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When using fixed focal length lenses, there are three ways to change the FOV of the system (camera and lens). The first and often easiest option is to change the WD from the lens to the object; moving the lens farther away from the object plane increases the FOV. The second option is to swap out the lens with one of a different focal length. The third option is to change the size of the sensor; a larger sensor will yield a larger FOV for the same WD, as defined in Equation 1.

where l 1 {\displaystyle l_{1}} and l 2 {\displaystyle l_{2}} are the characteristic dimensions of the format, and thus l 1 / l 2 {\displaystyle l_{1}/l_{2}} is the relative crop factor between the sensors. It is this result that gives rise to the common opinion that small sensors yield greater depth of field than large ones.

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Discounting photo response non-uniformity (PRNU) and dark noise variation, which are not intrinsically sensor-size dependent, the noises in an image sensor are shot noise, read noise, and dark noise. The overall signal to noise ratio of a sensor (SNR), expressed as signal electrons relative to rms noise in electrons, observed at the scale of a single pixel, assuming shot noise from Poisson distribution of signal electrons and dark electrons, is

Small body means small lens and means small sensor, so to keep smartphones slim and light, the smartphone manufacturers use a tiny sensor usually less than the 1/2.3" used in most bridge cameras. At one time only Nokia 808 PureView used a 1/1.2" sensor, almost three times the size of a 1/2.3" sensor. Bigger sensors have the advantage of better image quality, but with improvements in sensor technology, smaller sensors can achieve the feats of earlier larger sensors. These improvements in sensor technology allow smartphone manufacturers to use image sensors as small as 1/4" without sacrificing too much image quality compared to budget point & shoot cameras.[12]

Note: Horizontal FOV is typically used in discussions of FOV as a matter of convenience, but the sensor aspect ratio (ratio of a sensor’s width to its height) must be taken into account to ensure that the entire object fits into the image where the aspect ratio is used as a fraction (e.g. 4:3 = 4/3), Equation 7.

Most sensors are made for camera phones, compact digital cameras, and bridge cameras. Most image sensors equipping compact cameras have an 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 monitors without cropping.

Focal length

While it may be convenient to have a very wide AFOV, there are some negatives to consider. First, the level of distortion that is associated with some short focal length lenses can greatly influence the actual AFOV and can cause variations in the angle with respect to WD due to distortion. Next, short focal length lenses generally struggle to obtain the highest level of performance when compared against longer focal length options (see Best Practice #3 in Best Practices for Better Imaging). Additionally, short focal length lenses can have difficulties covering medium to large sensor sizes, which can limit their usability, as discussed in Relative Illumination, Roll-Off, and Vignetting.

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.[9] Such an exercise would in theory produce a lens with the same f-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[10]) the lens for a smaller sensor requires a greater resolving power. The development of the 'Tessar' lens is discussed by Nasse,[11] and shows its transformation from an f/6.3 lens for plate cameras using the original three-group configuration through to an f/2.8 5.2 mm four-element optic with eight extremely aspheric surfaces, economically manufacturable because of its small size. Its performance is 'better than the best 35 mm lenses – but only for a very small image'.

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 RX100 series, Panasonic Lumix TZ100 and Panasonic DMC-LX15. Canon has APS-C sensor on its top model PowerShot G1 X Mark III.

Due to inch-based sensor formats not being standardized, their exact dimensions may vary, but those listed are typical.[29] 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.[31][32] Film format sizes are also included, for comparison. The application examples of phone or camera may not show the exact sensor sizes.

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 l x = l m m 2 {\displaystyle \mathrm {lx=\,{\frac {lm}{m^{2}}}} } will change.

For calculating camera angle of view one should use the size of active area of the sensor. Active area of the sensor implies an area of the sensor on which image is formed in a given mode of the camera. The active area may be smaller than the image sensor, and active area can differ in different modes of operation of the same camera. Active area size depends on the aspect ratio of the sensor and aspect ratio of the output image of the camera. The active area size can depend on number of pixels in given mode of the camera. The active area size and lens focal length determines angles of view.[13]

Example 2: For an application using a ½” sensor, which has a horizontal sensor size of 6.4mm, a horizontal FOV of 25mm is desired.

