Airy Line versus Airy Disc
Posted 08 December 2012 - 02:53 PM
Back in the 90s when we saw Saturn compltely edge on I observed the stunning phenomenon of the Saturnian moons moving along in there orbits appearing like dew drops on the spider thread ring. Here was a text book example of airy discs versus linear diffraction .
I will say the ring was on edge for a disturbingly long time. Weeks went by from the date of absolute edge on but night after night and week after week it brightened a little but it became clear to me - this is the linear version of a diffraction pattern. Regardless of the magnifications it was constant cord from one end to the other. Now what was engaging g however was that Rhea and Dione and such were effectively unresolved points that shown as starry diffraction patterns BUT they were JUST large enough to appear THICKER than the ring and so appeared as points of light ever so slowly migrating the spiders thread. Some things made me wonder though - were they appearing resolved seperate from ring because they were ever so slightly out of plane or did their brightness create an airy disc that was larger than the airy *line*?
A note of the actual ring thinness and magnitude the day after absolute edge on was seeing Enceladus like a fragment of this ever thin and dim streak. It looked like a day after the plane crossing (or a couple days it was a while ago) that Enceladus was a perfect fragment or point source indicating actual ring surface brightness for that unit area. Subsequent weeks the rings brightened and then those moon transits along the line. It was a spectacle that was jaw dropping.
I mention this now since the discussion on Io and diffraction and MTF would seem to shed some light on this reoccurring series of events.
A conclusion to this observi program that had me setting up in numerous locales at 3am and such for a clear unobstructed view came on October 26th if I recall that week. It was partly cloudy and the seeing fuzzed now and then but I realized more and more this was a diffeaction effect and so possibly my typical planetary working mags of 200x to 240x were too conservative. With that I barlowed up to 364x and my jaw dropped again. After some 6 weeks of frustrated observing where no thickness was detected the rings finally budged. The answer were ever the the thin line but just before they reach the planets limb genuine thickness atlast!!!! Indeed the light and thickness dropped off the moment the crepe part entered in the profile but for a segment on each side true resolved thickness. It came with a sense of victory and a little sadness at missed opportunity: would the thickness had shown early if I used magnification typical of airy disc study? Early on in summers great seeing I had but the cooler weeks had their own limiting factor. Still I wonder if I could have done better.
Jus throwing it out there.
Posted 08 December 2012 - 11:44 PM
So why doesn't it?
Simple answer.... The magnitude is to low. When the rings are edge on, the magnitude is so low that they simply don't reflect enough light to be seen with just about anything on earth.
You would not be able to detect them until the brightness of the inclined rings reach the limiting magnitude of your scope. Only when they get wide enought to reach your limting magnitude would they show, and when this happens, they may appear thinner than the diameter of the Airy Disk of a bright star.
The problem is that they may have to get a fair amount of tilt depending on the limiting magnitude of the scope to be detected.
Even some professional telescopes that have imaged the rings edge-on don't show the edge of the rings, though they do show the shadow of the edge of the rings on the planet itself. Like a black line... But not the edge of the ring where it extends past the edge of the planet.
My guess is that the magnitude of the edge of the rings is 20 or 25 or something. Far to dim to be seen by anything bit very large telescoeps.
Posted 08 December 2012 - 11:59 PM
Thanks for your input on the details of the dynamics. I was sorry to see this past ring plane crossing offered no such similar view.
Posted 09 December 2012 - 12:05 AM
Edit: sorry, you said "dew" drop, not tear drop. That's all together a different appearance, like circular beads of moisture on a spider's silk strand.
If the rings were bright enough to produce a series of dim spurious discs, then the rings being edge on would have been resolved from the contrast difference against blackness of space. Since they are not, nothing was resolved. Nothing was seen. There would likely be no resolution of individual points along the ring'e edge, either, as there would be no contrast between those spurious discs.
If a brighter moon were seen against the ring's (sufficiently bright) edge, it would not be resolved in the classic sense of contrast between each point on the ring and the moon. But with the combined effect, it could be discerned and it would likely repeat that tear drop effect.
Nor sure this is right, it's more a "flux" property. As the rings tilt they present an extended object. Really, edge on could be an extended object, too, just a very tiny one with some angular size. Such a thin object could be 'effectively' linear if the angular size were quite small compared to the Airy disc. But, definitely extended with any amount of tilt. So, they become brighter as the combined flux increases. In my understanding, they are not linear no matter how thin they appear with tilt. Some degree of north to south optical path difference exists among some very dim spurious discs whose total flux increases with tilt.
...this is the linear version of a diffraction pattern.
Pete, you always ask the most difficult questions.