A photograph integrates change over time. Distinguish subject motion, camera motion, and electronic readout.
By the end: Predict blur length in a bounded model and choose a meaningful controlled comparison.
During exposure, a moving subject projects onto changing sensor positions. Its recorded light spreads along that path. If projected speed is constant, blur length is speed multiplied by exposure time. This speed is measured in the image, not necessarily in meters per second in the world.
The same runner produces different pixel speeds with different framing, distance, camera motion, and output resolution. There is no universally sharp shutter time for running. Decide whether the intended result freezes a face, preserves a readable body with moving limbs, or deliberately shows a trail.
Projected speed tells you how rapidly a feature crosses the picture. Imagine a marker moving 120 output pixels to the right between positions separated by 0.20 second. Divide 120 by 0.20 to get 600 output pixels per second. Assume that speed remains constant throughout the exposure and that the camera stays still. During 1/100 second, the marker travels 600 divided by 100, or 6 output pixels. During 1/500 second, it travels 600 divided by 500, or 1.2 output pixels.
For a chosen task, suppose motion may spread a high-contrast edge by at most 2 output pixels. Divide that allowance by 600 pixels per second. The maximum duration is 2/600 second, or 1/300 second. A 1/500 second exposure passes the ideal test, whereas 1/100 second fails it. This two-pixel allowance is a declared output criterion, not a universal definition of sharpness. Optical blur, focus error, and sampling can make the edge soft even when its motion contribution falls below the chosen allowance.
Direction matters as much as distance. A vertical edge translating horizontally spreads across its boundary. A long horizontal edge translating horizontally changes less away from its ends because its boundary moves along itself. A moving point traces the full path regardless. Motion blur can therefore hide some stripe orientations while leaving others readable. The diagram predicts an isolated feature's path. Actual appearance also depends on its brightness and the background over which that path falls.
The pixel unit must refer to a specific image size. Suppose the same captured frame is exported at 3,000 pixels wide and at 1,000 pixels wide. Every recorded displacement occupies one third as many pixels in the smaller version. A 6-pixel trail in the larger export becomes 2 pixels in the smaller one. The capture has not improved, but the smaller output may satisfy the task's tolerance. Enlarging a small preview on screen can conceal this distinction unless you know what image pixels the viewer is displaying.
Framing also changes the speed number. In an ideal projection from a fixed viewpoint, doubling focal length doubles the size of a subject and its lateral image displacement. Speed can rise from 600 to 1,200 output pixels per second at comparable output dimensions and sensor coverage. The two-pixel duration limit then halves to 1/600 second. Cropping and enlarging can produce the same output-speed increase without changing capture focal length. This is why one shutter recommendation cannot cover every framing of a moving person.
As a paper prediction, choose a feature crossing 90 pixels in 0.15 second. Its speed is again 600 pixels per second, despite the different measured interval. Halve the output width and ask whether 1/100 second now meets the same two-pixel allowance. The speed becomes 300 and the trail is 3 pixels, so it still fails. The needed duration is 2/300 second, or 1/150 second. This reasoning requires no camera control and makes the output assumption explicit before you judge a setting.
Camera shake can move the whole image, including a stationary background. Subject motion can blur a person while the background remains sharp. Stabilization mainly counters camera movement. It cannot generally freeze a moving person, though computational systems may attempt additional reconstruction.
Panning follows a subject during exposure. A well-matched pan can reduce that subject’s projected speed while streaking the background. Rotating limbs can still blur because they do not share one velocity. A tripod removes some camera motion but does not remove movement in the scene.
A stationary background provides a reference. A wall does not move in the world; its image still moves if the camera rotates during exposure. In a small central image region, a simple camera rotation can make many edges smear in approximately the same direction. Subject movement adds another displacement relative to that moving background. A single blurred frame cannot always separate these contributions, especially without fixed detail or with nearby objects at different depths.
Construct an additive image-speed example. Relative to a fixed camera, a person's face moves right at 200 output pixels per second and the wall stays at zero. Suppose camera movement contributes another 100 pixels per second rightward to both projected images. The wall then moves at 100 and the face at 300 pixels per second. In 1/50 second, their paths are 2 and 6 pixels. Supporting the camera removes that stipulated 100-pixel contribution, leaving zero for the wall and 4 pixels for the face.
The supported camera improves both, but the face still fails a two-pixel motion allowance. Its remaining speed of 200 pixels per second requires at most 2/200 second, or 1/100 second. Stabilization can also reduce some camera movement, within device-dependent limits, but it does not ordinarily cancel the person's independent motion. A sharp wall beside a blurred face is useful evidence for subject movement. It is not proof against a focus error, because the wall could also be the plane the camera actually focused on.
