Telescope Reviews: 100 Her at 8x

Lets stick with 100 Herc mag 5, and a 50mm binocular.

A 50mm lens has an Airy disk 138/50 = 2.76 arcsec. We can argue photopic or scotopic light, but lets not. That might change 2.76 to a 2.5 arcsec.

Assuming
a 50mm binoc, diffraction limited, will make stars into 2.76 arcsecond disks.
It would probably take about 60x to 75x to see that.

Resolution on a USAF line pairs chart would be about 70% (30% smaller than) that. So the same diffraction limited 50mm binoc at approx 75x sould be able to see 1.9 arcsec on a line pairs chart. We sometimes read that people are testing their binocs using a USAF chart and sometimes see a claim that they have reached the diffraction limit. What's missing here is they fail to address that the binoc should be able to see 30% smaller than the diffraction limit when using the line pair charts. No one that I'm aware of has ever reached the diffraction limit with any binocular when testing resolution on a line pairs chart.

As an example of this, I have two different 80mm diffraction limited scopes. Both have clearly resolved stars to the diffraction limit, about 1.7 to 1.65 arcseconds. Both have resolved down to 1.2 arcseconds using the line pairs charts. Both the line pairs readings and the point source (stars) resolution required approx 150x or even up to 200x to see it.

Keep in mind, when a scope employees enough power to resolve a pair of stars at the extreme diffraction limit, there is NO SPACE at all left between the disks. The star disks occupy 99.9% of the space.

If a 50mm lens were used at high enough power to approach the diffraction limit (2.76 arcseconds) and then back off just a little, say to 4 arcseconds, when viewing that 4 arcsec pair, the stars would occupy 70% of the space. If the stars were bright, say mag 3, then the stars might occupy 85% of the space, leaving only 15% of the space as the dark line separating the two components.

I’ve resolved 8 arcseconds on line pairs with a 10x50. I’ve resolved 3.0 arcsec on a line pairs chart at best with 10x50s boosted to 60 power with a small auxiliary scope. Also, I’ve seen 100 Herc, 14.2 arcsec mag 5 pair with 10x50s at best.

(Of special note here, I’ve resolved 3.2 arcseconds on a line pairs chart with the Takahashi 22x60 at it’s normal power of 22x and with the same binocular I’ve cleanly resolved 95 Herc, a 6.3 arcsec equal mag 5 pair).

So why can’t a low power binocular resolve pairs that are closer than 14 arcseconds ( speaking from my limit)? Why can’t a 10x50 see 2.76 arcseconds?

Well for one, you just can’t see that small at 10 power. But other reasons might be:

You are not seeing Airy disks with low power optics. You are seeing a star disk made up of the entire diffraction pattern, or at least some portion of the diffraction pattern. Even though a larger lens makes a smaller Airy disk than a smaller lens, neither lens at these powers is capable of seeing the Airy disk or the Airy pattern. And granted the rings get progressively dimmer, but the first ring might contain 15% of all the light, so at least some of the rings are include in the bloated star disk. This makes the star disk larger than the dimension calculated by the Airy disk formula.

Magnitude has a dramatic affect on the size of the visible disk, the central disk within the Airy pattern. In scope optics, at powers high enough to see the Airy disk, the visible disk of a mag 2 star might be 40% to 50% larger than that of a mag 6 star. However, other than the visible disk, magnitude does not have an effect of the overall dimensions of the elements of the diffraction pattern. But it might include more diffraction rings in the bloated disk. Considering this is a known phenomenon, it stands to reason that testing on a line pairs chart under too bright a light might have the same effect.

Combinations of fast optic aberrations swell the diffraction pattern to a larger size. Spherical and chromatic aberration and astigmatism would be likely culprits. There is no way that I know of to calculate the implications of these effects.

In binoculars, the combination of bright stars and fast optics swells stars to very large sizes. But indeed finer optics do produce smaller stars. Note the example from my recent tests of 22x binoculars. While the Takahashi 22x60 (note the considerable smaller aperture here) can resolve a 6.3 arcsec mag 5 pair, the GO Signature 22x85 can only resolve a 7.8 arcsec mag 5 pair. That would indicate that the star disks in the GO 22x85 are about 25%+/- LARGER than the Tak, whereas, due to the aperture, they should be 30%+/- smaller. The huge difference is due to the aberrations (or lack of) in the lens.

edz

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Edited by EdZ (10/14/09 07:21 AM)