Martin came to me with a customer problem earlier this week. The customer bought the "low cost" Phantom Miro camera to do high frame rate photography. Cool bit of kit that I hope to play with some time in the near future (*ahem*, Martin...). The problem is providing enough light for the camera at such fast shutter speeds. The customer already owns a tungsten 6k light, but even that's not enough.
I'm assuming that the customer bought the new Miro M320S which maxes out at about 1540fps in HD and has a native ISO of 1100 - oddball ISO rating, huh? Given these specs, which lights does the customer need to buy? That's actually fairly easy to calculate. A while back M. David Mullen, ASC published a simple formula which he uses to order up lights by using the foot-candle photometric data of the fixture. Good thing I published this to my personal blog just as a way to keep track of the formula!
foot-candles (approximately) = 25 x (T-stop)^2 / (ISO * shutter time)
So let's say the customer wants to operate the lens at a typical T/2.8. We're using cine lenses here; none of that f/# funny business! I'll assume the camera can operate with a near 360-degree shutter speed, but in truth I have no clue since I don't have any experience with the camera.
FC (approximately) = 25 x (2.8)^2/(1100* (1/1540)) = 267 foot-candles
Let's say the customer wants to use a more comfortable to focus T/4 with a typical 180-degree shutter angle.
FC (approximately) = 25 x (4)^2/(1100* (1/3080)) = 1120 foot-candles
From here it's pretty easy to know what lights to order since most vendors, like Arri, publish photometric data for their fixtures. The Arri 200W HMI provides approximately enough light to do what the customer needs, maybe even with diffusion involved, however that assumes a short throw distance. The customer will have to do his own research with photometric data when the light-to-subject distance is better understood. A Film Gear or Arri 575W HMI might be a safer, more versatile purchase.
The only real variable is how much light loss comes from different types of diffusion and bounce. That's something for a future blog article.
There is an easier way to do a back-of-the-envelope calculation when you need something quick and dirty. The rule of thumb is ISO 100, 180-degree shutter angle at 24p, T/2.8 equates to 100 foot-candles of light for proper exposure. So for instance if you have an Arri Alexa with a native ISO of 800 then you only need 1/8th that amount of light, or 12.5 foot-candles. If you want to operate the lens at T/4, then you need 200 foot-candles because that's half the amount of light/one stop less making it's way through the lens. Easy, yes?