Panning deliberately changes the camera's contribution. Suppose a moving torso projects at 600 pixels per second with a fixed camera. A matched pan contributes 600 pixels per second in the opposite direction. The torso's net speed approaches zero while the fixed background moves at 600 pixels per second. At 1/50 second, the background traces 12 pixels. If a hand's speed relative to the fixed camera is 900 in the torso's direction, subtracting the same pan leaves 300 pixels per second, producing a 6-pixel hand trail.
An imperfect pan may still help. If its compensating speed is 500 rather than 600 pixels per second, the torso retains 100 pixels per second and traces 2 pixels at 1/50 second. The background traces 10 pixels. These local constant-speed approximations cannot make every rotating body part sharp. Turning heads, swinging limbs, and changing distance produce different paths. Nor can a pan correct focus behind the person, even with a steady torso image.
For optional observation, compare a stationary textured background with a moving hand in comfortable light. Keep your position and framing similar, and first support the device safely. Then compare with a gentle handheld attempt if appropriate. Ask whether the background changed and whether the hand changed independently. Automatic exposure or multi-frame processing can differ between attempts, so inspect reported settings when available. Without a device, use the numerical speeds above to predict which edges should improve after support and which require a different duration or relative movement.
| Feature | Fixed-camera speed | After −600 px/s pan | Path in 1/50 s |
|---|---|---|---|
| Torso | +600 output px/s | 0 output px/s | 0 px |
| Hand | +900 output px/s | +300 output px/s | 6 px right |
| Fixed background | 0 output px/s | −600 output px/s | 12 px left |
| Torso, imperfect pan | +600 output px/s | +100 with −500 pan | 2 px right |
This is image-plane speed at a specified output size, not the subject’s world speed.
Selected trail: 6 pixels. Time 10 milliseconds.
| Observed result | Candidate cause | Useful next test |
|---|---|---|
| Whole frame smeared | Camera movement | Support camera; repeat |
| Background sharp, hand blurred | Subject movement | Shorten time at same framing |
| Straight object leans | Rolling shutter or perspective | Compare stationary subject and readout mode |
The original motion experiment keeps projected speed at 600 output pixels per second while time changes. It draws path length, not a photograph of a moving light. To reason about brightness along a path, assume an isolated source whose image is too small to resolve on a dark background supplies 1,000 detected signal units per second through the chosen opening. Ignore saturation, diffraction, read noise, and changes in source brightness. At 1/100 second the total signal is 10 units and the path is 6 pixels. At 1/25 second it is 40 units along 24 pixels.
Under uniform speed, each additional piece of trail receives light for approximately the same time as the source passes it. Dividing total signal by path length gives 10/6 or 40/24, both about 1.67 units per pixel of path. Thus four times the total collected light need not make every part of a moving point's trail four times brighter. It can instead make the trail four times longer. This thin-path average ignores image width, pixel overlap, and bright or textured backgrounds.
Contrast a stationary patch covering the same sensor positions throughout exposure. In the linear unsaturated model, each covered sensing area collects four times as much signal when time increases fourfold. An extended moving object differs. Its interior may cover one position throughout much of the exposure, while its leading and trailing edges sweep across positions for shorter intervals. The final image mixes different coverage durations. That is why a long exposure can show a readable body, blurred limbs, and a background visible through part of a moving edge.
Now impose a motion requirement. Starting from f/4 and 1/100 second, shorten time to 1/400 second at unchanged light. Collection from a stationary patch falls to one quarter. For the 600-pixel speed, the path falls from 6 to 1.5 pixels. Opening from f/4 to f/2 doubles pupil diameter and quadruples area, restoring ideal collection at the shorter time. It also changes depth of field. This remedy is available only if the lens actually offers that opening and the required subject depths remain acceptable.
Four times the subject illumination can also restore collection at f/4 and 1/400 second. Raising ISO fourfold cannot. It may restore a brightness target while leaving the captured signal at one quarter, with device-dependent noise and clipping consequences. Automation may combine these changes. State which physical variables changed rather than saying that the camera compensated. The equality of a displayed face's brightness does not establish equality of collected light or equality of fine detail after processing.
Keep aperture fixed and halve the model's 1/100 second time. The path becomes 3 pixels and steady-patch collection halves. Decide whether a two-pixel allowance is met before proposing any compensation. It is not, so another reduction is needed; 1/300 second would reach the stated limit and collect one third of the baseline. If controls are absent, consider a stiller moment or better illumination as a practical comparison. Better light may prompt a shorter automatic time, but check the actual decision.
| Capture choice | Steady-patch collection | Trail at 600 px/s |
|---|---|---|
| Baseline f/4, 1/100 s | 1 | 6 px |
| f/4, 1/400 s | 1/4 | 1.5 px |
| f/2, 1/400 s | 1 | 1.5 px |
| f/4, 1/400 s, light ×4 | 1 | 1.5 px |
| f/4, 1/400 s, ISO ×4 | 1/4 | 1.5 px |
Many electronic shutters expose or read different rows at different times. A moving object can lean or bend through rolling-shutter distortion, even when each row has a short exposure. Flickering lighting can produce bands. Mechanical shutters also have a traveling-slit regime at fast settings.
