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.

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

Florentin Millour: All you ever wanted to know about optical long baseline stellar interferometry, but were too shy to ask your adviser. arXiv:0804.2368v1 [astro-ph]

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).

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