Would this work? https://www.edmundoptics.eu/p/20mm-square-uncoated-b270-window/18799/

No it wouldn't work.. you need edges polished, not the top and the bottom.
I am not shipping out prism at the moment as they r not balanced yet (working on this). I am also working on a FPGA toolchain, will post an update on my progress here soon.

Can you recommend a specific polygon motor module on alibaba? I don't know if there are any differences and I'd like to order one. THanks!

Yes, you should buy exactly this motor https://nl.aliexpress.com/item/32824649951.html . It uses the NBC3111 chip. I had problems with other motors. Make sure you buy at least 2, although they are quite hard to break.

Dude, this is some pretty awesome work. I'd love to help refine some of the manufacturing and board designs, let me know how I can best help

Thanks! There are two other people who have shown interest. I need at least 10 people to do a run as I have to buy the prisms in bulk. Turn around time would be significant. Producing the prism takes at least a month.
I am fixing the low hanging fruits at the moment. It is hard to help with these as you don't have a laser head. I am building a new one but there is still only one in the world :-).
Things you could look in to;

- a better alignment system for the laser; this uses four screws and is over dimensioned --> see my free cad design files

- a better alignment system for the cylinder lenses; the screw system is not really comfortable --> see my freecad design files

-  how do i put my state machine on an fpga; I have been looking into https://github.com/m-labs/misoc as a replacer for the beaglebone.
This task seems rather complicated but I guess this knowledge could be really help full. The statemachine now runs on pru of the beaglebone and is limited at around 2 MHz.

- how do i balance the prism; i have done some preliminary experiments but still works needs to be done. You could also try to figure this out with a regular polygon motor. Add an imbalance and try to analyze this.

- the slicer or interpolater can only be run on a computer, as it overflows the ram of the beaglebone https://github.com/hstarmans/ldgraphy/blob/master/interpolator/interpolator.py . Remove this problem, optimize the code.

In the mean time, I am cleaning up the code, building a second head and still have to do more experiments.
I am also waiting for news on the hackaday prize. That's also why I have been quiet on the blog.

I'm wondering if there isn't a BLDC motor that could be substituted for the polygon motor, hopefully something that is more available. And then I'd need an encoder. I'll take a look at this, although I suspect going greater than 20k rpm requries air bearings and a custom design.

The rectangular prism does seem to be a challenge. I'll let you worry about that. Out of curiosity, do you know how much it'd cost for a custom order?

An FPGA should be able to handle the state machine. I'm working on the FPGA that's in the Hackaday Superconference badge, and it's got an open toolchain. It might be overkill though. The ICE40 may be better(and cheaper). I might be in the minority in that I'm not sure this is a huge priority, as your electronics are pretty cheap. It's probably a pretty significant time sync to rewrite the assembly for the PRUs into a state machine. I'd probably focus on a command and control system to interact with GCODE or something else.

 I could jump into the MCAD, but I only know Solidworks. I suspect someone else might be better suited for that.
At work, we have specifications for balancing motors for EVs. The most relevant standard is ISO1940. Let me know if that's useful for you. Usually a balancing machine is used to detect vibrations while the part is rotated. They're pretty rare and fairly expensive though. They do make some simple ones for balancing quadcopter props you could look into. Usually you have to add or remove material in a specific spot to make it work.

I already have some of the parts you've used. Perhaps it won't be as hard to duplicate some version of this as I expect.(expect for that lens).

-  i wouldn't substitute the motors; they have been used in this application for years by a large industry. Rotating polygon mirrors are produced in the tens of thousands. Motors can handle up to 21000 RPM.  This is more than what is needed at the moment, 2400 RPM, as the beaglebone can't go faster.
- custom order is around 500-600$ and MOQ is 10. for the prisms
- Henner zeller wrote a GCODE parser for the beaglebone called beagleg; my idea is that this used and you simply flip the machine between gcode mode and laser writing mode
- never heard of this standard good tip
- all parts are easy to obtain including lenses, motor etc; the only challenge is the prism and time. You will need time :-)

well you can count me in, i'm interested with this project

Congratulations on winning Hackaday Prize 2019!  (at least in my opinion)

Robert, thank you for supporting me! Winning the prize would be amazing.  My current target is to get other people to try out the technology, I am really trying to make it more accessible. I hope I can show an improved prototype of the scan head soon.

