smaller objective lens f-numbers are required to maximise the amount of light projected on the sensor. To combat the effect discussed above, smaller format pixels include engineering design features to allow the reduction in f-number of their microlenses. These may include simplified pixel designs which require less metallisation, 'light pipes' built within the pixel to bring its apparent surface closer to the microlens and '[[Back-illuminated sensor|back side illumination]]' in which the wafer is thinned to expose the rear of the photodetectors and the microlens layer is placed directly on that surface, rather than the front side with its wiring layers. The relative effectiveness of these stratagems is discussed by [[Aptina]] in some detail.<ref>{{cite web|last=Aptina Imaging Corporation|title=An Objective Look at FSI and BSI|url=http://www.eetrend.com/files-eetrend/newproduct/201101/100029156-17249-fsi-bsi-whitepaper.pdf|work=Aptina Technology White Paper|access-date=29 January 2012}}</ref>
==Common image sensor formats==
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Some professional DSLRs, [[Sony SLT camera|SLTs]] and [[mirrorless camera]]s use ''[[full-frame DSLR|full-frame]]'' sensors, equivalent to the size of a frame of 35 mm film.
Most consumer-level DSLRs, SLTs and mirrorless cameras use relatively large sensors, either somewhat under the size of a frame of [[Advanced Photo System|APS]]-C film, with a [[crop factor]] of 1.5–1.6; or 30% smaller than that, with a crop factor of 2.0 (this is the [[Four Thirds System]], adopted by [[
{{As of|2013|11}}, there
Many different terms are used in marketing to describe DSLR/SLT/mirrorless sensor formats, including the following:
* {{val|860
*
*
*
Obsolescent and out-of-production sensor sizes include:
* {{val|548
* {{val|548
* {{val|548|u=mm2}} area [[APS-H]] format for the high-end mirrorless SD Quattro H from [[Sigma Corporation|Sigma]] (crop factor 1.35)
* {{val|370|u=mm2}} area APS-C crop factor 1.5 format from [[Epson R-D1|Epson]], [[Samsung]] NX, [[Konica Minolta]].
* {{val|286 * {{val|225
* {{val|116
*
* {{val|30|u=mm2}} area 1/2.3" original [[Pentax Q]] (5.6 crop factor). ''Current Q-series cameras have a crop factor of 4.55.''
When [[full-frame digital SLR|full-frame]] sensors were first introduced, production costs could exceed twenty times the cost of an APS-C sensor. Only twenty full-frame sensors can be produced on an {{convert|8|in|cm}} [[silicon wafer]], which would fit 100 or more APS-C sensors, and there is a significant reduction in [[Semiconductor device fabrication|yield]] due to the large area for contaminants per component. Additionally, full frame sensor fabrication originally required three separate exposures during each step of the [[photolithography]] process, which requires separate masks and quality control steps. Canon selected the intermediate [[APS-H]] size, since it was at the time the largest that could be patterned with a single mask, helping to control production costs and manage yields.<ref name=canon-wp>{{cite press release
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Most sensors are made for camera phones, compact digital cameras, and bridge cameras. Most image sensors equipping compact cameras have an [[aspect ratio (image)|aspect ratio]] of 4:3. This matches the aspect ratio of the popular [[SVGA]], [[XGA]], and [[SXGA]] display resolutions at the time of the first digital cameras, allowing images to be displayed on usual [[computer monitor|monitor]]s without cropping.
{{As of|2010|12}} most compact digital cameras used small 1/2.3" sensors. Such cameras include Canon
As of 2018 high-end compact cameras using one inch sensors that have nearly four times the area of those equipping common compacts include Canon PowerShot G-series (G3 X to G9 X), Sony DSC
[[File:Sensor sizes area.svg|thumb|400px|right|For many years until Sep. 2011 a gap existed between compact digital and DSLR camera sensor sizes. The x axis is a discrete set of sensor format sizes used in digital cameras, not a linear measurement axis.]] Finally, Sony has the DSC-RX1 and DSC-RX1R cameras in their lineup, which have a full-frame sensor usually only used in professional DSLRs, SLTs and MILCs.
