Variables that affect exposure

Graphical concept: Eddy Talvala
Applet: Katie Dektar
Text: Marc Levoy
Technical assistance: Andrew Adams
Additional illustrations: Eddy Talvala

The amount of light recorded by a camera depends on the size of the lens opening (called the aperture) and the amount of time light is allowed to strike the film or sensor chip (called the exposure time). The former is controlled by varying the f/stop, a.k.a. F-number, and the latter is controlled by varying the shutter speed. In a digital camera it is also possible to vary its sensitivity to light by amplifying the voltage observed at each pixel position before converting that voltage to a number. The amount of amplification is called the ISO number. Unfortunately, each of these variables has a side effect: opening the aperture also decreases depth of field, lengthening the exposure time also increases motion blur (including motion blur due to camera shake), and increasing the ISO number also increases image noise. In this applet, we explore these tradeoffs.

Playing with aperture

The aperture of a camera is controlled by opening or closing a diaphragm, which is usually located in the middle of the lens assembly. The rules of geometrical optics allows us to replace this assembly with a single lens of appropriate shape if it simplifies our analysis. In this thin lens approximation, the diaphragm would be located just before or after the lens (along the optical axis). The aperture is then specified as an F-number N, defined by the well-known formula N = f/D, where f is the focal length of the thin lens (a.k.a. the effective focal length of the original lens assembly), and D is the diameter of the diaphragm opening. Doubling N while holding f constant halves the diameter D of the aperture, which in turn decreases its area by 4x. To make things more convenient, N is usually given as a sequence of square roots, e.g. f/4, f/5.6, f/8, f/11, f/16, f/22. Moving rightward in this sequence by one entry is called "closing down the aperture by one f/stop", e.g. from f/8 to f/11. Since f/11 is a smaller diameter than f/8 by sqrt(2), the area of the aperture is decreased by 2x. This halves the amount of light entering the camera - a factor that's easier to remember than 4x.

In the applet above, try dragging the aperture slider left and right. Each tickmark is 1/3 of an f/stop. The darker tickmarks have been rounded to the traditional numbers (e.g. f/1.4, f/2, f/2.8,...,f/22). Note that as you move to lower F-numbers, the image gets brighter, eventually turning white as it saturates the imaginary sensor in this visualization. Similarly, as you move to higher F-numbers, the image gets darker, eventually approaching black. The image should get twice as bright (or dim) with each f/stop of motion, but we've cheated on this so that the image doesn't disappear entirely. In other words, don't take the appearance of the image as being scientifically correct for each setting of the sliders; it's just a visualization.

As you move to higher F-numbers, note also that the foreground figure (in green) and background figure (in yellow) come into focus. This is the main side effect of changing the aperture - it increases depth of field. A full discussion of depth of field is beyond the scope of this applet, but an approximate formula is Dtot = 2NCU^2 / f^2, where N is the F-number, C is the allowable size of blur on the sensor, U is the distance to the scene, and f is the focal length of the lens. For example, for this picture of a pensive folk dancer, N = f/4, C = 2.5 microns (the width of one pixel on the Casio EX-F1 point-and-shoot camera that took this shot), U = 5.9 meters (19 feet), and f = 73mm. Plugging these into the formula, we get Dtot = 132mm (about 5 inches), which is barely the depth of the dancer's face. Note that 73mm on this camera is equivalent to 362mm on a 35mm SLR, i.e. a real telephoto shot. It is therefore not surprising that the depth of field is shallow. This makes it critical that the focus be good.

Playing with exposure time

The exposure time of a digital camera is controlled either by opening and closing a mechanical shutter lying near the sensor chip, or by controlling when the sensor pixels are reset to zero and when the electrons they have accumulated since being reset (due to the arrival of photons) is read off the chip. The latter is called an electronic shutter and is used in cell phone cameras and some point-and-shoot cameras. In either case, exposure time is measured in fractions of a second. (For this applet, let's assume that mechanical shutters can open instantly and close instantly, and that electronic shutters can reset and read off the entire chip at once. This allows us to ignore "focal plane distortion" and "rolling shutter distortion", respectively.

In the applet above, try dragging the exposure time slider left and right. Once again, the darker tickmarks have been rounded to the traditional fractional powers of two (e.g. 1/2, 1/4, 1/8,..., 1/500). Note that as you move to higher shutter speeds, the image gets darker. Now set the aperture to a high F-number, like f/16, and make the exposure time long, like 1/8 second. What happens to the visualization? It becomes blurred, reflecting the fact that most people cannot hold a camera steady enough to shoot at 1/8 second without using a tripod. This blur is called camera shake or handshake. Of course, if the object itself is moving, there will be additional blur, called motion blur. Both kinds of blur will be worse for long exposures than for short exposures. In the remaining paragraph, we use the phrase "motion blur" to denote both kinds of blur.

