Opposing Archimedean spirals.

[Anonymous]

Dear Sirs and Madams,

Before I start I should point out that I have extremely little skill when it comes to AutoCAD so I apologise if this is actually incredibly simple.

I am trying to use AutoCAD 2015 (for Mac) to generate two intertwined Archimedean spirals on a 2D plane, I have attached an image illustrating what I wish to achieve. The design will then be imported to a Direct Laser Writer (DLW) to create a photomask for optical lithography to microfabricate biosensors.

An example design: I wish for the line thickness of each of the two spirals to be 5 um, with a separation of 5 um between the intertwined spirals. The total width of the two spirals should be about 2 mm.

Using the 'HELIX' command to generate the spiral, and then using the 'PEDIT' command to attribute the line thickness, when I create the second spiral (rotated and then centre trimmed using 'TRIM' command) I find that the separation between the two intertwined spirals seem to change, almost randomly each time.

Is anyone able to assist?

Kindest regards,

Jules Hammond

[beyoungjr]

Hi,  Your sample graphic may not be a true representation of an Archmedian Spiral??

I created 3 versions of spiral forms in the attached DWG file.  I prefer creating the true boundaries vs. the Polyline shapes with width.  You can then fill the boundary with a gradient or solid hatch.

I placed a flat AutoCAD spiral inside each form to illustrate the growth differences.

1. The left-most example is simply arcs (Start-End-Angle).  I created several of these arcs, then joined them with rounds to create a Polyline boundary of zero width.  This is the cleanest spiral in my opinion.
2. The center example was created by offsetting the AutoCAD spiral and closing the form with arcs as Start-End-Angle.  Notice how it's cross-sectional distance is inconsistent at various positions around the axis.
3. The right-most example is two AutoCAD spirals created independently with a 5 micron difference in their start radius and in their end radius.  This example appears to maintain consitency but is a bit more difficult to terminate on the same axis with similar terminations.

I left .015 micron between the turns for your spacing.  For the repeat spiral I simply select the form and Rotate 180 with the Copy option.

I stayed small (few turns) with thses examples but they are produced at the size/scale you detailed.

Let me know if any of these capture your intent.

Cheers,

Blaine 

[Kent1Cooper · Accepted solution]

I got something more accurate, but when I tried to Hatch in a spiral, it blew my computer's mind, probably because at the dimensions you describe, it's a lot more turns than in your image.  And now it won't even Recover it, and I don't want to go through the whole process again.  But this is what I did:

There's a routine of mine called Spirals.lsp, available here.  In it is a command called SPEQ for a SPiral with EQually-spaced turns [an Archimedean one].  In a drawing with units set to Millimeters, I used SPEQ to make a spiral like this:

Center: [pick wherever -- I used 0,0, but it doesn't matter]

Starting/Inside radius: 0.005mm [= your 5um -- could be different, but I thought that gave a good result at the center]

Ending/Outside radius: 1mm [for your overall size of about 2mm]

Interval between turns:  0.02mm [4x eventual width to account for the second spiral and spaces between them]

Segments per turn:  48 [arbitrary but high, for good accuracy]

Starting angle from center:  [whatever you prefer -- I used 0, but it looks like about 60 degrees would give a result like your image]

Direction:  [whichever you prefer -- I used CCW as in your image]

Then:

I used PEDIT Fit on it to smooth it even more, and because without that, the Offsetting somehow result in a single Polyline in the outward direction.

I OFFSET it to both sides by .0025 for the half-width of a spiral.

I used the CE command from another routine of mine, called CapEnd.lsp, available here, with its Arc option, to round over the ends, which also joined the inner and outer ones together into one outline for the whole spiral.

I ARRAYed that outline in a Polar Array of 2 copies about the center [SPEQ puts a Point entity there that you can Osnap to, if you picked some arbitrary point].

That's where I tried to Hatch it and lost it, but in any case....  You could HATCH it Solid or not as required, and ARRAY either the Hatch or the outline or both.

It's pretty darned accurate about the spacings [I checked before trying to Hatch one], though because it's not a "true" spiral but a Polyline approximation [albeit with high accuracy], it's not absolutely precise.  When I checked distances perpendicular between edges, most came out at 0.0050, but a few at 0.0049 or 0.0051 -- nothing farther off than that.  If you used an even higher number of segments per turn to make the core spiral, it would be closer still, though also more likely to blow your computer's mind.