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Due to the size constraints of powerful zoom objectives, most current [[bridge camera]]s have 1/2.3" sensors, as small as those used in common more compact cameras. As lens sizes are proportional to the image sensor size, smaller sensors enable large zoom amounts with moderate size lenses. In 2011 the high-end [[Fujifilm X-S1]] was equipped with a much larger 2/3" sensor. In 2013–2014, both Sony ([[Cyber-shot DSC-RX10]]) and Panasonic ([[Lumix DMC-FZ1000]]) produced bridge cameras with 1" sensors.
=== Medium-format digital sensors ===
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}}</ref> later models of the 645 series kept the same sensor size but replaced the CCD with a CMOS sensor. In 2016, [[Hasselblad]] announced the X1D, a 50MP medium-format [[Mirrorless interchangeable-lens camera|mirrorless]] camera, with a {{convert|44|x|33|mm|abbr=on}} CMOS sensor.<ref>{{cite web|url=http://www.dpreview.com/news/1988725790/medium-format-mirrorless-hasselblad-unveils-x1d |title=Medium-format mirrorless: Hasselblad unveils X1D |first=Allison |last=Johnson |publisher=[[Digital Photography Review]] |date=2016-06-22 |access-date=2016-06-26}}</ref>
In late 2016, [[Fujifilm]] also announced its new [[Fujifilm GFX 50S]] medium format, [[Mirrorless interchangeable-lens camera|mirrorless]] entry into the market, with a {{convert|43.8|x|32.9|mm|abbr=on}} CMOS sensor and 51.4MP.
<ref>{{cite press release | title=Fujifilm announces development of new medium format "GFX" mirroless camera system | publisher
<ref>{{cite web | title = Fujifilm's Medium Format GFX 50S to Ship in February for $6,500 | url = https://petapixel.com/2017/01/19/fujifilms-medium-format-gfx-50s-ship-february-6500 | date = 2017-01-19}}</ref>
=== {{anchor|Table of sensor sizes}}Table of sensor formats and sizes ===
[[File:Ov6920-01.jpg|thumb|Different
Sensor sizes are expressed in inches notation because at the time of the popularization of digital image sensors they were used to replace [[video camera tube]]s. The common 1" outside diameter circular video camera tubes have a rectangular photo sensitive area about {{val|16|u=mm}} on the diagonal, so a digital sensor with a {{val|16|u=mm}} diagonal size is a 1" video tube equivalent. The name of a 1" digital sensor should more accurately be read as "one inch video camera tube equivalent" sensor. Current digital image sensor size descriptors are the video camera tube equivalency size, not the actual size of the sensor. For example, a 1" sensor has a diagonal measurement of {{val|16|u=mm}}.<ref>{{cite web|title=Making (some) sense out of sensor sizes|url=http://www.dpreview.com/news/2002/10/7/sensorsizes|work=Digital Photography Review|access-date=29 June 2012|author=Staff|date=7 October 2002}}</ref><ref>{{cite web|title=Image Sensor Format |url=http://www.spotimaging.com/resources/glossary/image-sensor-format.php |archive-url=https://web.archive.org/web/20150326051941/http://www.spotimaging.com/resources/glossary/image-sensor-format.php |url-status=dead |archive-date=26 March 2015 |work=Imaging Glossary Terms and Definitions |publisher=SPOT IMAGING SOLUTIONS |access-date=3 June 2015 |author=Staff }}</ref>
