Fresnel diffraction - a way of development of occulatation project

Slawomir Kruczkowski

Introduction

The purpose of my speech is a demonstration of possibility of application the Fresnel diffraction phenomena in amateur astronomy.
Some about the history… The first reference to diffraction phenomena appears in the work of Leonardo da Vinci but first accurately described by Grimaldi in a book, published in  1665. Huygens, the first proponent of the wave theory, seems to have been unaware of Grimaldi’s discoveries. The possibility of explaining diffraction effects on the basis of a wave theory was not noticed until about 1818. In that year there appeared the celebrated memoir of Fresnel in which we showed that the diffraction can be explained by the application of Huygens construction together with the principle of interference.
In 1909 P.A. MacMahon has been described first, in the note “On the determination of the apparent diameter of a fixed stars” (1908, MNRAS, 69, p. 126), application of the Fresnel diffraction phenomena in the astronomy. The works of A.E. Whitford’s (1939, ApJ, 89, p. 472) and J.D. Williams have been suggested that angular diameter of stars may be registered by photoelectric equipment.
The great evolution in photoelectrical registration astronomical phenomena was in the years that followed the Second World War. In the years 60’s and 70’s was observed great value of the lunar occultation, which had in view to calculate diameters of the stars.
At the beginning years 90’s to notice a disappearance of interest of using diffraction phenomena in astronomical observations. I suppose so, development HST, ESO observatories caused change of trends.
Well… I hope that the growing interest of dynamics small bodies the Solar System and possibility of collision will cause that we don’t forget about the Fresnel diffraction phenomena.

Phenomena

Fresnel diffraction is a special case of diffraction on any obstacles – describe diffraction on a straight edges. Fig. 1 show at one with the situation, when light source is a star and straight edge is edge of Moon disc.
 
 
Left side of the drawing show an area with filling in 40% of gray (not a white-ness of sheet) because is impossible to show bright-ness of light on right side.
It is important that actual time of occultation is, when density of light source amount 25% normal density. Often instead units of distance – d use be units of time. In case lunar occultation 1 m correspond with 1.1 ms.
Moreover, the observa-tions of the phenomena are better quality when light from the star will filtered, particularly by narrow-band filter.

Applications

In practice of amateur astronomy may be to apply the  Fresnel diffraction phenomena to:
a) central or graze occultation – improving of lunar limb profile by calculating of degree of the slope lunar limb profile. Fig. 2 show mechanics of phenomena, which consist in extended time of visibility the Fresnel diffraction on factor 1/cos ?,
b) central and graze occultation – calculating diameter of the stars, which have angular diameter between 0”.002 and 0”.020 (fig. 3),
c) asteroidal occultation – showing a problem of varying complexity. Fig. 4 present an example occultation: disappearance ? Geminorum by 381 Myrrha (1993, AJ, 105, p. 1553),
d) central and graze occultation – detecting double and multiple systems of stars. Fig. 5 present an example: double star, when elements have similarly brightness (1970, AJ, 75, p.575).

  

       Fig. 2                                                                                                Fig. 3

 
 

        Fig. 4                                                                                                Fig. 5

A way of development

Today haven’t technical obstacles, so that to execute showing earlier aims. The astronomical kit  telescope – recorder (especially when recorder is a photomultiplier) allows to recording the phenomena about brightness 12m – 13m.
Remain important question, yet:
a) wont the amateurs to go in this direction?
b) how much have an influence on this decision good intensions and how much – cost?
We remember, source of success in observation projects is a teamwork. If we wont to accomplish good results, many amateurs should be equipped with good quality telescope – recorder  kits. I now, that a lot of numbers of amateur astronomers haven’t so much money but my second speech has purpose to present solution of this problem.
 
 
Back to list of authors and abstracts.