Tuesday, June 14, 2011

Exposing the Lume

Some watch enthusiasts are proud of how bright the luminous paint is on their watches. They publish highly edited photos or use heavy exposure settings and then post a "lume shot" with the full intention of impressing the reader. Others, of a more pedantic persuasion, might wonder exactly how bright their lume is, as measured in (usually) milli-candelas per square meter i.e. mcd/m2. And not all watches are that bright - for example, older military watches that have the tritium paint can be quite dim after 20+ years. Like this 25-year old Altus:
Not quite up to the blinding images usually posted on watch fora by lume freaks, even though it's exposure was increased by 4 stops in PhotoShop! So, how could we measure the actual brightness of the hands and markers of this watch? There are several ways, some more technical than others - but in this post we will examine how a good camera might do the job, the example chosen being, of course,  my trusty Nikon D50 armed with a Nikkor 60mm f/2.8D Macro lens.
At first, it seemed easy . . just take a pic, note the camera's exposure settings and do a quick calculation of some sort. Note the vagueness implied by "some sort". (Like: - to get to the moon, we'll build "some sort of rocket"). The first problem was that the exposure meter found it quite difficult to measure what was, to it, almost total darkness. It was also difficult to mess with the resulting image so as to find the relative area of the fuzzy luminous paint to the surrounding area of darkness. It could all be done but it wasn't much fun ;-), so much not fun that I gave up on that approach.
Then it was thought that using the "spot" metering mode would allow a direct measurement without even having to take a pic. Fine in theory until it was found that watch hands aren't generally wide enough to fill the spot metering area, even with the lens set to maximum close-up. (The D50's spot metering field of view is two degrees which translates to 3.5mm at maximum close-up setting). Attempts to interpose magnifying lenses failed miserably due to a) focusing problems and b) a much dimmer image, it seemed. Therefore I gave up on that approach, too, although it did work on a WWII aircraft clock that I have by my bed.
So an approach was sought that involved no particular camera exposure setting and brought into use a picture's image pixel brightness but without those tedious lume versus total area calculations or equivalent editor trickery. The thought was that, if an image pixel brightness was known, then it should be possible to calculate the exposure at the sensor that resulted in such a pixel brightness.
It's quite hard to find detailed information about cameras. The great majority of websites only skim the surface of the subject, carefully avoiding any mention of scientific units, performance data, etc., that would actually be helpful in this task! However, some individuals such as Doug Kerr have written useful articles aimed at  less knowledgeable folks such as myself. With Doug's help, the following method was developed  . . .
Step 1)
As Mrs Beeton might have said "first, take your picture". Armed with the D50, a tripod and a completely dark room, I took this rather unimpressive shot:
As can been seen, the lume is not real bright on this 25-year old military watch. The original shot was taken in the RAW (Nikon's .nef) format, with the camera set manually to an arbitrary f/5.0, 13 seconds at ISO 400. The file was opened in PhotoShop Elements and everything that the camera had done was reset to zero. The white balance was reset to 6500K with no tinting. At this point, the on-screen image was color-picked within the hour hand area, and RGB readings of 5, 31, 6 were noted.
Step 2)
Now we estimate what photometric exposure  Ho  (i.e. at the face of the camera's CCD sensor) was necessary to cause the RGB readings noted above. Doug provided a spreadsheet which produced a relative luminance factor (y) which could be applied to the maximum or saturated exposure Hsat in order to determine the exposure Ho caused by the lume. Hsat  is derived from ISO 12232:2006 as being: Hsat = 55.56/Si, where Si is the camera's ISO setting. At a setting of ISO 400, Hsat comes out as 0.139 lux-seconds (lx.s). Cameras can vary in their implementation of the ISO standard, so 55.56 may not be correct for your camera . Running Doug's spreadsheet with RGB = 5, 31, 6 plugged in gave a value for the relative luminance as y = 0.0103. Therefore,  Ho =  Hsat times y = 0.139 x 0.0103 = 0.001431 lx.s.
Step 3)
Having found the photometric exposure at the face of the sensor, and knowing the camera settings, it is now possible to to work a photometric equation backwards to thereby find the object's luminance  Lo . The particular equation that relates Ho to Lo is:

Ho = 4/pi * t/N^2 * L* q  where t = exposure time, N = aperture setting (f/N),
and q = T * Vθ * cos^4(θ) where T = lens transmittance, V = vignetting factor and θ = the angle of the object from the lens' axis. An arbitrary value of 0.88 for q may well suffice if the object is less than 10 degrees off-axis.
The equation can be re-arranged to provided our desired result, namely  the object's luminance Lo   in cd/m^2:
Lo =  H/ (4/pi * t/N^2 * q)
Substituting Ho = 0.002575, t = 13, N = 5 and q = 0.88 gives  Lo = 0.0024561 cd/m^2
Therefore, the luminance of the watch lume is 2.46 mcd/m^2
For those who are not into heavy calculations like the above, I've added them to Doug's spreadsheet here.
Here's a shot of a Marathon military watch I have. It has 12-yr old tritium vial markers and does not need to be "charged up" under a lamp. It still glows well in the the dark.
Best regards,  xpatUSA