By: Adam Kingsley
Mentor: Dr. Durfee
When seeking more information about stars, one of the first things that astronomers want to know is, “How big is it?” It is not an easy question to answer. The ultimate challenge is always resolution. Resolution has a physical limitation because of the physical size of equipment. Rayleigh’s criterion defines this limitation based on the diameter of the lens of the telescope that is being used. To some extent it would seem a simple thing to build a larger telescope, however, this reaches practical limitations. Other techniques were developed to determine the angular size of stars. The Michelson interferometer was used for some time and was quite successful. However, creating large interferometers with enough stability placed a limit on even this method. It was during this time that
Hanbury-Brown with the assistance of Twiss created what was later called “intensity interferometry” (a somewhat misleading label). The idea was ingenious. Using two photodetectors with a variable distance between them, they showed that the correlation between the two photodetectors dropped off as the distance between them increased. The extent to which the detectors stayed correlated was related to the angular size of the light source. This same construction has the possibility of being duplicated in the laboratory on not stars but small light sources. The set-up, measurement and calculation to determine the size would be useful as an educational lab for undergraduates. Often the labs that undergraduates are asked to conduct are either too easy and nothing is learned or the lab is too difficult and nothing is accomplished. This lab has promise to be challenging but consistently possible so that the students can learn by working on a difficult lab as well as analyzing the outcomes.
One of the interesting requirements for this experiment is that the source be incoherent. If the source was temporally coherent then the correlation between signals would never drop off and the size would be indeterminable. Although the Hanbury-Brown Twiss (HBT) effect was called intensity interferometry, the interferometry part is not quite correct. After the detectors have gathered a signal, all phase information is lost and so nothing can “interfere” after this point. To be clear, the HBT effect is working with intensities not directly electric fields. This has the benefit that once the signal is gathered everything is conducted in electronics. This makes stability easy because instead of building stable optics, one can just run wires from the detectors. This also means that very large distance can be covered to resolve very small sources. However, the HBT effect is no longer used today in astronomy.
Michelson interferometers are created with arrays of telescopes that have the stability to create interference. The other problem with the HBT effect is due to signal to noise ratio. The correlation function requires that the two signals be multiplied before being time-averaged. However, all detectors perform some type of time averaging because the detector is not infinitely fast. This meant, in the

original experiment, that Hanbury-Brown and Twiss has a tiny signal above the noise and it required taking data for hours at a time for each separation distance. So what is needed to lower the noise is still a signal that is not perfectly coherent but perhaps has fluctuations on the time scale of what our detectors can pick up, instead of fluctuations that our detectors couldn’t possible detect. My plan to solve this problem is to take a laser and send the beam through a ground piece of glass. The piece of glass will be rotating because of a motor. By changing the speed of rotation we can effectively change the frequency of the fluctuations in the now somewhat incoherent beam. Some of the light coming through the glass would then be sent through a pinhole and the experiment would be conducted to find the angular size of the pinhole.
The next step that needs to be researched is to create a mathematical model so I can be sure that the experiment should work. I still need to know the speed that the motor needs to be spinning, the grain size on the glass and the size of the pinhole that will be the easiest to measure. I am acquiring electronics that can manipulate the signal from the photodiodes. The lab already has high-speed photodiodes that I can use for the experiment, as well as lasers I can use to test the apparatus. Within the month I should be able to begin constructing the circuit and completing a mathematical model. After that is accomplished, feasible sizes and speeds will be chosen and the circuit will need to be tested and optimized. This project is unique because it needs the electronics to be robust and the set-up to be repeatable as many students will be constructing this experiment. This means that once I have the experiment working that I will need to conduct numerous tests to be sure that some small detail will not inhibit the success of the experiment. Several copies of the circuit will also need to be constructed so that several groups can conduct the experiment simultaneously on the same pinhole.