All About Exposure
I wrote this article about exposure many years ago. I've updated it to reflect the change from film to digital which has happened since it was written, but that's about all the changes it needed. What was true then, is still true now
Shutter speed is, of course, measured in seconds or fractions of a second, and these are familiar units needing no explanation. Aperture, however, is measured by means of f-stops, and though I'm sure everyone is familiar with numbers such as f2.8 and f8, probably not everyone is clear on what these numbers actually mean.
The simplest way to explain f-stops is to consider a very simple lens system in which a single element lens is placed one focal length away from the film. Let's say we have a lens 75mm in diameter and 300mm in focal length. Now another term for f-stop is f-ratio, and the ratio referred to is the ratio of the focal length of the lens to its diameter. In this case the ratio is 300/75, or more simply 4.0! Thus such a lens has a photographic "speed" (also called "f-stop", "f-ratio" or "f-number") of f4. If we use a lens of only half the diameter (37.5mm), but the same focal length (300mm), it would then be an f8 lens. I think it's clear that the smaller diameter lens will collect less light than the larger one, and so the image formed by the smaller diameter f8 lens will be less bright than that formed by the larger diameter f4 lens.
Now real photographic lenses are complex designs which use many lens elements. Clearly they don't change their f-stop by varying the physical size of their lens elements. Instead an internal, variable diameter, iris (also called a "stop") is used to regulate the effective aperture. As the iris closes down to a smaller diameter, less light is allowed through the lens and the image formed by the lens becomes dimmer. Thus the brightness of the image formed by a complex 300mm f2.8 lens with a front element 107mm in diameter, when that lens is used at f4, is exactly the same as that formed by a simple, 75mm diameter 300mm focal length f4 lens. Moreover, the image formed by any f4 lens, whether 300mm, 50mm or 20mm in focal length will be the same brightness.
Where does the "normal" f-stop sequence come from?
You might wonder why the normal f-stop sequence is the way it is. Why f1, f1.4, f2, f2.8, f4, f5.6, f8, f11, f16, f22 and so on rather than some other set of numbers? Well, it's because the normal sequence represents a doubling or halving of image brightness. The brightness of the image depends on the effective area of the lens used to form the image. The f-stops (as described above) are related to the effective diameter of the lens used to form the image. The effective area is proportional to the square of the effective diameter, thus to increase the effective area by a factor of two (and therefore increase image brightness by a factor of two) you need only increase the effective diameter (or divide f-stop) by a factor of the square root of two, or 1.4 (1.414 to be more exact). To decrease image brightness by a factor of two, we must then divide the effective diameter (or multiply f-stop) by 1.4.So, starting out from f1.0 (which is a nice round number!) decreasing the image brightness by a factor of two gives us f1.4. Decreasing the image brightness by another factor of two gives f2.0, and so on to f2.8, f4, f5.6 and the rest. Changing the image brightness by a factor of two in this manner is called changing the exposure by "1 stop". Opening up the aperture to give a brighter image (and a smaller f-number) is called "opening up by one stop", while decreasing image brightness by a factor of two (and so going to the next larger f-number) is called "closing down by one stop".
Fractional f-stops
Of course some lenses can be set in 1/2 stop steps, or even 1/3 stop steps for very fine exposure control. While adjacent numbers in the full stop step sequence are related by a factor of 2√2 (1.414), as described above, adjacent numbers in the 1/2 stop sequence are related by a factor of 4√2 (1.189) and in the 1/3 stop sequence they are related by a factor of 6√2 (1.122).Thus a full stop sequence would be : f4, f5.6, f8 etc.
a 1/2 stop sequence would be : f4, f4.7, f5.6, f6.7, f8 etc.
a 1/3 stop sequence would be : f4, f4.5, f5, f5.6, f6.2, f7.2, f8 etc.
