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.

1 Exposure equation
2 Exposure value
3 The additive (logarithmic) system
4 APEX in practice
5 Use of APEX values in EXIF
6 Notes
7 References
8 See also
9 External links

[edit] Exposure equation

Until the late 1960s, cameras did not have built-in exposure meters, 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

$\frac {A^2} {T} = \frac {B S_x} {K}$

where

$A$ is the relative aperture (f-number)
$T$ is the exposure time ("shutter speed")
$B$ is the average scene luminance ("brightness")
$S x$ is the ASA arithmetic film speed
$K$ 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 $L$ . 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 and ISO standards have varied slightly over the years; this topic is discussed in greater detail under Exposure meter calibration in the Light meter article.

[edit] Exposure value

In the late 1950s, Hasselblad introduced lenses with coupled shutters and apertures, such that adjusting either the shutter speed or aperture made a corresponding adjustment in the other to maintain a constant exposure. Combinations of shutter speed and relative aperture that resulted in the same exposure were said to have the same exposure value $E v$ , a base-2 logarithmic scale defined by

$E_v = \log_2 {\frac {A^2} {T} } = \log_2 {\frac {B S_x} {K} }$

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 a camera with an $E v$ scale such as was included on some Hasselblad lenses. 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. Use of the $E v$ scale on such cameras is discussed briefly by Adams (1981, 39).

[edit] The additive (logarithmic) system

Although some photographers (Adams 1981, 66)^[1] 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, 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: $A v = 2$ $log 2$ $A$

$T v$ 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: $S v = log 2$ $(N S x)$

$B v$ is the luminance 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, $2 - 7 / 4$ ).^[2]

ASA standards covered incident-light meters as well as reflected-light meters; the incident-light exposure equation is

$\frac {A^2} {T} = \frac {I S_x} {C}$

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, ASA PH2.12-1961; current SI practice prefers the symbol $E$ .

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: $I v = log 2$ $(I / N C)$

[edit] 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, ANSI PH2.7-1973 and 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 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 cameras use 'Av' and 'Tv' to indicate relative aperture and shutter speed. 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 steps as "EV steps," as when adjusting exposure relative to what the light meter indicates. A compensation of +1 EV (or +1 step), for example, means to expose for a longer time or with a smaller $f$ -number. This usage can be confusing, because an exposure compensation of +1 EV actually calls for a smaller EV—a greater EV results in less exposure.

[edit] 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”; JEITA 2002) differs slightly from the APEX value of $2 - 7 / 4$ (0.2973); with the EXIF value, an ISO linear film speed of 100 corresponds exactly to a speed value^[3] $S v$ of 5.

The relationship between $B v$ and luminance depends on both the speed scaling constant $N$ and the reflected-light meter calibration constant $K$ :

$B_\mathrm {v} = \log_2 \frac {B} {NK}$

Because EXIF 2.2 records ISO linear speed rather than film sensitivity, the value of $N$ affects the recorded value of $B v$ 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 $B v$ = 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 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.

[edit] Notes

^ Ansel Adams described the exposure equation in a slightly different form: “To use the Exposure Formula, take the film speed number (on the ASA scale) and determine its approximate square root. This number is remembered as the key stop for that film. . . . At the key stop, the correct shutter speed is the reciprocalof the luminance expressed in c/ft².” The relationship to the ASA exposure equation may not be obvious; however, substituting for $A$ and $T$ gives

$\frac {A^2} {T} = LS$

The calibration constant $K$ might appear to be missing, but with luminance in c/ft², it was unity (greatly simplifying the calculation). With luminance in cd/m², $K$ = 10.8, slightly less than current recommendations.
^ The origin of the value of $2 - 7 / 4$ for $N$ is arcane, apparently so much so that ASA PH2.12-1961 included an explanation of what ASA PH2.5-1960 had intended.
^ EXIF 2.2 refers to $S v$ as “film sensitivity.”

[edit] References

Adams, Ansel. 1981. The Negative. Boston: New York Graphic Society. ISBN 0821211315

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.

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.