Additive Photographic Exposure System (APES)
Revised 20150927 by Bill Claff
The Additive Photographic Exposure System (APES) is a formulation that captures a first order approximation of the fundamental law of exposure. The formula is based on Exposure Value (EV) terms that represent the contribution of brightness (B), film speed (S), aperture (A), and shutter speed (T) to the exposure. Note that brightness in this context is scene luminance and not the "brightness" of the final image. The use of base‑2 logarithms (log_{2}) in the equations that follow is a convenience for practical use. The APES equation is:
EV_{B} 
 
EV_{X} 
+ 
EV_{S} 
= 
EV_{A} 
+ 
EV_{T} 
= 
EV 
Brightness 
 
Exposure
Compensation 
+ 
Speed 
= 
Aperture 
+ 
Time 
= 
Exposure 
The formulas for the EV terms are:
EV_{B} 
= 
log_{2}(B_{CSF}) 
where B_{CSF} is luminous brightness in candles ft^{2} 
EV_{X} 
= 

where X is exposure compensation in stops 
EV_{S} 
= 
log_{2}(S_{A}) 
where S_{A} is ISO arithmetic speed (ft^{2} candles^{ 1}sec^{1}) 
EV_{S} 
= 
(S_{L}  1) / 3 
where S_{L} is ISO logarithmic speed 
EV_{A} 
= 
log_{2}(A^{2}) 
where A is the aperture f‑number 
EV_{T} 
= 
log_{2}(T^{1}) 
where T is the exposure time in seconds 
Note that my definitions of EV_{B} and EV_{S} differ from the “standard” formulas. The “standard” formulas use 3.125 as an approximation for π so that EV_{S} values for common ISO arithmetic film speeds are whole numbers. Substituting 3.125 for π and remembering that candles ft^{2} = foot‑Lamberts / π, the “standard” EV_{B} and EV_{S} formulas are:
EV_{B} 
= 
log_{2}(B_{FL}) 
where B_{FL} is luminous brightness in foot‑Lamberts 
EV_{S} 
= 
log_{2}(S_{A} / 3.125) 
where S_{A} is ISO arithmetic speed (ft^{2} candles^{ 1}sec^{1}) 
EV_{S} 
= 
log_{2}(S_{A} * .32) 
where S_{A} is ISO arithmetic speed (ft^{2} candles^{ 1}sec^{1}) 
The “standard” formula for EV_{S} differs by only .127% arithmetic or .00764EV (about 1/131EV) from the “correct” formula. This difference is insignificant so either scheme can be used interchangeably. I prefer the “correct” formulas because they model the underlying physics exactly without introducing any “magic” number.
Also note that the “standard” formulas do not include EV_{X }and_{ }EV_{X} is assumed to be 0.
Using the initial formulas, replacing each EV term with its formula, and raising each side of the equation to the power of 2 we get the underlying equation in arithmetic rather than logarithmic terms:
B_{CSF} ∙ S_{A} ∙ 2^{X} 
= 
A^{2} ∙ T^{1} 
For a properly exposed photograph:
· Compute the required EV:
o Determine EV_{B} (internal or external light meter)
o Bias EV_{B} with any exposure compensation value (typically 0EV)
o Compute EV by adding EV_{S} to the biased EV_{B} to adjust for the sensitivity of the film
For cameras with built‑in exposure meters these computations are performed automatically.
· Set A and T so that EV_{A} plus EV_{T} equals EV
o In program (P) mode the camera sets A and T automatically.
o In aperture priority (A) mode you set A and the camera sets T.
o In shutter priority (S) mode you set T and the camera sets A.
o In manual (M) mode you set both A and T.
Cameras with built‑in meters generally display (EV_{B} – EV_{X} + EV_{S}) – (EV_{A} + EV_{T}).
The rule is: on a sunny day set your aperture to f16 and your shutter speed to 1 over your film speed.
Assuming EV_{X} = 0, why does this work?
· If EV_{B} = EV_{A} then EV_{S} = EV_{T}.
· If EV_{S} = EV_{T} then S_{A} = T^{1}; e.g. ISO 200 means 1/200^{th} shutter speed.
Does it make sense?
· If A = f16 then EV_{A} = 8 = EV_{B}.
· If EV_{B} = 8 then B_{CSF} = 256 candles ft^{2} = 2,758 candles m^{2} = 8,665 lumens m^{2} = 8,665 lux.
· If luminance is 8,665 lux for an average reflectance of 18% then illuminance is 48,139 lux; about right for full sun at an angle.
Note that if it’s cloudy you might do better with the “Cloudy 11 Rule” or if it’s bright perhaps the “Bright 22 Rule”.
EV_{S} is placed on the left‑hand‑side of the equation because after having chosen which film to load in the camera, the film photographer has no control over the film speed. In the absence of an exposure compensation dial or as al ternate method of exposure compensation the film photographer can change EV_{S} to differ from the speed at which the film will be processed. The film photographer also has the option of processing the film at other than its rated speed; generally at a higher speed, which is called pushing the film.
In the digital era the “film” is processed in the camera and it is if each frame is a new roll of film. The digital photographer is more likely to change film speed on a frame‑by‑frame basis than the film photographer. Some digital cameras have modes that automatically vary film speed, putting film speed on an equal footing with aperture and exposure time regarding exposure. Note that digital film speed is fixed at the native speed of the digital sensor and that raising speed on a digital camera does not change the sensitivity of the sensor array [there are some exceptions]; it's equivalent to pushing film.
In review, here's the APES equation for reference:
EV_{B} – EV_{X} + EV_{S} = EV_{A} + EV_{T}
Using Nikon DSLR terms, common to many cameras, the values can be varied automatically by the camera as follows:
None 
Manual Mode 
EV_{A} 
Shutter Priority 
EV_{T} 
Aperture Priority 
EV_{S} 
Manual Mode with ISO Auto 
EV_{A} and EV_{T} 
Program 
EV_{A} then EV_{S} 
Shutter Priority with ISO Auto 
EV_{T} then EV_{S} 
Aperture Priority with ISO Auto 
EV_{A} and EV_{T} then EV_{S} 
Program with ISO Auto 
Exposure bracketing, in any mode, varies the EV_{X}
term from frame to frame over a series of frames.
Flash bracketing in any mode, has the sideeffect of varying EV_{B }from
frame to frame over a series of frames.