Format factor

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The format factor is a term from photography . It indicates the length ratio between the diagonals of two recording formats .

application

Since the recording format , image angle and focal length are related to the set of rays , the format factor can be used to calculate which focal length a lens must have in order to be the same for a different recording format (image size) with a given focal length and the same distance to the subject (object size) To show image detail.

For digital SLR cameras based on 35mm predecessors, the 35mm format of 24 mm × 36 mm is used as a comparison format, which corresponds to a diagonal of around 43 mm. The diagonal of the light-sensitive surface of the image sensor multiplied by the format factor results in the diagonal of the small picture format. The diagonal of the recording format is in the same order of magnitude as the normal focal length for this recording format (see also normal lens ). With a format factor of 1.5 (based on the 35mm format), the image diagonal is 43 mm / 1.5 = 29 mm.

The same phenomenon occurs with the transition from large and medium format to 35 mm cameras. Instead of specifying the format factor , the camera lenses are classified as wide-angle , normal or telephoto lenses based on their angle of view for the respective format (although the tele construction alone does not affect the angle of view, but lenses with a small angle of view and long focal length are often tele constructions).

Focal lengths for an image angle of 69 ° with different recording formats (small image: 32 mm)

Alternative terms

The following terms are used synonymously in connection with the phenomenon of changing the image angle with the same focal length but different image sizes .

Crop factor

A reduction in the photosensitive surface results in a cropping of the image field (reduction of the angle of view). The format factor is also called the crop factor (from English to crop ). A reduction in the recording format corresponds to an enlarged section .

"Focal length extension factor"

The term “focal length extension factor ” is used synonymously with format factor , although it is misleading. The focal length of a lens is predetermined by its design and cannot be changed by reducing the recording format. Changing the recording format only changes the angle of view .

Zoom lens of a digital camera with an actual focal length f of 6.2 to 66.7 mm. The equivalent focal length values ​​from 28 to 300 mm based on the 35mm format are indicated on the setting ring.

35mm format equivalent focal length

The term 35mm format equivalent focal length is determined for the product of the actual focal length and the format factor related to the 35mm format. It refers to the focal length that results in the same angle of view in the 35mm format as the actual focal length of a lens on the respective recording format .

This term is also misleading as the equivalence only relates to the angle of view . For example, the course of the depth of field , the critical aperture , the achievable cooling capacity on the image sensor , the travel of the lens motors or the effect of the focusing error and many other imaging errors do not depend on the image angle, but on the size of the image sensor area.

Angle of view factor

The term angle of view factor, which is occasionally used, is an attempt to take into account the fact that it is not the focal length that changes with the recording format, but the angle of view used . However, it is often wrongly assumed that the format and angle of view factors are identical, but this is not the case: when the focal length is varied, the effective angle of view of a lens (see also zoom factor ) changes to different degrees, even if the recording format is changed. This means that when switching from a 35mm camera to a digital camera with a smaller sensor, for example, the angle of view used by a 20 mm wide-angle lens changes less than that of a 400 mm telephoto lens. Therefore, the change in the angle of view that is caused by the transition to a different recording format cannot be described by a factor that is valid for all focal lengths . The cause lies in the relationship between the recording format, focal length and image angle via the non-linear tangent function .

example

Format Factor.gif

The image sensor of many common digital SLR cameras is 1.5 to 1.6 times smaller (see section Common format factors ) than the usual 35 mm format of 24 mm × 36 mm, i.e. only 15.7 mm × 23.5 mm (so-called. APS-C format). With a lens with a focal length of 50 mm, the image sensor only “sees” a section of what the 35mm film “sees”. If you compare 9 × 13 cm prints of photos that were shot with this lens on a 35mm camera and a standard digital camera, it looks as if the picture was taken from a digital camera with a longer focal length. If you want to achieve the same section with the 35mm camera as with the digital camera, a focal length longer by the format factor, in this case 50 mm × 1.6 = 80 mm, must be used or a corresponding section enlargement must be made.

Other values, such as B. the depth of field, also change by the format factor or its reciprocal value, if you record with the same lens, but the recording format changes. When switching from a small image to a smaller image sensor, the depth of field is reduced by the format factor for the same focal length . But: With the same image section , i. H. with a correspondingly shorter focal length, the depth of field increases proportionally to the format factor.

