X-Message-Number: 19370 From: Date: Sat, 29 Jun 2002 10:16:13 EDT Subject: Intensity interferometer part 2 --part1_97.29c4e2b7.2a4f1b2d_boundary Content-Type: text/plain; charset="US-ASCII" Content-Transfer-Encoding: 7bit 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 image and adding one more would give access to the third dimension, something impossible in astronomy. Yvan Bozzonetti. --part1_97.29c4e2b7.2a4f1b2d_boundary Content-Type: text/html; charset="US-ASCII" [ AUTOMATICALLY SKIPPING HTML ENCODING! ] Rate This Message: http://www.cryonet.org/cgi-bin/rate.cgi?msg=19370