The resolution of all optical systems is limited by diffraction. One way of considering the effect that diffraction has on cameras using different sized sensors is to consider the modulation transfer function (MTF). Diffraction is one of the factors that contribute to the overall system MTF. Other factors are typically the MTFs of the lens, anti-aliasing filter and sensor sampling window.[7] The spatial cut-off frequency due to diffraction through a lens aperture is

Some professional DSLRs, SLTs and mirrorless cameras use full-frame sensors, equivalent to the size of a frame of 35 mm film.

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.

And, we might compare the depth of field of sensors receiving the same photometric exposure – the f-number is fixed instead of the aperture diameter – the sensors are operating at the same ISO setting in that case, but the smaller sensor is receiving less total light, by the area ratio. The ratio of depths of field is then

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.

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.

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.[14] 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 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 G o b j e c t i v e ≃ w p i x e l 2 ( f / # ) o b j e c t i v e , {\displaystyle G_{\mathrm {objective} }\simeq {\frac {w_{\mathrm {pixel} }}{2{(f/\#)}_{\mathrm {objective} }}}\,,} where wpixel is the width of the pixel and (f/#)objective is the f-number of the objective lens. The geometrical extent of the microlens / photoreceptor system is given by G p i x e l ≃ w p h o t o r e c e p t o r 2 ( f / # ) m i c r o l e n s , {\displaystyle G_{\mathrm {pixel} }\simeq {\frac {w_{\mathrm {photoreceptor} }}{2{(f/\#)}_{\mathrm {microlens} }}}\,,} where wphotoreceptor is the width of the photoreceptor and (f/#)microlens is the f-number of the microlens.

The sensors of camera phones are typically much smaller than those of typical compact cameras, allowing greater miniaturization of the electrical and optical components. Sensor sizes of around 1/6" are common in camera phones, webcams and digital camcorders. The Nokia N8 (2010)'s 1/1.83" sensor was the largest in a phone in late 2011. The Nokia 808 (2012) surpasses compact cameras with its 41 million pixels, 1/1.2" sensor.[19]

Note: As the magnification increases, the size of the FOV will decrease; a magnification that is lower than what is calculated is usually desirable so that the full FOV can be visualized. In the case of Example 2, a 0.25X lens is the closest common option, which yields a 25.6mm FOV on the same sensor.

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.[4] 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,[5] 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.

Note: Fixed focal length lenses should not be confused with fixed focus lenses. Fixed focal length lenses can be focused for different distances; fixed focus lenses are intended for use at a single, specific WD. Examples of fixed focus lenses are many telecentric lenses and microscope objectives.

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.[a]

In order to avoid shading, G p i x e l ≥ G o b j e c t i v e , {\textstyle G_{\mathrm {pixel} }\geq G_{\mathrm {objective} },} therefore w p h o t o r e c e p t o r ( f / # ) m i c r o l e n s ≥ w p i x e l ( f / # ) o b j e c t i v e . {\displaystyle {\frac {w_{\mathrm {photoreceptor} }}{{(f/\#)}_{\mathrm {microlens} }}}\geq {\frac {w_{\mathrm {pixel} }}{{(f/\#)}_{\mathrm {objective} }}}.}

Once the required AFOV has been determined, the focal length can be approximated using Equation 1 and the proper lens can be chosen from a lens specification table or datasheet by finding the closest available focal length with the necessary AFOV for the sensor being used.

As of November 2013[update], there was only one mirrorless model equipped with a very small sensor, more typical of compact cameras: the Pentax Q7, with a 1/1.7" sensor (4.55 crop factor). See Sensors equipping Compact digital cameras and camera-phones section below.

