Revised 2015-09-27 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. Note that brightness in this context is scene luminance and not the "brightness" of the final image. The use of base‑2 logarithms (log2) in the equations that follow is a convenience for practical use. The APES equation is:

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

The formulas for the EV terms are:

 EVB = log2(BCSF) where BCSF is luminous brightness in candles -ft-2 EVX = where X is exposure compensation in stops EVS = log2(SA) where SA is ISO arithmetic speed (ft2- candles -1-sec-1) EVS = (SL - 1) / 3 where SL is ISO logarithmic speed EVA = log2(A2) where A is the aperture f‑number EVT = log2(T-1) where T is the exposure time in seconds

Note that my definitions of EVB and EVS differ from the “standard” formulas. The “standard” formulas use 3.125 as an approximation for π so that EVS 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” EVB and EVS formulas are:

 EVB = log2(BFL) where BFL is luminous brightness in foot‑Lamberts EVS = log2(SA / 3.125) where SA is ISO arithmetic speed (ft2- candles -1-sec-1) EVS = log2(SA * .32) where SA is ISO arithmetic speed (ft2- candles -1-sec-1)

The “standard” formula for EVS 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 EVX and EVX 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 ∙ 2-X = A2 ∙ T-1

### Application to Photography

For a properly exposed photograph:

·        Compute the required EV:

o       Determine EVB (internal or external light meter)

o       Bias EVB with any exposure compensation value (typically 0EV)

o       Compute EV by adding EVS to the biased EVB 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 EVA plus EVT 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 (EVB – EVX + EVS) – (EVA + EVT).

### 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 EVX = 0, why does this work?

·        If EVB = EVA then EVS = EVT.

·        If EVS = EVT then SA = T-1; e.g. ISO 200 means 1/200th shutter speed.

Does it make sense?

·        If A = f16 then EVA = 8 = EVB.

·        If EVB = 8 then BCSF = 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

EVS 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 EVS 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:

EVB – EVX + EVS = EVA + EVT

Using Nikon DSLR terms, common to many cameras, the values can be varied automatically by the camera 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

Exposure bracketing, in any mode, varies the EVX term from frame to frame over a series of frames.
Flash bracketing in any mode, has the side-effect of varying EVB from frame to frame over a series of frames.