Mirror Making: DIY Spherometer Part 2, Calibrating and Using the Instrument
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- เผยแพร่เมื่อ 15 ก.ค. 2024
- In Part 2, Gordon shows how to calibrate the three-ball spherometer, and how to use the instrument to determine the radius of a telescope mirror.
- วิทยาศาสตร์และเทคโนโลยี
Gordon, thanks for these videos! Your lesson was easy to follow along with and made perfect sense. Can't wait to see more! I subscribed and encourage others to do so as well. Thanks again!
Mr Waite, Thank you for your videos, they have opened up an entire world for me.
Thanks! Enjoy your projects!
Great vid dude on the instrument. Last year I finished my first mirror and it turned out ok. It's FL is 56" and is within 1/10 of a wave on the Folcalt Tester.
great vid tyvm
*WHAT A FANTASTIC VIDEO, Thanks* (i have no idea if the math is correct,at this point,but it certainly seems to be).
Awesome thank you !! Wondering if there is a printable cheat sheet somewhere ?
Mmh, the formula in 7:33 looks strange to me. It says that Rₘ = (Rₛ² - s²)/2s - d/2. However, when I derive it from Pythagoras, I arrive at a formula where the minuses are replaced with pluses: Rₘ= (Rₛ² + s²)/2s + d/2. Why ? What we are having is a orthogonal triangle with the orthogonal parts being (a) the spherometer radius Rₛ and (b) the mirror-radius minus sagitta Rₘ - s, and (c) the hypotenuse is the full mirror-radius Rₘ, so written Pythagoras (c² = a²+b²) this is Rₘ² = Rₛ² + (Rₘ - s)². From there, we can resolve this for the mirror radius Rₘ = (Rₛ² + s²)/2s. The term +d/2 then is needed because we are actually measuring the radius a little bit short because the measurement essentially goes through the center of the balls, so we have to add that again sitting on the concave surface. So in this particular sample calculation with this new formula we'd arrive at 124.2" instead of 123.9" for the mirror radius. Not a huge difference, this is probably why it is not noticeable so much in the real world. After all, when we grind the mirror, we're only looking to be in the ballpark. Did I miss something ?
nice video iv been thinking of trying to make my own mirrors for a bit now look easy for the most part. where may i ask do u get the preformed mirror blank? and where do you get you qurtz blanks also? and is the qurtz good compared to pryrex? would you be willing to answer quistions if i have hicup along the way? thank josh
I have to ask you as a man in the trade so to speak what do you make of the Hubble kerfuffle and the messed up mirror. Was it an easily made mistake or does it boggle the mind how it could happen?
How can you get a constant radius from the the point of the spherometer to the circle that is circumscribed by the spherometer "feet" when you said in the first video that the "feet" do not need to be precisely placed an equal distance from the center of the pully. You WILL get the radius of the circumscribed circle, but won't the point of the dial indicator be 1000ths, or even 100ths of an inch from that radius?
Fantastic. Flipping us off a bit, however :)
Gordon- I was curious about your calculation formula for the radius. I decided to do a derivation and had a slightly different formula. How did you derive this formula self or referenced?
Are you looking for the radius of the spherometer feet, or the radius of the mirror?
Greetings, are you still available? And do you grind and figure optics for Maksutov-Cassegrain telescopes? Im on a journey to make my own Mak-Cass astrograph so im searching for someone willing to grind the corrector and mirrors, the corrector is 200mm and the primary mirror 208mm the overall focal ratio I am seeking is around f10-12 depending on what of those two end points give better correction to cover a full frame sensor.
The location of the feet doesn't need to be precise because the Z distance doesn't change very much at the center of the circle. Do a calculation of sagitta of 8" diameter, 120" radius, sag=.0667. If 7.95" diameter instead, sag=.0658. Diff is .0009 which is probably below measuring accuracy of a cheap dial indicator. Build it and calibrate it against a mirror of known focal length... plenty accurate enough for non-professional use.