What material is the prism made from? How is it manufactured?
Can i make it in my "maker lab"?

Prism has the following properties; 2 mm thick, 30x30 mm square,  faces 60/40 < 5 arc min, chamfers 0.10 – 0.30mm, edges Polished 60/40, top bottom polished 60/40.   You will have to discuss details with manufacturers in China over Alibaba. I made the first in a maker styled lab, a description of the process is in this log https://hackaday.io/project/21933-open-hardware-fast-high-resolution-laser/log/167433-how-to-be-transparent

I'm also interested in the possibility of using a motor from a hard disk drive instead of a breaking down a polygon motor.  HDD motors are cheap to buy and (as I understand it,) contain an encoder and have screw holes which makes affixing things easier.

HDD seem too slow.  They typically spin at 5400 or 7200 RPM.  At the moment, I can go up to 24000 RPM with polygon motor. For some applications, I would like 50000 RPM or 70.000 RPM, like the roadrunner sold by precision laser scanner. Also the motors are not too expensive, they are like 20 euros. I understand 20 euro's can still be a lot but if you look at total costs; you can better pay attention to other components.

Oh, I had no idea you were planning on high speed.  Where can you get the motors in the 20 euros range?

You can find polygon motors at alibaba (https://www.alibaba.com/showroom/polygon-motor-ricoh.html) .  The system is a proof of concept; for desktop PCB prototyping 2400 RPM is fine. If you plan to compete with Kleo https://www.youtube.com/watch?v=7R464iHaTQU . You will need at least 50K RPM.  An option would be to encase the prism and remove the air. This will reduce the drag. You could also fill the encasing with Helium as it has low drag and a high thermal conductivity.  Like the roadrunner the encasing windows would be tilted out of plane to minimize back reflections, see https://precisionlaserscanning.com/2016/03/road-runner-70000-rpm-polygon-scanner-solves-the-noise-problem/

My suggestion for this project is to isolate the scanner from the 3 axis robot part so that the scanner could be made into a tool that can be changed out.  I would also ditch using BB's PRU and instead use a dedicated chip (and maybe a RAM buffer) and connect it via CAN bus.

I intend to isolate the scanner, and design it for specific machines. I like the idea of having a dedicated chip. In the past I used a FPGA (Xula-LX25) with RAM as  bufffer. I can imagine there are even better options. The problem is that developing a dedicated board costs time, money and a lot of experience. Zeller made a very accessible code for the Beaglebone, so I went with that. You are looking at a proof of concept. It's a technology demonstrator. Anyway if you have recommendations; or some example code; feel free to share. 

Considering this is a project where accurate timing is vital, I think an XMOS processor (e.g. XS1-L4A) would be a good fit.  Each 100MIPS processing unit is 100% deterministic with fast GPIOs.  I don't know the rate of data throughput you need but it may be easier to just cache to workload on a local FLASH chip than stream it.

XS1-L4A is nice... but I rather like something with lot of support and examples... probably first gonna optimize the current code and balance my prism.

XMOS stuff actually does have lot of support (https://www.xcore.com), examples (https://github.com/xcore/) and even an IDE but I somehow missed the part where you wrote that didn't want to build a custom board.  Sorry about that.  XMOS chips make it easy to glue things together since it's 99% software so it doesn't take too much skill to make a board with them.  Consider enlisting help to make a board as there is a good chance it will alleviate timing related issues.  Good luck! :)

This is a good idea, but honestly I think the best thing is to focus on getting the precision as perfect as possible. There's no consumer grade PCB maker device that can give traces/spaces resolution down to 0.01mm. It's crazy we are still using tonner transfer and UV exposure. I'm planning to build a CNC gantry made from granite, magnetic actuators and air bearings to get the most accurate, friction free, repeatable long term PCB manufacturing with >0.7 traces and spaces. But yes, would be nice down the road to have the scanner head removed for another tool... but for now precision is priority. Precision & Resolution is the reason why this project brings my interest and everyone here.

