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Newtonian Focal Length Test Rig - Ideas/Pictures?

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22 replies to this topic

#1 xrayvizhen

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Posted 16 November 2015 - 01:05 PM

I'm in the middle, more or less, of my 12.5", F/5.2 (I think) project. Most of the carpentry is done and optical components are in-house. Since this is a solid tube Dob, I want to be particularly careful where I drill the hole in the tube for the focuser. The tube matches the reinforcement rings and flanges that I routed out exactly and if I screw up the location of the hole the odds of getting another cardboard tube from Lowes the exact same diameter is slim and none. So I want to measure the focal length of the mirror exactly and therein lies the problem. I measured it twice several weeks apart and got two different focal lengths. Either I don't know what I'm doing or I'm not being consistent.

 

The mirror is nominally F/5.2. It was made by Mr. Dodds at Nova Optical sometime in the 90s, weighs 30 lbs and is 2" thick. I used what I thought is the standard method of measuring by reflecting a clear light bulb onto the mirror and viewing the image on a white screen placed alongside the bulb. I used a clear bulb so I could place the screen and filament of the bulb exactly in line with each other. When the filament appeared on the screen in perfect focus I measured the distance to the mirror and divided by 2.

The first time I did this, I measured 130 3/8"  (FL=65.2). Yesterday I did it again and came up with 127 1/2" (FL=63 3/4). So something is wrong somewhere. The only thing different is the first time I had the mirror on a test stand. The second time I had the mirror in its cell mounted inside the mirror box. So the mirror is either F/5.2 or 5.1 and I'm not sure how much leeway I will have with the location of the focuser (a GSO from Agena Astro that I already had). I'd hate to mount the spider and focuser and end up with a scope that won't come to focus. I'm thinking I should measure two or three more times and take an average but other than that I'm stumped. My test apparatus is pretty simple. Mirror and cell on the floor and the light bulb and screen opposite with a tape measure in between.

Ideas anyone? Or if anyone has a picture of how they test (or tested) the focal length of their mirror or maybe a different method, I would certainly be interested in seeing.


Edited by xrayvizhen, 16 November 2015 - 01:12 PM.


#2 Pinbout

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Posted 16 November 2015 - 01:27 PM

the most accurate way to find the focal length is to take a knife edge reading to the center zone at the radius of curvature  and measure the distance from the center of the mirror to the ke then divide by 2.

 

similar to how we measure the rossnull lens to mirror distance. @ around 3:10 https://www.youtube....h?v=t3UkcF4LegY

 

 

the knife edge should look like this.

 

12.5 f5 focus distance.jpg



#3 Jeff Morgan

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Posted 16 November 2015 - 02:00 PM

Danny's method is of course the most accurate.

 

If you don't have the Foucault apparatus, or don't want to build it, your method should be able to achieve an accuracy of plus or minus 1/4" or so. Good enough for the task at hand.

 

Try a few more measurements.



#4 J A VOLK

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Posted 16 November 2015 - 02:08 PM

I have used the method you used (taught to me by John Dobson!) on dozens of mirrors with great consistency and accuracy.   Your mirror should be very close to "design" based on the maker.  I would guess you made some mistake on the second reading.  In any event I always leave some leeway to move the primary a bit so I can accomodate the focus points for my range of eyepieces.



#5 Richard O'Neill

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Posted 16 November 2015 - 02:23 PM

 "the most accurate way .... then divide by 2."

 

  Not really. Dividing the radius of curvature of a parabolic mirror by 2 will get you in the ball park but it won't be an accurate figure, only an approximation. For fast mirrors the actual focal length will be less than 1/2 R.

 

 There are formulas to calculate it based on F ratio but in my experience the more useful and accurate method is to image an infinitely distant object (for all practical purposes our moon will do nicely) and measure the distance between mirror center (or edge) and focus point.


Edited by Richard O'Neill, 16 November 2015 - 02:25 PM.


#6 SteveNH

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Posted 16 November 2015 - 04:50 PM

Actually, Danny said to measure the center zone's radius of curvature and divide by 2, and for all intents and purposes that would get you practically the closest measurable distance to the actual focal length given the equipment most of us have available at home. The typical size of the center zone for a 12.5" f/5 used in a Foucault test is relatively small, and reading meaningful variations of radius within it would be beyond the capability of the measuring tools we have available in a typical household.

 

Steve



#7 kfrederick

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Posted 16 November 2015 - 04:56 PM

 "the most accurate way .... then divide by 2."

 

  Not really. Dividing the radius of curvature of a parabolic mirror by 2 will get you in the ball park but it won't be an accurate figure, only an approximation. For fast mirrors the actual focal length will be less than 1/2 R.

 

 

    care to explain ???



#8 Richard O'Neill

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Posted 16 November 2015 - 06:38 PM

 Gladly, but to save time please consult this pdf for an in depth explanation.

 

http://scipp.ucsc.ed...parabolic09.pdf

 

 I'll grant that in some situations a little deviation from exactness might be acceptable but in the case of fast mirrors and stringent parts mounting requirements those differences could be important, especially if one needs to determine exact parts placement to ensure the focal plane ends up exactly where intended - prior to drilling holes.