Ha! Reminds me of high school.
Excellent video. How difficult would it be to integrate an Arduino board into this project to make a digital spherometer? I and likely many others would be extremely interested in a tutorial.
That wouldn't be too hard. You would need a dial indicator with a data port. Should be available at minimal cost. I'll see if I can scare up a solution along those lines. Thanks!
GordonWaite the cheap 20-25 buck ones typically have an rs232-ish data port on them. The same protocol on those as on the cheap digital calipers, I believe. Might be worth a try.
porque 2.7734? nos meus calculos obtive 35.0667
Gordon, did you do a video on how to determine the power of the telescopes?? The F number is good to know to build a telescope, but, how is the power in magnification determined? I have a bunch of mechanical and fluid engineering formulas I use, and I see nothing for magnification vs power in my engineering text. What is a good range of magnification - 20X, 40X, 100X?? is a 175X to 200X magnification a powerful magnification? I have a camera that has a 3.5X additional lense to make the 50X become 175X, and digital magnification I can go a little more, but it starts to become a bit fuzzy so I generally stop at about 175X to 180X. That is powerful enough to see the moon distinctly move in real time. I am considering to get a 5X or even a 10X to have 250X to 500X magnification.
Magnification has to do with the focal length of the mirror, and the focal length of the eyepiece you are using. If you have a mirror with a fl of 50 inches, and an eyepiece with a focal length of 0.5 inches, divide the mirror fl by the eyepiece focal length. 50/.5=100 power. For wide angle objects like open clusters, you want low magnifications like 50x to 75x. For planets or the moon, you might want magnification like 200x or even more. Just depends on what you want to observe.
Ok. Thanks!
Then you dive the apparent field of view listed on the eyepiece by the power the eyepiece gives in your telescope to find out the true field of view as seen through that eyepiece in that particular telescope.
That is correct!
Sorry but sometimes you point with the middle finger, is it a message in it ?
I've written an online calculator for this if anybody builds one of these: DDAmanda.com/Sphero.php
Added some more calculations to it.
You can input Gordon's values to verify that it works.
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Dear Mr.Gordon i have a mitutoyo dial indicator with 0.001 mm graduations with max measurement of 1mm. what could be the ideal size of a spectrometer body for this. i have access to lathe so i can turn aluminium block to any size. say i need to measure sagitta of a 12 inch f2 sphere. thanks
Nagarajan K Hi! Actually your dial indicator would have to be put in a quite small spherometer, as the travel is so small at 1 mm. To test a mirror with a 24" focal length, your spherometer would have to have a diameter of about 75 mm. Please email a photo after to make this instrument! -Gordon
GordonWaite So nice of you sir. now i know the size from the master. may be in a week ill get it done. thank you soo much
GordonWaite I have made my spherometer as per your guidance. thank you soo much. i have sent photos of it to your mail.
Oh I meant Foucault, yea.
Very good video. The balls have 1/2" diameter?
No, they are smaller. More like 1/4" diameter.
@@GordonWaiteThanks. I have a spheres with 5mm diameter . Could I use ones?
@@GordonWaite I need use exactly 1/4" diameter sphere?
One question, it may be a silly one. How do you know it's 31.5 thou and not 68.5 thou? I'm assuming the smaller dial(smaller needle) towards the bottom tells the number of rotations the main indicator needle has made...
Brett- Because the small dial vane was considered on the flat measurement. It is used as a reference on smaller measurements that the dial travels less than one full revolution for this dial indicator. When measurements larger than one full revolution of the large vane, then the small dial vane must be included to verify an accurate reading. Just watch if the large vane travels less than one full revolution. It may be possible to travel more than one revolution on a small mirror with very short F value - but my guess is that few would be that small of a radius.
