Newtonian diagonal sizes

Newtonian diagonal sizes

Telescope Myths Demolished _ Sky & Telescope February 2002

In the February 2002 issue of Sky & Telescope, under the telescope techniques topic, "Four Infamous Telescope Myths" - short focus Newtonians require larger secondary mirrors than long focus models, Gary Seronik argues that fast f/ratio Newtonians do not necessarily need a larger diagonal. In the article he states...."For example, all other things being equal, the same 1-inch secondary mirror will serve well for 6-inch reflectors from f/4 to f/10, in all cases producing essentially the same edge-of-field illumination _ one of the more important parameters to consider when you are selecting a secondary mirror." He then makes use of a diagram illustrating the vignetting profiles for 6-inch Newtonians from f/4 to f/10 across a 1-1/4 inch linear field. Although the reduction in illumination of the field boundary remains essentially constant for the different focal ratios considered, roughly 45%, it bizarrely depicts the 6-inch f/4 profile vignetting immediately off axis!

Just in case I was overlooking some vital point I went to Mel Bartels website again and downloaded diagonal.exe, which is the DOS6.2 version of his on-line diagonal sizing Java script programme.

The approach Seronik advocates is one with which I take issue. In order to correctly size the Newtonian diagonal it is necessary to consider either the minimum acceptable linear or angular unvignetted fov, and not just by how much the edge of the field of view is vignetted.

To illustrate my point I have run an experiment. One way of sizing a diagonal is to base it on an unvignetted fov of 1/2 degree, so the Moon is not vignetted on photographs. The following outputs are obtained:-

Mel Bartels' Diagonal
Calculator
http://www.efn.org/~mbartels/tm/diagonal.htm
Sunday, February 3, 2002

Constant unvignetted fov of 1/2 degree

10"f/4_L=8"_1/2deg fov ma=2".6
Off-Axis    Illum.    Light Loss
0.00 in    100.0%    0.00 mag
0.10 in    100.0%    0.00 mag
0.20 in    100.0%    0.00 mag
0.30 in    100.0%    0.00 mag
0.40 in    99.65%    0.00 mag
0.50 in    96.54%    0.03 mag
0.60 in    92.35%    0.08 mag
0.70 in    87.70%    0.14 mag
0.80 in    82.81%    0.20 mag
0.90 in    77.79%    0.27 mag
1.00 in    72.71%    0.34 mag

10"f/5_L=8"_1/2deg fov ma=2".4
Off-Axis    Illum.    Light Loss
0.00 in    100.0%    0.00 mag
0.10 in    100.0%    0.00 mag
0.20 in    100.0%    0.00 mag
0.30 in    100.0%    0.00 mag
0.40 in    100.0%    0.00 mag
0.50 in    99.59%    0.00 mag
0.60 in    95.63%    0.04 mag
0.70 in    90.19%    0.11 mag
0.80 in    84.07%    0.18 mag
0.90 in    77.62%    0.27 mag
1.00 in    70.99%    0.37 mag

10"f/6_L=8"_1/2deg fov ma=2".25
Off-Axis    Illum.    Light Loss
0.00 in    100.0%    0.00 mag
0.10 in    100.0%    0.00 mag
0.20 in    100.0%    0.00 mag
0.30 in    100.0%    0.00 mag
0.40 in    100.0%    0.00 mag
0.50 in    100.0%    0.00 mag
0.60 in    97.51%    0.02 mag
0.70 in    91.43%    0.09 mag
0.80 in    84.11%    0.18 mag
0.90 in    76.18%    0.29 mag
1.00 in    67.98%    0.41 mag

10"f/7_L=8"_1/2deg fov ma=2".25
Off-Axis    Illum.    Light Loss
0.00 in    100.0%    0.00 mag
0.10 in    100.0%    0.00 mag
0.20 in    100.0%    0.00 mag
0.30 in    100.0%    0.00 mag
0.40 in    100.0%    0.00 mag
0.50 in    100.0%    0.00 mag
0.60 in    100.0%    0.00 mag
0.70 in    96.80%    0.03 mag
0.80 in    89.42%    0.12 mag
0.90 in    80.55%    0.23 mag
1.00 in    70.99%    0.37 mag