 

 Some leeway in hole placement can be adjusted for with the focuser but a relatively small mounting error can prove crucial if a wide range of eyepiece, camera or bino-viewer accommodation is required with a limited range of focuser travel, hence my recommendation to avoid disappointment by measuring the focal length using an astronomical object.

 

 I hope that helps. Measure three times, cut and drill only once.


Edited by Richard O'Neill, 16 November 2015 - 06:39 PM.


#9 mark cowan

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Posted 17 November 2015 - 12:17 AM

The first time I did this, I measured 130 3/8"  (FL=65.2). Yesterday I did it again and came up with 127 1/2" (FL=63 3/4)

 

 

Re. the disagreements - Danny's method is the same as mine, and it is correct.  The paraxial focus of the center of any paraboloid is where the FL of the mirror is measured from on the bench, before being recorded on the finished mirror.  It will provide exactly the same focus distance (ROC/2) as it does for on-axis rays from infinite sources, like any spherical mirror would.  The speed of the mirror doesn't matter so long as you can measure the FL of the center.

 

Where the caution about a paraboloidal mirror does apply is when the tester is using the entire mirror to attempt to find a "focus" at ROC, of which there isn't one, it produces instead a caustic horn of focus points from different radii across the surface.   The overall depth of this caustic for a 12.5" f/5.2 is only about 7 mm for a fixed Foucault test, and 3.5 mm if you're moving the light source and target, as you were doing, so that's hardly going to account for the large discrepancy.

 

What I suspect you might have done though is measure one time to the back of the mirror and the other time to the front surface - it would explain the discrepancy -  or measured from the back and neglected to account for it.  Either way, check it several times until you get the same result repeatedly.

 

A method accurate to a few mm would be to set it up close to a stepladder where you can directly measure the FL while minimizing (with care!) the size of the suns reflection.  Or just put a mask on the mirror that exposes only the central few inches and use that with the flashlight test.  A coated mirror should be plenty bright for this.


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#10 xrayvizhen

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Posted 17 November 2015 - 08:39 AM

Thanks for the suggestions. I can assure you I did not measure to the back of the mirror but in reviewing my method there was one other inconsistency other than what I originally noted, mainly I used a 9 segment LED flashlight instead of a clear lightbulb. I doubt that would make much of  a difference though.

 

I'll try masking the off the outer zones of the mirror. I hadn't thought of that. Also I have an older mini-magliite with a single small bulb. I'm going remove the head of the flashlight and align the bulb to the screen and take the measurement from that point. I'll also try reflecting the sun off the side of my house. Bottom line, I'll record all the measurements until I start getting some kind of consistent reading.



#11 Pinbout

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Posted 17 November 2015 - 08:59 AM

 

I'll also try reflecting the sun off the side of my house

 

I only do that with an uncoated mirror.

 

https://www.youtube....h?v=_0JlYspvQlo

 

and because I have the mirror tilted funky, its not all that accurate for me.

 

I use this when I'm making the mirror after a flash polish to see if I messed up the focal length.



#12 Pinbout

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Posted 17 November 2015 - 09:02 AM

 

Re. the disagreements - Danny's method is the same as mine, and it is correct....

 

I have to agree with that 100% :lol:

 

from http://physics.stack...l-rays-question

 

 

<<The formula for the focus of marginal rays is given by R−Rcosθ   where θ  is the angle made by the marginal ray with the line joining it's point of incidence with centre of curvature. We can see that for marginal rays θ  is large hence the focus is small. Thus marginal rays converge close to the lens (for concave lenses) and diverge from a nearer point (for convex lenses). In fact, for paraxial rays θ  is approximately 0  and so F=R−Rcos(0) =R/2The formula for the focus of marginal rays is given by R−Rcosθ   where θ  is the angle made by the marginal ray with the line joining it's point of incidence with centre of curvature. We can see that for marginal rays θ  is large hence the focus is small. Thus marginal rays converge close to the lens (for concave lenses) and diverge from a nearer point (for convex lenses). In fact, for paraxial rays θ  is approximately 0  and so F=R−Rcos(0) =R/2>>


Edited by Pinbout, 17 November 2015 - 09:04 AM.


#13 dan_h

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Posted 17 November 2015 - 09:08 AM



I'll also try reflecting the sun off the side of my house.


Maybe not a good idea with a coated mirror. Anything at the focus is going to get really hot, really fast. It will only take a second or two to do damage to anything but concrete. Really. Don't do this.

If you want an accurate focal length, cast an image of a distant target (horizon, street lights, lighted sign, etc) onto a screen. It doesn't need to be at infinity distance. Once the target is over 1000 focal lengths distance the error will be less than you can quickly measure. If you use a screen about half the size of a playing card it can be on axis and your measurement will be very good.

dan

#14 mark cowan

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Posted 17 November 2015 - 03:31 PM

Thanks for the suggestions. I can assure you I did not measure to the back of the mirror but in reviewing my method there was one other inconsistency other than what I originally noted, mainly I used a 9 segment LED flashlight instead of a clear lightbulb. I doubt that would make much of  a difference though.

