Autocollimators 2: Formula for Resolution

In this episode of the Machine Tech Video Blog, I go through the mathematical formula used to determine the resolution of an autocollimator - an optical instrument capable of measuring tiny angles of less than an arc-second. I explain where the terms in the formula come from by discussing two important phenomena in optics: the law of reflection and lens focal length. To illustrate these points, I use a fun little optics discovery kit and I go on a field trip to the Port of Oakland! Finally, I use the formula to calculate the resolution of an actual autocollimator. To purchase the kit for your own use, do an eBay search for "Optical Concave Convex Lens Prism Set Physical Optical Kit Laboratory Equipment".
For further reading on this topic, check out "Metrology with Autocollimators" by K. J. Hume. It's a fantastic book, albeit hard to find.
Juicy jams by Sun Hop Fat - "Yègellé Tezeta": www.sunhopfat.com/
For daily posts on related content, check us out on Instagram @laneymachinetech
For more about Laney College, check out the website: laney.edu/machine_technology/​
AND BE SURE TO SMASH THAT "LIKE" BUTTON!

[@madnessguy010101]

This is channel is truly a gem for those interesting in machinist work

[@LaneyMachineTech]

So glad you think so!

[@ebrewste]

You are really hitting it out of the park teaching deeper than noob topics and still making them very accessible.

[@LaneyMachineTech]

Thanks! I’m so glad there are people out there who are interested in this sort of thing 😅

[@mykedindeal]

Oh boy.That was realy interesting.Looking forward for the next episode👍

[@LaneyMachineTech]

So glad you thought so!

[@vanguardcycle]

Please keep this kind of content coming!

[@LaneyMachineTech]

I’ll do my best 💪

[@HP_rep_mek]

Wov, clear and concise! I’m still following you and that’s all about your ability to educate in an easy to understand way👍 Thanks Adam🙏

[@LaneyMachineTech]

Thank you!

[@mikemichelizzi2023]

The way you present this definitely contributes to a more intuitive understanding of it. Amazing job!

[@LaneyMachineTech]

Thanks! 🙏

[@mazo691]

That was a super explanation, really no gaps. Thanks!

[@LaneyMachineTech]

Thanks!

[@WobblycogsUk]

Wow, that's honestly the best video I've watched in ages. There were two or three real light bulb moments for me, for example, I've wondered why telescopes are so long and now I know! Can't wait for the next video.

[@LaneyMachineTech]

So glad you enjoyed it! I’m editing the next video right now. It’s a DOOZY! Lots of detailed optical design info...

[@kevinrblodgett]

Cool! Hope you continue your other series as well

[@LaneyMachineTech]

You bet!

[@joshmyer9]

That… was a lot simpler than I was expecting (simple for a soft handed enginerd, at least). I'm really looking forward to the video on how the mirror works, but I might sit down and poke at it in python to see if I can figure it out. Also: the presentation was fantastic, and reminds me why I love community colleges and trade education in general. No pretentiousness, just getting down and dirty with the implementation of things. These demos are super clear, very approachable, and still tie back to the theory for anyone who's worrying about that kind of thing. This was a huge difference between my HS trades and CC science classes versus the few I took at University. The emphasis is flipped: lots of inscrutable theory, very little time spent building intuition. If you want a design that will never work despite having all the right parts, you want someone with lots of theory and no intuition.

[@LaneyMachineTech]

Thanks! I’m glad you’re enjoying the presentation style! As for the mirror math, it’s just simple trigonometry: use the sine of the angle you measure in the autocollimator, the length of the mirror base is the hypotenuse and then solve for the opposite side of a right triangle.

[@JontyCtheKing]

Thanks - what an excellent description of autocollimators. I didn't realise how simple they are; the cleverness of them is in the math. It would be really amazing if you could actually make one.

[@LaneyMachineTech]

I was also really attracted to their elegant simplicity 👍

[@ShopperPlug]

Excellent explanation. You made a video which people can actually learn from.

