Exposure: stops and the exposure value

A stop is a factor of two in light. Three controls set how much light makes the picture: the aperture (f-number $N = f/D$, the focal length divided by the entrance-pupil diameter, the apparent width of the lens opening: a small f-number means a wide opening), the shutter speed $t$ and the sensor gain, ISO $S$. Light through the lens is proportional to the pupil area, $\propto 1/N^2$, so the standard f-stops $1.4, 2, 2.8, 4, 5.6, 8, 11, 16, 22$ go up by $\sqrt2$ and each halves the light. The exposure value combines aperture and time:

A scene is correctly exposed when the camera’s $\mathrm{EV}_{100}$ equals the scene’s light level, $\mathrm{EV}_{100,\text{scene}}$. In this simulator the exposure error in stops is $\Delta = \mathrm{EV}_\text{scene} - \mathrm{EV}_{100} - n_\text{ND}$, where $n_\text{ND}$ is the number of stops of neutral-density filter. Positive $\Delta$ is overexposure; the light meter needle and the brightness of the render follow $2^{\Delta}$. Typical scene values: full sun ≈ 15, overcast ≈ 12–13, golden hour ≈ 11, blue hour ≈ 7, a lit city street at night ≈ 4.

Reciprocity: equivalent exposures

Any combination with the same EV gives the same brightness: $f/2.8$ at $1/1000$ s ≡ $f/4$ at $1/500$ ≡ $f/5.6$ at $1/250$. What changes is the look: aperture controls depth of field, shutter speed controls motion blur, ISO controls noise. That trade-off is the exposure triangle. The semi-automatic modes do the reciprocity for you: in Av (aperture priority) you choose $N$ and the camera picks $t$; in Tv (shutter priority) you choose $t$; P picks both along a program line; M is fully manual and the meter tells you how far off you are.

Depth of field

Depth of field (DoF) is the range of distances in front of and behind the focus point that still look sharp. Why it exists: a point not at the focus distance $s$ images as a small blur disc, and if the disc is small enough the eye cannot tell it from a point. With focal length $f$, the diameter on the sensor of the blur of an object at distance $d$ is

It counts as sharp if $b$ is smaller than the acceptable circle of confusion $c$ (≈ 0.030 mm on full frame, about $1/1500$ of the sensor diagonal). Setting $b=c$ gives the hyperfocal distance and the near and far limits:

Depth of field gets shallower with a wider aperture (small $N$), a longer focal length and a closer subject. Focusing at $H$ makes everything from $H/2$ to infinity acceptably sharp. In the render every layer (subject, cyclist, matatu, buildings, road, foreground leaves) is blurred by its own $b$, and point lights become bokeh discs (out-of-focus highlight shapes) of diameter $b$, hexagonal when the six-bladed aperture is stopped down.

Crop factor

Smaller sensors see a narrower angle with the same lens. The crop factor $k$ is the ratio of the full-frame diagonal (43.3 mm) to the sensor diagonal. Angle of view: $\alpha = 2\arctan\!\big(\tfrac{w}{2f}\big)$ for sensor width $w$. A 50 mm lens on APS-C ($k≈1.5$) frames like 75 mm on full frame; to get the same framing you step back, and the depth of field at the same f-number becomes deeper by about $k$, because $c$ shrinks with the sensor. The equivalent full-frame aperture for the same depth of field is $N\cdot k$.

Motion blur and camera shake

An object moving at speed $v$, at distance $d$, smears across the frame by $\approx \frac{f\,v\,t}{d}$ on the sensor. To freeze a cyclist at 18 km/h about 8 m away you need roughly $1/500$ s or faster. Hand-holding adds shake; the reciprocal rule suggests $t \le 1/f_\text{eq}$ (with $f_\text{eq} = k f$), and an image stabiliser buys about 3 stops. Panning (rotating the camera with the subject) keeps the subject sharp while the background streaks. For video, the 180° shutter rule sets the shutter to about $1/(2 \times \text{frame rate})$: $1/50$ s at 25 fps. This gives natural motion blur, so in bright light you control exposure with ND filters, not a faster shutter.

Noise and ISO

ISO does not add light; it amplifies the signal. Fewer photons means more shot noise (Poisson: $\sigma = \sqrt{n}$, so signal-to-noise $=\sqrt n$). Each doubling of ISO for a correct exposure halves the photons collected, so SNR drops by $\sqrt2$. Read noise from the electronics dominates in deep shadows. Smaller sensors collect fewer photons for the same picture, so they are noisier at the same ISO. The simulator models shot noise plus read noise per pixel at the displayed resolution.

Colour temperature and white balance

Light sources are described by their correlated colour temperature in kelvin: candle ≈ 1900 K, tungsten ≈ 3200 K, golden-hour sun ≈ 3500 K, noon daylight ≈ 5500 K, overcast ≈ 6500 K, shade and blue hour ≈ 7500–9000 K. The camera’s white balance setting divides out the colour of the light it assumes. If the WB setting is lower than the light’s temperature the picture turns blue; if higher, orange. Here the cast is computed from a black-body colour model: (light colour) ÷ (WB setting colour), channel by channel.

Model notes: the scene is drawn in depth layers rather than ray-traced, the blur is Gaussian except for the bokeh discs, and the meter is an average meter. Shutter speeds and apertures use nominal marked values.

1. Equivalent exposure

2. Scene EV from settings

3. Hyperfocal distance

4. Portrait depth of field

5. Background blur disc

6. Freezing motion

7. ND filter for panning in sunlight

Pick a challenge, set up the camera, and press the round shutter button. Each photo is checked automatically.

Experiments

1. Perspective compression. With “Keep subject framed” on, go from 14 mm to 200 mm. The subject stays the same size but the buildings loom larger and fewer fit in: background magnification is $\propto f$ when the subject size is fixed.
2. Equivalent exposures. In Av mode change the aperture from f/1.4 to f/16 and watch the camera lengthen the shutter one stop per stop, while the depth of field grows and the matatu begins to blur.
3. Crop factor. Keep 50 mm, f/2 and switch Full frame → Phone. The subject is framed the same (you walk back), but the background becomes much sharper.
4. White balance. In golden hour set WB to Daylight (warm) and then to Tungsten (blue). Auto white balance sits between.
5. Light trails. Night scene, tripod on, Bulb 8 s, f/8, ISO 100: the matatu becomes streaks of head- and tail-lights.
6. Hyperfocal focusing. Set 24 mm, f/11, untick “Focus follows subject”, and set the focus distance to the hyperfocal distance shown in the DoF panel.

Rule of thirds

Divide the frame into a 3 × 3 grid (switch on the grid overlay). Placing the subject’s eyes on or near an intersection usually gives a more dynamic picture than dead centre, and leaves “looking room” in the direction the subject faces. The subject in this scene stands on the left third line.

Lens choice and perspective

Perspective depends only on camera position. A telephoto lens used from further away makes the background appear larger relative to the subject (“compression”); a wide-angle lens used close exaggerates depth and distorts faces. Classic portrait lenses are 85–135 mm on full frame.

Separation

Separate the subject from the background with shallow depth of field, a darker or plainer background, a rim of light, or colour contrast. Watch for distracting elements “growing” out of the subject’s head, such as lamp posts.

Reading the histogram

The histogram plots how many pixels fall at each brightness from black (left) to white (right). A graph piled against the right edge means clipped highlights (lost detail, shown by the blinkies); piled at the left means crushed shadows. Night scenes legitimately sit to the left, snow scenes to the right: the meter averages to mid-grey, so use exposure compensation (+1 to +2 for snow, −1 for dark scenes).