You've certainly done your homework very thoroughly, and I see that in your application with very small optical cone angles (large focal ratio), the optical aberrations and field curvature appear to be tolerable.  That's great.

One question: You say that previous scan techniques require a large (and therefore expensive, you argue) f-theta lens, which must have one dimension at least as wide as the scan line.  In your approach, your polygons must be larger than the scan line length, but in *two* dimensions, making the volume of your optical element much larger.  Since either shape would use identical materials and fabrication processes in volume production (i.e. injection molding), one would naively expect the smaller element (the f-theta lens) to be cheaper.   How is this line of reasoning flawed?

A telecentric f-theta lens requires one dimension at least as wide as the scan line. A non-telecentric f-theta lens does not require that.  In my approach, the polygon must have one dimension longer than the scan line. The second dimension is 2 mm. An f-theta lens consists out of multiple lens elements, e.g. a 3 element f-theta lens. These elements have curved surfaces. The prism consists out of a single element with a flat surface. You can't make the f-theta lens out of plastic, so you would have to injection mold quartz. I am unfamiliar with the prizes for that. Besides most likely a higher price and the fact you have to use multiple elements, you also need to worry about patents. Envisiontec patented the usage of reflective polygons; US 9079355 B2 . Finally, you need a thick reflective polygon as thick polygons can deflect collimated bundles with a large diameter and these can be focused to smaller spots.  A transparent prism uses a focused bundle and therefore typically can be thinner, which keeps the price of the bearing lower.

You have clearly thought about this a great deal, and have your arguments worked out well.

I wasn't considering that you might be requiring quartz.  I would have guessed even BK7 would be overkill for this application.

I mention injection molding because I look around my offices and see several laser printers.  Each of them contain a laser scanning unit with a rotating (reflective) polygon and a f-theta lens arrangement, with the final element being very large (>200 mm long).  All the optical elements of the ones I have inspected appear to be injection-molded PMMA or similar plastic.  The entire laser scanning unit must cost considerably less than $50, given the prices of the printers (all less than $200, two less than $70).  Granted, these are produced in huge volumes, but they serve as existence proof that these scanning systems with large optical elements are not intrinsically costly.

PMMA absorbs light at 405 nm. The laser printers at your office use 800 nm and low power lasers. I use 405 nm and high power lasers. So yes; there is concrete proof that PMMA injection molded systems are not intrinsically costly. There is no proof that quartz systems are not intrinsically costly.  It's unclear what the prices of these systems would be .

A good variation on the usual way.  I build a few instruments based on this and similar methods between 1985-1989.  A couple of important notes:  

1. The scanned field is NOT flat: The optical distance to the target plane *increases* as the polygon rotates away from normal.  Not only is it geometrically longer, some of the increased  path length is in the high-index polygon too, increasing the path length even more.  The result is a curved focal or scan plane.  One of my instruments actually depended on this: a rotating polygon was used to tune the optical path length inside an optical resonator cavity, to adjust a tunable laser that was phase-locked to that cavity. 

2. You get some significant spherical aberration when you focus through a thick window like that, for similar reasons: the light rays at the periphery of the optical cone take a longer path to the target plane than rays going through the middle of the cone, with the result that they focus at a different depth.  For a laser at f/50 (or whatever it is), this probably isn't significant, but in an imaging system at f/2, it seriously degrades focus. 

Paul, thank you for your reply!
A transparent polygon scanner with a single laser bundle was first patented by Lindberg in 1962.  The scan field is not flat and you can get some significant optical aberrations. A full numerical model is available here https://github.com/hexastorm/opticaldesign . A description of this model is available in the technical presentation. The result shows that in practice the scan field is flat and the optical aberrations are not significant for the current spot size and line length.

Well this is the first comment! If Hackers are interested in transparent polygon scanning let me know :P ..