#settools

# Flicker free equation

There are two ways to deal with pulsating light sources, magic frame rates, or magic shutter angles. If you pick a magic frame rate, you can use whatever shutter angle you want to get the motion blur and exposure you want. If you have to use a non-magic frame rate, you're stuck to pick one of the shutter angles that are "magic" for that frame rate.

Light sources that pulsate due to AC power produce light on both the positive and negative half cycles, so they pulsate at twice the power frequency, 100 Hz in the UK, 120 Hz here in the US. Your goal is to get the same amount of light in every frame.

 The first way to do that is to choose a frame rate that divides evenly into the pulse rate. That way each complete exposure and pulldown cycle of the camera corresponds to an integer number of light pulses. So, the shutter always opens at the same point in the light pulse cycle, and closes after admitting the same amount of light. That allows you to use any shutter angle you want. 24 works here, because 120 = 5 x 24. 25 works there, because 100 = 4 x 25.

For over or under cranking, the possibilities are:

120 = 1 x 120 = 2 x 60 = 3 x 40 = 4 x 30 = 5 x 24 = 6 x 20 = 7 x 17.143 = 8 x 15 = 9 x 13.333 = 10 x 12 .... = 20 x 6, etc.

If you can't use one of the magic frame rates, you're stuck with the more difficult approach. You have to find the shutter angles that, at the required frame rate, have the shutter open for an integer number of light pulses. Suppose you must use 25 fps with 120 light pulses per second. In that case, you want a shutter angle A such that

(1/25) x (A/360) = (N/120) where N is an integer. The possible N values are 1, 2 ,3, and 4, because at N = 5, the exposure becomes longer than the cycle time, so your shutter angle would have to be over 360 degrees. Working the math, we get:

A = 75 x N

So, the possible angles are 75, 150, 225, and 300. (The next one would be 375, but that's impossible.)

It should be clear that magic frame rates are the easy way, and 24 is plenty close enough to 25.

If you have some reasonable way of recording and monitoring what you shoot, you should be able to test and play back on the set to be sure if you have a problem. A great many light sources such as incandescents and modern flourescents don't follow the mains frequency, and work fine without any extra math or magic. I've seen problems with neon signs and advertising displays, though. Particularly, some of the LED chasers use their own frequencies, so you may have to experiment with them, or just get them off the set.