Michelson star interferometer

Beam path in the Michelson star interferometer

The 20 foot wide Michelson star interferometer on the frame of the 2.5 meter Hooker reflector telescope at Mount Wilson Observatory , 1920

principle

The Michelson star interferometer is one of the earliest interferometers used in astronomy . It is based on the fact that the light of a star is received on two separate paths, which are brought to interference. The two paths are created by two slit-shaped openings that are spaced apart. Using two deflecting mirrors each, the two light paths reach the primary mirror of the telescope, from there to the secondary mirror and finally converge in focus. ${\ displaystyle D}$

If a star were a point source, the superposition of the two light paths would produce an interference pattern corresponding to the double slit experiment. An arrangement of stripes would result, which would be angularly spaced ( denotes the wavelength of the incident light). In fact, despite their great distances, stars have a tiny, but not negligible, angular diameter . Each point on the star's surface provides its own interference pattern, so that a multitude of stripe patterns is created. But these are shifted against each other, according to the angular distance of the corresponding points on the star's surface. The superposition of the individual stripe systems has the consequence that no more interference pattern can be recognized if the angular diameter of the star is the same . The measurement is carried out by varying the distance between the two slit openings until the interference pattern disappears. ${\ displaystyle \ lambda / D_ {0}}$ ${\ displaystyle \ lambda}$ ${\ displaystyle \ lambda / 2D}$ ${\ displaystyle D}$

Measurement accuracy

As a result of the turbulence in the air, the classic method is only moderately accurate by today's standards. According to Hale (1921) the accuracy of the first measurement of the angular diameter of Betelgeuse was about 0.005 ". According to Scheffler and Elsässer (1990), the measurement error can be up to 0.01 ″ (modern instruments achieve an accuracy of up to 0.00002 ″, as shown below, which is up to 500 times more precise than the classic interferometer). The uncertainty corresponds roughly to the angular diameter at which the sun appears from the nearest star. It is therefore clear that the Michelson star interferometer generally fails with main sequence stars , and even in the area of giants and supergiants, only relatively close objects with distances of up to about 100 parsecs can be reliably measured.

In order to derive the actual diameter of the star from the angular diameter, further effects must be taken into account. The so-called edge darkening represents a particular difficulty, as already pointed out by Hale (1921). The center of the star disc shines brighter than the edge, thus contributing more to the interference pattern. There is a tendency to underestimate the diameter of the star.

The giants and supergiants most accessible to interferometry, in particular , often have extensive photosphere and thus, in contrast to the sun, represent extremely diffuse objects. Now there is a tendency to overestimate the diameter, since the measurement is not only the actual star body, but also its shell includes. The resulting problem of how to define the diameter of such a star is discussed in detail in the article Star surface .

Of course, the distance to the star must also be known in order to convert the angular diameter into the actual one. When the Michelson star interferometer was used, the knowledge of the distance from giants and supergiants in particular was very uncertain. The distance information compiled by Pease (1921) for the red giant Arctur differed by more than 100% (6.3 to 13.5 parsecs, corresponding to 21 to 44 light years ). In the 1990s, the Hipparcos satellite was able to determine reliable distances for more than 100,000 stars of almost all types. However, the extensive photosphere of some stars represent a considerable limitation of the measurement accuracy even for today's instruments.

history

The Michelson star interferometer was designed by Albert A. Michelson in 1890 . More than 20 years earlier, Hippolyte Fizeau had already submitted a proposal for interferometry to stars to the French Académie des Sciences , which was then implemented by M. Stephan, the then director of the Marseille observatory . It is unclear whether Michelson knew about this preliminary work.

In 1891 Michelson carried out test measurements of the diameters of the four Galilean moons of Jupiter with a slit diaphragm on a 12-inch telescope , which showed excellent agreement with the values already determined in other ways. However, after this initial preparatory work, it took another 25 years until the first Michelson star interferometer was put into practical use: an arrangement with which light was reflected from plane mirrors about 6 meters apart into the 2.5-meter reflector telescope of the Mount Wilson observatory .