Depth of field

Due to the ever-changing constraints of semiconductor fabrication and processing, and because camera manufacturers often source sensors from third-party foundries, it is common for sensor dimensions to vary slightly within the same nominal format. For example, the Nikon D3 and D700 cameras' nominally full-frame sensors actually measure 36 × 23.9 mm, slightly smaller than a 36 × 24 mm frame of 35 mm film. As another example, the Pentax K200D's sensor (made by Sony) measures 23.5 × 15.7 mm, while the contemporaneous K20D's sensor (made by Samsung) measures 23.4 × 15.6 mm.

Three possible depth-of-field comparisons between formats are discussed, applying the formulae derived in the article on depth of field. The depths of field of the three cameras may be the same, or different in either order, depending on what is held constant in the comparison.

\begin{align}\text{AFOV} & = 2 \times \tan^{-1} \left( {\frac{50 \text{mm}}{2 \times 200 \text{mm}}} \right)  \\ \text{AFOV} & = 14.25° \end{align}

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.

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 16 mm on the diagonal, so a digital sensor with a 16 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 16 mm.[26][27]

As previously stated, some amount of flexibility to the system’s WD should be factored in, as the above examples are only first-order approximations and they also do not take distortion into account.

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.

While most sensors are 4:3, 5:4 and 1:1 are also quite common. This distinction in aspect ratio also leads to varying dimensions of sensors of the same sensor format. All of the equations used in this section can also be used for vertical FOV as long as the sensor’s vertical dimension is substituted in for the horizontal dimension specified in the equations.

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 {\displaystyle 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.

An alternative is to consider the depth of field given by the same lens in conjunction with different sized sensors (changing the angle of view). The change in depth of field is brought about by the requirement for a different degree of enlargement to achieve the same final image size. In this case the ratio of depths of field becomes

Focus distance

A fixed focal length lens, also known as a conventional or entocentric lens, is a lens with a fixed angular field of view (AFOV). By focusing the lens for different working distances (WDs), differently sized field of view (FOV) can be obtained, though the viewing angle is constant. AFOV is typically specified as the full angle (in degrees) associated with the horizontal dimension (width) of the sensor that the lens is to be used with.

The focal length of a lens defines the AFOV. For a given sensor size, the shorter the focal length, the wider the AFOV. Additionally, the shorter the focal length of the lens, the shorter the distance needed to obtain the same FOV compared to a longer focal length lens. For a simple, thin convex lens, the focal length is the distance from the back surface of the lens to the plane of the image formed of an object placed infinitely far in front of the lens. From this definition, it can be shown that the AFOV of a lens is related to the focal length (Equation 1), where $ \small{f} $ is the focal length and $ \small{H} $ is the sensor size (Figure 1).

focallength中文

Generally, lenses that have fixed magnifications have fixed or limited WD ranges. While using a telecentric or other fixed magnification lens can be more constraining, as they do not allow for different FOVs by varying the WD, the calculations for them are very direct, as shown in Equation 4.

As of December 2010[update] most compact digital cameras used small 1/2.3" sensors. Such cameras include Canon Powershot SX230 IS, Fuji Finepix Z90 and Nikon Coolpix S9100. Some older digital cameras (mostly from 2005–2010) used even smaller 1/2.5" sensors: these include Panasonic Lumix DMC-FS62, Canon Powershot SX120 IS, Sony Cyber-shot DSC-S700, and Casio Exilim EX-Z80.

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 {\displaystyle 1/{C}} where C {\displaystyle {C}} is the relative crop factor, making the overall scale factor 1 / ( N C ) {\displaystyle 1/(NC)} . Considering the three cases above:

where P {\displaystyle P} is the incident photon flux (photons per second in the area of a pixel), Q e {\displaystyle Q_{e}} is the quantum efficiency, t {\displaystyle t} is the exposure time, D {\displaystyle D} is the pixel dark current in electrons per second and N r {\displaystyle N_{r}} is the pixel read noise in electrons rms.[2]

Most of these image sensor formats approximate the 3:2 aspect ratio of 35 mm film. Again, the Four Thirds System is a notable exception, with an aspect ratio of 4:3 as seen in most compact digital cameras (see below).

