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Mak Focal Length Calculations

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#1 Asbytec


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Posted 03 November 2012 - 11:09 PM

Last year I did extensive star drift measurements to calculate 150 Mak TFOV for each eyepiece using a diagonal. I used Regulus to measure drift time through the center FOV. I also measured drift time using the shorty 2x Barlow inserted both before and into the diagonal. My data is attached.

Equation used: TFOV = 15.04*T*Cos(delta)

Where T is drift time and Cos(delta) is cosine of Regulus declination at 11.9 degrees.

According to the math, if one knows TFOV and AFOV, one should be able to work most of the numbers associated with a scope, right? For example, if TFOV = AFOV/Mag, then Mag = AFOV/TFOV. Once you know Mag and eyepiece focal length, you're off and running. From there, you can calculate your effective focal length.

My data is surprising, so can someone check the logic based on the actual TFOV figures I trust to be good? Something bugs me about the data, though. According to the 12mm w/1.6 power barlow, I should be observing Jupiter at nearly 300x. Maybe, but it does not feel right. Maybe something is wrong with the math or logic.

Now, I calculated the Barlow power, which should be 2x inserted into the diagonal and 3x before the diagonal. I took the ratio of drift times both with and without the diagonal and found the drift ratio to be 1.5x (with the barlow after the diagonal) and 2.2x (before the diagonal.) I think this is valid math.

I also found my scope to be operating effectively at f/15.5 to f/16 (~2300mm) with the diagonal. This seems a bit long, though not too surprising, since the scope is advertised at f/12 (~1800mm.) But, f/16 is the derived figure based on TFOV measurements and the best AFOV eyepiece data I could find.

Any discussion to lock this down would be greatly appreciated. Thanks in advance.

Edit: I understand TFOV = AFOV/Mag is an approximation and the eyepiece focal length can be off by some fraction of a mm. Also, the AFOV listed may not be accurate, either. But, I am just looking for a good ball park figure for visual work, to be comfortable saying the scope really was at ~300x.

I do not have a CCD to work the pixel method. Field stop information can vary, too, and is often hard to come by, IME. So, I prefer the star drift method, as it is reasonably accurate despite distortions.

Another method that sounds promising is knowing the lunar diameter and comparing it's size to that on the focal plane.

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#2 Jon Isaacs

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Posted 04 November 2012 - 06:15 AM


Since everything is dependent on the field of view of the eyepiece, I suggest using an eyepiece with a known field stop diameter. You can measure it yourself for simple eyepieces like orthos and Plossls. Then can you use

FLscope =(57.3 deg/rad) x Field Stop/TFoV


#3 Asbytec


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Posted 04 November 2012 - 07:23 AM

Thank you, Jon. I just read a few threads on it, you and David offering some nice conclusions. Didn't realize, but should have, this question pops up often.

#4 vahe



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Posted 04 November 2012 - 08:26 AM

Any discussion to lock this down would be greatly appreciated. Thanks in advance.

Assuming that your 6” Mak has a moving mirror focusing mechanism then the results should not be surprising.
The advertised F/12 applies to focus at 2” behind the eyepiece opening with moving mirror there are infinite focus points.

The case in point is my 6” f/12 TEC Mak, according to the manufacturer the primary mirror has a total movement of 7mm, 5mm forward and 2mm backward from the design optimized point of F/12, with these extreme mirror positions the Mak focal length varies from F/11 to F/14.


#5 Asbytec


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Posted 04 November 2012 - 09:22 AM

Thank you, Vahe. Yes, understood about the varying focal length in a moving mirror system. Mine has it. I just thought my calculations were a little over estimated (with the diagonal in place.) But, the drift timings are what they are and the remaining data is what it is at some level of accuracy. Another form of testing might shed some light.

Yea, Vahe, those mirrors do not move much. I was shocked how little mine moved during testing, full turns on the focuser were hardly noticeable. Amazing thing.

Thank you for replying, not really wanting to start another thread (after reading the very thorough ones posted fairly recently.)

