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Dec 20

Snowtonics: the photonics of snow?

Fresh snow is bright, white and opaque. What does this actually mean, optically?

Fresh snow is opaque

If you’ve seen snow, you will know this to be true. But why? Snow is made of, erm, snowflakes, which are made of ice, which is transparent, not opaque. Snow is what we call a multiple scatterer, in other words, most of the light that falls onto it is scattered around (inside the snow) several times before it gets out. The consequence of this is that light falling on the snow gets mixed up, randomised, and any information within it is scrambled. So, why you might be able to see distorted images through a clear block of ice, snow looks opaque white, just like a piece of paper, or the paint on your wall.

Why does this scattering occur? The refractive index of ice is about 1.31 and that of air is about 1. Any light beams hitting the interface between ice / air will be bent as a result of refraction (Snell’s Law) or reflection (Fresnel reflections or total internal reflection), depending on the angle of incidence. Do this a number of times to a beam of light and it undergoes a random walk within the bulk of the snow. Therefore snow is also a bulk scatterer.

Fresh snow is bright white

The reflectivity of snow changes little as a function of wavelength across the entire visible range. This has been shown for real snow by many studies including a highly cited piece of work by Teruo Aoki et al[1]. They used an optical fibre based light collector mounted on a tripod, and measured the collected light with a spectrometer, over real snow in 4 campaigns during February 1998 in Hokkaido, Japan. To ensure accuracy they compared their results to a diffuse reflectance standard made of SpectralonTM (for more see below). Their work also shows that the albedo (mean diffuse reflectivity) was around 90% across the visible region. In other words, highly reflective and with no colour - both bright and white.

Note that I said “fresh snow”. We all know that as snow gets older, it gets dirtier – basically, stuff lands on it. This reduces the albedo because a lot of the “stuff” is dark and absorbs the light.

How far does the light penetrate?

There’s no snow here right now so we’ll have to make do with some “ideal snow”, namely a piece of SpectralonTM (mentioned above for its use as a reflectance standard). In this photo I aimed a laser pointer at a slab of Spectralon and took a photo from the side. You can see that the beam has penetrated into the material by over 10mm. Note that SpectralonTM has a finer grain structure than snow does, and potentially lower absorption, but the same principles should apply.

Not a training photo for laser eye surgery

When light from the laser pointer hits the side of the Spectralon block, photons travel over 10mm into the material. Some of them leave the top surface, enter the camera, and show up as red on this image

The amount by which light penetrates into real snow depends an awful lot on its microstructure (different sized ice grains [1]) and can vary with the snow conditions, the snow’s age, and how wet it is (wetness between grains significantly reduces the refractive index change as the refractive index of water is around 1.33 – close to snow’s 1.31).This material has a diffuse reflectance of approximately 99%, one of the highest known. How does it achieve this? We can think about what happens to the photons entering the material. If the material was infinitely thick, they could bounce around a bit until they leave from the surface they entered, they could be absorbed by the material or by impurities, or they could … er … bounce around a bit more. So as long as there is lots of scattering and not very much absorption, the diffuse reflectivity will be very high. The consequence of this is that in order to achieve high reflectivity the material must be quite thick (the manufacturers say at least 10mm), or else the light will leave the far side, never to be seen again. And it must have a suitable microstructure with lots of refractive index changes, with very low levels of light absorption.

If we get any new snow in the near future, I’ll try and repeat the laser pointer experiment. Or get one and try it yourself! It works best in the dark.

Snowtonics and The-Future-of-Civilisation-As-We-Know-It

The reflectivity of snow is an important factor in the Earth’s energy balance[2] – more snow means more reflected sunlight and less global warming. And vice versa – as the planet warms and snow melts, more sunlight is absorbed and the planet warms further, which is why melting snow provides the potential for positive feedback to global warming. Understanding the amount of snow and the level of reflectivity it offers are important elements of the global climate models used to inform environmental policy and reports by the IPCC (Intergovernmental Panel on Climate Change). For example, scientists studying the Greenland ice sheet recorded record levels of ice melt during 2012 [3];

“The lowest surface albedo observed in 13 years of satellite observations (2000-2012) was a consequence of a persistent and compounding feedback of enhanced surface melting and below normal summer snowfall.”