Fractional Shutter Speeds
Shutter speeds are a little easier to understand. Again, the normal sequence of shutter speeds proceeds in factors of two. Starting from 1 second, decreasing exposure by a factor of two give 1/2 second, and decreasing by a further factor of two give 1/4 second. as we go along the sequence we find 1/8 second, 1/15 second (not quite a factor of two, but chosen to give "round numbers" further along the sequence), 1/30, 1/60, 1/125 (again not quite a factor of two!), 1/250, 1/500, 1/1000 and so on. The small "glitches" in the sequence (at 1/15 and 1/125) have no practical importance. Without them we would have 1/16, 1/32, 1/64, 1/128, 1/256, 1/512 and 1/1024 second shutter speeds. Though there are no physical "stops" involved with shutter speed, a change from one of the above speeds to the next is often referred to as changing the shutter speed by "1 stop". Just as with aperture stops, shutter speeds can be changed in fractional stops. Cameras are available which can set shutter speeds in both 1/2 and 1/3 stop units. Adjacent shutter speeds in a 1 stop sequence are related by a factor of two, in a 1/2 stop sequence they are related by the square root of 2 (1.414) and in a 1/3 stop sequence they are related by the cube root of 2 (1.26).Thus a full stop sequence is : 1/125, 1/250, 1/500 etc
a 1/2 stop sequence is: 1/125, 1/177, 1/250, 1/354, 1/500 etc.
a 1/3 stop sequence is: 1/125, 1/158, 1/198, 1/250, 1/315, 1/397, 1/500 etc.
Many modern cameras with electronic shutters are essentially "stepless", i.e. when used in automatic modes the shutter speed can be changed in very small steps of 1/10 stop or less, however the shutter speed displayed under these conditions is normally the nearest full, 1/2 or 1/3 step unit, depending on the camera.
Exposure Value (EV)
The correct exposure for a given scene is usually expressed as a combination of shutter speed and f-stop. An exposure meter, either built into the camera or a hand held external meter, is normally used to determine just what this correct exposure is. However, on bright sunny days, the correct exposure for a front-light mid-toned subject is given by the "sunny-f16" rule. Basically this states that the exposure under these conditions is 1/ISO (seconds) at f16. Thus at ISO 64, the exposure would be 1/60 at f16. At ISO 125, the speed would be 1/125 at f16.Of course that doesn't mean that you have to shoot at 1/125 and f16. If we open up to f11, we increase the image brightness by a factor of two, and if we change the shutter speed to 1/250 we halve the time for which the film is exposed to the image. These two effects cancel, and so 1/125 @ f16 and 1/250 @ f11 are the same exposure, as are 1/500 @ f8, 1/1000 @ f5.6, 1/2000 @ f4 and so on. There is, in fact, a single number which represents all these values. It is called the "Exposure Value" or EV. In this example, 1/125@f16, 1/250 @f11 and all the equivalent combinations of shutter speed and aperture can simply be represented by EV 15. A change of 1 EV unit is the same as a change of 1 full stop of aperture or one "stop" of shutter speed, thus if 1/125 @ f16 is EV 15, then 1/250 @f16 is EV 16 and 1/125 @f11 is EV 14. Higher EV numbers mean less exposure, lower numbers more exposure.
In order to relate EVs to absolute brightness levels, you have to define film speed. Thus using the sunny f16 rule, exposure at ISO 64 would be 1/60 @ f16, which is EV 14 ("EV 14 at ISO 64") while at ISO 125 it would be 1/125 @f16, which is EV 15 ("EV 15 at ISO 125"). You will see EVs used in this way in camera specifications where the operating range of the autofocus system and/or the built in exposure meter are expressed in terms of EV units. A range to EV 1 to EV 18 would be fairly typical. For reference, EV 15 at ISO 100 is a typical of a clear bright, sunny day. A brightly light office is usually at EV 7 or 8 at ISO 100 and a typical living room under artificial light is around EV 5 at ISO 100.