 

I'll try masking the off the outer zones of the mirror. I hadn't thought of that. Also I have an older mini-magliite with a single small bulb. I'm going remove the head of the flashlight and align the bulb to the screen and take the measurement from that point. I'll also try reflecting the sun off the side of my house. Bottom line, I'll record all the measurements until I start getting some kind of consistent reading.

 

 

 

It's just the Holmesian method, "Once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth."   :lol:

 

Actually, measuring from the back of the mirror, or some fixed point close to that on the test stand, is what I do.  Just subtract the edge thickness plus whatever and you're good, because the tape measure is then showing the same distance as it would if you could hook it onto the center of the face (treating the mirror as a sphere at ROC for this purpose :p

 

Yes, use a bare bulb tungsten flashlight for this, it's a lot more accurate.

 

FWIW a big coated mirror should not be used for the sun test - too dangerous and too bright.   With a mask that exposes just an inch of the center it'd be OK though.


Edited by mark cowan, 17 November 2015 - 03:41 PM.


#15 Joe1950

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Posted 17 November 2015 - 04:57 PM

Might a pinhole, reflected back to 1/4" of itself work? Maybe a little easier to measure position than a filament or flashlight.



#16 xrayvizhen

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Posted 17 November 2015 - 06:42 PM

After coming home from work I tried the mini-maglite with the head removed method. I measured 127 5/16, 127 1/4 and 127 3/8.  Mirror was on a stand, not it's cell, and I afixed the maglite to the white screen with the bulb flush with the screen. So it looks like whatever I did several weeks ago was wrong as these measurements, combined with what I did yesterday, seem more or less consistent. And yes I surmised that reflecting the sun onto the wall of my house (actually, it would have been my neighbor's house, due to the angle of the sun this time of the year) would not be a good idea. And right now the moon is a crescent and too low in the sky.

 

I need to refine my "test stand" because I nearly had a stroke before. The mirror flopped out of the stand, which was on the basement floor, with a loud clang. I let out a shreak and my wife called down and asked if she should call the paramedics. Thank God no damage.

 

By the way, I assume that the focus point is when the reflected light on the screen is the smallest, which with the mag-lite is just a small point of light?



#17 mark cowan

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Posted 17 November 2015 - 08:40 PM

So it's a f/5.1, depending on how you measure it.  If the bevel is, say 1/8" it's an f/5.2 for the optical diameter.

 

Yes the focus is when the point is smallest.



#18 xrayvizhen

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Posted 18 November 2015 - 12:00 PM

Ah, the bevel... maybe that's the crux of the problem! The original owner of the mirror thought it was a 5.2, which is what I've been using as the basis for all my drawings and diagrams. But I was basing my calculations on 12.5" x 5.2 = 65"FL, when in fact it's 12.25 x 5.2 = 63.7".  Now that makes sense and corresponds much more closely to the measurements I'm getting. That still doesn't explain how I screwed up the first time I measured several weeks ago, but I feel better now, regardless. Thanks for bringing that up.


Edited by xrayvizhen, 18 November 2015 - 12:02 PM.


#19 jtsenghas

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Posted 18 November 2015 - 01:20 PM

Errors on diameters and focal length due to neglecting to consider the bevel are common. Such errors also contribute to replacement mirrors sometimes not fitting existing cells. Some makers routinely increase the blank diameter to get the nominal optical diameter with a bevel in place. It really can make a difference as the difference in diameter would be multiplied by the f/number for the difference in focal length.

#20 Pinbout

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Posted 18 November 2015 - 02:39 PM

 

Errors on diameters and focal length due to neglecting to consider the bevel are common.

 

that should say focal ratio. 63.75" is still the same length no matter what diameter.

 

keeping a small bevel is nice

 

6in bevel.jpg

 

 

but having a rounded polished bevel is really cool to work with.

 

https://www.youtube....h?v=lGMLJNVXV2c


Edited by Pinbout, 18 November 2015 - 02:40 PM.


#21 mark cowan

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Posted 18 November 2015 - 02:46 PM

Errors on diameters and focal length due to neglecting to consider the bevel are common. Such errors also contribute to replacement mirrors sometimes not fitting existing cells. Some makers routinely increase the blank diameter to get the nominal optical diameter with a bevel in place. It really can make a difference as the difference in diameter would be multiplied by the f/number for the difference in focal length.

 

 

I only engrave the FL on mirrors, never the f/ratio.  Not possible to get the FL wrong. :p

 

I agree with Danny about rounded bevels, but there are endless numbers of people apparently who think the only good bevel is one with sharp edges... :lol:



#22 jtsenghas

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Posted 18 November 2015 - 03:15 PM

Oops! I meant to say "errors on diameter and focal RATIOS" not focal LENGTH.

I'm well aware that the focal length is measured and the the focal ratio calculated, not the other way around.

To my point, though, I've seen some excessive bevels that significantly reduce the diameter. Perhaps some of them were made to eliminate turned down edges.

#23 mark cowan

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Posted 19 November 2015 - 03:41 PM

No foul.  As I said, I only engrave the FL, the f/ratio can always be calculated with it from whatever people like (optical diameter or physical diameter).




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