Michelson and Francis G. Pease (1881–1938) used this device to carry out the first measurements of star diameters. The first such measurement concerned the diameter of Betelgeuse , which Michelson and Pearse determined in December 1920 to be 390 million kilometers. That corresponds roughly to the diameter of the Mars orbit ; this makes the red giant Betelgeuse around 300 times larger than the sun . Hale (1921) describes that when the two stomata were 6 feet apart, an interference pattern was clearly visible. At a distance of 8 feet this was already much less pronounced, and at a distance of 10 feet it was completely gone. With an average wavelength of 550 nm, an angular diameter of 0.045 "could be derived from this. ${\ displaystyle D}$

Six more star diameters followed. These initial successes were followed by the construction of an even larger device, the mirrors of which were now a full 15 meters apart. However, with this improved apparatus it was only possible to measure a single additional star diameter, and the corresponding observation series were discontinued in 1931.

Modern interferometer

Beam path in the Culgoora star interferometer

The Michelson star interferometer has been experiencing a renaissance since the 1990s. This was made possible by the adaptive optics , which allow real-time correction of the impairments caused by the unrest in the air. As an example, the Sydney University Stellar Interferometer SUSI operated at the Culgoora Observatory in Australia , which Davis et al. (1999) is described in detail.

Siderostats , which always reflect in the same direction regardless of the position of the star in the sky , serve as primary receiving mirrors , which define the distance . Their diameter is 20 cm, but only 14 cm effectively contribute to this, because the starlight is not incident perpendicular, but at a certain angle. The small size has been chosen deliberately: The resolution of the individual mirror is no longer limited by the turbulence in the air, but rather by the diffraction. As a result, the turbulence in the air no longer causes the constellation to "wobble" as it does with a large telescope, but only a back and forth wobble of the constellation as a whole, which is easier to analyze and correct using the adaptive optics . The instrument has 12 stationary siderostats, which are arranged linearly in north-south direction. By selecting a different pair of mirrors, different distances of 5–640 m can be achieved. ${\ displaystyle D}$ ${\ displaystyle D}$

The incident bundles of rays from the siderostats reach a collimator consisting of two parabolic mirrors . There, the diameter of the bundles of rays is reduced from the original 14 cm to 5 cm and thus adapted to the subsequent, rather small optical elements. Then they pass through a system that is not discussed further here, which corrects the effects of the refraction of light caused by the atmosphere .

In contrast to the primary slits of the classic interferometer, the siderostats of the Culgoora instrument are placed asymmetrically , which initially results in paths of different lengths for the two beams. This asymmetry is eliminated by a system consisting of two movable reflectors. Depending on how far they are from the optical axis, the path is shortened for one beam and lengthened to the same extent for the other. The correction of the light paths also includes an adaptive element. The mirrors shown with bold lines can be moved, thereby reducing the image movement caused by the turbulence in the air in real time.

The two beams now pass through a system for correcting the dispersion , which is also not explained in more detail here. Eventually they reach the heart of the instrument, which Davis et al. (1999) so-called “optical table”.

The "optical table" of the Culgoora star interferometer

In this "optical table" the rays are brought to interference. Before that, however, they each pass a polarizing beam splitter, which breaks them down into horizontally and vertically polarized components. The horizontally polarized components get into interference, the vertically polarized components are fed to wavefront sensors (see under adaptive optics ), which analyze the image movement.

Another beam splitter is used to cause the remaining horizontally polarized components to interfere. Two new rays emerge, but they have parts of both of the original bundles. Prisms redirect each of the new beams to a photomultiplier . However, not all of the incident energy is subject to refraction; a small part leaves the prism in the same direction. The latter is fed to a third wavefront sensor for one of the two new beams. By comparing with the results of the two other sensors (which examine the image movement before the interference), the influence of the air turbulence can also be analyzed after the original rays have been merged.

The angular diameter of the star is now determined by measuring the intensities of the two new beams and correlating them with one another over time. This correlation measurement must not be confused with that of the intensity interferometer . With the latter, the incident rays are converted into intensities before the interference, but with the Michelson interferometer only afterwards ! However, the correlation between the two intensities shows the same qualitative behavior for both types of instruments. If the distance between the primary receivers is very small, the two intensities are strongly correlated with one another over time. In the classical sense, this means that the interference pattern generated by the Michelson interferometer is clearly visible. If the distance is increased, the correlation, i.e. the visibility of the interference pattern, decreases. The larger the angular diameter of the star, the smaller the distance required to achieve a correlation drop. ${\ displaystyle D}$ ${\ displaystyle D}$

Due to the numerous correction elements, especially the adaptive optics , the SUSI achieves extraordinary accuracy. Davis et al. (2009) the angular diameter of the Cepheid 1 Car with a measurement error of only 0.00002 ″! This also makes it possible to precisely observe changes over time caused by pulsation. However, it still applies that the nominal angular diameter must be freed from the influence of the edge darkening and any extensive stellar atmosphere that may be present .

