Image sensor format: Difference between revisions

Revision as of 14:18, 19 February 2024

Revision as of 02:25, 1 March 2024

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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-f/|2}} it is interesting to compare performance of cameras with small and big sensors. A good cell phone camera with typical pixel size 1.1 μm (Samsung A8) would have about 3 times worse SNR due to shot noise than a 3.7 μm pixel interchangeable lens camera (Panasonic G85) and 5 times worse than a 6 μm full frame camera (Sony A7 III). Taking into consideration the dynamic range makes the difference even more prominent. As such the trend of increasing the number of "megapixels" in cell phone cameras during last 10 years was caused rather by marketing strategy to sell "more megapixels" than by attempts to improve image quality.

===Read noise===

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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 Ff-numbers are in the ratio <math>1/C</math>, so the scale factor for the diffraction MTF is 1, leading to the conclusion that the diffraction MTF at a given depth of field is independent of sensor size.

In both the 'same photometric exposure' and 'same lens' conditions, the Ff-number is not changed, and thus the spatial cutoff and resultant MTF on the sensor is unchanged, leaving the MTF in the viewed image to be scaled as the magnification, or inversely as the crop factor.

== 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 Ff-number and angle of view, with a size proportional to the sensor crop factor. In practice, simple scaling of lens designs is not always achievable, due to factors such as the non-scalability of [[manufacturing tolerance]], structural integrity of glass lenses of different sizes and available manufacturing techniques and costs. Moreover, to maintain the same absolute amount of information in an image (which can be measured as the [[space-bandwidth product]]<ref>{{cite book|last=Goodman|first=Joseph W|title=Introduction to Fourier optics, 3rd edition|year=2005|publisher=Roberts and Company|___location=Greenwood Village, Colorado|isbn=978-0-9747077-2-3|pages=26}}</ref>) the lens for a smaller sensor requires a greater resolving power. The development of the '[[Tessar]]' lens is discussed by Nasse,<ref>{{cite web|last=Nasse |first=H. H. |title=From the Series of Articles on Lens Names: Tessar |url=http://www.zeiss.com/C12578620052CA69/0/58D501E36518AFC9C12578D2004104E1/$file/cln_39_en_tessar.pdf |publisher=Carl Zeiss AG. |access-date=19 December 2011 |url-status=dead |archive-url=https://web.archive.org/web/20120513162446/http://www.zeiss.com/C12578620052CA69/0/58D501E36518AFC9C12578D2004104E1/%24file/cln_39_en_tessar.pdf |archive-date=13 May 2012 }}</ref> and shows its transformation from an {{f/|6.3}} lens for [[plate camera]]s using the original three-group configuration through to an {{f/|2.8}} 5.2&nbsp;mm four-element optic with eight extremely aspheric surfaces, economically manufacturable because of its small size. Its performance is 'better than the best 35&nbsp;mm lenses – but only for a very small image'.

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.

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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 [[Ff-number]]), but in practice are not directly proportional to [[image noise]] or resolution due to other limitations. See comparisons.<ref name="dxoa">[http://www.dxomark.com/index.php/Cameras/Camera-Sensor-Ratings Camera Sensor Ratings] {{Webarchive|url=https://web.archive.org/web/20120321161023/http://www.dxomark.com/index.php/Cameras/Camera-Sensor-Ratings |date=2012-03-21 }} DxOMark</ref><ref name="imac">[http://www.imaging-resource.com/IMCOMP/COMPS01.HTM Imaging-resource: Sample images Comparometer] Imaging-resource</ref><!-- PLEASE see above. Thank you. --> Film format sizes are also included, for comparison. The application examples of phone or camera may not show the exact sensor sizes.

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! scope="col" | Aspect Ratio

! scope="col" | Area (mm{{sup|2}})

! scope="col" | [[Ff-number#Stops, f-stop conventions, and exposure|Stops]] (area)<ref>Defined here as the equivalent number of stops lost (or gained, if positive) due to the area of the sensor relative to a full {{val|35|u=mm}} frame ({{val|36|x|24|u=mm}}). Computed as <math display="inline">\mathrm{Stops}=\log_{2} \left(\frac{\mathrm{Area_{sensor}}}{\mathrm{Area_{35\ mm}}} \right)\,.</math></ref>

! scope="col" | [[Crop factor]]<ref>Defined here as the ratio of the diagonal of a full {{val|35|u=mm}} frame to that of the sensor format, that is <math display="inline">\mathrm{CF} = \frac{\mathrm{diag_{35\ mm}}}{\mathrm{diag_{sensor}}}\,.</math></ref>

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