Tuesday, 9 October 2007

Guide Numbers vs. Watt Seconds

A post in the photosig forum was asking about a link between Guide Numbers and Watt Seconds, and whether there was a direct conversion.

It is possible to do calculations to do this conversion, but for most real-world situations, it's unbelievably complex, with light having to be simulated or otherwise modelled as it travels via reflectors etc. before heading in its final direction.

Guide numbers don't really give information about the power of a flash though. What they give is information about how bright they make a subject at a given distance, and therefore, how wide an aperture you should have to correctly expose that subject.

It is therefore possible to do a conversion directly to an Illuminance value in Lux.

Once you have this value, you then would need to model the light to give a value in Lumens or Lumenseconds. The only one you can really calculate is an imaginary light source which evenly lights in all directions (a point light source, a bit like a star). This never applies to any strobe though, so it's purely for interest sake.

If you're allergic to maths, look away now!

First of all, go have a read of this rather interesting page on Photometry of Strobes, and in particular the section called "Photographic Light Meters, Exposure Value and Guide Number" although almost everything before this section is of use in explaining the following calculations. This page is my source for the equations to calculate all of this, so I'm making the assumption this information is correct.

Here's the initial conversion from Guide Number to Lux, with a few assumed values added in to do the sample calculation.

And the following conversion to watt seconds for an ideal point source light is purely for interest sake.

Apologies for the poor hand-writing and hopefully I don't need to make any apologies for any mistakes in the maths! If you find any though, I'd like to know about them asap!


Strogoff said...

Sorry, I think you might be mistaken. A I see you have got a result in foot lamberts and done a conversion by the foot candle vs lux. I think you should multiply the foot lambert by the factor between luminance and illuminance as well to get illuminance. In this:
http://en.wikipedia.org/wiki/Exposure_value in Table 3. the luminance corresponds to your EV 14,5 but the illuminance does not.

n506 said...

Hi Strogoff

I've had a look at that wikipedia page. They're suggesting that an my EV of 14.6 would be an illuminance somewhere between 2048 and 4096cd/m^2. That works in close enough with my expected value of 2685cd/m^2.

So, as you say, it's the conversion to lux. I think it's a pretty simple explanation, but I could be wrong.

They're giving a lux value based on the definition of lux which is illuminance cast on a surface by a one-candela source at one metre away. However, rather unspecifically I guess, I kinda used a "lux equivalent" value, given I'm talking about a surface 10 metres away.

Roughly speaking, at 1 metre, this would be around 70,000lx on the table you mention if a quick in-head calculation is correct.

On the second page, you'll see I took account of the surface area of the 10 metre radius sphere, so I think it comes to the same.

Roughly speaking, I'd expect my 500W head at 3/4 power, sitting bare bulb, to give an exposure of about f/4-5.6 @ ISO 100 at 10 metres or somewhere thereabouts, so my resulting 350 wattsecond value does seem pretty realistic.

At their value of say 60,000lx or so, you're talking in the region of 2500wattseconds. But we think it's a metre only, so roughly, that'll be about 300wattseconds at 10metres. Given they're probably being fancy and taking account of some wavelength power distribution or something, I'm thinking we're not all that far apart.

If you think I'm a mile off though, I'm interested to hear it! :)

The fundamental point of this posting was to show that there's no simple conversion from guide number to watt seconds. It's related to a whole list of things such as the efficiency of the strobe, the light modifiers, and even the output wavelengths of the light from the strobe, and no doubt other smaller factors as well. Far from just a simple "multiply guide number by x to get watt seconds" conversion which people were asking for.

Strogoff said...

Hi, the relationship between illuminance as incident amount and luminance as reflected amount to the sensor is the 18%.

n506 said...

I think you're forgetting that a guide number (which we started with) is based on correct exposure, so that 18% gray card is already assumed, if I'm not mistaken?