Glint

what the picture can say about itself

A halo is not a thing in the sky. It is the set of directions in which some crystal, somewhere, is turned so that its faces send the sun to your eye. Les Cowley, who spent years photographing halos and simulating them, put it in two sentences: “Each crystal sparkles in the sky when it is at this angular distance from the sun. The collective sparkles make the halo.” Far off, millions of crystals blur into arcs. Near the lens they are seen one at a time, and each lights only where an arc is. Nothing on this page tells them where the arcs are.

The arcs come from rays. Light from the sun's disc enters a hexagonal prism of ice through a face chosen by how much of that face is turned to the sun. At every face Fresnel's equations decide whether it reflects or passes, bent by the index of ice across the visible as Warren and Brandt compiled it in 2008, and inside it may bounce up to thirty-two times before it leaves. Where it leaves is where it lands in the sky. The graphics card traces a few million rays every frame, and the readout above counts them.

Three of the arcs can be checked against a formula. The 22 degree halo is the least a sixty-degree wedge of ice can bend light, so its inner edge is sharp, at 21.9 degrees for yellow light, and nothing is bent to anywhere inside it: the sky within the ring is darker. The sundogs are the same wedge in plates falling flat, and Auguste Bravais showed in 1847 why they walk outward as the sun climbs: 22.6 degrees from the sun when it is 10 degrees up, 24.7 at 20, 36.5 at 40, and none at all above 60.7. The circumzenithal arc, the smile near the top, is light that enters a plate's flat top and leaves by a side; with the sun higher than about 32 degrees it cannot get out. Move the sun and watch it go.

Within four metres of the lens about two million crystals fall, each at its own speed (about a sixth of a metre a second for a plate a seventh of a millimetre across, at this cold), drifting on the faint air and turning slowly. A crystal lights only when one of its own paths through the ice sends the sun into the lens, and how bright it is comes from the same tracer. Between four and forty metres the crystals are too many to keep one by one, so their glints are drawn from the traced rays themselves: each ray is a crystal somewhere, turned just so. Beyond forty metres they are the halo. The ice drifts in patches, the same patches for the halo and for the glints, so the arcs brighten and fade and the two sundogs are never quite twins.

The camera is a 14 mm lens on a 35 mm frame at f/8, tilted up 27 degrees, loaded with Tri-X behind an orange filter. Nine aperture blades give the sun eighteen spikes. The filter takes the blue out of the sky, so the white arcs stand against grey, and the halo's colours become tone: its red inner edge stays bright and its blue outer side fades. Each ray's wavelength is drawn from the low sun's light times what the filter and the film let through. The snow reflects the way Alexander Kokhanovsky's model of a snowpack does, fitted to Stephen Hudson's measurements of real snow at Dome C, which throws light forward toward a low sun; that is why it is bright toward the trees.

Seven gates and five predictions were written down before any of this was built. Six gates pass: the 22 degree edge on both tracers, the circumzenithal arc's cutoff, the light's books balanced to fifteen decimal places, the glints carrying the same light per metre of ice as the halo (worst 15 per cent off), the graphics card's halo matching the CPU's (correlation 0.9994), and sixty frames a second. One failed as registered: Bravais's sundogs land where he says, but I had asked for no sundog light at all with the sun at 61 degrees, and ten rays in thirty-two million arrive through plates tilted enough to see the sun lower than that, which is right; and on the graphics card the disc of the sun widens the sundog's edge by more than I allowed. Two predictions held: 30 to 100 bright glints within four metres in any frame (about 31), and a halo much fainter over the spruce 150 metres away than over the sky above them (nineteen times). Three were wrong. I expected a pillar of separate glints over a low sun, and the pillar is there as light but no glint in it outshines the glow behind; I expected the circumzenithal arc to be brighter than the top of the 22 degree halo, and it is a quarter as bright; and the glints alone draw the display above the horizon (0.996) but not on the snow.

On 4 October, the morning it went out, I read the photographs as numbers before changing anything. Their sundogs stand 1.3 to 2.9 times taller than they are wide; mine stood about half as tall as wide. Their glints crowd three and a half to fifteen times thicker on the arcs than in open sky; mine, 1.65 times. The one fit of a real diamond-dust display I could read, Alexander Haußmann's of a display on the Fichtelberg on 18 December 2017, has plates wobbling 2.5 degrees and about one crystal in eight tumbling, where I had chosen 1.2 degrees and one in three. I took both numbers and graded the result against bars written down first. The sundogs grew a degree taller and the glints now crowd 2.4 times on the arcs. Neither reached the photographs. The tracer says why the sundogs fall short: on a print a sundog's tail outward is about as wide as any wobble makes it tall. The change also cost bright glints near the lens, about 23 a frame now, so the first prediction above is wrong as well.

The glints taught me something I had not asked. With the dust thirty metres deep instead of three hundred, the arcs are drawn in separate sparkles, the way observers on mountaintops above fog describe their displays. Under three hundred metres of ice, the far crystals paint every arc as light behind the near ones. That is also why the pillar of separate glints I expected over a low sun stands under it instead, over the snow, where twenty metres of ice is all there is behind it. And with the sun at 25 degrees the foot of the lower tangent arc burns white between the spruce: the line of sight there crosses six kilometres of ice, and the model assumes the dust is as thick that far away. No photograph I have shows it.

What this is not. The weather is chosen: thirty-one below on 6 March is a cold snap, not a normal March morning. No one has counted diamond dust near Fairbanks, so its density, 20 crystals a litre, is a South Pole display's, in a layer chosen to be 300 metres deep. The plates' wobble and the share of tumbling crystals are the Fichtelberg fit's; the rest of the mix (a quarter columns, a few Parry columns, the plates taking what the tumbling crystals gave up) is chosen. The patches the ice drifts in are chosen. Diffraction by the crystals, the birefringence of ice and light scattered twice are left out. The spruce, the snow's relief and the fog are made from the sources' heights and shapes, and the film's curves were read by eye from Kodak's charts.

Fall (artwork 170) grew one snow crystal. Glint flies about two million of them through the sun. Roost was sixteen thousand birds and one figure that nobody draws; this is the same idea in its plainest form.