Common format factors

Comparison of common sensor formats
Format factors of common sensor sizes relative to the 35mm format
Factor a Typical designation of
the sensor size b 		use Width
(mm) 		Height
(mm) 		Diagonal
(mm) 		Area
(mm²) 		Area (%)
based on KB
014.0 1 ⁄ 6 ″ (= 0.17 ″) Standard old 4: 3 camcorder 002.5 001.8 003.1 004.5 000.5
09.6 1 ⁄ 4 ″ (= 0.25 ″) some smartphones 003.6 002.7 004.5 009.7 001.1
07.7 1 ⁄ 3.2 ″ (= 0.31 ″) some smartphones 004.5 003.4 005.6 0015.3 001.8
07.2 1 ⁄ 3 ″ (= 0.33 ″) some smartphones and video cameras 004.8 003.6 006.0 0017.3 002.0
06.3 1 ⁄ 2.6 ″ (= 0.38 ″) some smartphones 005.5 004.1 006.9 0022.6 002.6
06.1 Super 8 no digital format 005.7 004.2 007.1 0023.9 002.8
06.0 1 ⁄ 2.5 ″ (= 0.40 ″) some smartphones and older 4 to 9 MP compact cameras (2005 to 2011) 005.8 004.3 007.2 0024.7 002.9
05.6 1 ⁄ 2.3 ″ (= 0.43 ″) some smartphones and compact cameras 006.2 004.6 007.7 0029 003.3
05.4 1 ⁄ 2 ″ (= 0.5 ″) Compact cameras, e.g. B. Fujifilm FinePix F770EXR with 16 MP from 2012 006.4 004.8 008.0 0031 003.6
04.85 1 ⁄ 1.8 ″ (= 0.56 ″) older 3 to 10 MP compact cameras (2002 to 2008) 007.2 005.3 008.9 0038 004.4
04.6 1 ⁄ 1.7 ″ (= 0.59 ″) some smartphones 007.6 005.7 009.5 0043 005.0
03.9 2 ⁄ 3 ″ (= 0.67 ″) EB and studio cameras while watching TV 008.8 006.6 011.0 0058 006.7
02.7 1 ″, CX d Noble compact cameras and older system cameras 013.2 008.8 015.9 0116 013.5
02.38 0.94 ″ (source?) BlackMagic Cinema Camera 015.8 008.9 018.1 0141 016.2
02 4 ⁄ 3 ″ (= 1.33 ″) , four-thirds , micro-four-thirds Premium compact cameras and system cameras 017.3 013.0 021.6 0225 026.0
01.94 1.5 ″ Canon, Multi-Aspect at 4: 3 017.9 013.4 022.4 0240 027.8
01.92 Canon, Multi-Aspect at 3: 2 018.7 012.5 022.5 0234 027.1
01.85 Canon 018.7 014.0 023.4 0262 030.3
≈1.6 APS-C mainly Canon ≈22.5 ≈15.0 ≈27 ≈335 ≈39
≈1.5 mainly Nikon (= DX format ), Sony, Fujifilm X series , Konica Minolta, Pentax, Ricoh, Samsung ≈23.7 ≈15.6 ≈28 ≈370 ≈43
01.3 APS-H older professional DSLR (digital single lens reflex cameras) 027.9 018.6 033.5 0519 060
01 35mm , full format , FX d Professional DSLR 036.0 024.0 043.3 0864 100
00.8 Medium format c S format (Leica) , 3: 2 045.0 030.0 054.1 1,350 156
00.79 Digital versions of some 645 cameras ( Fujifilm GFX series , Pentax) 043.8 032.9 054.8 1,441 167
00.72 z. B. Mamiya ZD 048.0 036.0 060.0 1,728 200
00.55 Roll film 120/220 6 × 6 (typical) 056.0 056.0 079.2 3.136 363
00.43 Roll film 120/220 6 × 9 (typical) 056.0 083.0 100.1 4,648 538
aThe format factor in this table corresponds to the ratio of the diagonals of the 35mm format to the specified diagonals of the light-sensitive surface of the image sensor. Some authors relate this to the larger side of the recording format instead, in order to better accommodate the different aspect ratios (2: 3 for 35mm and DSLR, 3: 4 for most sensors for compact digital cameras, 16: 9 for some newer models) Differences to information in other sources occur.
bThe size specifications in fractions of an inch traditionally refer to the size of video pickup tubes. A one-inch vidicon picture tube has an outer diameter of 25.4 mm, but only a usable screen diagonal of around 16 mm.
cAs with conventional roll film does not exist in digital photography that a medium format, even within a manufacturer's products sway the medium format sensors in their dimensions. Examples: Pentax 645Z: 43.8 × 32.8 mm, Pentax 645D: 44.0 × 33.0 mm, Hasselblad H5D-40: 32.9 × 43.8 mm, Hasselblad H5D-50: 36.7 × 49 ,1 mm; Hasselblad H5D-50: 40.2 × 53.7 mm, Hasselblad H5X: 41.5 × 56.0 mm
d CX, DX, FX are format names of the manufacturer Nikon

