Apex - its use and abuse

[Doug Kerr]

APEX, the Additive System of Photographic Exposure, is a clever system of representing numerous factors invoked in the matter of photographic exposure - shutter speed, aperture, ISO sensitivity, etc. - on a base 2 logarithmic basis.

When the system was introduced (in 1961), its driving concept was that it would allow photographers to "solve the standard exposure equation" using only addition and subtraction and without the need for any constants.

On a more pragmatic level, the system was intended to allow photographers to easily apply standard rules of thumb for exposure based on "described" lighting conditions (that is, without benefit of an exposure meter). A few cameras (notably from Polaroid) and LF camera lenses in fact had special scales to play along with this.

But the widespread availability of exposure meters (which of course mostly had their own little circular slide rules for solving the "standard exposure equation), and soon the emergence of automatic exposure systems, led to APEX being mostly of no real value. It never was formalized in a real standard, just being presented as a interesting scheme in an appendix of the 1961 issue of the American standard for exposure meters. It was gone from the next issue of that standard (1971), with a note that it had not been (recently, I guess) used on consumer products.

Nevertheless, the system of logarithmic representation of exposure factors is still today of considerable utility in scientific and technical work.

Sadly, in that twilight zone between actual science and practical photographic work, there is are practices seemingly related to APEX that are wholly wrong.

I this note, I will give some insight into the APEX system and discuss some of these aberrations.

The APEX representations for the various photographic factors all have "value" in their names (such as Time Value, Aperture Value, etc.) and are represented by symbols ending in "V" (sometimes done as a superscript, or a lower-case "V"), such as Tv, Av, etc. The appearance of the word "value", or the letter "V in the symbol, is a cue that the APEX logarithmic representation is what we see.

By virtue of the use of base 2 logarithms, we find that for any doubling (or halving) of a quantity, the APEX "value" changes by 1 unit. Thus the scales essentially work in "stops", a concept already familiar to most photographers.

Both positive and negative values can exist were appropriate. Fractional values can be used when needed.

Basic quantities

For many of the quantities, the starting point of the scale is a handy and obvious one. For example for exposure time (Time Value, Tv), the part of that scale near Tv0 is like this:

Time Tv
4 sec -2
2 sec -1
1 sec 0
1/2 sec +1
1/4 sec +2
1/8 sec +3

Note that an increase in the value is in the direction of decreasing exposure. This eliminates some pesky minus signs in the exposure equation.

In the case of the aperture (Aperture Value, Av), the actual quantity indicated is not the f-number but rather the relative aperture area (so it will fit into the exposure equation).

The part of that scale near Av0 is like this:

f-number Av

1.0 0
1.4 +1
2.0 +2
2.8 +3
4.0 +4
5.6 +5

Photometric quantities

Two photometric quantities are included. One is "measured scene luminance" (Brightness Value, Bv). This is of course used in the "reflected light" metering approach, in which the average luminance of the scene, together with the ISO sensitivity, "suggest" a combination of exposure time and aperture that together constitute a certain "photographic exposure".

Then other is "scene illuminance" (Incident Light Value, Iv). This is of course used in the "incident light" metering approach, in which the illuminance on the scene, together with the ISO sensitivity, "suggest" a combination of exposure time and aperture that together constitute a certain "photographic exposure".

The APEX scales for the photometric quantities do not have such obvious starting points, in part because they have to be defined in terms of both "traditional" and SI (metric) units, and because of the need to make the standard exposure equation very simple for both reflected light and incident light metering concepts.

These scales work in the direction of a greater value for greater luminance/illuminance. That makes the exposure equation simple , since of course for a greater luminance/illuminance (greater value), a shorter exposure time and/or smaller aperture (greater value) is needed.

ISO sensitivity

The value scale for ISO sensitivity (Speed Value, Sv) includes these entries:

ISO Sv
25 +3
50 +4
100 +5
200 +6
400 +7

Exposure Value

The exposure time and aperture have a joint effect on exposure, and together determine a quantity known as "photographic exposure" This has its own representation in APEX, "Exposure Value, Ev". It is defined thus:

Ev = Tv + Av​

You may have seen EV used in a way that suggests it has a different meaning. Forget that (I will get to it shortly).

The abuses

APEX contains a perfectly appropriate "value" for describing scene luminance, Brightness Value (Bv).

But years ago, some camera manufacturers, deciding how to describe how low a scene luminance was suitable for, for example, their automatic focus system to operate with, decided that Bv was not a good way to express it (since few photographers had ever encountered it), nor to just express it in photometric units (few photographers were familiar with them either).

Instead they adopted this scheme: to describe some critical scene luminance, they would state the Ev value that, for an ISO sensitivity of ISO 100, the standard exposure equation would "recommend" as the photographic exposure for a scene showing that luminance.

Ugh.

