APEX system
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APEX stands for Additive System of Photographic Exposure, which was proposed in the 1960 ASA standard for monochrome film speed, ASA PH2.5-1960, as a means of simplifying exposure computation.


Exposure equation

Until the late 1960s, cameras did not have built-in
exposure meter A light meter is a device used to measure the amount of light. In photography, a light meter (more correctly an exposure meter) is used to determine the proper exposure for a photograph. The meter will include either a digital or analog calcula ...
s, and many photographers did not have external exposure meters. Consequently, it often was necessary to calculate exposure from lighting conditions. The relationship of recommended photographic exposure to a scene's average luminance is given by the camera exposure equation :\frac = \frac \, where * A is the
f-number In optics, the f-number of an optical system such as a camera lens is the ratio of the system's focal length to the diameter of the entrance pupil ("clear aperture").Smith, Warren ''Modern Optical Engineering'', 4th Ed., 2007 McGraw-Hill Pro ...
(reciprocal of the relative
aperture In optics, an aperture is a hole or an opening through which light travels. More specifically, the aperture and focal length of an optical system determine the cone angle of a bundle of rays that come to a focus in the image plane. An ...
) * T is the exposure time (" shutter speed") in seconds * B is the average scene luminance ("
brightness Brightness is an attribute of visual perception in which a source appears to be radiating or reflecting light. In other words, brightness is the perception elicited by the luminance of a visual target. The perception is not linear to luminan ...
") * S_x is the ASA arithmetic
film speed Film speed is the measure of a photographic film's sensitivity to light, determined by sensitometry and measured on various numerical scales, the most recent being the ISO system. A closely related ISO system is used to describe the relation ...
* K is the reflected-light meter calibration constant Use of the symbol B for luminance reflects photographic industry practice at the time of ASA PH2.5-1960; current SI practice prefers the symbol L. German sources typically used k for the relative aperture. Many authors now use N and t for relative aperture and exposure time. Recommendations for the value of the calibration constant K in applicable
ANSI The American National Standards Institute (ANSI ) is a private non-profit organization that oversees the development of voluntary consensus standards for products, services, processes, systems, and personnel in the United States. The organi ...
and
ISO ISO is the most common abbreviation for the International Organization for Standardization. ISO or Iso may also refer to: Business and finance * Iso (supermarket), a chain of Danish supermarkets incorporated into the SuperBest chain in 2007 * Iso ...
standards have varied slightly over the years; this topic is discussed in greater detail under Exposure meter calibration in the
Light meter A light meter is a device used to measure the amount of light. In photography, a light meter (more correctly an exposure meter) is used to determine the proper exposure (photography), exposure for a photograph. The meter will include either a Di ...
article.


Exposure value

In an attempt to simplify choosing among combinations of equivalent camera settings, the concept of ''exposure values'' (German: ''Lichtwert'') was originally developed and proposed to other manufacturers by the German shutter manufacturer in the early 1950s. Combinations of shutter speed and relative aperture that resulted in the same exposure were said to have the same ''
exposure value In photography, exposure value (EV) is a number that represents a combination of a camera's shutter speed and f-number, such that all combinations that yield the same exposure have the same EV (for any fixed scene luminance). Exposure value is ...
'' E_v, a base-2
logarithm In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number  to the base  is the exponent to which must be raised, to produce . For example, since , the ''logarithm base'' 10 of ...
ic scale defined by :E_v = \log_2 = \log_2 \,. When applied to the left-hand side of the exposure equation, E_v denoted combinations of camera settings; when applied to the right-hand side, E_v denoted combinations of luminance and film speed. For a given film speed, the recommended exposure value was determined solely by the luminance. Once the exposure value was determined, it could be directly set on cameras with an E_v scale. Adjustment of exposure was simple, because a change of 1 E_v corresponded to a change of 1 exposure step, i.e., either a halving or doubling of exposure. Starting 1954, the so-called ''Exposure Value Scale'' (EVS), originally known as ''Light Value Scale'' (LVS), was adopted by
Rollei Rollei () was a German manufacturer of optical instruments founded in 1920 by and in Braunschweig, Lower Saxony, and maker of the Rolleiflex and Rolleicord series of cameras. Later products included specialty and nostalgic type films for the ...
,
Hasselblad Victor Hasselblad AB is a Swedish manufacturer of medium format cameras, photographic equipment and image scanners based in Gothenburg, Sweden. The company originally became known for its classic analog medium-format cameras that used a waist ...
,
Voigtländer Voigtländer () was a significant long-established company within the optics and photographic industry, headquartered in Braunschweig, Germany, and today continues as a trademark for a range of photographic products. History Voigtländer was f ...
, Carl Braun Camera-Werk, Braun, Kodak, Seikosha, Aires, Konica, Olympus Corporation, Olympus, Ricoh and others, introducing lenses with coupled shutter (photography), shutters and apertures, such that, after setting the exposure value, adjusting either the shutter speed or aperture made a corresponding adjustment in the other to maintain a constant exposure. On some models, the coupling of shutter speed and aperture setting was optional, so that photographers could choose their preferred method of working depending on the situation. Use of the E_v scale on such cameras is discussed briefly by #CITEREFAdams1981, Adams (1981, 39). Modern cameras no longer display exposure values as such, but continue to offer exposure modes, which support users in employing the concept of counter-adjusting shutter speed and aperture at a fixed point of exposure. This can be found in features such as Manual Shift on some Minolta AF, Minolta, Konica Minolta and Sony Alpha or Hyper Manual on some Pentax (D)SLRs since 1991, where the photographer can change one of the parameters, and the camera will adjust the other accordingly for as long as the Auto-Exposure Lock (AEL) function is activated. In a wider sense, functions like , Pa / Ps Creative Program Control (by Minolta, Konica Minolta and Sony) or Hyper Program (by Pentax) belong to this group of features as well.