Summary

If the recording format changes (for example when connecting a lens for a 35mm SLR camera to a digital SLR with a smaller sensor or by making an enlargement of a section):

Focal length
Stay constant. The actual focal length of a lens does not change. Likewise, the reproduction scale, which is independent of the recording format.
F-number
F-number , aperture width (or light intensity of the lens), luminous flux through the lens as well as the illuminance , the photometric light intensity and the luminance in the image remain constant, and thus also the exposure value and the combination of exposure time , f-number and sensitivity required for correct exposure .
Comparison of large image section (blue) and small image section (orange) in the image circle (black) of a lens. The effective distortion , the effective aperture errors and the number of optically resolved lines are smaller in the small image section than in the large image section.
Angle of view / image section
The angle of view used decreases with a format factor> 1 and increases with a format factor <1, ​​but not linearly to this over different focal lengths, but according to the tangent function . The longer the focal length, the smaller the change in the angle of view used. The maximum usable angle of view of the lens ( image circle ) remains constant.
The image section is reduced according to the angle of view used. A focal length of 50 mm with a format factor of 1.6 results in an image section like 80 mm for a 35mm camera.
Due to the trimming, imaging errors that tend to occur at the edges of the image , for example in the case of vignetting , have less of an effect the larger the format factor.
Resolving power
The optical resolution of the lens does not change. However, since a smaller section of the image is used, the effective resolution in the registered image changes by the format factor. If, for example , a certain contrast transfer is still achieved in the full format with a spatial frequency of 480 line pairs per image height (i.e. 40 line pairs per millimeter) , with the smaller image format APS-C only the spatial frequency of 360 line pairs per image height reduced by the format factor 1.5 ( so still at 40 line pairs per millimeter).
Blurring , motion blur
The rule of thumb for small images "1 / focal length (second) is still possible" must be extended to "1 / (focal length × format factor) is still possible". The change in the rule of thumb results from the changed image section (see above). Please note that this rule of thumb is intended for prints that are viewed at least at the distance of the image diagonals. Any image stabilization is also not taken into account.
The motion blur also changes according to the changed image section. The motion blur increases with a format factor greater than one.
Depth of field
  • With the same focal length and the same f-number , the depth of field is reduced with a format factor> 1.
    The absolute diameter of the circles of confusion remains constant, but they become larger in relation to the (smaller) recording format and angle of view . This reduces the depth of field. In order to still achieve the same depth of field, the f-number must be multiplied by the format factor: A 50 mm lens produces the same depth of field with the same object width at aperture 2 as with aperture 3 with format factor 1.5 or aperture 3.2 with Format factor 1.6.
  • With the same image section and the same f-number (i.e. same object width, same angle of view, shorter focal length), the depth of field increases with a format factor> 1.
    In order to reproduce the same image section, the focal length of the lens must be reduced by the format factor . The change in the focal length has a greater effect on the depth of field with the same f-number than the change in the recording format, so that the overall depth of field increases. In order to maintain the same depth of field as well as the image section, the f-number must be divided by the format factor : A 50 mm lens produces about the same depth of field and the same image section as a 35 mm lens at aperture 1.4 for format factor 1.5 (rounded to the usual values, diffraction effects neglected).
  • With the same image section and the same opening width (i.e. same object width, same angle of view), the depth of field does not change, and the same diffraction blur results on the image sensor . The f-number is reduced accordingly by the format factor.

See also

swell

  1. ↑ Summary of the crop factor
  2. ↑ a b Markus Bautsch: Effect of image size on image parameters Wikibooks digital imaging processes , see table columns 1 to 3, accessed on May 21, 2015

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