10"f/8_L=8"_1/2deg fov ma=2".25
Off-Axis    Illum.    Light Loss
0.00 in    100.0%    0.00 mag
0.10 in    100.0%    0.00 mag
0.20 in    100.0%    0.00 mag
0.30 in    100.0%    0.00 mag
0.40 in    100.0%    0.00 mag
0.50 in    100.0%    0.00 mag
0.60 in    100.0%    0.00 mag
0.70 in    99.91%    0.00 mag
0.80 in    93.84%    0.06 mag
0.90 in    84.42%    0.18 mag
1.00 in    73.65%    0.33 mag

10"f/9_L=8"_1/2deg fov ma=2".25
Off-Axis    Illum.    Light Loss
0.00 in    100.0%    0.00 mag
0.10 in    100.0%    0.00 mag
0.20 in    100.0%    0.00 mag
0.30 in    100.0%    0.00 mag
0.40 in    100.0%    0.00 mag
0.50 in    100.0%    0.00 mag
0.60 in    100.0%    0.00 mag
0.70 in    100.0%    0.00 mag
0.80 in    97.33%    0.02 mag
0.90 in    87.90%    0.13 mag
1.00 in    76.08%    0.29 mag

10"f/10_L=8"_1/2deg fov ma=2".25
Off-Axis    Illum.    Light Loss
0.00 in    100.0%    0.00 mag
0.10 in    100.0%    0.00 mag
0.20 in    100.0%    0.00 mag
0.30 in    100.0%    0.00 mag
0.40 in    100.0%    0.00 mag
0.50 in    100.0%    0.00 mag
0.60 in    100.0%    0.00 mag
0.70 in    100.0%    0.00 mag
0.80 in    99.65%    0.00 mag
0.90 in    91.03%    0.10 mag
1.00 in    78.34%    0.26 mag

Note that whereas the minimum minor axis remains, within practical limits, 2-1/4 inches between f/10 and f/6, it then begins to increase significantly between f/6 and f/4.

If the experiment were conducted for an unvignetted fov of 1-3/4" to cover the diagonal dimension of a standard 35mm frame (24mmx36mm), acceptable for deep sky astrophotography the following is obtained:-

Constant unvignetted fov of 1-3/4 inches

10"f/4_L=8"_s=1".75 ma=3".3
Off-Axis    Illum.    Light Loss
0.00 in    100.0%    0.00 mag
0.10 in    100.0%    0.00 mag
0.20 in    100.0%    0.00 mag
0.30 in    100.0%    0.00 mag
0.40 in    100.0%    0.00 mag
0.50 in    100.0%    0.00 mag
0.60 in    100.0%    0.00 mag
0.70 in    100.0%    0.00 mag
0.80 in    100.0%    0.00 mag
0.90 in    98.31%    0.01 mag
1.00 in    94.98%    0.05 mag

10"f/5_L=8"_s=1".75 ma=3".0
Off-Axis    Illum.    Light Loss
0.00 in    100.0%    0.00 mag
0.10 in    100.0%    0.00 mag
0.20 in    100.0%    0.00 mag
0.30 in    100.0%    0.00 mag
0.40 in    100.0%    0.00 mag
0.50 in    100.0%    0.00 mag
0.60 in    100.0%    0.00 mag
0.70 in    100.0%    0.00 mag
0.80 in    100.0%    0.00 mag
0.90 in    98.43%    0.01 mag
1.00 in 94.15%  0.06 mag