Update: The moon tonight is 30.03" arc and is 17mm focused on wax paper. My previous measurements were 33.43" and 19mm, respectively. Both calculations give an effective focal length of ~1950mm (f/13) at the diagonal. This seems more reasonable and is more consistent with observation, for example Jupiter at 160x and not 200x. It's also more in line with other CAT test results. Close enough for government work.

Not sure why this seems to work better, but the method used: s=FL x tan(angle radians)

#6 Starman1


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Posted 19 November 2012 - 03:17 PM

Here is an article with formulae on the focal length change in moving mirror catadioptrics with back focus distance:
You might check out the final page to get a visual view of the changes with distance.

#7 Eddgie



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Posted 19 November 2012 - 06:26 PM

Calculating Barlow magnificatoin factors for a telescope with a moving mirror can be difficult

The reason is that for a given eyepeice, even putting in the Barlow and taking it out makes you have to move the primary mirror to re-focus the scope, which changes the focal length.

Generally, if you put in an eyepeice and focus, then pull out the eyepeice and insert your Barlow and eyepeice back in, you have to now have to turn the focuser counterclockwise to move the mirror backwards to bring the focal plane (which is now to far back) forward back to reach focus.

And this movement alone causes the focal ratio of the telescope to change.

Now, after you refocus, if you move the Barlow to the front of the diagonal, the focal plane is once more behind the field stop of the eyepiece, so to get the focal plane to move forward, you have to crank the focuser even more counter-clockwise, which once again, changes the focal length.

Calculating the exact magnificatoin factor you will get with a Barlow lens in a scope with a moving mirror will be very difficult because you have to keep moving the mirror and hence the focal lenght when you change add or change the position of the Barlow.

This could make it hard to know if your calculations are using valid data. You would have to measure the back focus for every combination and correct the actual focal lenght being used at the primary.

Also even a millimeter here or there, or a slight difference from stated magnification of an eyepiece could cause an outsized error when you are dealing with such long focal lenghts.

But the Barlow power factor is problematic because your mirror spacing keeps changing every time you change the position or remove the Barlow.

Sorry if I did not do a very good job of explaining this.

#8 Ed Holland

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Posted 19 November 2012 - 06:59 PM

As mentioned earlier in the thread, another good way is to use an EP with known field stop. That is what I did last year with the 127mm Mak when making FL calculations. I used a digital caliper to measure the field stop. I was also careful to ensure the star drifted across the stop through the centre of the field, not at some chord to the circle of view - that part was more challenging than I expected. Repeated measurements gave me an idea of the uncertainty in data collected this way. Drift time was long enough that the other uncertainty - deciding when the star was in & out of view - was not significant in relation to the accuracy I sought, or the effect of intentional changes made in the system as part of the testing.

All good science! Have fun :)

#9 Asbytec


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Posted 19 November 2012 - 10:28 PM

Don, its a great article. Too much math for me, but it definitely shows the effect Eddgie described. In fact, the effect is even more amazing when one realizes the mirror move is almost imperceptible.

Eddgie, absolutely. In fact, comparing the drift times (they are what they are, and the ratio is the same) did give variances of 1.4x to 1.6x. And the same small variance around 2.2x inserted prior to the diagonal. All eyepieces focus rather closely despite the different designs. So, only minor turns on the focuser knob were necessary in any Barlow configuration. (Adding the Barlow changed it, but refocus movement remained small once inserted.) So, to have some variance between eyepiece designs is not surprising. The ratio of the drift times with and without the Barlow offered some idea of the magnification. Close enough.

Ed, yea if I had reliable field stop data I would have tried it. Internet searches turned up scant information and I just decided not to buy calipers for this one task. Even when I used what was available, it seemed even a small deviation (from stated and actual) made a big difference. I toyed with the numbers to see this change in the answer.

I have to be happy with the method I finally settled on, measuring the moon on the focal plane. It seems much more consistent with observation and your own results than the (AFOV) errors inherent in the methods I used. And, again, I just did not have accurate enough field stop data.

I wasn't after an exact figure, just something reasonably ball park that I could apply across the board. Something more accurate than the stated f/12. Seems it varies between f/12.8 and f/13.1. So, F/13 it is...close enough and no reason to doubt it. (And its pretty consistent with the article Don posted above showing an expected longer focal length.)

Thank you for replying.

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