# lux level calculations for key and fill

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### #1 Ollie Bartlett

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Posted 26 November 2008 - 06:26 AM

Hi there,

Ive been looking at millarsons 'lighting for television and film', and come across an equation for calculating fc / lux ratings for key and fill light.

(25 x f/ x f/) / (asa x 1/shutter speed) = total FC

10.764 x total FC = total lux

firstly id like to ask where the 25 comes from? its not explained in the book, and so i can only assume its a given number. Could it be anything to do with frame rate? Would i change this if i was shooting 60 fps? Would it make any difference anyway if the shutter speed was always half the frame rate?

Secondly, millarson says that the final outcome will give you a total figure from which to work out your key and fill ratios. If i end up with a number of say, 800, would a 4:1 ratio mean 800:200, ie the total lux gives key, then fill is worked out after that?

or would 800 be divided into 5 parts of 160, and then the ratios adjusted accordingly? ie 640:160

hope this isnt too muddled to be understood. Cheers guys for any imput.

Ollie

PS... if anyone has any other equations for lighting, lenses etc etc id love to hear them. i dont get as much chance as id like to be out there shooting and so a lot of the time i have to rely on my fascination behind the art and science of cinematography to tide me through.
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### #2 Serge Teulon

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Posted 26 November 2008 - 12:06 PM

Hi Olllie,

The 25 represents frames per second.
Maths is not my strong point but I would say that you seem to have understood what Millarson is saying.

I must confess that, unless I'm trying to work out photometrics of a particular light, I very rarely use these calculations in a practical sense.
Normally I ascertain my look through testing.

Above all, I always trust my eye together with the zonal system. And, touch wood, to date it hasn't let me down.
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### #3 Ollie Bartlett

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Posted 26 November 2008 - 01:47 PM

The thing is, every other part of the equation has an explanation. ASA, shutter speed, f/T stop, all of which are variables. I cant understand why frame rate, another variable, wouldnt be given an explanation. He doesnt say that this number should be altered accordingly if you're shooting 24, 29.97, 30, 50, 60 fps or whatever... its just the number "25".... odd.

As i said, i dont get as much chance to shoot as id like, so im trying to get my head around the photometrics of it all. Using this formula i should be able to get key lux level. Using another will tell me how far away a given light would need to be in order to hit key (as long as you initially know its lux output at a given distance). Then, knowing how many stops difference you'd like between highlights, shadows, objects etc etc you can work out required lux levels for other areas of the frame, how much light will be hitting them already as spill, and how to top that up / cut it down to whatever you need in order to create good contrast within the image.

Still using 800 foot candles as a reference, millarson says if you'd like a 3:1 contrast ratio (a stop and a half?), key would be 520fc and fill would be 280fc. This only seems like a 2:1 difference to me. Any thoughts on where im going wrong here? Is there a slight inaccuracy in the book, or am i just going completely down the wrong track?

I know that the science plays only a very small part in what id like to do, and i shouldn't worry so much about the technical stuff, but working 11 hours a day in an equipment house leaves very little time for the art of it. I'd love to get out and shoot, but at the moment these technical ramblings are about all i can fit in, so anyone who can point out where my mistake is to me has my deepest thanks.
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### #4 Joshua Jackson

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Posted 28 November 2008 - 05:12 AM

Be careful! This "25" does not mean frames per second. It's a predesignated value according to ANSI standards to represent that the footcandles given in the equation will illuminate an object of 17.67% reflectance to be captured as the medium value of the recording medium's individual latitude. If you plugged in 60, you'll overexpose by about 1.4 stops!
The fps comes in the equation later:
Footcandles (lumens/feet² ) = 25(f/stop² )/[(ASA)/(Shutter Speed)]
The Shutter speed, at a 180° shutter angle, is simply one divided by two times the frames per second:
Shutter Speed = (1)/2(fps)
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### #5 Joshua Jackson

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Posted 28 November 2008 - 05:18 AM

Sorry. More ISO than ANSI.
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### #6 Joshua Jackson

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Posted 28 November 2008 - 05:23 AM

Footcandles (lumens/feet² ) = 25(f/stop² )/[(ASA)/(Shutter Speed)]

Correction:
Footcandles (lumens/feet² ) = 25(f/stop² )/[(ASA)(Shutter Speed)]

Sorry, I type too fast for myself!

Edited by Joshua Jackson, 28 November 2008 - 05:24 AM.

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### #7 Joshua Jackson

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Posted 28 November 2008 - 05:49 AM

According to ISO 2720:1974 ,
This "calibration constant" is suggested to fall between 22-37.
So what's the calibration of your meter?

Constant = [(Footcandles)(ASA)(Shutter Speed)] / (f/stop²)
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### #8 Joshua Jackson

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Posted 28 November 2008 - 06:00 AM

Still using 800 foot candles as a reference, millarson says if you'd like a 3:1 contrast ratio (a stop and a half?), key would be 520fc and fill would be 280fc. This only seems like a 2:1 difference to me. Any thoughts on where im going wrong here? Is there a slight inaccuracy in the book, or am i just going completely down the wrong track?

Ok. Imagine the key light coming from the left of the frame. Let's say that you position it to hit only the right side of his face (Let's assume no light is reflecting from the walls, etc. onto the subject). The key reads 520 Footcandles on the right side of his face and nothing on the left side of his face.