[[File:Apple and Samsung image sensor sizes.png|alt=The increasing image sensor sizes used in smartphones plotted|thumb|The development of different format image sensors in the main cameras of smartphones]]
Sizes are often expressed as a fraction of an inch, with a one in the numerator, and a decimal number in the denominator. For example, 1/2.5 converts to 2/5 as a [[Fraction (mathematics)#Simple fraction|simple fraction]], or 0.4 as a decimal number. This "inch" system gives a result approximately 1.5 times the length of the diagonal of the sensor. This "[[optical format]]" measure goes back to the way image sizes of video cameras used until the late 1980s were expressed, referring to the outside diameter of the glass envelope of the [[video camera tube]]. [[David Pogue]] of ''The New York Times'' states that "the actual sensor size is much smaller than what the camera companies publish – about one-third smaller." For example, a camera advertising a 1/2.7" sensor does not have a sensor with a diagonal of {{cvt|0.37|in|mm}}; instead, the diagonal is closer to {{cvt|0.26|in|mm}}.<ref>{{cite news| url=https://www.nytimes.com/2010/12/23/technology/personaltech/23pogue.html?ref=technology | work=The New York Times | first=David | last=Pogue | title=Small Cameras With Big Sensors, and How to Compare Them | date=2010-12-22}}</ref><ref name="dpreview-sensor-sizes" /><ref>{{Cite web|url=http://www.dpreview.com/articles/8095816568/sensorsizes|title=Making (Some) sense out of sensor sizes}}</ref> Instead of "formats", these sensor sizes are often called ''types'', as in "1/2-inch-type CCD."
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|archive-url=https://web.archive.org/web/20130125090640/http://www.dpreview.com/glossary/camera-system/sensor-sizes
|archive-date=2013-01-25
}}</ref> <!-- Every word or number of the following two sentences is VERY carefully selected. PLEASE see talk page, think twice about the physics of optics before you change anything. Thank you very much. -->The listed sensor areas span more than a factor of 1000 and are [[Proportionality (mathematics)|proportional]] to the maximum possible collection of light and [[image resolution]] (same [[lens speed]], i.e., minimum [[
<!-- To recompute these with Scientific Python:
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-->
{{sticky header}}
{| class="wikitable sortable sticky-header plainrowheaders" style="text-align: center;"
|+ Sensor format types and dimensions
|-
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! scope="col" | Aspect Ratio
! scope="col" | Area (mm{{sup|2}})
! scope="col" | [[
! scope="col" | [[Crop factor]]
|-
! scope="row" | 1/10"
|1.60||1.28||0.96||4:3||1.23||{{val|-9.46}}||27.04
|-
! scope="row" | 1/8" (Sony DCR-SR68, DCR-DVD110E)
|2.00||1.60||1.20||4:3||1.92||{{val|-8.81}}||21.65
|-
Line 338 ⟶ 332:
|9.50||7.60||5.70||4:3||43.30||{{val|-4.32}}||4.55
|-
! scope="row" | 1/1.6" ([[F200EXR|Fujifilm
|10.07||8.08||6.01||4:3||48.56||{{val|-4.15}}||4.30
|-
Line 368 ⟶ 362:
|14.54||12.52||7.41||5:3||92.80||{{val|-3.22}}||2.97
|-
! scope="row" | 1" ([[Nikon CX format|Nikon CX]], [[Sony RX100]], [[RX10|Sony RX10]], [[
|15.86||13.20||8.80||3:2||116||{{val|-2.89}}||2.72
|-
! scope="row" | 1" [[Digital Bolex]] d16
|16.00||12.80||9.60||4:3||123||{{val|-2.81}}||2.70
