Indium Blog

Calculating Oddly-Shaped Aperture Area Ratios

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  • Phil Zarrow: Ron, we've moved to where area ratio is what we're typically using for our stencil apertures, as opposed to aspect ratio, but we've come up with some very unusually shaped apertures these days.
    Dr. Ronald C. Lasky: Yeah, a reader wrote in and asked me to calculate the area ratio for an elongated D-shaped aperture.
    Phil Zarrow: And you did? And how did you do it?
    Dr. Ronald C. Lasky: Yeah, I did that. Well, you know, Phil, the area ratio is the area of the opening over the area of the sidewalls, so I went back to my 10th-grade geometry. It's a little complex, but I was able to develop a formula, which itself is a little complex.
    Phil Zarrow: Let me ask you this, with regard to what we've been using, the area ratio as being greater than 0.66, we've used that for circular and square apertures. Did that work out with the D?
    Dr. Ronald C. Lasky: Really, they've got to collect some data, and that's what I suggested to the person that wrote in. But even though the 0.66, as you're aware, that's not a law, that's a practice.
    Phil Zarrow: Right, right.
    Dr. Ronald C. Lasky: It really surprises me in that I had just recently analyzed a lot of data, hundreds of thousands of data points, and boy, it's surprising how the transfer efficiency will be going along just like this, say around close to 1 and then drops right off at about 0.66, so I'm expecting for this elongated D aperture that it will also be 0.66.
    Phil Zarrow: Very good, and you're going to be doing work with other shapes too, right?
    Dr. Ronald C. Lasky: Yeah. As a matter of fact, I'd be excited if any viewers out there have an interesting aperture shape, send me an email at, and I'd be happy to calculate the area ratio for them.
    Phil Zarrow: Very good, and this work is of course on your blog. Where can we find that?
    Dr. Ronald C. Lasky: My blog is at
    Phil Zarrow: Ron, thank you for this great work and ongoing work too. It's much appreciated.
    Dr. Ronald C. Lasky: Thank you.