The additive (logarithmic) system

Although some photographers (#CITEREFAdams1981, Adams 1981, 66) routinely determined camera settings using the exposure equation, it generally was assumed that doing so would prove too daunting for the casual photographer. The 1942 ASA exposure guide, #CITEREFASAZ38.2.2-1942, ASA Z38.2.2-1942, featured a dial calculator, and revisions in 1949 and 1955 used a similar approach. An alternative simplification also was possible: ASA PH2.5-1960 proposed extending the concept of exposure value to all exposure parameters. Taking base-2 logarithms of both sides of the exposure equation and separating numerators and denominators reduces exposure calculation to a matter of addition: :E_v = A_v + T_v = B_v + S_v \,, where * A_v is the ''aperture value'': A_v = \log_2 A^2 * T_v is the ''time value'': T_v = \log_2 (1/T) * E_v is the ''exposure value'': E_v = A_v + T_v. * S_v is the ''speed value'' (aka ''sensitivity value''): S_v = \log_2 (N S_x) * B_v is the ''luminance value'' (aka ''brightness value''): B_v = \log_2 (B / N K) * N is a constant that establishes the relationship between the ASA arithmetic film speed S_x and the ASA speed value S_v. The value of N is approximately 0.30 (precisely, 2^). * K is the reflected-light meter calibration constant ASA standards covered incident-light meters as well as reflected-light meters; the incident-light exposure equation is : \frac = \frac \,, where * I is the scene illuminance * C is the incident-light meter calibration constant The use of I for illuminance reflects photographic industry practice at the time of the 1961 ASA standard for exposure meters, #CITEREFASAPH2.12-1961, ASA PH2.12-1961; current SI practice prefers the symbol E. #CITEREFASAPH2.12-1961, ASA PH2.12-1961 included incident-light metering in the APEX concept: :E_v = A_v + T_v = I_v + S_v \,, where * I_v is the incident-light value: I_v = \log_2 (I / N C) (German sources typically use LW (for ''Lichtwert'' or ''Belichtungswert'' — but not to be confused with the English term light value) instead of the exposure value's symbol E_v. Consequently, the aperture value A_v is referred to as ''Blendenleitwert'' LWk, and the time value T_v as ''Zeitleitwert'' LWt. The film speed value S_v is named ''Empfindlichkeitsleitwert'', and the brightness value B_v is known as ''Objekthelligkeit''.)


APEX in practice

APEX made exposure computation a relatively simple matter; the foreword of ASA PH2.5-1960 recommended that exposure meters, exposure calculators, and exposure tables be modified to incorporate the logarithmic values that APEX required. In many instances, this was done: the 1973 and 1986 ANSI exposure guides, #CITEREFANSIPH2.7-1973, ANSI PH2.7-1973 and #CITEREFANSIPH2.7-1986, ANSI PH2.7-1986, eliminated exposure calculator dials in favor of tabulated APEX values. However, the logarithmic markings for aperture and shutter speed required to set the computed exposure were never incorporated in consumer cameras. Accordingly, no reference to APEX was made in #CITEREFANSIPH3.49-1971, ANSI PH3.49-1971 (though it was included in the Appendix). The incorporation of exposure meters in many cameras in the late 1960s eliminated the need to compute exposure, so APEX saw little actual use. With the passage of time, formatting of APEX quantities has varied considerably; although the v originally was subscript, it sometimes was given simply as lower case, and sometimes as uppercase. Treating these quantities as acronyms rather than quantity symbols probably is reasonable because several of the quantity symbols (E, B, and I for exposure, luminance, and illuminance) used at the time APEX was proposed are in conflict with current preferred SI practice. A few artifacts of APEX remain. Canon (company), Canon, Pentax and Leica Camera, Leica cameras use 'Av' and 'Tv' to indicate relative aperture and shutter speed as well as to symbolize aperture priority and shutter priority modes. Some Pentax DSLRs even provide a 'TAv' Digital camera modes, exposure mode to automatically set the Film speed, ISO speed depending on the desired aperture and shutter settings, and 'Sv' (for sensitivity priority) to pre-set the ISO speed and let the camera choose the other parameters. Some meters, such as Pentax spot meters, directly indicate the exposure value for ISO 100 film speed. For a given film speed, exposure value is directly related to luminance, although the relationship depends on the reflected-light meter calibration constant K. Most photographic equipment manufacturers specify metering sensitivities in EV at ISO 100 speed (the uppercase 'V' is almost universal). It is common to express exposure increments in EV, as when adjusting exposure relative to what a light meter indicates (#CITEREFRay2000, Ray 2000, 316). For example, an exposure compensation of +1 EV (or +1 step) means to increase exposure, by using either a longer exposure time or a smaller f-number. The sense of exposure compensation is opposite that of the EV scale itself. An ''increase'' in exposure corresponds to a ''decrease'' in EV, so an exposure compensation of +1 EV results in a smaller EV; conversely, an exposure compensation of −1 EV results in a greater EV.


