APEX system
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 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 where Use of the symbol formula_4 for luminance reflects photographic industry practice at the time  of ASA PH2.5-1960; current SI practice prefers the symbol formula_8. German sources typically used formula_9 for the relative aperture. Many authors now use formula_10 and formula_11 for relative aperture and exposure time. Recommendations for the value of the calibration constant formula_6 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. 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" formula_13, a base-2 logarithmic scale defined by When applied to the left-hand side of the exposure equation, formula_13 denoted combinations of camera settings; when applied to the right-hand side, formula_13 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 formula_13 scale . Adjustment of exposure was simple, because a change of 1 formula_13 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, Hasselblad, Voigtländer, Braun, Kodak, Seikosha, Aires, Konica, Olympus, Ricoh and others, introducing lenses with coupled 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 formula_13 scale on such cameras is discussed briefly by 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, 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 (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, 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: where ASA standards covered incident-light meters as well as reflected-light meters; the incident-light exposure equation is where The use of formula_43 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 formula_46. ASA PH2.12-1961 included incident-light metering in the APEX concept: where 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 formula_59 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 (formula_46, formula_4, and formula_43 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, Pentax and 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' exposure mode to automatically set the 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 formula_6. 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 (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 formula_64 -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 formula_10 given in the  Exif 2.2 specification ("Exif 2.2"; JEITA 2002) differs slightly from the APEX value of formula_40 (0.2973); with the Exif value, an ISO arithmetic film speed of 100 corresponds exactly to a speed value formula_67 of 5. The relationship between formula_68 and luminance depends on both the speed scaling constant formula_10 and the reflected-light meter calibration constant formula_6: Because Exif 2.2 records ISO arithmetic speed rather than film sensitivity, the value of formula_10 affects the recorded value of formula_68 but not the recorded film speed. Exif 2.2 does not recommend a range of values for formula_6, presumably leaving the choice  to the equipment manufacturer. The example data in Annex C of Exif 2.2 give 1 footlambert for formula_68 = 0. This is in agreement with the APEX value for formula_4, but would imply formula_77, or 3.125 with formula_4 in footlamberts. With formula_4 in cd/m, this becomes 10.7, which is slightly less than the value of 12.5 recommended by and currently used by many manufacturers. The difference possibly arises from rounding formula_4 in the example table; it also is possible that the example data simply were copied from an old ASA or ANSI standard.