The dial indicator needle always rotates counter clockwise on the spherometer, after being calibrated. It is a bit counter-intuitive. The needle of the dial indicator travels clockwise when the plunger is pushed up. On the spherometer the plunger goes down from the reference position so the needle rotates counter clockwise.
Youd said the balls are 1/4" dia. and you subtract 1/4"from the OD, you don't end up at the center of the ball but the inside dim between the balls....or did I miss something?
AffordBindEquipment You are looking to get the diameter of the circle that includes the centers of the three balls. So you need to take off half the diameter of one ball ON EACH SIDE, so that means to get the diameter of the circle, you have to take the diameter of the outside, then subtract half the diameter of a ball on each side. Since 1/2 plus 1/2 is 1, you subtract the diameter of one ball to get the measurement of the circle you want.
+AffordBindEquipment - If there is 0.125 ball radius, minus 0.125 ball radius, then taking the outside measurements minus the 0.250 will give you the centers.... Subtracting both diameters (0.500) will give you the Inside Diameter. Or, take the OD and subtract the ID and divide by 2 and it will give you the center to center.
I am guessing all this yap is to measure that you have dished the glass evenly ?
You measure both that it is even, and also that it is the right depth.
I have most of the popular texts on ATM. Can anyone please tell me from where these formulas came so I can have a literal reference rather than trying to write this down from a dynamic video ? thanks.
Just hit the "pause" button and take your time writing things down.
@@GordonWaite Ya I did that and put it in a spreadsheet and then it got messed up and didn't work in reverse. I was hoping this came from a text so I could see more of the math behind it.
OK so these didn't come from a text ?
@@SmeeUncleJoe The math is pretty easy to derive yourself. Easiest of all is to just use one of the online calculators that people have written to calibrate a homebrew spherometer. A good example is at mwganson.freeyellow.com/spherometer/ just put the three length measurements into the three slots at top left and hit the "submit" button. Just above the big circle, you'll see the calculated value for the spherometer radius. Once you've got that, there are a thousand places to put in the radius of a spherometer and your dial indicator readings to determine the radius of your glass. If that isn't enough for you, go to Wolfram MathWorld and put in "circumcircle" there. More math than you will even need to make a spherometer!
@@GordonWaite I like your layout better. I'll just draw a nice labelled sketch in Autocad with formulas and try and remember to send it to you or post it on Cloudy Nights. Cheers and thanks again for all these great videos.
I find it funny that someone who grinds parabolic mirrors talks about buying a surface plate, since a surface plate is made by lapping three plates flat against one another.
I have made many a flat by grinding A-B-C! And I've always wanted to learn how to flatten a surface plate by the scraping process. Yet another thing on my bucket list.
@@GordonWaite look up Vintage machinery.org here on youtube. He also hosts classes in scraping if you want it more hands on.
Why go through so much calculation? After finding the lengths of the three sides, If the triangle created by the three balls is approximately an equilateral triangle, you can just divide the mean length by sqrt(3) and arrive at the same answer. In your case, it comes out to r=2.77339
actually r comes out to 2.7734O ,rounding off properly,the same that the author got; thanks for your alternate method.
The term "thou" is commonly misbelieved to be shorthand for 0.001" (THOUsandth of an inch. It is actually a TENTH of a thousandth of an inch, 0.00001".)
Important distinction in the world of machinists and critical in the world of optics.
Doc - 0.00001 as you show it is 1/100,000. 1/10,000 is written as 0.0001. And with 0.001 dials, it is not too difficult to calculate the space between the lines at 0.0002 increments or even 0.0001 after a little practice.
thou is short for a thousandth of an inch... and for ten thousandth you say tenth..
Too Good
You're doing astronomy but you're not in metric?
The joy of astronomy. Mirror diameters are in inches. Eyepiece focal lengths are in mm. Radius of a mirror normally is inches. Thickness of mirror glass is in mm. SiC abrasive is sold in pounds. AlOx abrasive in kg.