Use of APEX values in Exif

APEX has seen a partial resurrection in the Exif standard, which calls for storing exposure data using APEX values. There are some minor differences from the original APEX in both terminology and values. The implied value (1/3.125) for the speed scaling constant N given in the Exif 2.2 specification ("Exif 2.2"; #CITEREFJEITA2002, JEITA 2002) differs slightly from the APEX value of 2^ (0.2973); with the Exif value, an ISO arithmetic film speed of 100 corresponds exactly to a speed valueExif 2.2 refers to S_\mathrm as "film sensitivity." S_\mathrm of 5. The relationship between B_ and luminance depends on both the speed scaling constant N and the reflected-light meter calibration constant K: :B_\mathrm = \log_2 \frac \,. Because Exif 2.2 records ISO arithmetic speed rather than film sensitivity, the value of N affects the recorded value of B_ but not the recorded film speed. Exif 2.2 does not recommend a range of values for K, presumably leaving the choice to the equipment manufacturer. The example data in Annex C of Exif 2.2 give 1 footlambert for B_ = 0. This is in agreement with the APEX value for B, but would imply K = 1/N, or 3.125 with B in footlamberts. With B in cd/m2, this becomes 10.7, which is slightly less than the value of 12.5 recommended by #CITEREFISO2720:1974, ISO 2720:1974 and currently used by many manufacturers. The difference possibly arises from rounding B in the example table; it also is possible that the example data simply were copied from an old ASA or ANSI standard.


Notes


References

* Adams, Ansel. 1981. ''The Negative.'' Boston: New York Graphic Society. * ANSI PH2.7-1973. ''American National Standard Photographic Exposure Guide''. New York: American National Standards Institute. Superseded by ANSI PH2.7-1986. * ANSI PH2.7-1986. ''American National Standard for Photography — Photographic Exposure Guide''. New York: American National Standards Institute. * ANSI PH3.49-1971. ''American National Standard for general-purpose photographic exposure meters (photoelectric type)''. New York: American National Standards Institute. After several revisions, this standard was withdrawn in favor of ISO 2720:1974. * ASA PH2.5-1960. ''American Standard Method for Determining Speed of photographic Negative Materials (Monochrome, Continuous Tone)''. New York: United States of America Standards Institute. * ASA PH2.12-1961. ''American Standard, General-Purpose Photographic Exposure Meters (photoelectric type)''. New York: American Standards Association. Superseded by ANSI PH3.49-1971. * ASA Z38.2.2-1942. ''American Emergency Standard Photographic Exposure Computer''. New York: American Standards Association. * ASA Z38.2.6-1948. ''American Standard for General-Purpose Photographic Exposure Meters (Photoelectric Type)''. New York: American Standards Association. Superseded by ASA PH2.12-1957. * ISO 2720:1974
''General Purpose Photographic Exposure Meters (Photoelectric Type)—Guide to Product Specification''. International Organization for Standardization.
* Japan Electronics and Information Technology Industries Association. 2002
JEITA CP-3451, Exchangeable image file format for digital still cameras: Exif Version 2.2
(PDF). Japan Electronics and Information Technology Industries Association.
* JEITA. ''See'' Japan Electronics and Information Technology Industries Association. * Ray, Sidney F. 2000. Camera Exposure Determination. In ''The Manual of Photography: Photographic and Digital Imaging'', 9th ed. Ed. Ralph E. Jacobson, Sidney F. Ray, Geoffrey G. Atteridge, and Norman R. Axford. Oxford: Focal Press. {{ISBN, 0-240-51574-9


External links


Doug Kerr's in-depth description of APEX
Photographic techniques