APEX (photo)

APEX , Apex - Additive system for determining exposure ( Eng. Additive system of Photographic Exposure ), proposed in the United States in 1960 to simplify the calculation of exposure parameters when photographing ^[1] . The ASA PH2.5-1960 standard provided for a special sensitivity scale designed for use with the system.

Content

Exposure calculation

Until the late 1960s, cameras and movie cameras were rarely equipped with built-in exposure meters , and most photographers and cameramen determined exposure parameters from tables or based on personal experience. The system, based on the logarithmic nature of most sensitometric laws, as well as on the properties of the binary logarithm , made it possible to reduce complex calculations to simple addition and subtraction operations. Basic exposure calculations for photographic materials of any type are performed using the equation:

{\frac {A^{2}}{t}}={\frac {LS_{x}}{k}}\,,

{\ displaystyle {\ frac {A ^ {2}} {t}} = {\ frac {LS_ {x}} {k}} \ ,,}

Where

$A$ ${\ displaystyle A}$ - aperture number ;
$t$ ${\ displaystyle t}$ - exposure in seconds ;
$L$ ${\ displaystyle L}$ - averaged brightness in foot lamberts;
$S_{x}$ ${\ displaystyle S_ {x}}$ - arithmetic value of photosensitivity ;
$k$ ${\ displaystyle k}$ - calibration factor of the exposure meter;

The concept of “ exposure number ” developed by the German developer of shutters Friedrich Deckel was the basis of the APEX system, allowing simplification of the above calculation ^[2] . For this, the main parameters - aperture , shutter speed, brightness and photosensitivity - were expressed using a logarithm with a base of 2 . In this case, the exposure number for the light reflected from the subject $E_{v}$ ${\ displaystyle E_ {v}}$ determined by the sum ^[3] :

E_{v}=A_{v}+T_{v}=L_{v}+S_{v}\,,

{\ displaystyle E_ {v} = A_ {v} + T_ {v} = L_ {v} + S_ {v} \ ,,}

Where

$A_{v}$ ${\ displaystyle A_ {v}}$ - logarithmic diaphragm value: $A_{v}=$ ${\ displaystyle A_ {v} =}$ $\log _{2}$ ${\ displaystyle \ log _ {2}}$ $A^{2}$ ${\ displaystyle A ^ {2}}$
$T_{v}$ ${\ displaystyle T_ {v}}$ - logarithmic value of the shutter speed: $T_{v}=\log _{2}$ ${\ displaystyle T_ {v} = \ log _ {2}}$ $(1/t)$ ${\ displaystyle (1 / t)}$
$S_{v}$ ${\ displaystyle S_ {v}}$ - logarithmic value of photosensitivity: $S_{v}=\log _{2}$ ${\ displaystyle S_ {v} = \ log _ {2}}$ $(NS_{x})$ ${\ displaystyle (NS_ {x})}$
$L_{v}$ ${\ displaystyle L_ {v}}$ - logarithmic brightness value: $L_{v}=\log _{2}$ ${\ displaystyle L_ {v} = \ log _ {2}}$ $(L/Nk)$ ${\ displaystyle (L / Nk)}$

Coefficient $N$ ${\ displaystyle N}$ determines the relationship between the arithmetic value of photosensitivity $S_{x}$ ${\ displaystyle S_ {x}}$ and its logarithmic correspondence $S_{v}$ ${\ displaystyle S_ {v}}$ in different sensitometric systems. For ASA, the constant takes on value $2^{-7/4}$ ${\ displaystyle 2 ^ {- 7/4}}$ (approximately 0.3).

APEX Scales

The shutter speed and aperture values in logarithmic terms differ from the generally accepted ones and for the APEX system own scales were developed ^[3] :

Table 1. APEX Shutter Speed Scale
Seconds Exposure	one	1/2	1/4	1/8	1/15	1/30	1/60	1/125	1/250	1/500	1/1000
APEX T _v	0	one	2	3	four	five	6	7	eight	9	ten

Table 2. APEX Relative Hole Scale
Diaphragm	f / 1,0	f / 1.4	f / 2.0	f / 2.8	f / 4.0	f / 5.6	f / 8.0	f / 11	f / 16	f / 22
APEX A _v	0	one	2	3	four	five	6	7	eight	9

