## Sunday, May 17, 2009

### Experimental Interferometry

Yesterday night, I've made a nice experiment. Here is the view from the frontyard of my appartment building along the street, photographed with my old digital camera mounted on a tripod:

(Click for larger view or the original photo)

There is the roof of a parked car in the foreground, and a bright street light about 100 metres away. The dimmer white and blueish lights are street lights on a hill, about 1 kilometre away, and the yellow lights are illuminated windows.

For the experiment, I have equipped the camera with a double-slit aperture, fabricated by printing two letters "l" in sans-serif against a black background on an old-fashioned overhead slide:

The two slits are a bit less than 1 millimetre wide each, and separated by a bit more than 1 millimetre.

I have then fixed the aperture on the lense of the camera with adhesive tape - the casing of the lense is big enough to allow this without glueing the lense. Here is photo of the camera with the double-slit aperture. The quality is not very good, because I have only one camera, so this is a self-portrait in a mirror of the camera equiped with the double-slit aperture:

Now, I have taken another photo of the same nightly street scene, using the double-slit aperture:

(Click for larger view or the original photo)

There is less light entering the camery, so the photo is darker. But wait: The distant street lights now show a very clear interference pattern! Instead of one spot of light, there are three distinct fringes.

I was quite amazed by the result when I looked at the photos on my computer. Here is a detail of the photo:

This startling little experiment demonstrates the principle of interferometry, as it is used in astronomy to measure the diameter of stars, for example.

Actually, I got the idea of the experiment from the chapter Basic concepts: a qualitative Introduction in Labeyrie, Lipson, and Nisenson's An introduction to optical stellar interferometry.

Here is a rough sketch of what is going on:

The double-slit aperture is shown in black, the lens system of the camera in grey, and the CCD chip in blue. The camera is focussed "on infinity", which means that parallel rays of light are bundeled onto one spot on the chip in the focal plane. This is shown for the two yellow rays of light, which may hit the camera from one of the distant street lights.

So far, this is all geometrical optics. But as we know, light is a wave, and the aperture creates the situation of Young's double-slit experiment: According to Huygens' principle, each point of the two slits can be considered as the origin of a spherical wave, which, at a distance, combine again to plane wave fronts. But now, there will be not only the wave front in the direction of the incoming light rays, but also additional, slightly deflected wave fronts. In all these deflected wave fronts, the path difference Γ has to be an integer multiple of the wavelength, λ. The deflected waves will also be focussed on one spot by the lenses. This is shown by the dotted orange lines. In the experiment, there is one clearly visible extra spot on each side of the central spot, meaning that Γ, shown in lightblue, is just one wavelength of visible light.

The angle α between the the two spots is easy to calculate – it is (in radians) just the wavelenght of light, λ, divided by the distance d of the two slits: α = λ/d.

Taking for simplicity λ ≈ 600 nm = 0.6 µm and d = 2 mm = 2000 µm, this is α = 0.0003 ≈ 1' arc minute = 1/60°.

There is an interesting twist to these considerations: When the angular size of the light source is bigger than the angle α, one cannot expect to see the interference pattern, because the image of the source in the focal plane is already as big as the distance between the spots.

So, at a distance of, say, 100 m, the light source should be smaller than 0.0003 · 100 m = 3 cm for the interference pattern to show up. A typical street light is bigger than that, hence, there is no interference pattern visible for the nearby street light. However, for a distance of 1 km, the light source will show the interference fringes if it is smaller than 0.0003 · 1000 m = 30 cm – and this condition is fulfilled for the street lights on the distant hill!

The French physicist Hippolyte Fizeau has suggested in the 1850s to use this method to determine the angular diameter of stars: Spotting a star in a telescope with a two-slit aperture with a small distance beteeen the slits, one would expect to see interference fringes, as stars are very much point-like sources of light. However, increasing the distance between the slits, the critical angle for the loss of the interference pattern shrinks, and from the distance of the slits when the interference pattern disappears, one can calculate the angular diameter of the star.

Edouard Stéphan, astronomer at the observatory of Marseille in France, was the first to put this method in practice, but he always saw interference patterns: He only could establish upper bounds on the angular size of stars.

The first successfull application of the method was by Albert Michelson and Francis Pease in 1920: They could measure the diameter of Betelgeuse, the bright red star in the constellation Orion. It is 0.05 arcseconds, or the size of a street light in a distance of 1250 km.

For such measurements, I'll need better equipment.

Basic concepts: A Qualitative Introduction in Antoine Labeyrie, Stephen G. Lipson, Peter Nisenson: An introduction to optical stellar interferometry.

Florentin Millour:

Edouard Stéphan: Sur l'extrême petitesse du diamêtre aparent des étoiles fixes. Comptes Rendus de l'Académie des Sciences 78, 1008-1012 (1874).

Albert A. Michelson, Francis G. Pease: Measurement of the diameter of alpha Orionis with the interferometer. Astrophys. J. 53, 249-259 (1921).

Neil' said...

I've seen some pictures of the type of interferometry that combines data to get higher detail and not just diameters. I'm impressed with how the positions of multiple stars etc. show well even through the Earth's atmosphere. (IOW, better than even if you had a huge telescope on the Earth.)

