Calculating flash contribution

Watching the Maconcampus webinar: Blending Flash and Ambient Light for Beautiful Outdoor Portraits it was clear that to someone who either wasn't robotically familiar with common situations, or someone afraid of numbers, Joe Brady's descriptions of why, for example, flash being f/8 and ambient being f/11 would be a 33% flash contribution. Joe Brady, great host that he is, even made a few not-quite-mistakes (sloppy rounding one might say) in his humbers a couple of times (however, he was recording live, not scripted, they could be just slips of the tongue).

Note - I am a mathematician at heart, I juggle numbers very easily, and I apologise of this is just a sea of figures. Work through a few examples by hand, and become familiar with them.

Absolute Basics - Why is f/2 to f/2.8 "a whole stop", and f/2 to f/4 "two stops"?

Woh, this is too basic old stuff - show me the new bits.

First I'll answer something more fundamental:

Nomenclature - Why did I use "f/2" rather than "f2"?

In simple terms, assuming we are not sharing lenses between fundamentally different types of cameras, because the f-stops measure the ratio of the aperture to the focal length of the lens. We represent that focal length with the letter 'f', and if the aperture is half as wide as that, then it has value "f/2" - half f. A quarter f, "f/4" is smaller than half f. "Stopping down" is decreasing the aperture's size, perhaps to "f/8" or "f/16", which are clearly getting smaller. However, if you use the notation "f2", "f4", "f8", "f16", etc. then stopping "down" made the numerical value seem to increase, which is illogical.

People generally say "eff-two" as a shorthand, rather than "eff-over-two", but when writing it down there's no reason not to write it with the slash. I prefer the logical notation in every context. I'm like that.

So why is f/2 to f/2.8 "a whole stop", and f/4 to f/8 "two stops"?

Because the apertures are a linear measure, and the amount of light that gets through the lens to the sensor is proportional to area, so the square the linear measure. A "stop" is a halving or doubling of the light levels, as seen in the areas in the following table:

To calculate ratios, absolute values do not matter

The heading basically says it all. If your light meter says that f/8 is the correct apperture for the flash, and f/8 would be the correct apperture under only ambient light, then that's saying they're providing equal lighting. The same is true if the meter was saying f/5.6 for both, or f/4.0 for both. The absolute values do not matter, only the ratio between them, or the difference in number of stops.

Ditto f/5.6 flash and f/3.2 ambient (1 1/3 stops) is the same ratio as f/9 flash and f/5 ambient (as it's also 1 1/3 stops).

Because of this, as long as you scale all values by the same ratio, you have the option of map at least one of the values onto one which you are more comfortable calculating with. For example, to a near-by full stop (f/2, f/2.8, f/4, etc..

Calculating flash contribution

We know:

• The light reaching a scene, or reaching the camera, will be the sum of the light coming from each of the sources.
• The higher the denominator in the apperture ratio, the brighter the scene is, in proportion to the square of that number.

From that we deduce:

• The light contribution is proportional to the square of that denominator.
• We can sum those squared terms, and calculate the contribution of each component

E.g.: From the ambient light the light meter recommends f/2.5, and for the flash it recommends f/5.6.

The ambient light contribution is 2.52 = 6.3 and the flash contribution is 5.62 = 32. Therefore the flash will contribute 32/(32+6.3) = 84% of the light. (You may consider dialing down the flash power and/or increasing the exposure time in this instance, the foreground will be entirely dominated by the flash.)

E.g.: From the ambient light the light meter recommends f/10, and for the flash it recommends f/8.

The ambient light contribution is 102 = 100 and the flash contribution is 82 = 64. Therefore the flash will contribute 64/(100+64) = 39% of the light. (Unless you've got a soft diffuser, this will still look "flashy", but may be OK for dramatic effect.)

Assuming we have a known calibrated flash, and can fix its contribution (say, for example, at 1/4 power, your flash produces enough light to correctly illuminate a scene 3 meters away at f/8 when the camera's at ISO 160), then we can generate a table of these ratios for easy reference:

Update: 2014-10-23 - This article is hereby placed in the public domain. It may be reproduced in any form and/or modified without any obligation to link back here, mention me, or anything. Share freely.