10"f/6_L=8"_s=1".75 ma=2".75
Off-Axis    Illum.    Light Loss
0.00 in    100.0%    0.00 mag
0.10 in    100.0%    0.00 mag
0.20 in    100.0%    0.00 mag
0.30 in    100.0%    0.00 mag
0.40 in    100.0%    0.00 mag
0.50 in    100.0%    0.00 mag
0.60 in    100.0%    0.00 mag
0.70 in    100.0%    0.00 mag
0.80 in    100.0%    0.00 mag
0.90 in    97.19%    0.03 mag
1.00 in    91.33%    0.09 mag

10"f/7_L=8"_s=1".75 ma=2".6
Off-Axis    Illum.    Light Loss
0.00 in    100.0%    0.00 mag
0.10 in    100.0%    0.00 mag
0.20 in    100.0%    0.00 mag
0.30 in    100.0%    0.00 mag
0.40 in    100.0%    0.00 mag
0.50 in    100.0%    0.00 mag
0.60 in    100.0%    0.00 mag
0.70 in    100.0%    0.00 mag
0.80 in    100.0%    0.00 mag
0.90 in    96.82%    0.03 mag
1.00 in    89.67%    0.11 mag

10"f/8_L=8"_s=1".75 ma=2".5
Off-Axis    Illum.    Light Loss
0.00 in    100.0%    0.00 mag
0.10 in    100.0%    0.00 mag
0.20 in    100.0%    0.00 mag
0.30 in    100.0%    0.00 mag
0.40 in    100.0%    0.00 mag
0.50 in    100.0%    0.00 mag
0.60 in    100.0%    0.00 mag
0.70 in    100.0%    0.00 mag
0.80 in    100.0%    0.00 mag
0.90 in    96.91%    0.03 mag
1.00 in    88.60%    0.13 mag

10"f/9_L=8"_s=1".75 ma=2".4
Off-Axis    Illum.    Light Loss
0.00 in    100.0%    0.00 mag
0.10 in    100.0%    0.00 mag
0.20 in    100.0%    0.00 mag
0.30 in    100.0%    0.00 mag
0.40 in    100.0%    0.00 mag
0.50 in    100.0%    0.00 mag
0.60 in    100.0%    0.00 mag
0.70 in    100.0%    0.00 mag
0.80 in    100.0%    0.00 mag
0.90 in    96.02%    0.04 mag
1.00 in    86.11%    0.16 mag

10"f/10_L=8"_s=1".75 ma=2".4
Off-Axis    Illum.    Light Loss
0.00 in    100.0%    0.00 mag
0.10 in    100.0%    0.00 mag
0.20 in    100.0%    0.00 mag
0.30 in    100.0%    0.00 mag
0.40 in    100.0%    0.00 mag
0.50 in    100.0%    0.00 mag
0.60 in    100.0%    0.00 mag
0.70 in    100.0%    0.00 mag
0.80 in    100.0%    0.00 mag
0.90 in    98.66%    0.01 mag
1.00 in    89.01%    0.12 mag

Here again the diagonal minor axis increases steadily as the f/ratio gets faster, and increasingly so as it becomes faster than f/7. One could choose a different linear unvignetted fov, but the results would be similar.

As I understand what he is saying, vignetting is acceptable, even from the field centre, providing it is less than a certain amount (which he does not specify), but just to give him the benefit of the doubt, lets say 30%. In other words the edge of the maximum fov can be 70% less illuminated than the field centre. And because the illumination at the edge of the unvignetted fov falls off more rapidly at slower f/ratios, this value is reached over a shorter linear margin of the out field. 

To test this theory I also ran the same calculations keeping the minor axis constant at 2-1/4 inches, with the following result:-

Constant 2.25-inch minor axis

10"f/4_L=8"_ma=2".25
Off-Axis    Illum.    Light Loss
0.00 in    100.0%    0.00 mag
0.10 in    100.0%    0.00 mag
0.20 in    98.94%    0.01 mag
0.30 in    94.80%    0.05 mag
0.40 in    90.02%    0.11 mag
0.50 in    85.02%    0.17 mag
0.60 in    79.95%    0.24 mag
0.70 in    74.86%    0.31 mag
0.80 in    69.78%    0.39 mag
0.90 in    64.74%    0.47 mag
1.00 in    59.76%    0.55 mag

