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  H_o  (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 H_sat in order to determine the exposure H_o caused by the lume. H_sat  is derived from ISO 12232:2006 as being: H_sat = 55.56/S_i, where S_i is the camera's ISO setting. At a setting of ISO 400, H_sat 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,  H_o =  H_sat 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  L_o . The particular equation that relates H_o to L_o is:

H_o = 4/pi * t/N^2 * L_o * q  where t = exposure time, N = aperture setting (f/N),
and q = T * V_θ * 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 L_o   in cd/m^2:

L_o =  H_o / (4/pi * t/N^2 * q)

Substituting H_o = 0.002575, t = 13, N = 5 and q = 0.88 gives  L_o = 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.

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Best regards,  xpatUSA

SandY Seconds Hand - is it balanced?

The later Stocker & Yale military watches had this ugly seconds hand with a huge paddle on it:

I've read that the paddle acts as a counter-balance to the much longer arm with the arrow on it - but you can't really judge by just looking at it. However, it can be calculated if you know the areas of the various geometrical figures that go to make up the seconds hand's outline.

So I took a macro photo of the hand, brought it into PhotoShop and measured the needed dimensions (in pixels). Then, like a pilot checks the Weight and Balance of an aeroplane before taking off, I calculated the moments of area for each arm of the seconds hand. It's OK to use area instead of weight because the hand is made of thin sheet steel which means that, if the areas balance, so will the weights. The units end up as pixels cubed - because area was measured from the image as pixels squared and the distance of each geometrical figure from the center was also in pixels. Ordinarily, moments are given in units of force x distance - for example Newton-meters.

The paddle side came out at 1.73 Mpx³ and the arrow side came out at 3.29 Mpx³, almost twice as much. So, it's not balanced, even though it looks like it. The specification for the movement, a Ronda 715, states that the out-of-balance for the seconds hand is to be less than 0.04 μNm. So, some unbalance is allowed but, to check compliance, it would be necessary to use real units of mass instead of the above pixel-area short cut. I'll do it one day, just out of curiosity.

Best regards, xpatUSA

Smooth Sweeping Seconds - an alternative

Many of us like to see a smoothly-moving seconds hand, as opposed to that of a quartz watch which clunks it's way around the dial, only occasionally aligning with the marks thereon. And a good few of us think that the higher the beat rate the smoother it will be - which is true to an extent, but why? One could be forgiven for thinking that our so-called "persistence of vision" has something to do with it but, sorry to say, that is not the case. There might be a smooth running appearance if the beat was over 16 per second or even 24 per second like old movies but that would mean a beat rate of 86,400 bph!!

Yep, the hand does seem to run smoother on a 28,800 bph watch but only because it moves in smaller steps and takes more steps to go once round the dial. You can still see the steps, though. That got me to wondering how small a step would give apparently smooth motion. Well, apart from persistence of vision, another property of vision is that "visual acuity". Put simply, this is the ability of the eye and brain to distinguish between two objects that are very close together. Like the bars on the letter "E" when you visit your optician or optometrist.

Apparently most folks can distinguish objects quite easily if they are more that a certain angle apart. By "angle", I mean relative to the eyeball. That magic angle is 1/60 of one degree, also known as 1 minute of arc. At 20 feet distance, it is no coincidence that a person with 20/20 vision (6/6 in metric countries) should be able to read an "E" that is 0.35" tall at that distance because it is apparently 5 minutes of arc in size and each bar or gap is 1 minute of arc as seen by the eye.

However, when we glance at our watch, it's a little closer than 20 feet! Switching to metric, let's say 300mm, just less than a foot. This is the only information we need in order to calculate how far apart are two successive step positions of the tip of the hand that can be easily distinguished. Trigonometry tells us that the distance is 0.087mm. Less than a tenth of a millimeter!

Next, let's have a sweep seconds hand that is 13mm long from center to the tip. More trigonometry tells us that the tip of this hand sweeps a circumference of 81.681mm every minute. From here, we can go several ways but it might be instructive to calculate the beat rate in bph for the step distance of 0.087mm established in the preceding paragraph. It comes to 938 beats/min which is 56,267 bph. This tells us that, even at this very high beat rate, a person with normal vision will still see the seconds hand ticking!

Well now, what about those old-fashioned sub-seconds hands? They seem to run smoother too, huh? I have a watch with a sub-seconds hand 3mm long. Ergo, it sweeps a circumference of 18.85mm. That works out, for the same step distance, to only 13,000 bph. The watch actually ticks at 15,000 bph, so it is no surprise that the hand motion (to my less that perfect eyes) seems quite smooth with no apparent ticking discernible.

Best regards, xpatUSA

A Perfect Watch is always Fast

Let's say that you bought a perfect watch on January 1, 1972. By perfect, we mean that each and every second measured by this hypothetical watch is exactly equal to a SI second - defined in 1967 as "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom". Let's say also that, comforted by this extreme accuracy, you've never adjusted the watch or had to change to battery or wind it up or whatever. After all it is a perfect watch, right?