|-
! scope="row" | 1" [[Kodak DCS]]-200
|16.81||14.00||9.30||3:2||130.2||{{val|-2.73}}||2.57
|-
! scope="row" | 1.1" Sony IMX253<ref name="Sony-IMX253">{{cite web
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|34.50||30.7||15.8||35:18||485.06||{{val|-0.83}}||1.25
|-scope=row style="background:#ddd;"
! scope="row" style="background:#ddd;" | '''[[Full-frame digital SLR|35 mm film full-frame]]
|43.1–43.3||35.8–36||23.9–24||3:2||856–864||
|-
! scope="row" | [[Arri Alexa|ARRI ALEXA]] LF
|44.71||36.70||25.54||13:9||937.32||
|-
! scope="row" | [[Red Digital Cinema Camera Company|RED]]
|46.31||40.96||21.60||17:9||884.74||
|-
! scope="row" | [[Leica
|54||45||30||3:2||1350||
|-
! scope="row" | [[Pentax 645D]], Hasselblad X1D-50c, Hasselblad H6D-50c, CFV-50c,
{{cite web
|url=https://cdn.hasselblad.com/datasheets/x1d-II-50c/x1D-ii-50c-data-sheet.pdf
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|date=2019-06-01
|access-date=2022-04-09}}
</ref>
{{cite web
|url=https://fujifilm-x.com/global/products/cameras/gfx-50s/specifications/
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|date= January 17, 2019
|access-date=2022-04-09}}</ref>
|55||43.8||32.9||4:3||1452||
|-
! scope="row" | [[70 mm film#Technical specifications|''Standard 65/70 mm'']]'' film frame''
|57.30||52.48||23.01||7:3||1208||
|-
! scope="row" | [[Arri Alexa|ARRI ALEXA]] 65
|59.86||54.12||25.58||19:9||1384.39||
|-
! scope="row" | Kodak KAF 39000 CCD<ref>{{Citation
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| access-date=2014-02-09
| url = http://www.kodak.com/ek/uploadedFiles/Content/Small_Business/Images_Sensor_Solutions/Datasheets(pdfs)/KAF-39000LongSpec.pdf}}</ref>
| 61.30 || 49 || 36.80 || 4:3 || 1803 ||
|-
! scope="row" | Leaf AFi 10
| 66.57 || 56 || 36 || 14:9 || 2016 ||
|-
! scope="row" | [[Medium format (film)|Medium-format]] ([[Hasselblad]] H5D-60c, Hasselblad H6D-100c)<ref>{{Citation
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| access-date=2013-06-19
| url = http://www.bhphotovideo.com/c/product/893195-REG/Hasselblad_H5D_60_DSLR_Camera_With.html}}</ref>
| 67.08 || 53.7 || 40.2 || 4:3 || 2159 ||
|-
! scope="row" | Phase One [[Phase One (company)|P 65+]], IQ160, IQ180
| 67.40 || 53.90 || 40.40 || 4:3 || 2178 ||
|-
! scope="row" | Medium-format 6×4.5 cm (also called ''645 format'')
| 70 || 42 || 56 || 3:4 || 2352 ||
|-
! scope="row" | Medium-format 6×6 cm
| 79 || 56 || 56 || 1:1|| 3136 ||
|-
! scope="row" | [[70 mm film#IMAX .2815.2F70.29|''IMAX'']]'' film frame''
|87.91||70.41||52.63||4:3||3706||
|-
! scope="row" | Medium-format 6×7 cm
| 89.6 || 70 || 56 || 5:4 || 3920 ||
|-
! scope="row" | Medium-format 6×8 cm
| 94.4 || 76 || 56 || 3:4 || 4256 ||
|-
! scope="row" | Medium-format 6×9 cm
| 101 || 84 || 56 || 3:2 || 4704 ||
|-
! scope="row" | Large-format film 4×5 inch
| 150 || 121 || 97 || 5:4 || 11737 ||
|-
! scope="row" | Large-format film 5×7 inch
| 210 || 178 || 127 || 7:5 || 22606 ||
|-
! scope="row" | Large-format film 8×10 inch
| 300 || 254 || 203 || 5:4 || 51562 ||
|}
{{notelist-ua}}
==See also==
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* [[Field of view]]
==Notes
{{notelist}}
==Footnotes and references==
{{Reflist|30em}}
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