WP's SloMo

Nyquist-Shannon-Kotelnikov Theorem of Sampling

Trajectory evaluation: translation, rotation,
velocity, acceleration and stick-figure animation

Escaping strobe effect is not as simple as it seems. Especially not with a high-speed camera. Illumination sources you would never expect suddenly start to blink. (It seems you do not need a strobe at all. ;-)

Effective or nominal mains voltage of 115 V or 230 V alternates 60 or respectively 50 times per second. Illumination devices directly driven by mains are pumping more or less with this alternating current (AC) frequency of 60 Hertz or 50 Hertz. (1 Hz (Hertz) = 1/sec). Possibly even with 120 or 100 Hertz, because there may be two zero-crossings due to sine oscillation.

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Why illumination may flicker

Evidently usual light bulbs or similar illumination sources are just too sluggish to clearly show the frequency of AC mains power supply. And of course, our eyes are too slow to perceive these variations. Also a video camera usually does not take notice of these flickers.
Even so-called direct current (DC) lamps, where electronics rectify or smoothen the AC current, can show a certain ripple or oscillation of higher frequencies a movie or a video camera does not note, but a high-speed camera of sufficient frame rate does.

Sequence and flickering illumination

That's the cause for a frequent, but incorrect fault report: »The camera flickers and jitters!«.

Namely the high-speed camera is definitely not responsible for that. The reason is connected with the so-called Nyquist-Shannon-Kotelnikov theorem of sampling, see the figure on the left. Not until one measures a changing variable with more than its double frequency, one will be able to reconstruct its curve shape.

In the figure on the left the video camera runs almost with half the frequency of the ripple of the illumination source, whereas the high-speed camera is factor four to five faster again. The gray areas give the amount of light per frame. The white areas show the read-out time or inactive phases.
It is clearly to see how ups and downs of the intensity compensate themselves more or less, the video camera is integrating over them. Usually this is independent of the phase shift, i.e. the temporal delay.
The frames of the high-speed camera, however, are exposed with varying values. The sequence will flicker, when replayed in slow motion. Something one can often notice in slow motion sequences of sports event broadcasted on TV under artificial light or directly the headlights of racing cars, because these are operated pulsed.

Only if one (strictly) reduces the time of exposure of the video camera, narrower gray and wider white areas in the figure above, one will be able to make it flicker as well. With clever adjusted frequencies (synchronized), however, it may not necessarily happen.

Using a frame rate of some 100 frames/sec one is able to shoot the pumping of fluorescent tubes. Therefore this kind of illumination is not very suitable for high-speed cameras. The sluggish light bulbs at AC mains are less affected. But merely lamps driven by a battery (DC current) are really safe from high-speed cameras.

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Stroboscopy and translation

Essential approach is to synchronize the flash frequency towards the cyclic event, e.g. to m turns + x°. Flashing at a gear wheel each turn (= 360°) plus x° results in a progression of x°. Of course, x° can also be zero, then a frozen image seems to be obtained. (With m turns minus x° the well-known wagon wheel effect happens, see below.)
There is the chance, however, to gain much more. The multiple exposure of an photo - indeed of just one single frame - enables to shoot a translatory trajectory.
One can carry it to the extremes: just imagine you use a ball canon to shoot numerous tennis balls against a wall and you manually make a photo of each shot, thus randomly, without using automatic triggers like a photoelectric barrier. You receive any desired plenty of photos showing the individual tennis ball in a different phase of flight. If you sort the photos according to their distance between ball and wall you will get a »movie« with very high temporal resolution. It is, however, not the trajectory of one and the same ball. (But there is just no need to mention it. ;-)

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Wagon wheel optical illusion

Effect well-known - the coach moves forward, its wheels turn backward - is a consequence of the sampling theorem as well. Between two succeeding movie images the wheel rotates by slightly less than one full turn or at least one or more spoke segment(s). Or by some full turns whereas the last turn is not completely finished. That is a special case of the stroboscope effect where one tries to capture a still image of a rotating object by shooting integer multiples of a single turn. One's brain interprets these images then in the wrong way as pseud movement or just as no movement.
You can perceive the same effect with rotating propellers or helicopter rotors. (There the rolling shutter effect is evident, see below.)

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Rolling shutter artifacts

Extreme strange shots can occur using a rolling shutter, as provided by many video sensors. Different from the global shutter (freeze frame shutter) a single frame is not shot at one and the same time, but some kind of curtain relatively slowly falls over the sensor. Whereas since the cathode ray tube (CRT) era one inserts in interlaced mode two of these half-frames (= fields) separated by 1/50 or 1/60 seconds line by line in each other like a comb, now there are quite a number of image stripes shot at different times each single frame is consisting of. Even a progressive mode 100 Hz or 200 Hz monitor is not able to suppress this effect afterwards.
As a consequence rotating propeller blades look sickle-shaped, disappear from time to time or seem to jump fore and back. Also to use for artistic approach, for example water seeming to stream down to ground spirally.

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Jutter replay

Except for technical defects, there are two causes. At first the replay rate can be so low that a fluent sequence is not given. One must offer one's eyes 14 frames/sec at least in order to prevent them from visualizing the single frames and to keep up the movie illusion.
On the other hand a very short shutter time (time of exposure; in each frame x shown in the figure above just one single small gray column and much white space in between) compared with frame rate or movement, resp. can cause the movement appearing choppy because too much location change happens from frame to frame, thus from photo to photo and so too much is cut out. (Whereby we are at the flip book again.)
The sometimes odd appearance and alleged strange behavior of small water waves in movies or on TV are again caused by the Nyquist-Shannon-Kotelnikov theorem.