[@phillipmcguffie1183]

I am the Technical Manager of a metrology lab and will more than likely use your videos as an intro learning tool for training over surface plate calibration. Understanding these key fundamentals is incredibly important to understanding what you are calibrating. Well done on the video's. Extremely insightful. However, it leads my mind into wonder on what else you may know or cover. I am working on something pretty interesting. If you have a moment of time, would you allow me to bounce a few ideas off you?

[@hairyfro]

Great to see this is turning into a series! It would be great to see an example of practical use for measuring flatness of a surface plate or straightness of ways. There are a number of other videos out there that have done it but then more-or-less glossed over the technical details. It would also be interesting to explain the requirements of the target mirror -- why does it need to be so flat? Thanks again for the great in-depth discussion.

[@LaneyMachineTech]

I will definitely do a video on using an autocollimator to measure straightness/flatness. Maybe it will just be a simplified example of inspecting a straightedge or something like that. I think the math required to tie all the readings together is very interesting. I will also say that Robrenz and Abom79 have made some really good videos specifically about testing and reconditioning surface plates recently.

[@ericbeyer8229]

This is a great series Adam! Keep it up!

[@LaneyMachineTech]

Thank you! I'll do my best to keep up the pace.

[@4n2earth22]

Most excellent information conveyance. Very well done, understandable, and thorough overview with enough technical and specific information to flesh out the bones. Thank you for your skill and willingness to give.

[@LaneyMachineTech]

Thank you for your kind words!

[@arpeggi2999]

Enjoy your videos, don't stop!

[@LaneyMachineTech]

Thank you!

[@arlingtonhynes]

I’m enjoying the hell out of these videos, and I think I’ll enjoy them even more when I find out what auto-collimators are actually good for.

[@LaneyMachineTech]

🤣 Hopefully it will all come together in the end. The original plan was to use the autocollimator prototype to evaluate and align the ultraprecision lathe I want to build.

[@arlingtonhynes]

@@LaneyMachineTech Looking forward to the rest!

[@ronrinock6943]

Great series! I remember there was a multi part article in Modern Engineers Workshop magazine years ago, somewhere around issue 72ish, about building a autocollimator. I was collecting parts to build one but a couple Hilger & Watts units just like the one in your video thumbnail popped up on Craigslist for cheap so that project went to the back burner. Still would be a fun project.

[@LaneyMachineTech]

Yep! “An Autocollimator from the Scrap Box” in Issues 73, 75 and 76. It’s a great series of articles. I like his design, although I’m going a different way with mine.

[@DK-vx1zc]

excellent explanation.. very well done!!!!! thanks for putting this all together.. looking forward to the next video :)

[@LaneyMachineTech]

Thank you! 🙏

[@Mr30friends]

Do you plan on continuing the air bearing project?

[@dizzolve]

good question

[@LaneyMachineTech]

Yep! I just started editing that series again. It’s gonna take a minute though. This series and that series are all part of the same ultraprecision lathe project.

[@captcarlos]

Fantastic Adam. Looking forward to the designs, hoping to make one!

[@LaneyMachineTech]

Awesome! 🙌

[@EatRawGarlic]

I think I'm going to build one using my 3D printer. They never told me about such a device in university, but in hindsight, I know projects that could've benefitted from having one.

[@LaneyMachineTech]

That’s a great idea! I’d love to see it!

[@JekaMazurovskiy]

Thank you. Your explenations are priceless!

[@LaneyMachineTech]

Thanks! I’m having a lot of fun 😁

[@xero110]

Now I understand john Carmack's use of inverse square law 'Fast InvSqrt()' much better. Thank you very much, a great video.

[@LaneyMachineTech]

Glad to hear it!

[@reiniertl]

I learned a lot. Thanks for the video!

[@LaneyMachineTech]

You bet!

