Image sensor format

In digital photography, the image sensor format is the shape and size of the image sensor. The image sensor format of a digital camera determines the angle of view of a particular lens when used with a particular sensor. Because the image sensors in many digital cameras are smaller than the 24 mm × 36 mm image area of full-frame 35 mm cameras, a lens of a given focal length gives a narrower field of view in such cameras. Sensor size is often expressed as optical format in inches. Other measures are also used; see table of sensor formats and sizes below. Lenses produced for 35 mm film cameras may mount well on the digital bodies, but the larger image circle of the 35 mm system lens allows unwanted light into the camera body, and the smaller size of the image sensor compared to 35 mm film format results in cropping of the image. This latter effect is known as field-of-view crop. The format size ratio (relative to the 35 mm film format) is known as the field-of-view crop factor, crop factor, lens factor, focal-length conversion factor, focal-length multiplier, or lens multiplier.

In digital photography, the image sensor format is the shape and size of the image sensor. The image sensor format of a digital camera determines the angle of view of a particular lens when used with a particular sensor. Because the image sensors in many digital cameras are smaller than the 24 mm × 36 mm image area of full-frame 35 mm cameras, a lens of a given focal length gives a narrower field of view in such cameras. Sensor size is often expressed as optical format in inches. Other measures are also used; see table of sensor formats and sizes below. Lenses produced for 35 mm film cameras may mount well on the digital bodies, but the larger image circle of the 35 mm system lens allows unwanted light into the camera body, and the smaller size of the image sensor compared to 35 mm film format results in cropping of the image. This latter effect is known as field-of-view crop. The format size ratio (relative to the 35 mm film format) is known as the field-of-view crop factor, crop factor, lens factor, focal-length conversion factor, focal-length multiplier, or lens multiplier. In practice, if applying a lens with a fixed focal length and a fixed aperture and made for an image circle to meet the requirements for a large sensor is to be adapted, without changing its physical properties, to smaller sensor sizes neither the depth of field nor the light gathering \mathrm{lx = \, \frac{lm}{m^2}} will change. \mathrm{SNR} = \frac{P Q_e t}{\sqrt{\left(\sqrt{P Q_e t}\right)^2 + \left(\sqrt{D t}\right)^2 + N_r^2}} = \frac{P Q_e t}{\sqrt{P Q_e t + D t + N_r^2}} where P is the incident photon flux (photons per second in the area of a pixel), Q_e is the quantum efficiency, t is the exposure time, D is the pixel dark current in electrons per second and N_r is the pixel read noise in electrons rms. Each of these noises has a different dependency on sensor size. ===Exposure and photon flux=== Image sensor noise can be compared across formats for a given fixed photon flux per pixel area (the P in the formulas); this analysis is useful for a fixed number of pixels with pixel area proportional to sensor area, and fixed absolute aperture diameter for a fixed imaging situation in terms of depth of field, diffraction limit at the subject, etc. Or it can be compared for a fixed focal-plane illuminance, corresponding to a fixed f-number, in which case P is proportional to pixel area, independent of sensor area. The formulas above and below can be evaluated for either case. ===Shot noise=== In the above equation, the shot noise SNR is given by \frac{P Q_e t}{\sqrt{P Q_e t}} = \sqrt{P Q_e t} . Apart from the quantum efficiency it depends on the incident photon flux and the exposure time, which is equivalent to the 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 it is interesting to compare performance of cameras with small and big sensors. A good 2018 cell phone camera with a typical pixel size of 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=== The read noise is the total of all the electronic noises in the conversion chain for the pixels in the sensor array. To compare it with photon noise, it must be referred back to its equivalent in photoelectrons, which requires the division of the noise measured in volts by the conversion gain of the pixel. This is given, for an active pixel sensor, by the voltage at the input (gate) of the read transistor divided by the charge which generates that voltage, CG = V_{rt}/Q_{rt} . This is the inverse of the capacitance of the read transistor gate (and the attached floating diffusion) since capacitance C = Q/V . Thus CG = 1/C_{rt} . In general for a planar structure such as a pixel, capacitance is proportional to area, therefore the read noise scales down with sensor area, as long as pixel area scales with sensor area, and that scaling is performed by uniformly scaling the pixel. Considering the signal to noise ratio due to read noise at a given exposure, the signal will scale as the sensor area along with the read noise and therefore read noise SNR will be unaffected by sensor area. In a depth of field constrained situation, the exposure of the larger sensor will be reduced in proportion to the sensor area, and therefore the read noise SNR will reduce likewise. ===Dark noise=== Dark current contributes two kinds of noise: dark offset, which is only partly correlated between pixels, and the shot noise associated with dark offset, which is uncorrelated between pixels. Only