By the way, for such an "Ev", the corresponding value of Bv (a real measure of luminance) is given by:

Bv = "Ev" - 5​

So "Ev" = Bv + 5 (we'll run into that a little later).

Just today I discovered another "curiosity". A question by a forum member called to attention the "program curve charts" for the Ricoh GR camera. These charts show how the camera's automatic exposure system , faced with a certain measured scene luminance, decide how to play the required photographic exposure (from the standard exposure equation, it turns out) as a specific shutter speed and specific aperture.

I was hoping not to find the scale of scene luminance in terms of Ev (as we sometimes do). No it wasn't. It was in terms of Lv. What is that?

Well, some manufacturers, chastised (par moi?) for calling Bv + 5 "Ev", invented a new, bogus APEX-like value, Lv (Light Value), which is defined as - you got it, Bv +5.

So yet, this is our abused "Ev", with a new name so it is not "wrong" - just bogus.

Shame!

If you want more detail on APEX (there are a number of dirty little secrets and curiosities I have not mentioned here), you may find this paper of interest:

http://dougkerr.net/Pumpkin/articles/APEX.pdf

Best regards,

Doug

 

[Doug Kerr]

A related issue is what is the "unit' of the various APEX values.

In fact, the Apex values are dimensionless and unitless; that is, they are just numbers. That is natural, since they are logarithms (which always are dimensionless and unitless).

Note in fact that when an APEX value is stated no unit is given. But they are stated with an unusual syntax.

For example, if I was operating at f/5.6, and was asked, "what Av are you using", the formal answer is not "5"; it is "Av 5". We should not write in a specification: Av = 5. We might write Av = Av 5.

This is comparable to the special formal syntax for ISO sensitivity. If I was operating at ISO 200, and was asked, "what ISO sensitivity are you using",. the formal answer is not "200", it is "ISO 200".​

And of course we can always say that the unit of all APEX quantities is "the stop".

If one felt the need to say that there was a special unit for, for example, Av, one could perhaps say that the unit was "the Av" (or "one Av"). But that's not really so. Remember, f/5.6 is not "4 Av". It is "Av 4".

But somehow the habit has emerged of thinking that the unit for all APEX-like values is "the Ev" (probably since that's the only APEX value anybody has heard of). So we hear of "reducing the scene brightness by 2 Ev" by cutting back the lights, to avoid overexposure, or that some manufacturer's rating of the ISO sensitivity of his cameras is "consistently 0.5 Ev low".

In fact, I would describe that situation as "0.5 units low", or (even though this is not discussed by what passes for the formalities of APEX), "0.5 stop low".

Best regards,

Doug

 

[Asher Kelman]

..and I thought they were telling the truth!

So what are the rules for summing up the various Apex and pseudo Apex settings? Do we ever have to take account of the "+5" correction id we just have Av, Tv and ISO or only when we use a lightmeter and get EV?

Asher

 

[Doug Kerr]

Hi, Asher,

..and I thought they were telling the truth!

So what are the rules for summing up the various Apex and pseudo Apex settings? Do we ever have to take account of the "+5" correction id we just have Av, Tv and ISO or only when we use a lightmeter and get EV?

The use of the bizarre value "Lv" (or the misuse of "Ev") is only a matter of how luminance is stated in specifications or on charts. It has no effect (thankfully) on the working of the exposure metering, whether via an internal AE system or an external exposure meter. So the"+5" never has to be taken account of (unless of course we are trying to understand the theory of a program line chart or a specification for AF low-light sensitivity!).

It is as if the maker of per-mixed concrete tells us that one bag will make 15 minutes of concrete, but by that he means 1.2 cubic feet. It doesn't affect the concrete.

The "standard exposure equation" for reflected-light metering is:

Av + Tv = Bv + Sv​

where Av is the logarithmic expression of exposure time (shutter speed), Av is the logarithmic expression of aperture, Bv is the logarithmic expression of measured average scene luminance ("brightness"), and Sv is the logarithmic expression of the ISO sensitivity (ISO speed, to be specific).

This can be written as:

Ev = Bv + Sv​

so we do not need to be concerned how we "swap out" shutter speed and aperture.

Now if we are doing incident light metering, the equation becomes:

Av + Tv = Iv + Sv​

where Iv is the logarithmic expression of the measured illuminance on the scene.

This can be written as:

Ev = Iv + Sv​

It may seem odd that the two equations are essentially identical, given all the baloney about assumed average scene reflectance and the like.

The fact is that all that folklore has been built into the definitions of the scales for Bv, Iv, and Sv, so the equations will be essentially identical and "beautifully simple".

If we want to slightly change the "metered exposure strategy" from the one on which the equations are predicated, you would think that would require putting a "fudging constant" in the equations. But that's not how it works.

The equations stay just as they are (beautifully simple), but we tweak the definitions of of Bv and/or Iv to apply the "fudge".

Aargh!

