PAGE 14
Copyright – P. J.
Smith
But permission is given
to distribute this material in unaltered form as long as it is not sold for
profit.
Focal
Plane Correctors for
Very
Large Fast Newtonians.
by
Peter John Smith.
Various possible designs compared for correcting a 20 to 30 mm
field with a 1.6 m. F:3 primary mirror.
Rationale.
A 1.6 m F:3 Newtonian has a focal length of 4.8 m. If used with a 20 mm efl eyepiece, the magnification is 4.8 m / 20 mm. or 240 X. This results in an exit pupil of 1.6 m. / 240 or 6.6 mm.
Very few observers will have a larger eye pupil so this represents about the lowest magnification which effectively uses the full light gathering capacity of the 1.6 m. aperture.
Depending on the apparent field of view of the eyepiece used, a linear field of about 20 to 30 mm is indicated.
For the most critical visual use, the on axis image should be diffraction limited if possible. The outer portions can degrade and still be acceptable. Of course, if a telescope builder elects to consider the instrument limited by atmospherics rather than the theoretical diffraction limit, this indicates a more liberal image quality criterion.
A hyperboloidal primary mirror is easier to correct than a Paraboloidal one. Both possibilities will be considered.
More complex designs will always theoretically produce better corrected and wider fields but somewhere a line must be drawn. Priority here is the simplest design which performs a useful function and is doable by an advanced ATM.
Three Basic Options.
Among the many correcting systems I have investigated three were chosen as promising. None are overly complex so an ATM may realistically consider fabrication. One of particular interest uses some off the shelf catalogue lenses if desired. Two require Hyperboloidal primaries but the third uses a simple Paraboloid.
(a) A Ross type corrector (configuration 11). A simple Ross corrector would produces only mediocre visual results over the field size required. This variation uses different glass types and acts in a slight compression mode. It needs a mild Hyperboloidal Primary to achieve useful but not brilliant results. The glass types are a little unusual but certainly available. Unfortunately, the lenses are large thin meniscii. This is by no means beyond the capability of the advanced ATM.
(b) Type two uses two achromats of very common glass and a very mild Hyperboloidal primary mirror. Performance is excellent.
(c) The last option uses three separate elements of standard glasses in conjunction with a Paraboloidal primary mirror. Performance is excellent. Because the lenses are single elements, there exists the option of working stock catalogue lenses into the design. The last PlanoConvex lens is a standard Edmond catalogue item and the deep meniscus element may be produced by modifying an M Griot stock catalogue lens. Its convex surface is retained so only the concave requires generating and finishing. This leaves only one lens (the centre element) to be made from scratch. Fortunately, about 3, 4, or even 6 of these can be combined and made on one block.
Modifying the M Griot lens so as to utilize the convex surface would be an interesting exercise. Protect surface, hold lens, generate new surface and work it, etc. One thing which will help is that this lens is very much overdiameter to start with so damage to the edge area will not matter.
Of course the entire lens could be fabricated from scratch. This would also allow for a slightly improved design.
Details of the catalogue lenses are –
It is easy to see how the larger meniscus may be made from a catalogue lens.
Designing for a Paraboloidal primary mirror gives the option of star testing the primary as an intermediate step. This allows easier diagnosis by localising possible problems.
Performance
Comparison.
Performance is compared with an uncorrected Newtonian and another option which has been mentioned by Stuart Field being a Sub-Aperture Schmidt like Aspheric corrector plate placed in the vicinity of the diagonal mirror. Projected performance of this is also included to allow comparisons.
Simplifying approximations have been made. Since each system works at a slightly different F:NO, angular fields are not quite equal. The effect is, however, minor.
This departure from the original F:3 provides another degree of freedom as does the consequent necessity of introducing another glass type.
Although the Parabola + 111 system is plotted out to a semifield of 17.5 mm, the catalogue Edmond lens diameter will not quite allow this coverage unless the back focus is reduced slightly with subsequent redesign. I suspect 50 mm of back focus is more important than extra field width, especially as an eyepiece using this extra field cannot successfully transfer full illumination to the eye.