You can easily calculate EV from shutter speed and aperture using the formula:
EV = AV + TV
Where AV is the aperture value and TV is the time value as shown below:
| Speed | 1 | 1/2 | 1/4 | 1/8 | 1/15 | 1/30 | 1/60 | 1/125 | 1/250 | 1/500 |
| TV | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| F # | f1 | f1.4 | f2 | f2.8 | f4 | f5.6 | f8 | f11 | f16 | f22 |
| AV | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
Brightness Value (BV)
There is another unit of exposure which doesn't include film speed. This is the unit of "Brightness Value" or BV. On the BV scale "sunny f16" corresponds to BV 10. To get BV units, take the EV and subtract 3 for ISO 25, 4 for ISO 50, 5 for ISO 100, 6 for ISO 200, 7 for ISO 400, and so on. BV units don't seem to be used much, but if you ever see them, at least you now know what they are!
ISO Setting
In the days of film ISO setting (which is a measure of the sensitivity to light of the recording medium) wasn't much of a variable. You would chose your film, which had a fixed sensitivity, then use shutter speed and aperture to control exposure. With the advent of digital imaging, ISO is now as easily changed as shutter speed and aperture. It does affect image quality, higher ISO settings having more noise than lower setting (just as high ISO film shows more grain than low ISO film), but it does allow one more "degree of freedom" in exposure.The ISO setting is a linear function of sensitivity. By that I mean that if you double the ISO setting (say from 100 to 200), you only need 1/2 the exposure. So if the exposure was 1/100s at F8 and ISO 100, at ISO 200 the exposure would be 1/200s at f8 (expose for 1/2 as long) or 1/100s at f11 (reduce the amount of light by a factor of two). Each doubling or halving of film sensitivity is still called a change of one stop. So ISO 200 is 1 stop faster than ISO 100 and ISO 400 is one stop slower than ISO 800.
By tradition, fractional stop changes in ISO are done in 1/3 stops, never in 1/2 stops. The 1/3 stop sequence of ISO changes is a sequence based on multiplication by the cube root of 2 (1.26), though the numbers are rounded. Thus 1/3 stop faster than ISO 100 would be 100 x 1.26 = 126. In fact this is usually given as 125. Similarly 2/3 stop faster is 100 x 1.26 x 1.26 = 159, usually given as 160. Here's the sequence from ISO 50 to ISO 1600 in 1/3 stop steps.
50, 64, 80, 100, 125, 160, 200, 250, 320, 400, 500, 640, 800, 1000, 1250, 1600
Neutral Density Filters
A fourth way of modifying exposure in addition to shutter speed, aperture and ISO setting
is by the use of an external neutral density filter on the lens. This filter absorbs all wavelengths (colors) of light equally and so doesn't change the color balance of the image. Neutral density filters are most often used to allow longer shutter speeds for special effects, such as time exposures which can turn flowing water into a "silky stream" as shown here on the right which was shot with a 1 second exposure.
There are three systems of specifying how much light a filter absorbs and this can lead to some confusion. Filter strength can be expressed in stops, which if you understood the rest of this article should be a familiar measurement by now. Filter strength can also be expressed as a filter factor. In this system a 2x filter needs 2x more exposure, a 4x needs 4x more exposure and an 8x needs 8x more exposure. Since a stop is defined as doubling or halving exposure, it's clear that a 2x filter is also a 1 stop filter, a 4x is a two stop and an 8x is a 3 stop. There's also a third way of expressing filter strength called Optical Density, OD (or sometimes, less correctly, Neutral Density, ND)). In this system the change in exposure is given by 10 raised to the power OD. So for a 0.3 OD filter the change in exposure is 10 raised to the power 0.3 (100.3), which is 1.995, or 2 when you round it off. So a 0.3 OD filter is the same as a 2x filter, which is the same as a 1 stop filter. The table below shows some common values for ND filters.
| Stops | 1 | 2 | 3 | 6 | 8.65 | 10 |
| Filter Factor | 2x | 4x | 8x | 64x | 400x | 1024x |
| Optical (Neutral) Density | 0.3 | 0.6 | 0.9 | 1.8 | 2.6 | 3 |
If you buy an "ND2" or "2ND" filter, just be sure whether that "2" is a filter factor (in which case it's a 1 stop filter), a stop factor (in which case it's a 2 stop filter) or an OD factor (in which case it's a 6 and 2/3 stop filter).
• [NEXT - Part II - Determining Correct Exposure]
Further Reading
