Intensity interferometer

The intensity interferometer , also known as a correlation interferometer , is an optical device ( interferometer ) for determining the angular diameter of astronomical objects (usually stars ) that can not be resolved with direct observation .

Beam path in the intensity interferometer

Intensity interferometry of α Lyrae ( Wega ) and β Crucis ( Mimosa )

principle

The intensity interferometer consists of two spatially separated telescopes , on each of which the arrival times of the photons arriving from a bright star are registered by means of a photomultiplier , which is practically done by recording the temporal course of the two currents occurring there. These are combined in a correlator, which examines the two time courses for coincidences. The correlation between the two currents can be used to determine the angular diameter of the star (see further explanations below).

Robert Hanbury Brown and Richard Twiss recognized in the mid-1950s that the exit times of the electrons at different points on a photocathode illuminated by a plane wave are correlated with one another. They showed that this effect - which is called the Hanbury Brown-Twiss effect after its discoverers - can be interpreted both by the classical wave theory of light and by its quantum nature.

According to the work of 1957, the correlated exit times of the electrons, seen from a classical perspective, reflect correlated intensity fluctuations that occur at different points of the incident wave. These are due to the interference of various frequency components of the incident light. From a quantum mechanical point of view, the effect is based on the fact that photons follow the Bose-Einstein statistics and thus show a tendency to occur more frequently (which is often referred to as photon bunching ).

In a subsequent paper, the two researchers demonstrated how the effect they discovered can be used to measure the angular diameter of a star. If the two currents are strongly correlated with one another (which means that photons often arrive at both receivers at the same time), the observed star has not yet been resolved. This is the case when the distance between the two telescopes is too small. If this is increased, the correlation between the currents (i.e. the arrival times of the photons) decreases. The angular diameter of the star can be determined from the decrease in the correlation with increasing distance . This is a function of the term ( denotes the wavelength of the incident light). Has a star z. B. twice the angular diameter compared to another, you only have to pull the telescope half as far apart to observe the same drop in correlation. ${\displaystyle D}$ ${\displaystyle \theta }$ ${\displaystyle \pi \theta D/\lambda }$ ${\displaystyle \lambda }$

Finally, a practical example should be mentioned with the stars α Lyrae ( Wega ) and β Crucis ( Mimosa ). With the former, the correlation of the individual currents drops to practically zero at a telescope distance of around 20 m. With the latter you have to move them about 100 m apart to achieve the same effect. Consequently, Vega has a far larger angular diameter than Mimosa.

Measurement accuracy

The correlated intensity fluctuations caused by the arrival times of the photons are superimposed by much stronger, non-correlated fluctuations. One source of these additional fluctuations is the unrest in the air, which causes the everyday twinkling of the stars ( scintillation ), and another is the shot noise of the currents emanating from the two photomultipliers . The fluctuations caused by this far exceed the correlated fluctuations actually sought, by about a factor of 100,000! The non-correlated additional fluctuations can be "averaged out" by very long observation times, but exposure times of up to 100 hours were required even for very bright stars that were easily visible to the naked eye (not less than 2nd magnitude)! An extraordinary stability of the measuring electronics, in particular of the correlator, is therefore extremely important for the instrument.

Fortunately, the turbulence in the air has little influence on how quickly the correlation between the individual currents drops with increasing distance between the telescopes. The unrest in the air thus forces very long exposure times, but does not falsify the appearance of the curve (and thus the angular diameter of the star derived from it), which describes the correlation as a function of and . ${\displaystyle D}$ ${\displaystyle \theta }$

The accuracy with which the angular diameter of a star can be determined is given by the ratio of the light wavelength to the maximum telescope distance. With = 440 nm and = 188 m (for the instrument of the 1960s) one expects = 0.0005 ". In practice, Hanbury Brown achieved a somewhat better accuracy, namely 0.0002" on average. The intensity interferometer thus far surpasses the classic Michelson star interferometer and also allows the inclusion of main sequence stars close to the sun . While the resolving power of the Michelson star interferometer is limited by the turbulence in the air (it depends on the image of the star in the form of an interference pattern), this is not the case with the intensity interferometer. It is only the intensity of the star that is of interest, not its visual representation. ${\displaystyle \lambda /D_{\mathrm {max} }}$ ${\displaystyle \lambda }$ ${\displaystyle D_{\mathrm {max} }}$ ${\displaystyle \lambda /D_{\mathrm {max} }}$