10"f/5_L=8"_ma=2".25
Off-Axis    Illum.    Light Loss
0.00 in    100.0%    0.00 mag
0.10 in    100.0%    0.00 mag
0.20 in    100.0%    0.00 mag
0.30 in    100.0%    0.00 mag
0.40 in    99.82%    0.00 mag
0.50 in    95.95%    0.04 mag
0.60 in    90.43%    0.10 mag
0.70 in    84.24%    0.18 mag
0.80 in    77.74%    0.27 mag
0.90 in    71.09%    0.37 mag
1.00 in    64.41%    0.47 mag

10"f/6_L=8"_ma=2".25
Off-Axis    Illum.    Light Loss
0.00 in    100.0%    0.00 mag
0.10 in    100.0%    0.00 mag
0.20 in    100.0%    0.00 mag
0.30 in    100.0%    0.00 mag
0.40 in    100.0%    0.00 mag
0.50 in    100.0%    0.00 mag
0.60 in    97.51%    0.02 mag
0.70 in    91.43%    0.09 mag
0.80 in    84.11%    0.18 mag
0.90 in    76.18%    0.29 mag
1.00 in    67.98%    0.41 mag

10"f/7_L=8"_ma=2".25
Off-Axis    Illum.    Light Loss
0.00 in    100.0%    0.00 mag
0.10 in    100.0%    0.00 mag
0.20 in    100.0%    0.00 mag
0.30 in    100.0%    0.00 mag
0.40 in    100.0%    0.00 mag
0.50 in    100.0%    0.00 mag
0.60 in    100.0%    0.00 mag
0.70 in    96.80%    0.03 mag
0.80 in    89.42%    0.12 mag
0.90 in    80.55%    0.23 mag
1.00 in    70.99%    0.37 mag

10"f/8_L=8"_ma=2".25
Off-Axis    Illum.    Light Loss
0.00 in    100.0%    0.00 mag
0.10 in    100.0%    0.00 mag
0.20 in    100.0%    0.00 mag
0.30 in    100.0%    0.00 mag
0.40 in    100.0%    0.00 mag
0.50 in    100.0%    0.00 mag
0.60 in    100.0%    0.00 mag
0.70 in    99.91%    0.00 mag
0.80 in    93.84%    0.06 mag
0.90 in    84.42%    0.18 mag
1.00 in    73.65%    0.33 mag

10"f/9_L=8"_ma=2".25
Off-Axis    Illum.    Light Loss
0.00 in    100.0%    0.00 mag
0.10 in    100.0%    0.00 mag
0.20 in    100.0%    0.00 mag
0.30 in    100.0%    0.00 mag
0.40 in    100.0%    0.00 mag
0.50 in    100.0%    0.00 mag
0.60 in    100.0%    0.00 mag
0.70 in    100.0%    0.00 mag
0.80 in    97.33%    0.02 mag
0.90 in    87.90%    0.13 mag
1.00 in    76.08%    0.29 mag

10"f/10_L=8"_ma=2".25
Off-Axis    Illum.    Light Loss
0.00 in    100.0%    0.00 mag
0.10 in    100.0%    0.00 mag
0.20 in    100.0%    0.00 mag
0.30 in    100.0%    0.00 mag
0.40 in    100.0%    0.00 mag
0.50 in    100.0%    0.00 mag
0.60 in    100.0%    0.00 mag
0.70 in    100.0%    0.00 mag
0.80 in    99.65%    0.00 mag
0.90 in    91.03%    0.10 mag
1.00 in    78.34%    0.26 mag

At f/ratios faster than f/6, vignetting would be noticeable. Visually, this might be acceptable but only for stargazing purposes. It would not for example be feasible for variable star work using a comparison field, nor would it be desireable for either solar or lunar photography, and it most certainly would not be at all desireable for 35mm deep sky astrophotography.

