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Exponentials - The Relationship between Aperture, Shutter Speed and ISO

Introduction

Once you start using the full manual mode on a camera (or to a much lesser extent, the shutter and aperture priority modes), it becomes increasingly important to understand how Aperture, Shutter Speed and ISO settings affect exposure as well as their relationship with each other.

Most people with small compact cameras will leave their camera in 'automatic' mode. Set as such, the camera will automatically calculate settings to "optimise" the exposure. The aperture, shutter speed and (on some cameras) ISO is adjusted within certain parameters, and the flash triggered if necessary. All that is required for the operator to do is to point the lens at a scene, and press the shutter button.

In fact, some cameras (both film and digital) lack any form of manual control at all. As distinct from compact cameras, some of which do offer partial or complete manual control, these cameras are known colloquially as "point and shoot" cameras (although this tag is often used - erroneously - to refer to all compact cameras).

However, there's times when controlling your camera manually can be useful, if not essential. For example, there are times when triggering a flash would be completely inappropriate (in restaurants or at concerts if photography isn't banned), forbidden (in many art galleries, for obvious reasons) or pointless (if you're taking a photo of the moon, for example).

On the other hand, you might like to keep the shutter open for an extended period of time if you were capturing star trails or the trails of car lights passing by. Similarly, the aperture setting of a lens controls not only the amount of light that is allowed through, but also the depth of field, as discussed in this article.

Aperture and shutter speed affect each other, and both follow exponential scales. A third variable, ISO, also affects exposure in the same exponential manner. How does it all hang together? As it turns out, quite neatly...

Aperture

Much like the iris of a human eye, camera lenses (along with microscopes, telescopes and other precision optics) contain a diaphragm that can vary the aperture diameter of the lens. The purpose of this diaphragm is identical to that of the iris - it increases or decreases the size of the aperture, effectively controlling the amount of light that can pass through the lens.

Of course, in the context of photography, referring to "wider" and "narrower" aperture diameters without any further method of measuring the aperture size would make it difficult to control the exposure of any given photograph. This isn't to say that just because it's a bad idea, it hasn't been done - for example, some Polaroid cameras sported aperture levers without any associated scale.

F-Numbers

Given the large variation of lens sizes from relatively small optics like a 50mm lens to extremely large 400mm or 600mm telephoto lenses, simply measuring the diameter of the diaphragm opening isn't a consistent metric indicative of the cone angle, and therefore the amount of light passing through the lens. Instead, the f-number scale is used.

The f-number of a lens is the result returned when the focal length of the lens is divided by the diameter of the aperture diaphragm, when both the focal length and the aperture opening are measured in the same units. Being a ratio, the f-number of a lens is a dimensionless number, much like the decibel scale familiar to many people as a measure of sound pressure. By convention, the f-number is written as f/x, where x is the f-number.

Looking at the definition of the f-number, it is immediately evident that the value of the f-number will be inversely proportional to the diameter of the diaphragm opening, making these numbers counter-intuitive to those unfamiliar with them. By convention, f-numbers are used in f-stops, where an increase or decrease of one stop doubles or halves the intensity of light passing through the lens respectively. Given that the intensity of light passing through the lens is directly proportional to the area of the diaphragm opening, this corresponds to this area doubling or halving.

Given that the area of a circle is defined as πr² (where r is the radius of the circle), some simple maths will then show that to double the area of the (circular) diaphragm opening, its radius (and therefore the diameter) must be increased by a factor of √2. Likewise, the halve the area of the diaphragm opening, its radius will need to be divided by √2. The table below shows typical full-stop, half-stop and third-stop scales between f/1.0 and f/8. Note that, for the purposes of photography, f-number values are rounded to one decimal place. Of course, lenses have minimum apertures much smaller than f/8, with lenses commonly closing up to f/32, and some closing further still.

It is, of course, possible to create lenses with f-numbers less than one, although such lenses are relatively rare and when available, very expensive. The lens with the widest aperture (f/0.7) was created by Carl Zeiss AG for NASA and was used during the Apollo program to photograph areas of the moon not well illuminated by the sun. Interestingly, surplus copies of this same lens were used by Stanley Kubrick for use in the movie Barry Lyndon ^[1]. Other notable lenses with wide apertures include the Leica Noctilux 50mm (f/1.0), and the Canon EF 50mm f/1.0L, which although discontinued, remains the fastest autofocus lens made by Canon (the Canon f/0.95 "Dream Lens" sold with the Canon 7 Rangefinder was manual focus only, like the Noctilux).

It should be noted that when lens aperture is described in marketing or technical material, the maximum aperture of the lens is described. In the case of zoom lenses, the maximum f-number of the lens can change depending on the focal length. Such a lens will therefore have the changes in its maximum aperture noted (for example f/4-5.6). High-end zoom lenses will often maintain the same f-number through their zoom range. Such lenses are called constant aperture zoom lenses even though the size of the physical aperture will obviously need to change with the focal length to maintain the same f-number.