Flash introduces another time scale. With little ambient contribution, a short flash pulse can define the effective illumination interval. Ambient light may still create a ghost trail. Flash synchronization limits and high-speed modes vary by camera; do not infer flash behavior from the shutter number alone. For practice, compare a stationary background and moving hand at two times if your device allows control.
A short exposure for each image row does not imply that all rows describe the same instant. Construct a rolling-readout example with 20 milliseconds between the start of the top row and the start of the bottom row. Give every row an exposure duration of 1 millisecond, or 1/1,000 second. The top row records approximately the interval from 0 to 1 millisecond, while the bottom records 20 to 21 milliseconds. A global simultaneous exposure would give the rows the same interval instead. These invented timings do not specify your device.
Let a vertical object translate right at 500 output pixels per second. During each row's 0.001-second exposure, its local motion path is only 0.5 pixel. Between the top and bottom row start times, however, it moves 500 multiplied by 0.020, or 10 pixels. The assembled object can therefore lean by about 10 pixels from top to bottom while each local piece remains comparatively crisp. Halving each row's duration halves local blur, but it does not halve that lean if the 20-millisecond readout span stays unchanged.
This example separates shape distortion from integrated smear. Real objects can rotate or accelerate, and scan direction varies. Perspective can also make a stationary vertical line lean when the camera is tilted. Compare a stationary object at the same viewpoint first. Repeating under steadier illumination can help distinguish geometric distortion from lighting bands. With flickering light, rows recorded at different times can receive different illumination, producing brightness differences that shortening exposure does not necessarily remove.
Flash adds a second interval over which light reaches the sensor. Suppose ambient light would record a hand moving at 600 pixels per second throughout 1/50 second, giving a 12-pixel path. Add a flash whose effective light pulse lasts 1/2,000 second in this constructed case. During that pulse the hand moves 0.3 pixel. If flash dominates the recorded hand signal, it may provide a comparatively crisp image even though the shutter remains open much longer. The shutter setting did not determine the dominant illumination's duration.
If ambient light contributes substantially, the same capture can contain a narrow flash-defined image and a faint 12-pixel trail. Its appearance depends on the relative recorded contributions, background, pulse shape, and flash timing within the exposure. This is not a device recipe. Synchronization limits, traveling shutters, flash modes, and automatic multi-frame processing vary. Some flash modes illuminate for longer than a single brief pulse. Shutter time alone cannot prove that a subject must blur or that flash will freeze it.
To classify a result, compare several kinds of evidence. Directional trails around stationary background detail suggest camera movement; a sharp background with a trailing hand suggests subject movement. A crisp but slanted moving object suggests different row times, after viewpoint effects are considered. A narrow image plus a faint trail suggests differing illumination intervals. These remain candidates. Without making new captures, use the 1-millisecond and 20-millisecond example to explain why requesting a faster shutter may reduce smear yet leave the shape distorted.
A point moves at 600 output pixels per second. Compare 1/100 s and 1/25 s.
Multiply by seconds, not by the denominator.
| Time | Image speed | Trail |
|---|---|---|
| 1/100 s | 600 px/s | 6 px |
| 1/25 s | 600 px/s | 24 px |
The trails are 6 and 24 pixels. The longer time collects four times as much light from the steady source but spreads the moving point across a longer path. This model omits acceleration, optical blur, and sampling.
The buildings are sharp but a walking person is blurred. Would a tripod alone solve it?
Identify what moves relative to the camera.
| Intervention | Camera movement | Subject movement |
|---|---|---|
| Tripod | Usually reduced | Still present |
| Shorter time | Less integrated movement | Less integrated movement |
Not generally. The person still changes image position during exposure. Shorten the time, alter the timing or relative motion, or accept the blur as intentional. Extra light or a wider aperture can compensate for lost collection; higher ISO alone cannot replace those photons.
The lessons and answers stand alone. These optional secondary references explain the optics and imaging concepts. Numerical examples are constructed, not measured camera specifications. Visual judgments depend on the intended image; the course does not claim a universal aesthetic score.
Secondary overview of exposure, time, aperture, and sensitivity conventions. Our light-collection and brightness ratios are simplified teaching models, not camera calibrations.