[vignetting.pdf] is a spreadsheet and charts for each of the cases considered.

Consider case 1, an unvigetted half degree fov; note that the choice of minor axis sizes gives a pretty constant slope to the fall off in illumination for the different f/ratios. Likewise for case 2, a constant linear fov.

Consider case 3, a constant 2-1/4-inch minor axis diagonal, the vignetting commences nearer the field centre at f/4, and is greater at the edge of the linear field of view.


Vignetting debate

In his article Seronik concludes, "You can fine-tune the size of the secondary to suit a particular observing program. Planetary observers are fanatical about keeping the size of the secondary as small as possible to minimize image harming diffraction effects, while variable-star observers want larger diagonals for larger fully illuminated fields." Personally I would not dream of using a short focus 6-inch f/4 Newtonian as a dedicated planetary 'scope. However to give him the benefit of the doubt, for the purposes of discussion consider a hypothetical 6-inch f/4 Newtonian with a 1-inch minor axis flat. If we’re prepared to accept vignetting immediately off the optical axis, we need not bother considering the field lens diameter in the minor axis calculation.

Sizing of the flat then collapses to:-

where: l = flat to prime focus separation
           a = flat minor axis

If we put a = 1” then l = 4” for an f/4 system. If l is greater than 4” the flat is not big enough to see all the primary even on axis, and in effect stops down the entrance pupil. This means the eyepiece has to lie only 1-inch less than the radial offset of the tube from the edge of the primary. Its feasible, but the tube must be only marginally wider than the primary, say 7-inch OD and tube currents will begin to manifest themselves, and so will veiling glare. Not insurmountable, but serious design shortcomings nonetheless.

Now lets consider useable fields and powers. The 1-inch minor axis flat minimizes contrast loss due to Fraunhofer diffraction, so we don’t want to compromise anything that would negate the miniscule enhancement over a fully sized flat (sized to the field stop).

The highest practicable powers must therefore be achieved without using a Barlow lens or an eyepiece with additional air/glass surfaces due to either a built in Barlow or a Smyth converter, yet capable of working at f/4 without introducing noticeable spherical or spherochromatic aberration or spherical aberration of the exit pupil.

An ideal high power eyepiece capable of meeting these criteria would be either a Zeiss Abbe Orthoskop, or a Clave Plossl. The shortest useable focal length in this class of ocular is 4mm, yielding an exit pupil of 1mm, meeting the so-called Whittaker rule for the minimum power needed to barely see all the detail resolved in an extended image. So far so good, the field lens would be roughly 3mm (1/8-inch) diameter, and the edge of the field of 15arcmin would be vignetted by only 0.13mv.

Now consider the lowest feasible power. One of the great benefits of a 6-inch f/4 RFT is its ability to provide wide fields at a wide exit pupil. Suppose we wanted a 6mm exit pupil, corresponding to a 24mm focal length eyepiece, and further suppose we wished to maximize the available field, by using one of the latest exMoD 5 element Galoc-Berthele hybrids with a 32mm field lens and a 90 degree apparent field of view. At x24 the real field would correspond to 3.75 degrees, a semi-field of 112.5 arcmins. Vignetting at the outfield would be 1.55mv. Peters & Pike considered anything greater than 0.50mv to be objectionable, based on their visual trials. If we accept this to be so, all the outfield beyond 50 arcmin radius would be unacceptably vignetted and in fact there would be little point trying to use an eyepiece with a field stop wider than 0.7-inches. Even if we did however, not only would the outfield still be vignetted by an additional 1.0mv, the observer, if he moved his eye only a fraction of an inch away from the optical axis, would see right past the flat into the tube wall opposite. Again, not an insurmountable problem, but nonetheless a glaringly obvious shortcoming of the undersized flat.

