July 28, 1921] 



NATURE 



685 



The Application of Interference Methods to Astronomy. 



By H. Spencer Jones, Chief Assistant, 



''F'HE recent measurement at the Mount Wilson ' 

 ■»■ Observatory, California, with the aid of an ! 

 interferometer, of the angular diameter of the star 

 Betelgeuse has attracted much attention, and has ^ 

 incidentally illustrated the advantages to be de- 

 rived from the application of interference methods 

 to astronomical measurement. In view of the 

 striking success of this application, it is some- 

 what surprising that the possibilities of the 

 method have been generally overlooked by astro- 

 nomers, for the principles underlying the methods , 

 are by no means new, and their application to the 

 determination of the angular diameters of the 

 stars was indicated by Fizeau so long ago as 

 1868. It is of interest to recall the exact words 

 used bv Fizeau, the suggestion being thrown out 

 by him incidentally in a report on the Bordin prize 

 of the Acaddmie des Sciences : — 



"II existe, pour la plupart des ph^nom^nes d'intet- 

 f^rence, tels que les franges d 'Young, celles des ', 

 miroirs de Fresnel, et celles qui donnent lieu ^ la 

 scintillation d'aprfes Arago, une relation remarquable 

 et n^cessaire entre la dimension des franges et celles 

 de la source lumineuse; en sorte que les franges, d'une 

 t^nuit^ extreme, ne peuvent prendre naissance que 

 lorsque la source lumineuse n'a plus que des dimen- 

 sions angulaires presque insensible; d'ou, pour le dire 

 en passant, il est peut-etre d'esp^rer qu'en s'appuyant 

 sur ce principe et en formant, par exemple, au moyen 

 de deux larges fentes tr^s dearths, des franges d'inter- 

 f^rence au foyer des grands instruments destines ^ 

 observer les ^toiles, il deviendra possible d'obtenir 

 quelques donnas nouvelles sur les diam^tres angu- 

 laires de ces astres." 



St^phan was the first to attempt the determina- j 

 tion of the angular diameters of stars in this 

 way. He worked out an approximate theory, 

 based upon elementary considerations, of the 

 interference phenomena obtained in the focal plane 

 of an objective when a uniformly illuminated i 

 circular disc, of small angular diameter a, is 

 viewed through it, the objective being covered by 

 an opaque screen in which are two parallel narrow 

 rectangular apertures. The conclusion was 

 arrived at that, in general, a series of parallel 

 and equidistant interference fringes would be ob- 

 tained, but that the fringes would disappear if the 

 distance apart of the shts I satisfied the relation- 

 ship a = xfl,^ \ being the mean wave-length of the 

 light. A determination of the distance apart of 

 the slits for which the interference fringes dis- 

 appeared is therefore sufficient to enable the 

 angular diameter of the object to be deduced. 

 The practical difficulty arises that in attempting 

 to determine in this way the angular diameter of '. 

 a star, the loss of light due to the restriction of | 

 the aperture to two narrow slits is so great that 

 the fringes would in general be very faint. 

 St^phan removed this difficulty by showing that ■ 

 extended apertures could be used without serious | 

 error provided that they were equal and possessed 



1 A rigid mathematical investigation replaces this by the relationship 

 «=I'22 A//. 



NO. 2700, VOL. 107] 



The Royal Observatory, Greenwich. 



two axes of symmetry at right angles to each 

 other, one of these axes passing through the 

 centres of the two apertures, and that their width 

 was small compared with their distance apart. 



With the 8o-cm. Foucault refractor of the Mar- 

 seilles Observatory, Stephan, in 1874, examined 

 Sirius and other stars. The fringes were obtained, 

 but they did not vanish even with the maximum 

 possible separation of the slits. The least dia- 

 meter measurable by this method with this instru- 

 ment was o"i6, but from the appearance of the 

 fringes Stdphan was able to conclude that "les 

 experiences cities ne prouvent pas seulement que 

 le diamfetre apparent des 6toiles examinees est 

 inf^rieur k o"-i6, elles montrent encore que ce 

 diam^tre est une tr^s faible fraction du nombre 

 precedent." 



The subject was taken up again by Michelson, 

 who, in 1890, gave a more rigid theoretical dis- 

 cussion of the method than Stephan had done. 

 Three cases of interest were examined, and the 

 principal results obtained may be summarised 

 thus : — 



(i) If the object is a circular disc of uniform 

 brightness, of apparent angular diameter a, the 

 series of interference fringes produced in the focal 

 plane of the objective when the aperture is limited 

 to two narrow rectangular and parallel slits will 

 vanish when the distance apart of the slits I is 

 given by l=i-22\/a. 



(ii) If the object is not of uniform brightness 

 this relationship is modified. The precise modifica- 

 tion for any given law of variation of brightness 

 can be easily determined. If, for instance, the 

 illumination falls off towards the limb according 

 to the law of darkening observed for the sun, the 

 relationship becomes Z=i-33\/o. 



(iii) If the object is a double source, with an 

 angular separation of the components of amount o, 

 the fringes vanish for a distance apart of the slits 

 given by ^\/a, provided that the two components 

 are of equal brightness, that their distance apart 

 is large compared with their separate diameters, 

 and that the length of the slits is perpendicular 

 to the line joining the centres of the two sources. 



The method has practical application in the 

 measurement of the angular diameters of small 

 bodies such as planetary satellites and asteroids, 

 and more recently of the angular diameters of 

 stars, and also in the measurement of the separa- 

 tions and position-angles of close double stars or 

 spectroscopic binaries. 



The angular diameters of small bodies such as 

 satellites are usually measured with a filar micro- 

 meter. The measurement is possible only under 

 conditions of the best atmospheric definition, and 

 even then the probable error of observation is 

 relatively large, since the width of the finest 

 spider web is comparable with the linear dimen- 

 sions of the image in the focal plane of the tele- 

 scope. Using the interference method, it is found 



