I’m not trying to be a cheapskate here, but a can of compressed air costs like five bucks, and I got air at home. Like, a whole lot of it, just floating around, not paying rent. Can’t I just shove that into a can? I think you see where this bit is going.

Compressed Aircan for PC

So if you plot the spot radius as a function of $\frac{f^2}{s-f}$ for different values of $s$ you should get a straight line whose slope is the tangent of the numerical aperture.

I am constantly surprised by the number of people who do not have an electric duster, but everyone who has converted sings their praises. Jess Weatherbed doesn’t have the XPower but has a CompuCleaner and noticed a similar improvement in basic air quality. Another person online recommended the Metrovac DataVac ESD (a duster meant specifically for data centers) since at least one of Metrovac’s models also functions as a vacuum cleaner. I have not had a chance to do extensive side-by-side testing with these models, but I would bet those things blow pretty hard, too.

EDIT Since your lens is connected to a CMOS sensor, the above approach will not work for you. I recommend instead that you put a point source in front of the lens at a controlled (variable) distance, and measure once again the spot size.

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Now the numerical aperture is usually the $\sin$ of the angle - so if you care about the difference (which is important as NA gets larger) you need to do a bit of math:

A simple setup would focus a point source of light onto a ground surface (a focusing screen) that is mounted on an optical rail (so you can move it along the optical axis). Once you have found the focal point, you move the surface a known distance away, and measure the size of the focal spot (I would recommend using an eyepiece graticule to make the measurement straightforward). Repeat this for a few different distances, and determine the slope of the straight line through the plot of spot radius vs distance to focal point. This slope represents the tangent of the half-angle of the iris subtended at the focal point.

This does require you to know the focal length of the lens, and the lens to be focused on infinity. Measuring the distance to the optical center of the lens can be tricky - a zoom lens is a composite lens, and they don't always have an obvious "center". You can use the distance to the focal plane instead - that should be $s+f$ .

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I am not absolutely sure that these formulas work for compound lenses... perhaps somebody can either confirm this or point out the correction that is needed.

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Now we can use the formula for the distance to the focal point. If the source is a distance $s$ from the lens, and the focal length is $f$, then we expect the point to come into focus at a distance $d$ where

I was ambiently aware of the XPower a while ago because I looked up various methods for keyboard cleaning (including this weird goo). I had seen it on the shelf at Micro Center and, like many things in that wonderful store, I thought, “Wow, that sure does sound really useful. I should buy that sometime.” Micro Center stocks two similarly priced models — this one and an almost identical-looking model, both of which are also available on Amazon — but I went with the latter because it had the word “cyber” on the box and, thus, was better. It turned out to be so good that I immediately sold several friends on it, including my friend who works at a cafe and needs to clean up coffee grounds all the damn time. They also make it in a bunch of fun colors, and the same company makes heavier-duty models specifically for pet grooming that are available through XPower and Amazon.

The iris is marked with some repeatable settings labelled 1-5. I can't find any documentation to tell me what the actual size of the iris is at these settings but I need to work out the NA at each one. Is there a simple way of doing this?

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I have a lens system made up of some components of the Leica Z16 APO zoom system. This includes a built-in iris diaphragm to adjust the Numerical Aperture (NA) and therefore the depth-of-field (DOF).

Assuming you know the focal length, and that you focused the lens on infinity (so you set $d' = f$), then your imaging plane would be away from the in-focus plane by a distance $d - f$. In the small angle approximation, the point would become a circle with a radius $r = NA\cdot (d-f)$.

If my tone has been a little cheeky in this post, it’s because it’s hard to overstate just how much I use this guy. I’m constantly reaching for it while doing projects. In the span of writing this post, I blasted decades of gunk out of an old eBay VCR using my XPower. I feel like a corny TV pitchman right now, but it really is that useful.

As the name implies, it is also a duster, which does not sound as important until you realize how much dust is inside the average human home. It’s a lot, and it loves hiding in places. I have a significant dust allergy, so I am anal when it comes to air quality. For a fun time, put an N95 mask on, turn on your air purifier of choice (I have a Coway Mighty because that’s the one everyone collectively agreed to buy), and go hog wild on the hard to reach places in your room of choice. You will be shocked by the amount of revolting gunk that you will discover in your house and how much the basic air quality will improve.

Get an electric duster. It’ll clean your computer, it’ll clean your home, and hell, it may even clean your very soul. (Warning: individual souls may vary.)

Compressed AirStaples

AirDuster

I have always had a complicated relationship with canned compressed air. For a neat freak, it’s a vital tool. It keeps your keyboards clean, it blasts dust out of your gaming PC, and it gets gunk out of those hard to reach parts of devices. It’s an invaluable tool, an ally — heck, even a friend.

Say hello, dear reader, to the XPower A-2S Cyber Duster. I want to tell you how much I love this little guy. I love it more than most tools in my home. I love it more than I love some of my relatives. Imagine, if you will, a tiny vacuum cleaner but in reverse. It’s a pretty straightforward concept. It has two power settings (pretty powerful and very powerful), a brush attachment, and a shorter nozzle that I can’t find right now but is probably in the cabinet where I keep all of my tools. It is an absolute game-changer.

$$\begin{align}d - f &= \frac{s\cdot f}{s - f} - f \\ &= \frac{s\cdot f}{s - f} - \frac{f(s-f)}{s-f}\\ &=\frac{f^2}{s-f}\end{align}$$

An electric duster is not a one-to-one replacement for compressed air. Compressed air cans come with a thin plastic straw that comes in real handy when trying to get into very hard to reach places, and that’s just really hard to replicate. But what my duster lacks in precision, it makes up for in sheer power and cost savings. You don’t have to ration your electricity the way you do canned air, so it becomes very useful for making casual, quick cleaning sweeps. At its highest setting, this thing blasts away. You can knock stuff off of your nightstand at a distance with this bad boy.

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Now you can repeat this measurement for different settings of the focal length of the zoom lens, and for different values of the iris setting. Note that by defocusing to various points and measuring the slope you avoid the problem of not knowing the focal length of the lens.

The answer linked by @tmwilson26 is certainly helpful, but it may not be what you are looking for. There are a couple of different ways to approach this problem, and it depends a little bit on the equipment you have available. Note that if you have a zoom lens, leaving the iris at a fixed value will not, in general, result in a constant NA - instead the NA will depend on the focal length as well as the iris aperture.

Update January 18th, 6:52PM ET: This post has been updated with Amazon links to several products, including XPower’s A-2S Electric Duster.

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