CN FORUMS ARCHIVE Telescope Reviews: reading license plates at five miles

Well, let's take my test data a little further. And along the way i'll mention a few things about resolution.

Above I noted that the Megrez 80 could resolve 2.7 arcseconds at 40x and 2.1 arcsec at 66x. This is real data. This is line pairs resolution. We really could take line (not pairs) resolution into consideration. So the thin line resolution of the Megrez 80 is 1.35 arcsec at 40x and 1.05 arcsec at 66x. this is an 80mm scope. More recoreded data shows it gets better as magnification increases.

We know from tests performed by astronomers far more worthy than I, that a line can be resolved as thin as 1/10th to 1/15th of normal point source resolution values. Remember this discussion from the resolving a thin wire thread a long time ago. So while I have only used up to 66x in my Megrez and I got down to 1.05 arcseconds, it can see a much thinner line. In fact I have seen the Cassini Division (0.75 arcsec) with a scope operating at 40mm at 110x. Many people report being able to see the Cassini division with small scopes.

When visual resolution is measured with a Snellen letter chart it is the letter height that gives the resolution value, not the thickness of the lines that make up the letter. 5mm tall letters viewed at 20 feet is approx 3 arcmin resolution. The point here is that the eye can see the thickness of the lines or it would not be able to recognize the letter. For example, for the letter E, the thickness of the lines is one fifth the height of the letter. This can be seen in the three horizontal bars that make the E, where the width of the spaces are equal to the thickness of the lines.

I have also measured the height of the letters on my plates. They are 70mm high by 30mm wide by 7mm line thickness. Spacing varies a lot, from 10mm up to 40mm.

7mm line thickness at 5 miles is 0.18 arcseconds. That fits easily within the parameters of thin line resolution. It's finer than the Snellen chart, but astronomers have shown a thin line can still be detected even when much thinner than Snellen thickness.

So the letters 70x30x7, at a distance of 26,400 feet measure (in arcsec) 1.8x0.53x0.18. Once again, spacing varies.

For this example, I won't even go so far too say the scope can see line thickness at 1/10th point source resolution, although it has been shown achievable to 1/15th. A fine example of thin line resolution is documented in the Resolving a Thin Wire thread, where a 0.3mm wire is seen at 100 meters using a 10x50 binocular. That is an angular width of 0.7 arcseconds and at 10 power, an apparent size of only 7 arcseconds! Let's just say we have a scope that can see 1/5th point source resolution, the same as the line thickness in Snellen resolution criteria. To see that thin 0.18 arcsec line, the scope needs resolution of 0.18 x 5 = 0.9 arcseconds resolution. That's the most difficult criteria, the thickness of the line.

Solving for a scope that can very easily see this = 138/0.9 = 150mm scope.

Now how much magnification is needed? Average eyesight is about 3 arcminutes resolution. So you need enough magnification to get the letter size up to 180 arcseconds. Following the same pattern as the Snellen chart, that is the height of the letter, not the width and not the thickness (although we'll come back and check on the thickness).

The 70mm high letter at 5 miles is 1.8 arcseconds tall. Let's give our poor person some help here and let's say we'll enlarge the letter to an apparent size of 240 arecseconds. 240/1.8 = 133x. A magnification of 133x should make this letter big enough for anyone to read it.

How about the thickness. It's 0.18 arcsec. On a Snellen chart, seeing 3 arcmin means that the thickness of the letter E is 180/5 = 36 arcseconds thick apparent size. So to accomodate average eyesight, I need to raise the thickness at least to 36 arcseconds. So to see a thickness of 36 arcsec I need to use a magnification of 36/0.18 = 200x.

Using a 150mm scope with a magnification of 200x, the apparent thickness will be enough to see it and the apparent letter height will be more than enough to see it. But note that above in my calculations I was very conservative and said we'll only use half of the known ability of a scope. So it could very likely be done with much smaller.

Can it be done with my 80mm scope? Possibly, but that would certainly be pushing to the extreme limits. The Megrez 80 could see the letter height, but might have a problem with the line thickness. For my eyes, I require only 150 arcseconds resolution, but that's on point sources. On line pairs in daylight I require only 90 arcseconds. That would be 45 arcseconds for line thickness. So I only need a magnification of 90/1.8 = 50x to see the letter height and I need 90/5 = 18, or 18/.18 = 100x to see the line thickness.

BTW it was said above that five miles by Topo Map is a lot closer as when you measure as the crow flies. That is incorrect. 5 miles on a topo map IS the distance as the crow flies. You would need to calculate the slope distance for all the vertical rise and fall of the topo contour lines over that 5 miles to determine how much further than 5 miles you would need to walk to cover that distance as the crow flies.

edz

edit
this morning I went out to test out letter visiblity. I used a sheet of newsprint. It was not as contrasty as I would like, sort of less than black on less than white, but it works. Lighting was less than desirable. It was cloudy and still completely grey out at 6:30 AM.

Back to my standard mailbox disatance which is 125 feet. I taped up the newsprint.

I was easily able to read letters that measured 6mm x 6mm x 1.5mm thick.
I was still barely able to read letters 5mm x 3.5mm x 1mm thick. So I'm going with this reading, because I could still read most of it. I know from previos testing where I compared a half dozen binoculars in less than ideal light that I lose about 20% apparent resolution when compared to what they can see in bright light. So this is more than conservative, in other words it's easily doable in bright light.

Spacing between the letters varies, but for some letters it was 1mm.

So these letters at 125 feet result in an angular size (in arcseconds) of 27 x 17.5 x 5.4.

I was using a 7x50 binocular. So the apparent size that I was able to read was 189 x 123 x 38 arcseconds apparent, with 38 arcsec spacing between letters.

How does that compare to my license plate numbers. Well, they are 70x30x7mm, at a distance of 26,400 feet measure (in arcsec), that would be 1.8 x 0.53 x 0.18. Once again, spacing varies, but it's wider than line thickness. At 200x, that would be 360 x 106 x 36 arcseconds apparent. Give me some sunlight to see those letters and I could improve by 20%.

Throughout this analysis I have pointed out test and practical measurements shown to be achievable. Then I go on to point out that some of these require a very well seasoned observer, so I back off to a lesser ability to see. So what can we expect. Usually these types of little problems show that the claims are BS and cannot be substantiated. But, as I've learned long ago, you never know and you sure can't guess.

So in answer to the original question, What size scope is this guy using?

Under the best conditions with the best equipment used by a well seasoned observer this might be seen with an 80mm scope at 80x to 100x. But as I show above here, for the average observer meeting an easier criteria, one could see these size letters with a 150mm scope at a magnification of 160x to 200x.

edz

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Edited by EdZ (11/17/05 12:22 PM)