Additive Photographic Exposure System (APES)
Revised 2007-12-14 by Bill Claff

APES Theory

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. The use of base‑2 logarithms (log₂) in the equations that follow is a convenience for practical use. The APES equation is:

EVB	+	EVS	=	EVA	+	EVT	+	EVX	=	EV
Brightness Value	+	Speed Value	=	Aperture Value	+	Time Value	+	Exposure Compensation Value	=	Exposure Value

The formulas for the EV terms are:

EVB	=	log2(BCSF)	where BCSF is luminous brightness in candles -ft^-2
EVS	=	log2(SA)	where SA is ISO arithmetic speed (ft^2- candles^-1-sec^-1)
EVS	=	(SL - 1) / 3	where SL is ISO logarithmic speed
EVA	=	log2(A^2)	where A is the aperture f‑number
EVT	=	log2(T^-1)	where T is the exposure time in seconds
EVX	=		where X is exposure compensation in stops

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:

EVB	=	log2(BFL)	where BFL is luminous brightness in foot‑Lamberts
EVS	=	log2(SA / 3.125)	where SA is ISO arithmetic speed (ft^2- candles^-1-sec^-1)
EVS	=	log2(SA * .32)	where SA 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:

BCSF ∙ SA

=

A^2 ∙ T^-1 ∙ 2^X

Application to Photography

For a properly exposed photograph:

· Compute the required EV:

o Determine EV_B (internal or external light meter)

o Compute EV by adding EV_S to EV_B to adjust for the sensitivity of the film

o Adjust EV with any exposure compensation value (typically 0EV)

For cameras with built‑in exposure meters these computations are preformed 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_S) – (EV_A + EV_T + EV_X).

The “Sunny 16 Rule”

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”.

The Digital Era

Note that in formula initially presented that EV_X is placed on the right‑hand‑side of the equation along with the other values that are chosen by the film photographer. This also makes EV_X a positive value in keeping with the additive nature of the formulas.

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; it s equivalent to pushing film.

For discussion purposes I find it useful to rearrange the APES equation so that the values that can be automatically varied by the camera for a given frame are on the right‑hand‑side.

EV_B – EV_X = EV_A + EV_T - EV_S

Using Nikon DSLR terms the values on the right‑hand‑side can be varied as follows:

None	Manual Mode
EVA	Shutter Priority
EVT	Aperture Priority
EVS	Manual Mode with ISO Auto
EVA and EVT	Program
EVA then EVS	Shutter Priority with ISO Auto
EVT then EVS	Aperture Priority with ISO Auto
EVA and EVT then EVS	Program with ISO Auto

Finally, exposure bracketing can be used to vary the EV_X term from frame to frame over a series of frames.