Modern Michelson star interferometers not only overcome the deficiency of their classic predecessor (the comparatively high uncertainty of the angular diameter), they also avoid the handicap of the intensity interferometer (the very low sensitivity). While the intensity interferometer could only be used for very bright stars up to size 2, stars up to size 8 can be measured with SUSI. This means that several 10,000 objects of practically all spectral types are accessible, the distances of which are mostly known thanks to the measurements made by the Hipparcos satellite.

From interferometry to aperture synthesis

The principles developed by Michelsons star interferometer led from the 1950s to the development of aperture synthesis for radio telescopes by Martin Ryle , and from the 1960s to the development of optical interferometric methods, the modern descendants of which are telescopes such as the Large Binocular Telescope and the VLT interferometer .

The basic idea of aperture synthesis is to bring not only two, but at least three primary beams to interference. The resulting very complex interference pattern not only allows the angular diameter of the observed object to be determined, but also its intensity distribution (i.e. it can actually be represented as a body that appears flat). In the radio sector, in which disturbances from the atmosphere play no role, this method has been used for several decades. In visible light and near infrared, it was the adaptive optics of aperture synthesis that paved the way. The work by Haubois et al. (2009) who used an interferometer consisting of three telescopes to resolve the surface of Betelgeuse in the near infrared.

In view of the lack of a solid crust, the question of what is actually meant by a star's surface must generally be considered in interferometric star measurements . This is discussed in the relevant article.

literature

J. Davis, WJ Tango, AJ Booth, TA ten Brummelaar, RA Minard, SM Owens: The Sydney University Stellar Interferometer: I. The instrument . In: Monthly Notices of the Royal Astronomical Society 303, 1999, pp. 773ff
J. Davis, AP Jacob, JG Robertson, MJ Ireland, JR North, WJ Tango, PG Tuthill: Observations of the pulsation of the Cepheid l Car with the Sydney University Stellar Interferometer . In: Monthly Notices of the Royal Astronomical Society 394, 2009, pp. 1620ff
X. Haubois, G. Perrin, S. Lacour, T. Verhoelst, S. Meimon, L. Mugnier, E. Thiébaut, JP Berger, ST Ridgway, JD Monnier, R. Millan-Gabet, W. Traub: Imaging the spotty surface of Betelgeuse in the H band . In: Astronomy and Astrophysics Volume 505, 2009, pp. 923ff
GE Hale: The Angular Diameter of Alpha Orionis . In: Monthly Notices of the Royal Astronomical Society Volume 81, 1921, pp. 166ff
A. Labeyrie, SG Lipson, P. Nisenson: An Introduction to Optical Stellar Interferometry . Cambridge University Press, Cambridge 2006, ISBN 0-521-82872-4 .
FG Pease: The Angular Diameter of Alpha Bootis by the Interferometer . In: Publications of the Astronomical Society of the Pacific Volume 33, 1921, pp. 171ff
H. Scheffler, H. Elsässer: Physics of the stars and the sun . BI Wissenschaftsverlag, Mannheim / Vienna / Zurich, 2nd edition 1990, ISBN 3-411-14172-7 .

The article uses information from the entry Michelson stellar interferometer on the English language Wikipedia, as of December 8, 2008.

Individual evidence

↑ Labeyrie et al. 2006, p. 2f.
↑ Labeyrie et al. 2006, p. 4ff.
^ M. Ryle: Radio Telescopes of Large Resolving Power . Nobel Prize Lecture, December 12, 1974. For information on the LBT, see K. Jäger, Scientific observations started at the LBT . In: Stars and Space Vol. 7/2007, pp. 16-18. For the VLT interferometer see A. Glindemann: Das VLT interferometer . In: Stars and Space, Vol. 3/2003, pp. 24–32.

[1] Labeyrie et al. 2006, p. 2f.

[2] Labeyrie et al. 2006, p. 4ff.

[3] M. Ryle: Radio Telescopes of Large Resolving Power . Nobel Prize Lecture, December 12, 1974. For information on the LBT, see K. Jäger, Scientific observations started at the LBT . In: Stars and Space Vol. 7/2007, pp. 16-18. For the VLT interferometer see A. Glindemann: Das VLT interferometer . In: Stars and Space, Vol. 3/2003, pp. 24–32.