Best regards,

Doug

 

[Doug Kerr]

As an aside, note that several attributes that are part of the Exif metadata structure are encoded in an Exif/DCF file in terms of APEX values. These include shutter speed, aperture, maximum aperture, exposure bias, brightness, and ISO sensitivity. Their tags have names including "value" (e.g., ShutterSpeedValue).

The encoding is given in Annex C of CIPA-DC-008-2012 (Exif version 2.3). It references APEX, even though there is in fact no standard or specification for such.

The data type used is SRATIONAL (a signed rational, given as a numerator and denominator of the SLONG data type), except for the aperture and maximum aperture quantities, in which case the data type is RATIONAL (unsigned rational, given as a numerator and denominator of the LONG data type).

That means that the largest aperture that can be encoded is f/1.0.

Best regards,

Doug

 

[Doug Kerr]

Exposure metering constants in APEX

We don't hear much discussion about it these days, but the ISO standards for free-standing photographic exposure meters do not prescribe a unique "calibration" of the meter.

By "calibration" I mean what photographic exposure (combination of shutter speed and aperture) will the meter "recommend" for a certain measured average scene luminance (for the "reflected light" mode) or scene illuminance (for the "incident light" mode) together with the exposure index (what we tell the meter is the ISO sensitivity of the film or digital camera).​

Rather, the "exposure equation" used by the meter includes a calibration constant (K for the reflected light mode, C for the incident light mode) which may be chosen by the meter manufacturer over a fairly generous range.

This of course respects the quite reasonable tradition that there is no single "proper" exposure equation. (Discussions today about "exposure strategy" reflect this.)

The ISO standard for automatic exposure systems, however, in fact prescribe a unique "exposure equation", and thus essentially a certain value of K (although the equation is not stated in those terms), albeit with a generous "tolerance".​

Now in APEX, there is no "calibration constant" visible in the exposure equations, suggesting at first that a unique equation is "suggested". But as we look deeper, we find one of the dirty little secrets of APEX.

For both Brightness Value (Bv), the average scene luminance (pertains to "reflected light" metering) and Incident Light Value (Lv), the scene illuminance (pertains to "incident light" metering), the definition of the value has in it a "calibration constant" (in fact, K for Bv, C for Iv). As before, the meter manufacturer may choose values of K and C that will fulfill their adopted "exposure strategy".

(Of course, in APEX we are not necessarily talking about meters; this is a supposedly a system of describing physical properties! But this all is a historico-political accommodation.)

Commonly-seen tables of the specific luminance or luminance values for various integer values of Bv or Iv are in fact predicted on some specific value of K or C, although that is rarely mentioned.​

Thus, for example, an "APEX output" exposure meter, which reports the luminance or luminance as APEX values, will in so doing reflect the meter manufacturer's choice as to the "ideal" exposure equation.

I have "reverse engineered" my only free-standing exposure meter (a Miranda Cadius), based on tables nicely provided on the back of the meter) to determine the values of K and C it uses.​

Now, when a camera manufacturer shows curves that explain the strategy of their automatic exposure system, with one input being luminance (Bv), what value of K do they have in mind?

Probable answer: the value assumed by the widely-used tables.

Of course, in reality, camera manufacturers, in the context I mention, often use as the luminance parameter the value "Bv +5", which they label "Ev" (not a measure of luminance) or "Lv" (a name invented to legitimatize the practice of using Bv + 5 as the parameter of the exposure equation).​

The definition of BrightnessValue in the Exif specification gives the formal (APEX) mathematical definition of Brightness Value, including the calibration constant K , but then gives an explicit "encoding" table (the one that is commonly used, implying a certain value of K, which is never mentioned).

Talk about folklore!

Best regards,

Doug

 

[Doug Kerr]

In order to get some idea how the APEX scales for luminance and illuminance relate to familiar photographic practice, I will give an APEX interpretation of the "sunny 16" rule.

That rule suggests that, for midday full sun (in some unmentioned part of the world!), an appropriate exposure would be a shutter speed of 1/S (where S is the ISO sensitivity in use) and f/16 (or of course any equivalent photographic exposure).

If we plug these into the APEX "standard exposure equation", we learn that the "sunny 16" environment is one where the assumed incident solar illumination is, in APEX terms, Iv 9.6 (about 50k lux), and so, based on the average scene reflectance assumed by the APEX equations, the scene luminance would be Bv 9.6.

Note that this scene luminance would be identified, in the repulsive Lv notation, as Lv 14.6, or in the even more repulsive "Ev for luminance" notation as "Ev" 14.6.

So we would expect that the recommended photographic exposure, for ISO 100 (the premise of the "Ev for luminance" notation), would be Ev 14.6.

Following the "sunny 16 rule" for ISO 100, we would use (for example) 1/100 sec and f/16. For 1/100 sec, Tv is 6.6. For f/16, Av is 8. Thus Ev would be 14.6.

Quod erat demonstrandum.

Best regards,

Doug