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From:  var s1 = "Azt28"; var s2 = "aol.com"; var s3 = s1 + "@" + s2; document.write("<a href='mailto:" + s3 + "'>" + s3 + "</a>");
Date: Sat, 29 Jun 2002 10:16:13 EDT
Subject: Intensity interferometer part 2

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The basic idea to make pictures from an interferometer is not straightforward
to say the last. This message aim is to give the basic concepts underlying
that technology.

The simplest case is a light point source, if we take that light at two point
and bring the two beams together, they'll interfere, that is, they'll produce
a set of bright and dark strips on a screen. If the two beams are taken at a
distance D from each other and if the light wavelenght is L, then the source
angular diameter must be smaller than L/D (counted in radians, or arc length
equal to the diameter of a circle) so that it looks point-like. This is the
way the first stellar diameter where metered: Two mirrors was moved apart
until the interference finges disapear, that given the distance D in L/D so
that the star was no more a single point. Many things can go wrong in such a
mesurement, the basic problem is that there are two beams and so 2 error
sources and only one mesurement. If we try to get ride of the errers we have
an equation with 2 unknowns, this can't be solved.

A way out, it to start with 3 beams not on the same line. there are 3
unknowns and 3 interferences and so, 3 equations. A system with 3 equations
and 3 unknowns is solvable. You can think of the 3 beam captors as the sumits
of a triangle and the interference as the side of the triangle. When 2 sides
are used, the 3rd simply close the triangle, so from the first 2 mesurements
the 3 rd can be predicted. What is effectively mesured on it don't agree with
the prediction, the difference is the error introduced in the system. So, not
only a physical quantity, the interference pathern is metered, but its (first
rank) error is known too. Because, starting with the first beam, we get back
to it at the 3rd interference mesurement, this technics is known as "phase
closure". Interferences are about wave phase mesurement and this systen bring
back to the initial phase, so it close it.

This system gives the state of a wave at the triangle center, not a picture.
If we add a fourth beam, more triangles with phase closure may be built. The
wave can then be tested at a second point. Moving the fourth beam allows to
move that second point along a line giving a line. that line is an one
dimensiona picture of the light source. Adding a 5th moving beam give another
line. this system may scan a surface and so build back a picture the way a TV
one is made on a screen. More beams may be used to correct errors beyond the
first order ones, for example the french Director of the Observatoire de
Haute Provence has promoted for years the idea of an interferometer using 27
telescopes.

All these systems are two waves interferometers, intensity interferometers or
2x2 waves interferometers are another breed: The basic idea is that photons
are gregarious, they follow the Bose Einstein statistics. When they come from
a single point source, they fall in the same quantum state and travel
together, so they come in packets or bunched. If we look at the arrival time
of a photon set, we can say if the source is a single point  or a resolved
object, for example a disk. A point source will give bunched photons, on the
contrairy, a resolved source will produce random arrival time. Assume the
entrance aperture of the photon counter is small enough so that photons are
bunched. We can put nearby a second photon counter. If the distance D between
counter don't resolve the source, a bunch in the first counter will be
matched by another in the second. Now, if D resoves the source, then bunches
in one counter will refer to a point different from the one defined by
bunches in the second counter. Here, bunches coincidence has taken the place
of interference fringes.

What is interesting is that photon bunches have long tails, so we can see
them even with a modest time resolution. At the end of WWII, R. Hanbury-Brown
has been the first to build an intensity interferometer in UK. With only a
100 Mhz time resolution, he was abe to mesure the diameter of some stars. The
intensity interferometer has far less perturbations than its two waves
counterpart, so phase closure is not a requirement in astronomy. If we would
built a picture from a dispersive media such a biological body, then that
technics would be useful. As before, 5 counters would build a two dimensional
impossible in astronomy.

Yvan Bozzonetti.

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