Turn off the key light. Alright, let's put in some fill from the camera's position. It reads (by itself) at 280 Footcandles. It washes both sides of his face, so that the left side gets 280 and the right side gets 280.

Alright, turn back on the key light. Now that key light is adding 520 Footcandles to the right side of his face, but nothing to the left side of his face. With both lights on, the right side now has 800 Footcandles and the left (only affected by the fill) gets 280 Footcandles. 800fc : 280fc. Little under 3:1.
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### #9 Joshua Jackson

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Posted 28 November 2008 - 06:37 AM

For Lux, replace that "25" with a "269."
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### #10 Chris Keth

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Posted 30 November 2008 - 12:29 PM

That's a lot of work. For the same purpose, I always remember the rule that for 100 asa film, a 100 footcandle key gives a stop of f/2.8. You can move in any direction from this to get your asa and desired stop.
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### #11 Joshua Jackson

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Posted 01 December 2008 - 04:50 AM

That's a lot of work.

Well, if you ever need a nerdy AC, let me know (*snort)

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### #12 Joshua Jackson

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Posted 01 December 2008 - 05:57 AM

Ollie, here a few more formulas regarding photometry that might keep you busy on rainy days (of course, what you DO with these formulas will have a greater impact than just "knowing" them).

Footcandles = (Candelas)/(Distance in feet²)
Lux = (Candelas)/(Distance in meters²)
*Both based on Inverse Square Law (E=I/d²) Intensity per unit area is inversely proportionate to the square of the distance.
1 Footcandle = 10.76 Lux

Luminous Flux (measured in Lumens) is a measure of the power of visible light. If the light evenly distributed over 360 degrees (isotropic), then:
1 Lumen = 12.56 Candelas
If the light is not evenly distributed over 360 degrees, you'll need to find the steradians of the solid beam angle:

Ω= 2*Pi[1-cos(Beam Angle/2)]
And then,
Lumens = (Candelas)(Ω)

Candelas is luminous intensity. (measured in lm/steradians).
Illuminance is a measure of luminous flux per unit area. This is measured in footcandles (lumens/feet²) and lux (lumens/meter²).

Luminance is the luminous intensity given off by a surface.
For a Lambertian (perfectly diffused) surface:
Footlamberts = (footcandles)(reflectance %)
-reflectance in decimal form (100% is 1.00)

For lenses:

Angle of View of lens:

Angle = [2 * (arctan ( L / (2f) ) ) ]
where L is the length(mm) of the frame in the direction you want the reading. Horizontal dimension for horizontal AOV and vertical dimension for vertical AOV. f is the focal length of the lens.

The ASC manual has a ton more. Peace.
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### #13 Ollie Bartlett

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Posted 02 December 2008 - 08:19 AM

Guys thank you so much... might have to try and get a copy of the ASC manual of the internet.

As you said Joshua, its not what you know but what you do with the information thats important, but all these bits of knowledge that i can gather will just help me that little bit more on the few times i actually make it to set.

Gonna check out that rule later Chris once we close up at work and i can get a dark room.

Cheers once again,

Ollie

Edited by Ollie Bartlett, 02 December 2008 - 08:20 AM.

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### #14 Stuart Brereton

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Posted 19 December 2008 - 07:39 PM

I don't think you should get too hung up on maths. Just about every DP uses a meter reading in f-stops to measure the keylight, and judges fill by eye. There's not really time on set to bring out your slide rule and start doing algebra to determine your contrast ratios....

I'm not saying that there is no need to learn this stuff. Photometrics are extremely important when (pre)lighting large sets, but you shouldn't worry too much the hard maths involved.
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### #15 Ollie Bartlett

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Posted 20 December 2008 - 07:23 PM

If youre still in Bristol Stuart you fancy making me a camera trainee on your next project

Then i can get out of the kit room for a bit and hopefully learn from the person who made me want to be a DP in the first place.

Ollie
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### #16 Chris Keth

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Posted 20 December 2008 - 11:38 PM

If youre still in Bristol Stuart you fancy making me a camera trainee on your next project

Then i can get out of the kit room for a bit and hopefully learn from the person who made me want to be a DP in the first place.

Ollie

Perhaps you can carry Stu's slide rule. I saw it in his bag along with his glasses with the scotch tape on the bridge of the nose.
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### #17 Ollie Bartlett

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Posted 21 December 2008 - 01:35 PM

Thats fine.

I dont need both hands to carry around his tea or coffee so I'd have one going spare.
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### #18 Simon Wyss

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Posted 21 December 2008 - 05:02 PM

But why the 17.67 percent ? Couldn't it be 16⅔ or 18 ?
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### #19 Joshua Jackson

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Posted 27 December 2008 - 01:53 AM

But why the 17.67 percent ? Couldn't it be 16⅔ or 18 ?

17.67% (0), 25% (+1 stop), 35.35% (+2), 50% (+3), 70.71% (+4), 100% (+5)
12.5% (-1), 8.84% (-2), 6.25% (-3), 4.4% (-4), 3.12% (-5)
It's logarithmically mapped.

Mapping to an 11 zone system. Of course, 100% is only "white," while real-world elements push far beyond this, upwards to 600% on a film's shoulder. Sometimes more.
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### #20 Simon Wyss

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Posted 28 December 2008 - 06:09 AM

O, thank you for the definition.
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