Fractional values correspond to intermediate settings $A_{v}$ ${\ displaystyle A_ {v}}$ and $T_{v}$ ${\ displaystyle T_ {v}}$ written in decimal. The f / 3.5 aperture in this case is expressed by a value of 3.67. Using these scales, you can easily match a known exposure number to the desired combination of shutter speed and aperture. For example, with an exposure value of 12 relative to the aperture of f / 5.6, which is expressed as 5, there corresponds a shutter speed of 1/125 second, which has a value of 7 on the APEX scale. At the same time, the corresponding photosensitivity scale, logarithmic values, were proposed $S_{v}$ ${\ displaystyle S_ {v}}$ which can be compared with units of any sensitometric system ^[4] ^[3] .

Table 3. Correspondence of photosensitivity units of different sensor systems to APEX values
ISO	DIN	GOST	APEX S _v
0.8	0 °	0.7	−2
1,6	3 °	1.4	−1
3	6 °	2,8	0
6	9 °	5.5	one
12	12 °	eleven	2
25	15 °	22	3
50	18 °	45	four
100	21 °	90	five
200	24 °	180	6
400	27 °	350	7
800	30 °	700	eight
1600	33 °	1440	9
3200	36 °	2880	ten

During shooting, the exposure number can be determined from the tables for most lighting conditions with an accuracy sufficient for black and white negative photographs . Its calculation of the measured brightness gives even higher accuracy, sufficient for color negative and even reversed films. However, the introduction of the system required marking the main scales of cameras in logarithmic units. Such an innovation did not reach the camera, since the appearance of APEX standards coincided with the beginning of the mass distribution of photoelectric exposure meters, which give a more accurate estimate of the exposure without any calculations. Some companies have introduced a separate scale of exposure numbers, but its presence was limited to equipment with a central shutter ^[5] . In the USSR, a group of GOI developers also proposed a new GOST photosensitivity scale of a similar type, but it did not find practical application ^[4] .

Only individual elements of the system have survived to this day, mainly the exposure number used to mark the exposure compensation scales and describe the sensitivity range of exposure meters and autofocus . Some manufacturers of camera equipment use the symbols “Av” and “Tv” inherited from the corresponding terms to indicate the aperture priority and exposure priority modes of exposure automation $A_{v}$ ${\ displaystyle A_ {v}}$ and $T_{v}$ ${\ displaystyle T_ {v}}$ . Logarithmic values of the shooting parameters are also used in EXIF metadata files ^[6] .

Notes

↑ Douglas A. Kerr. APEX — The Additive System of Photographic Exposure (English) (August 4, 2007). Date of treatment October 23, 2015.
↑ Photokinotechnics, 1981 , p. 431.
↑ ¹ ² ³ John A. Lind. Exposure The Science of Photography . Tripod.com Date of treatment October 23, 2015.
↑ ¹ ² Shulman M.Ya. Development of devices for automating the installation of expositions in cameras (Russian) . Photographic equipment . State Optical Institute named after S.I. Vavilov (1958). Date of treatment October 24, 2015.
↑ Cameras, 1984 , p. 78.
↑ Sergey Shcherbakov. Metadata in digital photography (Russian) . Image in numbers . iXBT.com (January 26, 2005). Date of treatment October 23, 2015.

Literature

E.A. Iophis . Photokinotechnics. - M.,: “Soviet Encyclopedia”, 1981. - S. 431. - 449 p.

M. I. Shulman. Cameras / T. G. Filatova. - L.,: "Mechanical Engineering", 1984. - 142 p.

[1] Douglas A. Kerr. APEX — The Additive System of Photographic Exposure (English) (August 4, 2007). Date of treatment October 23, 2015.

[_1e6b3ae896ffe1e7-2] Photokinotechnics, 1981 , p. 431.

[sien-3] ¹ ² ³ John A. Lind. Exposure The Science of Photography . Tripod.com Date of treatment October 23, 2015.

[ssr-4] ¹ ² Shulman M.Ya. Development of devices for automating the installation of expositions in cameras (Russian) . Photographic equipment . State Optical Institute named after S.I. Vavilov (1958). Date of treatment October 24, 2015.

[_9766660932aefc2f-5] Cameras, 1984 , p. 78.

[6] Sergey Shcherbakov. Metadata in digital photography (Russian) . Image in numbers . iXBT.com (January 26, 2005). Date of treatment October 23, 2015.