One should keep in mind that there is always room for compromise. Axial definition may usually be improved at the expense of field coverage. The compromises presented are considered a reasonable balance by the author but there is no reason modifications cannot be made to suite different tastes.
As an example, if the concept of using some off the shelf lenses and surfaces is discarded, noticeable performance improvement is possible.
Remember - the figures given are for RMS Spot Radii, NOT
Diameter.
Probably the best simple standard is a comparison with the
Airy disk.
Some evaluation of the Parabola + 111 system indicates performance on a 100 inch scope at F:2.6 is reasonable and I doubt anyone will front up with one of these too soon. This assumes the useable linear field will be limited to the original - thus angular field is reduced.
Some problems and tolerances.
With a corrector of this type the back focus must be maintained. For example, with the Paraboloid and 111 system, it can be no more than 0.25 mm out before some noticeable loss of performance and 1 mm introduces considerable degradation. The other lens based systems are similar.
Interestingly, the sub diameter Schmidt corrector system is more tolerant before its performance degrades noticeably. About +/- 2 mm is tolerable. Of course, performance is not as good to start with.
The restriction on back focus variation can be overcome either by zero temperature coeff. expansion spacers or, for visual work, frequent readjustment.
There must be two focusing mechanisms. One for the entire corrector unit and one for attachments behind it.
A precision unit that goes on the rear with a ground glass screen or fine cross hairs at exactly 50 mm. will be needed. It can have a permanently mounted eyepiece. After this unit is quickly mounted on the rear of the corrector, the entire unit is focused and locked. With temperature variations on the Al struts this will need readjustment occasionally during an observing session.
Prescriptions.
Hyperboloid + 11 (improved Ross)
For a field of 21 mm. This can be increased somewhat.
|
Radius |
Thickness |
Glass |
Diameter |
Conic |
|
-9599.989 |
-4592.138 |
MIRROR |
1600.151 |
-1.179838 |
|
-132.003 |
-4 |
LF5 |
89.40888 |
0 |
|
-112.8391 |
-14 |
|
87.08705 |
0 |
|
1193.501 |
-4 |
BALF4 |
85.88316 |
0 |
|
410.415 |
-181.0434 |
|
85.52466 |
0 |
|
Infinity |
|
|
20.90055 |
|
..............................................................................................................................................................................................
Hyperboloid + 22
|
Radius |
Thickness |
Glass |
Diameter |
Conic |
|
-9600 |
-4625.282 |
MIRROR |
1600.209 |
-1.093802 |
|
-125.5915 |
-8 |
F5 |
86.27969 |
0 |
|
-172.7581 |
-5 |
BK7 |
83.66001 |
0 |
|
-86.90826 |
-65.99688 |
|
79.19222 |
0 |
|
Infinity |
-5 |
F5 |
67.30263 |
0 |
|
-220.6403 |
-8 |
BK7 |
66.31803 |
0 |
|
220.6403 |
-100 |
|
65.95151 |
0 |
|
Infinity |
|
|
30.25836 |
0 |
..............................................................................................................................................................................................
Paraboloid + 111
Uses some catalogue lenses with slightly compromised performance.
|
Radius |
Thickness |
Glass |
Diameter |
Conic |
|
-9599.989 |
-4625.98 |
MIRROR |
1600.175 |
-1 |
|
-67.434 |
-8 |
BK7 |
84 |
0 |
|
-91.11688 |
-38.1949 |
|
84 |
0 |
|
-145.3271 |
-4 |
SK2 |
60 |
0 |
|
-53.71081 |
-73.97254 |
|
60 |
0 |
|
-103.36 |
-5.07 |
BK7 |
50 |
0 |
|
Infinity |
-50 |
|
50 |
0 |
|
Infinity |
|
|
26.42399 |
0 |
If the design is not constrained by using off the shelf components, noticeable improvement is possible.
..............................................................................................................................................................................................
GOTO TOP
GOTO INDEX