[Anonymous]

Thank you both so much for your prompt solutions.

@ Blaine

Thank you for posting these solutions Blaine. I should apologise for the image I uploaded as it was simply taken from Google to ensure anyone reading my post would have a rough idea of what I was trying to do (my explanations can be somewhat erratic). In fairness, any of your solutions would probably be acceptable for me, but I worry my lack of skill/experience would mean it would take me too long to replicate or adjust the design in future.

@ Kent 

Kent, thank you sincerely for your solution. It took me a bit of fiddling to import the .LSP file but I eventually got it to work. In the long-term I believe your solution will offer me the best accuracy with minimal effort (as I mentioned in my initial post, my AutoCAD skills are almost non-existent!).

Great script- I assume you had to code it yourself.  

I haven't tried to HATCH yet as I'm on my laptop, but I'm hopeful that my Mac Pro (2015) should cope - given that I purchased it solely for COMSOL simulation. I shouldn't require higher resolution than the +/- 100 nm you mention for 48 segments as the beam of the direct laser writer (used to pattern the photoresist) around ~635 nm, meaning +/- 100 nm will be more than accurate enough. Furthermore I may be able to avoid using your CE script as a smooth end is not entirely necessary for my application, but have downloaded and installed anyway just in case.

Again, thank you both for solving my problem and enjoy the rest of your weekends.

Kindest regards,

Jules

[Anonymous]

@ Kent

I am hoping you will see this. After successfully drawing the spirals using your SPEQ function (again, thank you), I am now having issues when importing into CleWin 4 software.

I save my AutoCAD drawing in .dxf format and then open it using CleWin 4 - this is so that I can then save in the correct formats for our direct laser writer (DLW) in the nanofabrication facility. (.gds or .cif).

My problem is that when I import the .dxf into CleWin, the spiral is cropped (~0.35 mm diameter) and I have some unusual artifacts. I assume this is associated with the number of elements in the spiral (0.1 mm diameter spiral is imported correctly). Can you see anything obvious that I am doing wrong?

The process in AutoCAD that I am using is as follows:

SPEQ 1 (0 degrees rotation, 50 arc segments per turn, 2 mm diameter)
SPEQ 2 (180 degrees rotation, 50 arc segments per turn,  2 mm diameter)
PEDIT {fit} (I assume this smooths the line)
PEDIT {width} (5 um)
SAVE (.dxf 2013)

I also now realise that I can use CleWin 4 to attribute a width to the line, I tested this with a single spiral and the result after import is shown in attachment 'After_Import_Single'. The width of the line is correct, the spiral is still cropped (~1.3 mm diameter) and I still have a strange diaganol line.

[Kent1Cooper]

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@Anonymous wrote:

.... After successfully drawing the spirals using your SPEQ function (again, thank you), I am now having issues when importing into CleWin 4 software.

I save my AutoCAD drawing in .dxf format and then open it using CleWin 4 ....

My problem is that when I import the .dxf into CleWin, the spiral is cropped (~0.35 mm diameter) and I have some unusual artifacts. ....

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Very interesting result....  If they're being drawn correctly in AutoCAD, then it must be something in the export/import process through other file formats and into the other program that's causing the problem.  I know nothing about those other file types or programs, and have almost never even worked with .DXF files, so I'm afraid I can't help you there -- I hope someone else has some ideas.

[By all means it makes a lot of sense for you to just use SPEQ and give the result width, instead of offsetting it both ways and capping the ends with arcs as I did, if you don't need the ends to be rounded.  It uses a lot less memory, and avoids the blow-your-mind aspect of Hatching in such a thing.  And yes, the PEDIT Fit smooths the Polyline further, which helped increase the precision in my Offset-both-ways approach, and without it, Offsetting came out in separate pieces on the outboard side.  You may not need it if you use a single center-path Polyline with width, and a high enough number of segments per turn for the level of accuracy you need.  But since the spiral commands make their arc segments by defining the second point within each arc, rather than just the next vertex -- again for higher accuracy especially near the inside end -- the ends of the arc segments are not always perfectly tangent.  That means that with width applied, there can be tiny little wedges of gap on the inside or outside at the vertices.  They are only visible if you Zoom way in, and you would need to determine whether they would interfere with your process later on.  Those are eliminated by the PEDIT Fit operation, since that results in truly tangent transitions everywhere, even if you don't need that for the precision of the spacing between spirals.]