Sorry to tell you that your watch is now 24 seconds fast. Yep. You see, measuring the passage of time is not quite the same as telling the time. Time itself is but a concept, a human observation of change if you will. On the other hand, "the time" [of day] is our expression of an agreed instant in the passage of time. In fact, the time of day, or the definition thereof, has been messed around with ever since the first non-sundial clock was invented.

You would think that the invention of atomic clocks would clear everything up. After all, atomic clocks are almost as good as the perfect watch that you bought back in 1972. Unfortunately, we still have the same problem in modern times that the ancients had. Days are still varying in length - not just the period of daylight versus night, but also the actual length of each day varies during the year. Not to mention that the wobble of our planet (about once every 26,000 years) causes a change in the length of each year and that the planet itself is slowing down due to tidal friction.

Before the second was re-defined in 1967, it was defined with respect to the mean solar day and thus measured the passage of ephemeris time. However, the first atomics clocks proved that even ephemeris time was not perfectly constant so, up until 1967, they were actually adjusted to keep ephemeris time, known quaintly as "ET".

These days we still match "the time" to our planetary motion but now it is done by adding leap-seconds when required by our slowing planet. It is only by adjusting atomic time with leap-seconds do we arrive at the familiar UTC which is now truly "the time", as far as everyone on the planet is concerned. In 1972, when UTC was invented, it was already slow to the atomic clock by 10 seconds and since then 24 leap-seconds have been added - which is why your perfect watch is now 24 seconds fast!

Best regards, xpatUSA

A Made-up Military Watch

My Military Frankenwatch

Sorry, this article has been moved to my website, please click here

Best regards,

xpatUSA

Fixed my Military Navigator Watch

Made by the Swiss Gallet Watch Co for Marathon, the 6 prototypes were called "Desert Storm" on the dials. I wonder why? This one is a 1990, steel-bodied, signed "Marathon".

Have a look:

The Harley-Ronda 373 movement was ticking - but only moving the seconds hand back and forth, even with a fresh battery. A spare movement from my parts bin fixed that problem. The bi-directional bezel was sloppy and not clicking as it should. The internal spring was distorted and had a segment missing. It measured as 0.015" thick so I stole a guitar string from my studio and made a 0.016" replacement which was a little harder to refit the bezel but, once on, a much nicer fit and feel.

Eagle-eyed folks will notice the considerable bending up of the hands near the posts. I could have swapped the taller posts over from the dead movement but anyone who has attempted this on a Harley-Ronda 373 will understand exactly why I didn't. This watch was already built from a pile of parts and it's my current beater, not for sale, so it's really no sin to do things like that.

Best regards, xpatUSA

Arts and Crafts Door Casing

My First Built-up Door Casing Our 12x24 ft. Shack is of plain construction, more or less Southern Country style, conventional wood framing with a shed roof, supported on concrete blocks. Inside, it is equally plain. Thin, faux white pine walls and no trim work until now. After several years of living under 2x6 rafters and drooping insulation held up by staples, a start was finally made on the ceiling - which now supports 4x4 ft. squares of 3/8 ply wall panels, the kind that has grooves machined every 4" to look like boards. Then, next up would be wall/ceiling trim strips (cornices being too grand a name for what we had in mind). But "what kind of trim?", was the question. To go "Country" would comprise of simple 1x2 strips nailed up there but it wouldn't have looked all that good. On the the other hand, polystyrene crown moulding slapped up and glued into place would have just looked stupid - plus, the ceiling panels themselves were none too straight and needed to be forced up in some places. In the end, we bought a dozen 1x6 cedar fencing boards and ripped a load of 2" strips at the trusty Chinese table saw. To fancy it up a little, a chamfer was put on the bottom side. The strips went up OK, for an amateur. Next up for action was the entrance door which now needed a casing. Some research revealed that perhaps the most appropriate style to the Shack is the so-called "Arts and Crafts" style, proposed by the Englishman William Morris as a reaction to the excessively ornate Victorian style then in vogue. His movement caught on and was popular here in the USA from approx.1900 to 1930. Here is an example of both a door and a window casing in that style, but . . . . . . a pity about those light switches! Still, the nice thing is the lack of mitered joints - not the easiest kind of joints to make in boards that wide. And the header sets off the door better than just a piece that is the same section as the sides. I found a similar design in a book that we already had - a Home Depot "how to" book on trimwork. Unusually for me, I kept the design as-is and followed the instructions to the letter. I used more cedar fencing boards, quarter-sawn oak not being readily available at the local hardware store and also it's bloody expensive! Over there at Vincik's in Bellville, the nice man out in the yard lets me sort through the cedar boards to find the good 'uns. The header turned out OK but it did not stand out against the background. So I found some dark oak stain in the barn and used it to darken the casing a bit. Here's the finished job below, contrasting nicely with the "white pine" wall panels. This was also the first time I've routed my own mouldings. I've learning to rout in stages; the first try was terrible, lots of tear-out. Although the casing looks overly dark at first, the plan is eventually to try and match to the door's wood. I bought the door used from a garden center many years ago for ten bucks. While nailing up the header just now, I noticed that the grain where the doorbell used to be is showing very close growth ring spacing, see below. It's about ten rings per centimeter - some more, some less - which makes this door quite old and certainly worth stripping the paint off for a look. It needs to be re-glued anyway.