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How to Calculate the Focal Length of an SCT

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This question comes up fairly often, particularly when people are interested in knowing the actual magnification they are using while viewing with an SCT. It has come up in the Double Star forum in threads where people compare lowest powers to see a particular pair split. It comes up in binoviewer discussionss when people can't figure out why sometimes the view is muddy, but they don't realize they are underestimating power by 25%. And it comes up in eyepiece discussions when eyepieces are being compared between different scopes but the user may not be aware of the true power in the SCT.

Often people miscalculate the power when using an SCT. WHY? Because an SCT has a movable mirror and a secondary mirror that changes the steepness (and therefore the effective focal length) of the light cone. Every time you move the mirror in an SCT (or a Mak) to achieve focus, you change the operating focal length. Because of that changing shape of the light cone, you cannot simply add the length of the accessories you've added on the back end of your SCT. The operating focal length must be recalculated.

There is a great article by Chris Lord on his website that provides a great deal more in formulas, charts and explanation. Here, I have outlined a simpler do it yourself at home, for your configuration, check of the focal length.

Why would you need to do this?

Well, here are some examples:
  • My C5 with a standard 1.25" visual back and a 1.25" TV dielectic diagonal operates at a focal length of F=1367mm, not the nominal f/10=1250mm.
  • My C5, as it is currently configured with a 1.5" long extension tube (to get clear of the focus knob) and a 2" Astrotech dielectric diagonal, operates at a focal length of F=1540mm, f/12.3.
  • My C8 with a screw-on Crayford focuser and a 2" diagonal operates at about 2550mm approx f/12.5.

      Determining the Operating Focal Length of an SCT

      Use two different scopes, your SCT needing testing (in the configuration you would normally use it) and a refractor of known focal length. We'll assume the refractor has a shorter focal length than the SCT.

      Pick 3-4 eyepieces with a variety of focal lenghts and fs diameters (for example, 10,15,20, 25 or 30). To be sure that vignette is not an issue, try not to select eyepieces with very wide field stops that might possbly be vignetted by some portion of the SCT tube. I'd expect youd be fine with plossls up to 32mm.

      Hang a tape measure on a telephone pole, perhaps 100 yds away.

      Record the dimension across the fov for each eyepiece, first in the refractor. Then, record for each eyepiece in the SCT.

      I did this with a TV85 and my C5. I picked 4 eyepieces a 7.5, 12.5, 18 and 24mm. Set up a measureing tape. Using the eyepieces in a TV85 refractor of known focal length, recorded the extent of visible field (to as fine a division as could be seen) for each eyepiece. Next I brought out my C5 with the standard 1.25" diagonal. ran all 4 eyepieces through the C5/1.25"diag and recorded the extent of fov again.

      I then compared the reading for each eyepiece in the TV85 to the reading in the C5. Got near exactly the same ratio of drop in fov for all 4 eyepieces. This is good consistent data for the 4 eyepieces. So what that shows so far is only one thing changed, the POWER. And because only power changed, all 4 eyepieces have exactly the same ratio reduction in the fov. Variances here were on the order of 0% to 1%.

      So, Determine factor for each eyepiece dimension across fov in ref is to dimension across fov in SCT equals power in ref is to power in SCT. Smaller dimension reading in the SCT(assuming SCT is longer) is due entirely to higher power, nothing else.

      Multiply refractor power by factor to get SCT power. Having calculated operating powers in SCT calc backwards to get operating focal length.

      The factors should be near exactly the same for all eyepieces. If not, recheck. If so, you can establish the operating power of your SCT. Very minor differences may be seen due to a few mm difference in operating focal length of SCT to accommodate placement of field stops. Parfocalizing eyepieces would eliminate any differences, but is not necessary as error is very small, on the order of 5-10mm.

      This may seem like a lot of work, but takes perhaps only 15-20 minutes, and you are done forever.

      The accuracy of this method is well within 1%. Focal length will be slightly (not significantly) different at infinity. The farther away you put your test scale, the closer you will be to infinity, but you are probably within 1-2% even when testing at just a few hundred feet.

      Post in the Cats Forum related to Calculating the Focal Length of a C5 with a spacer and a 2" diagonal installed on back end



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