Photometry of lunar eclipse

On early morning, Wed Oct 28, 2004 (saint Thaddeus, and a legal holiday in Czech Republic -- remembering the birth of Czechoslovakia etc.), there was a lunar eclipse. The weather was rather poor in Brno, but the Moon was visible through the thin clouds since midnight.

I realised no sooner that at three o'clock in the morning, when I wake up spontaneously, that I should make a photometry of the phenomenon. I used a Fuji S5000 camera, for which I have a photometric calibration, including spectral sensitivity of its R, G, B filters (see ev. my poster g_camer.pdf), taking images from a window of our home and then from the garden. Examples of the results are given below (for luminance computation, dark frames are subtracted).

Photopic luminances are coded by colours, each colour corresponding to an order of magnitude. Blues are around 1 kcd/m², yellows around 100 cd/m², greens around 10 cd/m², etc. (blue is used twice, for the lowest luminances around 1 mcd/m² a second time). Within each colour, the brightness steps are logarithmic, each further is 10^1/5 or some 1.58 times brighter (in astronomic parlance, this is exactly 0.5 mag). For seeing details, load the images separately into a image viewer and magnify them (zgv with its ability to change gamma quickly is my favourite one).

To simplify luminance numbers, I'll write nit instead of candela per square metre further, 1 nt = 1 cd/m².

		01:18 UTC. Some five minutes before the Moon immerses to the ``earth shadow''. The upper left part of the Moon already, deep in semi-shadow is no more visible, due to the moonlight dispersed by the cloud. Exposure 1/2000 s, f=1/3.2, ISO 200. The brightest blue in the luminance-coding image corresponds to 1.6 knt, the less bright ones to 1 knt, 0.6 knt, 0.4 knt. Yellow begin at 0.25 knt, then continues through 0.16 knt etc. again. The darkest part of the Moon is too noisy already, with luminances below thirty nits (coded by green already). Even the well displayed part of the Moon, immersed in semi-shadow, shows very pronounced luminance scale, spanning more than a factor of ten. The total luminous flux density by the clouded Moon was 0.04 lx at the moment (would be 0.24 lx without the Earth shadow and the cleanest possible air).
		An image with 16x longer exposure (1/125 s) is overexposed already (giving false yellow in the overexposed part), one step lower exposure would be better. The limb near to the umbra is still not visible, being twice less luminous than the cloud. The luminance of the sky around the moon is shown without noise here, Penumbral luminances span more than a factor of 30.
		01:46 UTC. The part of the moon illuminated just by sunlight going through the earth atmosphere is visible faintly. 1/125 s exposure. The luminances in the umbral part are mostly due to the light dispersed in the cloud, just a slight contribution of the Moon itself is apparent.
		02:08 UTC, 1/30 s, even the brightest parts are not overexposed, so the luminances could be computed. The apparent edge of the shadow is the region, where the luminances diminish abruptly by an order of magnitude (in the image, it's the region from 3 nt to 30 nt, coded by greens).
		1/8 s shows the umbral parts better, with less noise in the luminances.
		02:17 UTC, 1/8 s is just below being overexposed.
		2 s show the umbral part well. Their luminances go down to decinit values.
		03:04 UTC, 2 s, through a heavier cloud. The deepest eclipse. The least illuminated limb of the moon is almost in the centre of the Earth's shadow. From there, a uniform ring of orange, refracted sun would be visible around the Earth, almost infinitely thin (less then three seconds of arc).
Even with the longest, 2s exposure, there few light and a lot of noise in the signal. However, the averages over one thousand pixel groups (R, G, G, B) are still rather accurate. These are given in the bottom of the tiles (the middle number is the median G value).		We may conclude, that the cloud has some 22 mnt (millnits) just left from the Moon and the darkest part of the Moon itself appears with some 40 mnt. This may be near to its extraterrestrial luminance: even if its contribution to the image is just some 18 mnt, we may guess that its light is attenuated to perhaps one half by the air.

Let's discusse this value. A very crude guess is that the luminance of the refracted Sun could be diminished by atmospheric extinction some 7.5 mag, or to 1e-3. The Sun is a ring just 0.04' thin, but four times larger than the usual Sun. The usual sun has some 800 square minutes, the refracted one some 4 square minutes, 5e-3. The illumination produced by it should be then 5e-6 the usual one, which was 1.4e5 lx before the eclipse. So in the centre of the shadow, there should be still some 3/4 lx.

Full moon has luminance (observed outside the atmosphere) of almost 5 knt (you may compute it by lun_illum.php), dispersing the sunlight mostly backwards. Multiplying it by 5e-6, we arrive at 25 mnt, not far from the measured value.

More elaborate reasoning about luminances, with implications to the actual transparency of the atmosphere in the regions where the sunlight squeezed around the Earth surface, would be possible if the photometry would be performed under clear air with well-determined extinction properties. Still, the observation done by me shows at least that the ``shadow margin'' is that region on the Moon, where the luminance falls from tens of nits to units of nits, within a strip of just several arcminutes width.

Such a photometry done at many places in the world would be a unique possibility to compare different cameras, even to calibrate them. Moon can become a luminance normal which can be used simultaneously over almost half of the Earth. When in penumbra, it offers a wonderful grayscale, in the umbra, colour photometry could be checked.

Quite probably, even non-raw data could be used for photometry, if the non-linear transformations used to produce them would be known or guessed. Like those wonderful images available within NASA gallery of this eclipse.