Using diffusely reflective materials in our work

We have used diffusely reflective materials like the SpectralonTM above in our gas detection work. The gas cells we designed are easier to align than traditional cells, which should make them more field robust [4]. One of the key considerations for our research was to understand the resulting laser speckle from materials like Spectralon and to minimise the noise that it adds to our data [5]. An image of laser speckle from SpectralonTM is shown below.

Fuzzy optics.. not fuzzy like a car

Image of laser speckle in an expanded beam from a laser pointer

I think of this as “fuzzy optics”, by analogy with fuzzy logic.

Other groups working on this approach include Siemens in Munich, who developed an oxygen monitor for use in industrial boiler flues [6], and a group at Lund University who have measured gases from within various scattering media including biological tissue [7], pharmaceutical pills [8] and engineered ceramics [9].

You can try the laser speckle experiment yourself with a laser pointer and a piece of paper (in the dark). The sparkly bits are laser speckle. Now bend your forefinger round to make a small hole and place this in front of your eye while looking at the speckle. As you make the hole smaller, the speckles should get bigger. This proves that laser speckle size is a property of the viewing aperture and not the reflective material. If you want to take a photo, aim to use your camera with its lowest NA (highest F/#). In the image above, we used an aperture of f22.

Finally, I used these materials to make an inside-out snowman – more tomorrow!

References


[1]       T Aoki, T Aoki, M Fukabori, A Hachikubo, Y Tachibana and F Nishio. Effects of snow physical parameters on spectral albedo and bidirectional reflectance of snow surface. Journal of Geophysical Research 105 (D8), 10,219-10,236, 2000.

[2]       AJ Dietz, C Kuenzer, U Gessner and S Dech. Remote sensing of snow – a review of available methods. International Journal of Remote Sensing 33 (13), 4094–4134, 2012.

[3]       JE Box, J Cappelen, C Chen, D Decker, X Fettweis, E Hanna, NT Knudsen, T Mote, K Steffen, M Tedesco, RSW van de Wal and J Wahr. Greenland Ice Sheet. Artic Report Card: Update for 2012. November 28, 2012. Available at http://www.arctic.noaa.gov/reportcard/greenland_ice_sheet.html.

[4]       J Hodgkinson, D Masiyano and R P Tatam. Gas cells for tunable diode laser absorption spectroscopy employing optical diffusers. Part 1: Single and dual pass cells. Applied Physics B 100 (2), 291-302, 2010.

[5]       D Masiyano, J Hodgkinson and R P Tatam. Use of diffuse reflections in tunable diode laser absorption spectroscopy: implications of laser speckle for gas absorption measurements. Applied Physics B 90, 279-288, 2008.

[6]       J Chen, A Hangauer, R Strzoda and M-C Amann. Laser spectroscopic oxygen sensor using diffuse reflector based optical cell and advanced signal processing. Applied Physics B 100 (2), 417-425, 2010.

[7]       M Lewander, ZG Guan, K Svanberg, S Svanberg and T Svensson. Clinical system for non-invasive in situ monitoring of gases in the human paranasal sinuses. Optics Express 17 (13), 10849-10863, 2009.

[8]       T Svensson, M Andersson, L Rippe, S Svanberg, S Andersson-Engels, J Johansson and S Folestad. VCSEL-based oxygen spectroscopy for structural analysis of pharmaceutical solids. Applied Physics B 90 (2), 345-354, 2008.

[9]       T Svensson, E Adolfsson, M Lewander, CT Xu and S Svanberg. Disordered, Strongly Scattering Porous Materials as Miniature Multipass Gas Cells. Physical Review Letters 107 (14), 143901, 2011.