Because the unvignetted fov is zero, in theory even the highest power would be effected by veiling glare. The actual effect is additionally influenced by the tendency of an observer to look obliquely across the optical axis due to saccadic motion of the eye pupil. As the observer’s pupil oscillated around the Ramsden disc, it would produce a shadowing effect not dissimilar to spherical aberration of the exit pupil. This is a congruent design fault to that found in the Short Gregorian, which could only be overcome by using a pin hole eyestop. In other words whatever miniscule gain is to be had due to the smaller flat enhancing contrast by minimizing diffraction effects is more than offset by veiling glare, and extreme difficulty maintaining one’s eye at the optimal viewing position.

I have prepared a CAD drawing showing the dimensions adopted in making my point that vignetting due to an undersized flat is not acceptable, and that this is not simply a matter of personal opinion. If you choose to obstinately ignore these facts, you end up with an inferior telescope exhibiting the various faults I have described.

I have also prepared a comparison spreadsheet based on Peters’ & Pike’s formulae. Notice how the vignetting when compared over equal angular fields is much greater in the system with the smaller flat. This is contrary to the false impression created when running Alan Adler’s sec.exe which plots linear field radius against vignetting.

This brings me to one minor, but not trivial point, where matters are taken to extremes. Peters’ & Pike’s equations are based on two assumptions. There is no field curvature, and the observer always looks straight along the optical axis to the primary centre, from the optical axis (centre of the Ramsden disc). Vignetting increases when, at fast f/ratios it is calculated on the Petzval surface. It is marginal on the field centre, but increases as the 4th power of the field angle. If a ray trace were to be performed through the eyepiece, backwards through the system, from Ramsden disc to entrance pupil, vignetting would be significantly worse for a case where the observer’s eye was directed to the edge of the field and marginally off axis.

To summarize: whilst I accept the general point Seronik makes, that there is no direct correlation between f/ratio and flat size; there is for a given field angle, flat to focal plane separation, and unvignetted angular field coverage. So, is the old saw, "short focus Newtonians require larger secondary mirrors than long focus models" a myth? I hope you can see from the examples I have given that it isn't. If you want a Newtonian reflector "fine-tuned" to planetary observation build one with an f/10 or even an f/12 primary and a diagonal less than 1/5th the primary. That way you'll end up with an excellent planetary 'scope. If you choose to flout the conventions adopted over the past century or more, you will, not surprisingly, end up with an inferior telescope.


To emphasize my argument I have rewritten Alan Adler's sec.exe programme to plot vignetting against the angular field radius, and run Pike's and Peters' calculations (ref Sky & Telescope March 1977) for a 6-inch f/4 Newtonian with 1-inch; 1-1/2-inch; 2-inch and 2-1/4-inch minor axis flats. When a comparison of vignetting over the full possible field angle of a 2-inch focal plane is made, the small flat obviously vignetts to an horrendous extent.

[6-inch f/4 RFT.pdf]
[6-inch_f/4_comparison.pdf]



If you would like to run your own comparisons download the spreadsheet [Newtonianvignettingtemplate.hqx] (MAC Appleworks v6) or [Newtonianvignettingtemplate.zip] (WIN98 Xcel2001) Please note that since this spreadsheet was created on an Apple Mac computer the embedded charts will only be available if you run AppleWorks v6. Xcel 2001 users will only be able to open the worksheets.


To give you a good idea as to what a realistic vignetting profile should look like I have prepared a spreadsheet and chart of my 10-inch f/10.6 Calver which has a 2-inch minor axis flat and a 17.25-inch flat to focal plane separation. The unvignetted field of view has an angular radius of 7 arcmins. The vignetting at the edge of a 30 arcmin field radius is only 0.6 magnitudes. Even so this does manifest itself when observing either the sun or full moon and putting their images at the field boundary. The light loss corresponds to 42.5%.

[Calver-f/10.6-vignetting.pdf]


The correct way to size a Newtonian diagonal is provided on "How to size a Newtonian Diagonal". Here you will find charts that enable you to select the appropriate sized diagonal depending on the aperture, focal ratio and working distance between the focal plane and the tube wall.


This page was created by SimpleText2Html 1.0.2 on 3-Feb-102.


 

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