[@irfanashraf1238]

Very informative and easy to understand how auto collimating works. I notice you have changed your machine tool hinges with more stable ones, wise decision .

[@lakramjaggai6084]

I subscribed to this channel when I was in university wow its been a while

[@LaneyMachineTech]

I know...

[@dizzolve]

Really enjoyed this one

[@LaneyMachineTech]

Great to hear!

[@heinrichhemker8123]

Thank you! Simply superb!

[@LaneyMachineTech]

Thank you!

[@zZDeGaNsk8eRZz]

Please go on , very usefull information

[@In3xorable]

Very cool. Optics are a really cool subject.

[@LaneyMachineTech]

I totally agree!

[@danielepatane3841]

So in other words Is it correct to say that the more the focal length the better the resolution in arcsec of the autocollimator?

[@car9167]

How do they manage to create autocollimator with 1 sec precision or even 1/10 of a second in a small package? Is there a way to compact it by enlarging somehow optically the focal distance so you don't end up with meters long autocollimators?

[@intjonmiller]

I work in sales and play in my machine shop. I love having physics toys on my desk for customers to play with when they have to wait, and to identify the geeky/nerdy type customers (my people!) who can be the most difficult customers for sales people who don't know how to relate to or talk to them. The triple laser and lens kit would be fantastic in my collection, but I'm having trouble finding the laser. I know you said ebay but can you give me any more tips? Having trouble on any site.

[@BigBoss-rh7zq]

Instructive, thanks.

[@LaneyMachineTech]

👍👍👍

[@mitchwright1558]

Great series! Is there a scan or pdf of the catalog?

[@LaneyMachineTech]

Not that I know of! Some of the data sheets are still available on the Davidson Optronics website, but not all of them. I should make a copy of the catalog. It’s really REALLY cool.

[@mitchwright1558]

@@LaneyMachineTech yes, please

[@timzowada2867]

Wonderful! 😊

[@LaneyMachineTech]

🙏

[@lachlanbird9688]

Very interesting .

[@LaneyMachineTech]

Glad you thought so!

[@wojtekszelag123]

Great video! I'd love to see if it's possible to DIY an autocollimator instead of buying one :D

[@LaneyMachineTech]

I’ll try my hardest!

[@Steve_Just_Steve]

Want a Video on your DIY scraper!

[@LaneyMachineTech]

I have another five of them to make, so I should do a video. I’ll put it on the list 😂 And if you haven’t already, check out the detailed build notes on Instagram.

[@tessblog3384]

Wow what a skills thanks for the support please don't skip my ads🌹🌹🌹

[@parkermusselman9824]

👏

[@LaneyMachineTech]

🙏

[@treverkirk8110]

nice

[@LaneyMachineTech]

🙏

[@thiagosanchez4453]

🖖

[@LaneyMachineTech]

💪

[@gavendb]

but, what to light rays SMELL like??

[@LaneyMachineTech]

These smell like lemon and bubble gum 🤣

[@soranuareane]

Relating angle to distance directly, without using a trigonometric function? Small-angle approximation strikes again!

[@LaneyMachineTech]

This comment launched me into an internet research spiral. Thank you 😂👍

[@soranuareane]

@@LaneyMachineTech This pleases me tremendously. The small-angle approximation is a wonderful tool to machinists and engineers as it trivializes otherwise terrible calculations. However, it's only an approximation and is only usable for, as its name suggests, small angles--anything less than a few degrees (depending on application). That said, it royally pisses off the mathematicians when exact answers are preferable.

[@airman2468]

My physics senses were tingling. Just had to make sure someone mentioned this.

[@Steve_Just_Steve]

Like

[@LaneyMachineTech]

Nice!

[@oddsman01]

Who wants to adapt an autocollimator to a round column mill’s z-axis adjustment?

[@stevewright454]

Incidence equals reflection

[@LaneyMachineTech]

You’re darn right it does, Steve! 🤣

[@stevewright454]

Nice job Adam 👍🏼