In order to correctly interpret the measurement results of the intensity interferometer, as with the Michelson star interferometer, the edge darkening (the drop in intensity of the star disk from the center to the edge) must be taken into account. According to Hanbury Brown's publications from 1967, this has the consequence that the correlation of the two individual currents falls more slowly when the telescopes are pulled apart than one would expect with a uniformly shining star disc, i.e. H. the angular diameter is underestimated. The type of mathematical law between correlation and telescope distance remains unchanged, however, it is only given a longer scale with regard to . The interferometer therefore provides an effective angular diameter - which the star would have if its disk shone uniformly with the same overall intensity. In order to be able to determine the actual angular diameter from the effective angle, a model of the stellar atmosphere is required. In the main sequence stars measured by Hanbury Brown (1967b), however, the modification of the angular diameter is only a few percent. ${\displaystyle D}$

history

After the theoretical preparatory work in the 1950s, a successful test measurement of the Sirius was soon achieved . The first fully operational device of its kind went into operation in 1962 in Narrabri (Australia). The construction and commissioning of the interferometer turned out to be a difficult challenge; this phase alone stretched over almost two years. Another two-year phase of test measurements of several main sequence stars followed; the actual observation program did not start until 1965. In 1967 the angular diameters of 15 main sequence stars were first published. In total, the angular diameters of 32 main sequence stars were determined by 1972.

The interferometer consisted of two reflectors, each 6.7 m in diameter, each composed of 252 hexagonal individual mirrors. The two instruments could be separated from each other by up to 188 m on a track circle.

In 1990 the Sydney University Stellar Interferometer SUSI was put into operation as a follow-up instrument. It is located at the Culgoora Observatory near Narrabi. However, this is not an intensity interferometer, but a modern Michelson interferometer, which, through adaptive optics , overcomes the deficiency of the classic interferometer, the disturbance of the interference pattern caused by the unrest in the air. At the same time, it is far more sensitive than the Narrabi interferometer, it allows the measurement of stars up to about the 8th magnitude. The maximum distance between the light paths brought to interference is 640 m. A description of the SUSI can be found under Michelson star interferometer .

The measurement of the angular diameter of a star and thus, if the distance is known, its radius as well, inevitably leads to the question of what is actually meant by the surface of a star. This problem, which is anything but trivial in view of the lack of a solid crust, is discussed under the surface of the stars.

swell

• Hanbury Brown R .: A Test of a new Type of Stellar Interferometer on Sirius , in: Nature Volume 178, pp. 1046ff, 1956
• Hanbury Brown R., Twiss RG: Correlation between Photons in two Coherent Beams of Light , in: Nature Volume 177, pp. 27ff, 1956
• Hanbury Brown R., Twiss RG: Interferometry of the Intensity Fluctuations in Light. I. Basic Theory: the Correlation between Photons in Coherent Beams of Radiation , in: Proceedings of the Royal Society of London Volume 242, pp. 300ff, 1957
• Hanbury Brown R., Twiss RG: Interferometry of the Intensity Fluctuations in Light. III. Applications to Astronomy , in: Proceedings of the Royal Society of London Volume 248, pp. 199ff, 1958
• Hanbury Brown R., Davis J., Allen LR: The Stellar Interferometer at Narrabi Observatory. I. A Description of the Instrument and the Observational Procedure , in: Monthly Notices of the Royal Astronomical Society Volume 137, pp. 3 75ff, 1967a, bibcode : 1967MNRAS.137..375H
• Hanbury Brown R., Davis J., Allen LR, Rome JM: The Stellar Interferometer at Narrabi Observatory. II. The Angular Diameters of 15 Stars , in: Monthly Notices of the Royal Astronomical Society Volume 137, pp. 393ff, 1967b, bibcode : 1967MNRAS.137..393H
• Hanbury Brown R., Davis J., Allen LR: The Angular Diameters of 32 Stars , in: Monthly Notices of the Royal Astronomical Society Volume 167, pp. 121ff, 1974, bibcode : 1974MNRAS.167..121H
• Davis J., Tango WJ, Booth AJ, ten Brummelaar TA, Minard AR, Owens SM: The Sydney University Stellar Interferometer - I. The instrument , in: Monthly Notices of the Royal Astronomical Society Volume 303, pp. 773ff, 1999

Web links

• Private website about the Hanbury Brown-Twiss effect . Note: The statements made there with regard to photon bunching and the Bose-Einstein statistics contradict the work of Hanbury Brown and Twiss (1957)!

Individual evidence

1. ↑ see Hanbury Brown and Twiss (1956) and Hanbury Brown and Twiss (1957)
2. ↑ see Hanbury Brown and Twiss (1958) and also Hanbury Brown et al. (1967a)
3. ↑ according to the work from 1967
4. ↑ by Hanbury Brown et al. (1967b)
5. ↑ according to Hanbury Brown et al. (1967a)
6. ↑ see Hanbury Brown et al. (1967b)
7. ↑ according to Hanbury Brown et al. (1967a)
8. ↑ ^{a b} Hanbury Brown et al. (1967b)
9. ↑ see Hanbury Brown (1956)
10. ↑ according to Hanbury et al. (1967a)
11. ↑ see Hanbury Brown et al. (1974)
12. ↑ Hanbury Brown et al. (1967a)
13. ↑ see Davis et al. (1999)