Another interesting trick are ways to beat classic resolution limits, through near-field imaging or metamaterials. This site makes amazing claims:
http://cmbi.bjmu.edu.cn/news/0703/67.htm

Superlenses like this might allow biological objects such as individual viruses or molecules of DNA to be imaged — something that once seemed inconceivable with optical microscopy. "There's a huge amount of potential in this area," [physicist John Pendry of Imperial College in London] says. Of course I think that is "really cool" but it seems to cause trouble for the uncertainty principle: remember the "Heisenberg microscope" used to illustrate the UP? I haven't time to detail it here, just reflect on its implications so to speak if you know of it. Are metamaterials problematical in that regard, why or why not?

Andrei Kirilyuk said...

Thank you for confirming the wave nature of light and very successfully reproducing these surprising results of the 19th century physics. It shows that despite all spoiling influence of industrial progress on modern youth, the explorative power of our best minds is still here. However, closer to today's problems, the real physical nature of photon, a competing nature of light, remains absolutely mysterious. If it's each single photon that “interferes with itself” (as it seems to be confirmed, but maybe not without contradiction), then how can it be a “point particle” and an “extended wave” simultaneously? And if it's some “encompassing” electromagnetic wave that interferes and brings individual photons to a distribution of its density, then the situation becomes even more complicated. There is apparently no consistent solution to these real problems of modern science and they are far from being merely “interpretative” ones: for example, the whole modern cosmology (completely flawed within its standard framework) depends very critically on the photon problem solution. Needless to say, that's exactly why such kind of problem is very thoroughly excluded from activity of those luxurious centres and departments of “advanced” fundamental science, actually concentrating all serious material resources of the world invested in science... Nice clip-making and surprising discoveries to everybody!

Plato said...
This comment has been removed by the author.
Phil Warnell said...

Hi Stefan,

An excellent demonstration using what is considered today as ordinary household items. Can you imagine if you could travel to the past to show this to Young how perplexed he might be with the instrumentation, other then of course the paper with the two slits that is. Now if we could only come up with a cosmological object(s) that had reliably a identifiably consistent size rather than say simply brightness for which we already have a candidate we would be better able to calculate distance using such methods. Reading through the links you provided one finds that they still place Betelgeuse being at only approximately 640 light years out, which exemplifies this limitation to our current ability to measure.

Best,

Phil

Successful Researcher: How to Become One said...

Nice :)

Arun said...

Can you do Venus?

stefan said...

Hi Neil

... to beat classic resolution limits, through near-field imaging or metamaterials.

Thanks for the link. I have never followed this metamaterials story. Curiously, today's Physics also mentions them, Metamaterial brings sound into focus: "... Zhang et al. show that they can focus a point source of sound to a spot size that is roughly the width of half a wavelength and their design may allow them to push the resolution even further."

Hi Phil,

Can you imagine if you could travel to the past to show this to Young how perplexed he might be with the instrumentation, other then of course the paper with the two slits that is.

Well, even the preparation of the two-slit aperture might have perplexed him: Typing two "white" letters l in a Wordprocessor against a black background, and fixing this on an overhead slide with a laser printer ;-)

Hi Arun,

Can you do Venus?

Cool suggestion! The angular diameter changes between 10 an 66 arcseconds, so it may even be that depending on the relative position, the pattern is visible or not. I should try this.

Cheers, Stefan

Phil Warnell said...

Hi Stefan,

Yes true even the creation of the two splits would have most likely confounded him. As you can imagine along with others this wave/particle nature of light fascinates me. Of course there is always the one slit experiment which can have destructive interference for light be recognized and all that’s required for this is to look through fingers that are just a little not so tightly squeezed together. Now that could be considered using only materials you have on handBest,

Phil

Peter Shor said...

Hi Stefan

Neat experiement. What kinds of streetlights are these? They must have predominantly a single wavelength in their spectra, or you wouldn't get such nice interference patterns.

Peter Shor said...

Arun,

I suspect Venus wouldn't work, because there aren't enough sodium streetlights on Venus.

stefan said...

Hi Peter,

thanks for the comment - good point, I haven't yet given much thought to that. This could indeed spoil the experiment for Venus. On the other hand, Michelson and Pease didn't use colour filters?

The street lights are some kind of mercury vapour lamps. Actually, using the CD-ROM spectroscope, the spectrum looks pretty much like the first one given on that page; there are bright lines in the green, orange, and red, and one in the blue.

Cheers, Stefan

Peter Shor said...

Wow, sans-serif interferometry and CD-ROM spectrometry. I am indeed impressed.

I have no idea whether Michelson and Pease used color filters. A spectrum of Betelgeuse I found on the web shows a broad peak between 500 and 600 nm. This might have been enough for the experiment to work.

Peter Shor said...

Hi Stefan,

Of course, Betelgeuse is a red giant, so now I'm confused.

stefan said...

Hi Peter,

I'll have a closer look at the Michelson/Pease paper, perhaps the use of a filter is discussed somewhere.

Naively, I would guess that the interference pattern is washed out when the spectrum of the light source is flat over at least one octave, so maybe the Planck spectrum is peaked enough for the method to work? Actually, some contrast between the fringes is sufficient, it is not necessary that there is no intensity at all in between.

Maybe I could try some experiments with sunlight through a tiny hole in a cardboard...

Cheers, Stefan