Due to the size constraints of powerful zoom objectives, most current bridge cameras 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.

The focal length of a lens is a fundamental parameter that describes how strongly it focuses or diverges light. A large focal length indicates that light is bent gradually while a short focal length indicates that the light is bent at sharp angles. In general, lenses with positive focal lengths converge light while lenses with negative focal lengths cause light to diverge, although there are some exceptions based on the distance from the lens to the object being imaged.

If wphotoreceptor / wpixel = ff, the linear fill factor of the lens, then the condition becomes ( f / # ) m i c r o l e n s ≤ ( f / # ) o b j e c t i v e × f f . {\displaystyle {(f/\#)}_{\mathrm {microlens} }\leq {(f/\#)}_{\mathrm {objective} }\times {\mathit {ff}}\,.}

Be aware that Equation 6 is an approximation and will rapidly deteriorate for magnifications greater than 0.1 or for short WDs. For magnifications beyond 0.1, either a fixed magnification lens or computer simulations (e.g. Zemax) with the appropriate lens model should be used. For the same reasons, lens calculators commonly found on the internet should only be used for reference. When in doubt, consult a lens specification table.

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 f/1.5–2 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.

The largest digital sensors in commercially available cameras are described as "medium format", in reference to film formats of similar dimensions. Although the most common medium format film, the 120 roll, is 6 cm (2.4 in) wide, and is most commonly shot square, the most common "medium-format" digital sensor sizes are approximately 48 mm × 36 mm (1.9 in × 1.4 in), which is roughly twice the size of a full-frame DSLR sensor format.

If the required magnification is already known and the WD is constrained, Equation 3 can be rearranged (replacing $ \small{ \tfrac{H}{\text{FOV}}} $ with magnification) and used to determine an appropriate fixed focal length lens, as shown in Equation 6.

Using the same absolute aperture diameter for both formats with the "same picture" criterion (equal angle of view, magnified to same final size) yields the same depth of field. It is equivalent to adjusting the f-number inversely in proportion to crop factor – a smaller f-number for smaller sensors (this also means that, when holding the shutter speed fixed, the exposure is changed by the adjustment of the f-number required to equalise depth of field. But the aperture area is held constant, so sensors of all sizes receive the same total amount of light energy from the subject. The smaller sensor is then operating at a lower ISO setting, by the square of the crop factor). This condition of equal field of view, equal depth of field, equal aperture diameter, and equal exposure time is known as "equivalence".[1]

When 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 8 inches (20 cm) silicon wafer, which would fit 100 or more APS-C sensors, and there is a significant reduction in 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.[18] Newer photolithography equipment now allows single-pass exposures for full-frame sensors, although other size-related production constraints remain much the same.

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, C G = V r t / Q r t {\displaystyle 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 {\displaystyle C=Q/V} .[3] Thus C G = 1 / C r t {\displaystyle CG=1/C_{rt}} .

CameraFOV calculator

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 0.37 in (9.4 mm); instead, the diagonal is closer to 0.26 in (6.6 mm).[28][29][30] Instead of "formats", these sensor sizes are often called types, as in "1/2-inch-type CCD."

Field of view describes the viewable area that can be imaged by a lens system. This is the portion of the object that fills the camera’s sensor. This can be described by the physical area which can be imaged, such as a horizontal or vertical field of view in mm, or an angular field of view specified in degrees. The relationships between focal length and field of view are shown below.

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.[b]

Sensor size is often expressed as optical format in inches. Other measures are also used; see table of sensor formats and sizes below.