the shot-noise component Dt is included in the formula above, since the uncorrelated part of the dark offset is hard to predict, and the correlated or mean part is relatively easy to subtract off. The mean dark current contains contributions proportional both to the area and the linear dimension of the photodiode, with the relative proportions and scale factors depending on the design of the photodiode. Thus in general the dark noise of a sensor may be expected to rise as the size of the sensor increases. However, in most sensors the mean pixel dark current at normal temperatures is small, lower than 50 e- per second, thus for typical photographic exposure times dark current and its associated noises may be discounted. At very long exposure times, however, it may be a limiting factor. And even at short or medium exposure times, a few outliers in the dark-current distribution may show up as "hot pixels". Typically, for astrophotography applications sensors are cooled to reduce dark current in situations where exposures may be measured in several hundreds of seconds. ===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 DR = Q_\text{max} / \sigma_\text{readout} (note, the read noise \sigma_{readout} is the same quantity as N_r referred to in the SNR calculation ). \xi_\mathrm{cutoff}=\frac{1}{\lambda N} where λ is the wavelength of the light passing through the system and N is the f-number of the lens. If that aperture is circular, as are (approximately) most photographic apertures, then the MTF is given by \mathrm{MTF}\left(\frac{\xi}{\xi_\mathrm{cutoff}}\right) = \frac{2}{\pi} \left\{ \cos^{-1}\left(\frac{\xi}{\xi_\mathrm{cutoff}}\right) - \left(\frac{\xi}{\xi_\mathrm{cutoff}}\right) \left[ 1 - \left(\frac{\xi}{\xi_\mathrm{cutoff}}\right)^2 \right]^\frac{1}{2} \right\} for \xi and 0 for \xi \ge \xi_\mathrm{cutoff} The diffraction based factor of the system MTF will therefore scale according to \xi_\mathrm{cutoff} and in turn according to 1/N (for the same light wavelength). 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 1/{C} where {C} is the relative crop factor, making the overall scale factor 1 / (N C) . Considering the three cases above: For the 'same picture' conditions, same angle of view, subject distance and depth of field, then the f-numbers are in the ratio 1/C , 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 f-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. G_\mathrm{objective} \simeq \frac{w_\mathrm{pixel}}{2{(f/\#)}_\mathrm{objective}}\,, where is the width of the pixel and is the f-number of the objective lens. The geometrical extent of the microlens / photoreceptor system is given by G_\mathrm{pixel} \simeq \frac{w_\mathrm{photoreceptor}}{2{(f/\#)}_\mathrm{microlens}}\,, where is the width of the photoreceptor and is the f-number of the microlens. In order to avoid shading, G_\mathrm{pixel} \ge G_\mathrm{objective}, therefore \frac{w_\mathrm{photoreceptor}}{{(f/\#)}_\mathrm{microlens}} \ge \frac{w_\mathrm{pixel}}{{(f/\#)}_\mathrm{objective}}. If , the linear fill factor of the lens, then the condition becomes {(f/\#)}_\mathrm{microlens} \le {(f/\#)}_\mathrm{objective} \times \mathit{ff}\,. 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. 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 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. ==Common image sensor formats== === Table of sensor formats and sizes === CMOS sensors: an OV7910 (1/3") and three OV6920 (1/18") sensors, both types with composite video (NTSC) outputs]] 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 tubes. The common 1" outside diameter circular video camera tubes have a rectangular photo sensitive area about on the diagonal, so a digital sensor with a 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 . 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 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 ; instead, the diagonal is closer to . Instead of "formats", these sensor sizes are often called types, as in "1/2-inch-type CCD." Due to inch-based sensor formats not being standardized, their exact dimensions may vary, but those listed are typical. The listed sensor areas span more than a factor of 1000 and are proportional to the maximum possible collection of light and image resolution (same lens speed, i.e., minimum f-number), but in practice are not directly proportional to image noise or resolution due to other limitations. See comparisons. Film format sizes are also included, for comparison. The application examples of phone or camera may not show the exact sensor sizes. ==See also== Full-frame digital SLR Sensor size and angle of view 35 mm equivalent focal length Film format Digital versus film photography List of large sensor interchangeable-lens video cameras List of sensors used in digital cameras Angle of view Crop factor Field of view ==Notes== ==Footnotes and references== ==External links== Eric Fossum: Photons to Bits and Beyond: The Science & Technology of Digital, Oct. 13, 2011 (YouTube Video of lecture) Joseph James: Equivalence at Joseph James Photography Simon Tindemans: Alternative photographic parameters: a format-independent approach at 21stcenturyshoebox Compact Camera High ISO modes: Separating the facts from the hype at dpreview.com, May 2007 The best compromise for a compact camera is a sensor with 6 million pixels or better a sensor with a pixel size of >3μm at 6mpixel.org [https://cdn.hasselblad.com/datasheets/x1d-II-50c/x1D-ii-50c-data-sheet.pdf] at hasselblad.com

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