Playing with ISO

As mentioned earlier, a digital camera can be made more sensitive to light by amplifying the voltage observed at each pixel position before converting that (analog) voltage to a (digital) number, i.e. before A/D conversion. These numbers are arbitrary, so it was decided to use the same system originally defined by the International Standards Organization (ISO) to denote the sensitivy of film, a.k.a. film speed. This system was derived from an earlier standard for film speed established by the American Standards Association (ASA), a.k.a. the American National Standards Institute. The system says that a doubling of the ISO number denotes a doubling of sensitivity. In a digital camera this means an amplification by 2x of the voltage. By convention ISO 100 refers to no special amplification (beyond that normally done when the chip is read off), so it is the lowest ISO number available on most digital cameras. The maximum ISO varies from camera to camera. In addition, some cameras use multi-stage amplification, and other cameras switch at some point from analog amplification before A/D conversion to digital multiplication afterwards. In this applet we ignore these variations.

In the applet above, try dragging the ISO slider left and right. The tickmarks are powers of two beginning with 100 (i.e. 100, 200, 400). Note that as you move to higher ISO numbers, the image gets brighter. Now set the aperture to a high F-number, like f/16, so that the image is dark, and move the ISO slider rightwards. What happens to the visualization? It gets brighter, but it also becomes noisy! Noise means random variation in the intensity of pixels that should be the same color. It is beyond the scope of this tutorial to describe the various causes of image noise in a digital camera; it suffices to say that if you amplify the voltage levels coming from a sensor chip, you also amplify any random variation in these levels. A similar effect occurs when moving to films of higher speed, i.e. higher ASA, although for somewhat different reasons; it leads to graininess in the developed negative and hence in the photographic print.

Choosing the best aperture, shutter speed, and ISO

So given this labyrinth of variables (i.e. camera settings) and side effects, how should a photographer set up for a shot? The graph below shows the three main variables: aperture, exposure time, and ISO, and the four main effects: brightness, depth of field, motion blur, and noise. Click on the thumbnail image to get a larger version. If you change one of these settings at a time, you're following one of the solid lines on the graph. We've already talked about these paths. If you change two settings at once, you're following one of the dashed paths. These paths represent tradoffs between two variables. Assuming you have an SLR, the "Av/A", "Tv/T", and "P" modes help you make these tradeoffs intelligently. Let's go through each tradeoff one at a time.

First, let's consider the tradeoff between F-number and shutter speed. If you want control over depth of field, but you don't care about motion blur, then set your SLR to "Av" (called aperture priority), select the F-number you want (low F-number = shallow depth of field), and let the camera adjust the shutter speed so that total exposure is correct. To try this using our applet, click on "Av/A" (it's called "A" on some cameras), then fiddle with the F-number. As F-number gets low, depth of field becomes shallow; as F-number gets high, depth of field becomes deep but motion blur kicks in. To see the highest depth-of-field without also seeing motion blur, raise the ISO a few notches and try again.

If on the other hand you want control over freezing the motion (or deliberately creating motion blur), but you don't care about depth of field, then set your SLR to "Tv" (shutter priority), select the shutter speed you want (high speed = minimal motion blur), and let the camera adjust the F-number to compensate. To try this using our applet, click on "TV/S" (it's called "S" on some cameras), then fiddle with the exposure time. You should see the same tradeoffs as before. This similarity in behavior doesn't mean the two priority options are interchangeable. Our imaginary scene has a constant brightness. In the real world, these options let you fix one of these variables, and the camera will adjust the other variable according to the measured brightness of the scene.

By the way, most SLRs also have a "P" (program) mode, in which the camera choosing a reasonable combination of F-number and shutter speed, and with a single dial you can simultaneously change both of them in opposition, such that the total exposure stays constant. Finally, for the brave there is "M" (manual) mode, in which you separately control everything and need to watch a meter visualization to keep the exposure correction, and for the cowardly or lazy there is "A" (automatic), which adjusts everything for you. Our applet has a "Manual" mode, but we didn't implement the "P" or "A" modes because for a scene of constant brightness, they don't do anything interesting.

Finally, we come to the vexing question of how to factor ISO into this mix. A mathematical analysis of image noise is beyond the scope of this applet, but it turns out that while raising the ISO increases noise, it increases the signal faster. In other words, raising the ISO improves the signal-to-noise ratio (SNR) of the image. Moreover, it does so more effectively than brightening the image in Photoshop, because ISO-based brightening is performed in the camera before A/D conversion, while the signal is still an analog voltage, thereby minimizing what's called quantization noise. So should you raise the ISO until the noise is only barely tolerable, then then fiddle with F-number and shutter speed as described earlier? This is not an unreasonable approach, but there is a better one.

A further analysis shows that raising exposure time improves SNR faster than raising the ISO. Basically, getting more light into the camera is a good thing. Thus, the optimum strategy is: (1) maximize exposure time (by adjusting F-number and shutter speed) subject to the limits you are willing to tolerate on depth-of-field blur and motion blur (including blur due to camera shake), making sure not to saturate the sensor (i.e. avoid excessively blown-out highlights), then (2) to the extent your image is still not bright enough to fill the available range of intensities, increase the ISO until it does. You can judge this range of intensities by looking at a digital viewfinder, or by looking at a histogram of image intensities if your camera provides one. In practice this two-step strategy is difficult to perform, especially if you're in a hurry, but fortunately modern digital cameras do it for you, at least in "A" (automatic) mode.

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© 2010; Marc Levoy
Last update: June 8, 2010 11:19:55 PM
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