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

Another way to change the FOV of a system is to use either a varifocal lens or a zoom lens; these types of lenses allow for adjustment of their focal lengths and thus have variable AFOV. Varifocal and zoom lenses often have size and cost drawbacks compared to fixed focal length lenses, and often cannot offer the same level of performance as fixed focal length lenses.

CameraSize comparison withlens

Knowledge Center/ Application Notes/ Imaging Application Notes/ Understanding Focal Length and Field of View

In general, however, the focal length is measured from the rear principal plane, rarely located at the mechanical back of an imaging lens; this is one of the reasons why WDs calculated using paraxial equations are only approximations and the mechanical design of a system should only be laid out using data produced by computer simulation or data taken from lens specification tables. Paraxial calculations, as from lens calculators, are a good starting point to speed the lens selection process, but the numerical values produced should be used with caution.

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 D R = Q max / σ readout {\displaystyle DR=Q_{\text{max}}/\sigma _{\text{readout}}} [6] (note, the read noise σ r e a d o u t {\displaystyle \sigma _{readout}} is the same quantity as N r {\displaystyle N_{r}} referred to in the SNR calculation[2]).

The 14.25° derived in Example 1 (see white box below) can be used to determine the lens that is needed, but the sensor size must also be chosen. As the sensor size is increased or decreased it will change how much of the lens’s image is utilized; this will alter the AFOV of the system and thus the overall FOV. The larger the sensor, the larger the obtainable AFOV for the same focal length. For example, a 25mm lens could be used with a ½” (6.4mm horizontal) sensor or a 35mm lens could be used with a 2/3” (8.8mm horizontal) sensor as they would both approximately produce a 14.5° AFOV on their respective sensors. Alternatively, if the sensor has already been chosen, the focal length can be determined directly from the FOV and WD by substituting Equation 1 in Equation 2, as shown in Equation 3.

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.

Available CCD sensors include Phase One's P65+ digital back with Dalsa's 53.9 mm × 40.4 mm (2.12 in × 1.59 in) sensor containing 60.5 megapixels[20] and Leica's "S-System" DSLR with a 45 mm × 30 mm (1.8 in × 1.2 in) sensor containing 37-megapixels.[21] In 2010, Pentax released the 40MP 645D medium format DSLR with a 44 mm × 33 mm (1.7 in × 1.3 in) CCD sensor;[22] 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 camera, with a 44 mm × 33 mm (1.7 in × 1.3 in) CMOS sensor.[23] In late 2016, Fujifilm also announced its new Fujifilm GFX 50S medium format, mirrorless entry into the market, with a 43.8 mm × 32.9 mm (1.72 in × 1.30 in) CMOS sensor and 51.4MP. [24] [25]

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.

for ξ < ξ c u t o f f {\displaystyle \xi <\xi _{\mathrm {cutoff} }} and 0 {\displaystyle 0} for ξ ≥ ξ c u t o f f {\displaystyle \xi \geq \xi _{\mathrm {cutoff} }} [8] The diffraction based factor of the system MTF will therefore scale according to ξ c u t o f f {\displaystyle \xi _{\mathrm {cutoff} }} and in turn according to 1 / N {\displaystyle 1/N} (for the same light wavelength).

In many applications, the required distance from an object and the desired FOV (typically the size of the object with additional buffer space) are known quantities. This information can be used to directly determine the required AFOV via Equation 2. Equation 2 is the equivalent of finding the vertex angle of a triangle with its height equal to the WD and its base equal to the horizontal FOV, or HFOV, as shown in Figure 2. Note: In practice, the vertex of this triangle is rarely located at the mechanical front of the lens, from which WD is measured, and is only to be used as an approximation unless the entrance pupil location is known.

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.

so the DOFs are in inverse proportion to the absolute aperture diameters d 1 {\displaystyle d_{1}} and d 2 {\displaystyle d_{2}} .

Most consumer-level DSLRs, SLTs and mirrorless cameras use relatively large sensors, either somewhat under the size of a frame of 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 Olympus and Panasonic).