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# Lens with Angular Markings (Attachable)

For making photots that can be used to compute various things
 (+1) [vote for, against]

Before getting to the Idea, here is the problem it hopes to solve.

I live in a place where jets fly above, and make a lot of noise. Some years ago I discovered that there was a Rule to the effect that the jets were supposed to fly at least 1000 feet (about 305 meters) above the ground, but they actually often fly only a little higher than the tree-tops.

Now, consider the Inverse Square Law. If a noise is generated 1000 feet off the ground, and an equal noise is generated at half that altitude, the noise-energy received at the ground is 4 times higher for the lower-altitude noise generator.

If the plane flies at 333 feet (1/3 of 1000), the noise- energy will be 9 times higher than from a plane at 1000 feet.

Trees generally don't grow as high as 100 feet around here, so planes can fly fairly safely at 100 feet (1/10 of 1000) and thus the ground receives 100 times the sound- energy as from a plane flying at 1000 feet.

To be fair, there is another factor, in that human hearing is "logarithmic", not "scalar". Encountering 100 times the noise energy is not the same as experiencing a 100- times- louder sound. Nevertheless, the lower-flying planes are certainly louder!

The military presence in this town extends into its political life; there are a lot of retired people here who don't mind the jets making all that noise. So, there is no easy way to enforce the 1000-foot flying Rule. That's where this Idea comes in.

One well-known way to measure the distance to something involves its "angular diameter". Consider a TV --if you sit far from it, it appears smaller than if you sit close to it - - but you know it is the same size. Your overall "field of view" has less of it occupied by the distant TV than is occupied by the near TV. You can imagine an angle from your eyes to the left and right edges of the TV; that angle is smaller for the distant TV.

Now imagine a camera lens engraved with angular markings, rather like the circles of a bulls-eye. Any image you make will include those markings in the finished photograph, and no matter if the finished photo is enlarged or shrunk, the markings will accurately indicate the degree to which something in the photograph occupies the field of view.

So, take a picture of a jet flying by, at some modest distance, maybe a half-kilometer. The physical dimensions of the jet are public knowledge, and your picture now includes its angular diameter. You can use those two data items to compute exactly how far the jet is, away from the camera.

More, there is another angular measurement in the picture, the height of the jet off the ground. When you know the exact distance of the jet, that height can be computed easily. So now you have evidence you can take to the Legal System, to make the case that the pilots who don't fly at least 1000 feet can be caught and punished.

(Lenses marked as described here almost certainly exist. I'm asking that ordinary/common cameras, like on cell phones, be given an easy way to attach such a lens.)

 — Vernon, Mar 30 2014

Jeffrey's Exif viewer http://regex.info/exif.cgi
Highly recommended, you probably already have all the info you need [mitxela, Mar 30 2014]

 So, what happened when you phoned the airbase, without photographic evidence?

Also, what's to stop you from using a lens with different angular measurements?
 — MaxwellBuchanan, Mar 30 2014

 I'm not sure how accurate this will be. If you take a photo exactly perpendicular to the longitudinal axis of the jet, then it will be accurate. However, if you are at an angle to the jet your calculations will underestimate the distance.

Have you tried to do a measurement with commercially available range finders?
 — xaviergisz, Mar 30 2014

If your camera doesn't have an optical zoom then, given the models of both phone and airplane, the height is a matter of pretty basic math.
 — FlyingToaster, Mar 30 2014

Or just paintball the plane - that should settle any arguments.
 — MaxwellBuchanan, Mar 30 2014

Or just hold your thumb up at arms length as you snap the plane. If your thumb looks smaller than the plane, the plane is probably too close.
 — MaxwellBuchanan, Mar 30 2014

 Even the cheapest digital cameras include lens focal length in the exif data, which when coupled with sensor size (also usually in the exif) gives you all the information you would get from physically marking the lens. My camera also records the phase detection's guess at pupil-to-object distance, but naturally this becomes less and less accurate as the object is moved further away.

To calculate distance from angular size, you will of course need to take distortion into account - angular size is very rarely uniform across the frame. I suppose it depends on how much accuracy you need, longer focal lengths generally will be more accurate.
 — mitxela, Mar 30 2014

 [xaviergisz], you can take multiple photographs. The planes tend to fly in curved paths (pilots are practicing for landings on the short deck of an aircraft carrier), and you can almost always get a good full-side-view of the plane.

 As for range-finders, these are MILITARY jets. The pilots won't appreciate being "targeted" by a range-finder.

 [FlyingToaster], I will assume the Legal System will want more evidence, or better evidence. We want to get past the "reasonable doubt" issue.

 [MaxwellBuchanan], if such lens-attachments as I've described in the main text were common, lots of people could independently provide data for the Legal System. It would not be reasonable to think that ALL of them were using "rigged" angular-measurement scales.

[mitxela], it is possible, based on your remark and that of [FlyingToaster], that the angular-diameter markings don't have to be part of the lens, and can be added by the image-processing software of the camera. On the other hand, this is more susceptible to "rigging"....
 — Vernon, Mar 30 2014

Depth of field will defeat this. The markings in or near the lens will be far enough out of focus to be unusable.
 — MechE, Mar 30 2014

 Nobody appreciates being "painted" by a laser, but there are passive systems: artillery binoculars, etc.

But a bit of digging in your cellphone manual might turn up something useful as towards angular whatsis.
 — FlyingToaster, Mar 30 2014

 Louder, but for a shorter period....

I don't think any simple passive marking system on the lens will be in focus.
 — Ling, Mar 30 2014

 Another way to prove you haven't used falsified markings is for someone to go stand where you stood when you took the picture, which is provable by the angular relationships of near and far objects on the ground, and check that the angular sizes of objects on the ground match your lens's markings.

 // Depth of field will defeat this. The markings in or near the lens will be far enough out of focus to be unusable. //

 // I don't think any simple passive marking system on the lens will be in focus. //

True, but a problem well solved in gun sights. IIRC, some of them use some sort of hologram to make it appear that the red dot is infinitely far away, while others achieve the same with a relatively simple lens arrangement (probably just a collimator, come to think of it). (In that application, the main goal is to make the dot appear to lie on the line in space along which the bullet will travel, even when you move your eye off-axis, which a simple red dot in the middle of the eyepiece would not do.) The same might be doable with this. It would likely need some off-axis optics, and a beamsplitter to superimpose the artificially infinitely far away image on top of the real scene. That would add a bit to cost, but this is going to be a specialty item anyway. Most people who want to know the AGL altitudes of planes are going to check an ADS-B website, and most people who want to measure the sizes of or distances to things with a camera are going to use a fixed-focal length lens and a camera calibration toolbox.
 — notexactly, May 28 2019

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