Radial Density Filter
The intensity of the solar corona declines rapidly with distance from the limb of the Sun [1,2]. For this reason one photographic exposure cannot record the full coronal structure. Short exposures must be used to record details in the inner corona with much longer exposures for the outer regions. It is possible to combine many exposures electronically to build up a complete image of the corona as reported recently in Sky & Telescope . However this does involve taking many exposures, using valuable eclipse time. A more elegant solution is to filter the light from the corona selectively by using a radial density filter (RDF) enabling structure in the solar corona to be seen from the Sun's limb to the edge of the field of view in one image.
There are two approaches to constructing an RDF. The first involves coating a glass plate by evaporating metal in a vacuum jar containing the plate and controlling the process so that the greatest density of deposition is at the centre of the plate with the thickness reducing smoothly towards the edge. Controlling the process to achieve a specified density profile is very difficult and hence the plates are expensive; for this reason the technique is limited to professional astronomers, but the results can be stunning, see for example the results reported in Fred Espenak's eclipse pages or by Jonathan Kern in Sky & Telescope . The second approach is to put an opaque disc in the light path of the telescope. By suitable choice of the diameter of the disc and its position in front of the film, the effects of an expensive metal-on-glass radial density filter can be simulated; the big advantage for amateur astronomers is that the filter is very cheap to make and easy to use. The idea has been around for many years [5-7] and Francisco Diego of University College London introduced me to it in 1996 ; it is the approach that I used for the eclipse on 26 February 1998 which I observed from Venezuela.
The diameter of the disc and the appropriate distance to place it in front of the film can be calculated from the following equations:
d = D(B+A)/(2D+B-A)
s = F(B-d)/(B+D) x 1.8
d = diameter of opaque disc suspended at distance s in front of the focal plane,
D = diameter of telescope lens,
F = focal length of telescope,
A = Ds x 0.99 where Ds is the linear diameter of the Sun's image on the focal plane,
B = Ds x 3.92.
For example, in my telescope with a focal length of 890 mm, the opaque disc was 17.7 mm in diameter and 111 mm in front of the film plane.
Note that the telescope must be a refractor (or unobstructed reflector) as the central obstruction in a Newtonian or Cassegrain, for example, would change the radial density function.
Having modified the filter for use in Cornwall at the 11 August 1999 eclipse, I was unable to use it due to rain! However, the dimensions of the disc and separation from the film are within a few hundredths of a millimetre of those required for the 21 June 2001 eclipse. As a result, it's ready to go. The only things that will have to be changed are the angle of the polar axis of the heliostat, to 15° and, of course, the direction of the motor drive as we will be south of the equator.
||H. Zirin, The Astrophysics of the Sun, 1998, p.222 figure 8.5.
||L. Golub & J. Pasachoff, The Solar Corona, Cambridge University Press,
1997, p.5 figure 1.3.
||Eclipse Photography in the Digital Age, Sky & Telescope, January 1998, pp.117-120.
||Jonathan Kern, Sky & Telescope, May 1998, p.33.
||Allen, A New Technique for Eclipse Observations of the Solar Corona, in
METEORS (A Symposium on Meteor Physics), p.147 of Special Supplement to J. Atmos. Terr. Phys., Vol.2, 1955.
||George East, Use of a Vignetting Disk, Sky & Telescope, May 1973 p.322.
||Steve Edberg, Capturing More Corona, The Eclipse Chaser's Digest, Vol.1, p.2, 1994.
||F. Diego, JBAA, to be published.