Typically, a prime lens (that is, a lens with only one focal length, as opposed to a zoom lens) will open to wider apertures than a zoom lens of the same focal length. This makes prime lenses more usable in low-light situations, and opens creative opportunities with respect to a shallow depth of field. Some photographers prefer the opportunities offered by prime lenses, while others will prefer the versatility of a zoom.

Shutter Speed

Traditionally, cameras have shutters that sit over the film plane, blocking the passage of light. When a photograph is taken, the shutter opens for a specified period of time, exposing the film behind (or in the case of digital cameras, the image sensor) to the required amount of light before closing once more. Obviously, the longer the shutter remains open, the more light will reach the film or image sensor.

However, there are limits to how long a photographer can keep the shutter on their camera open. For example, if the camera is not on a tripod and you are not using a stabilised lens, leaving the shutter open for even seemingly short periods of time (for example, half a second) will result in images being blurred due to "camera shake", since it is physically impossible to hold a camera completely still. Likewise, if you are shooting an object that is not stationary or moving in a predictable manner, then keeping the shutter open will result in blurred photos due to subject movement, even if the subject movement is not easily perceptible to the human eye.

On the flipside, you may want to keep the shutter open for a longer period, in order to capture startrails, or merely to pan the camera with a subject, blurring the background and giving the perception of motion. This photo provides a good example of the effect gained by panning.

Assuming a relatively constant light source, the amount of light that reaches the flim/image sensor will be directly proportional to the amount of time the shutter remains open. Therefore, halving the time the shutter remains open will result in the amount of light reaching the film being reduced by half. Likewise, doubling the time the shutter remains open doubles the amount of light being captured by the camera.

Ignoring other effects caused by longer shutter times and aperture, it is therefore evident that for any given exposure, increasing the aperture size by one stop and halving the shutter time will result in the same exposure. Likewise, decreasing the aperture size by one stop and doubling the shutter time will also result in the same exposure.

ISO (formerly "Film Speed")

Sometimes, there isn't enough light for a camera to take a correct exposure using the aperture settings and the shutter speed selected by the photographer. In the film age, this problem was countered (assuming the flash wasn't being used) by loading different films with different sensitivity to light. Such film speed was measured in two different ways, known as the ISO Arithmetic Scale and ISO Logarithmic Scale. These scales are defined in ISO 5800:1987, a standard ratified by the International Organisation for Standardisation (its proper name, as opposed to "International Standards Organisation" which many incorrectly assume to be the case). The ISO Arithmetic scale was formerly known as the ASA scale, while the ISO Logarithmic scale was formerly known as the DIN scale. Out of the two, the ISO Arithmetic scale made the successful transition into digital photography and will be discussed further in this article.

In the ISO Arithmetic scale, a doubling of the ISO value represents a doubling of the film speed. This means that a film rated as ISO 200 is twice as sensitive to light as that rated ISO 100. To maintain the same exposure, this would also correspond to one aperture stop, or halving/doubling the time the shutter remains open.

However, this doesn't necessarily amount to "free light", since there is a price to pay for this extra speed. Films with higher ISO ratings are susceptible to film grain which is the phenomenon of the physical granules of silver halide used inside film showing up in the final photograph. Faster films required larger silver halide particles, which become increasingly large and obvious as film speed increases.

In the digital age, film speed is simulated by increasing the sensitivity of the sensor by adjusting the signal gain in the camera's internal signal amplifier. While this phenomenon is being gradually improved in newer digital camera bodies, increasing the ISO, especially to higher values (like ISO 800 and above) will result in the introduction of image noise to a photograph. While such noise can be used to artistic effect, it is generally seen as undesirable. As such, photographers generally strive to use the lowest ISO possible, while still obtaining the photographs desired. Obviously, a slightly "noisy" photo is better than no photo at all!

Altering exposure through other means

There are other ways that photographers alter the amount of light entering a photo, independently of the camera controls, some of which may or may not be available to them at any one time. The method most familiar with most people is the use of a flash strobe to add additional light into a dimly-lit scene.

The opposite problem - too much light - is also commonly encountered, especially when shooting landscapes or in bright daylight. In this case, neutral density filters. These basically work as 'sunglasses' for a lens, although a neutral density filter ideally will not introduce any colour tinting into an image. These filters have an ND rating which indicates the amount of light reduced by the filter. This rating is often written in the form ND 2^x, where x is the number of stops of light reduced by the filter. Therefore, an ND2 filter will have reduced one stop of light, an ND4 two stops. Extremely strong filters do not obey this convention, with an ND1000 being a ten-stop filter (rather than ND1024) and an ND10000 being a 13-stop filter.

Graduated Neutral Density filters are similar to Neutral Density filters, except that the strength of the filter varies across its surface. Graduated Neutral Density filters are clear on one end, with the filtered surface on the other end. These are often used when filming landscapes, especially at sunrise or sunset when the sky can be very bright, and the rest of the scene quite dark, exceeding the dynamic range of the film or image sensor.

Citations

• ^[1] Wikipedia - Lens Speed, Retrieved 12 September, 2009