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Detecting a dark spot -
Detecting a dark spot -
How would someone go about calculating the theoretical limit of the smallest dark spot detectable (naked eye) for any given diameter aperture? Not resolving two spots (as in using Dawes limits/Rayleigh criterion ), but detecting one spot. Meanings and some considerations: Smallest - in diameter Naked eye - assume 20/20 vision and dark adapted Dark spot - e.g. small crater on the Moon or shadow of a Jovian moon on Jupiter. No detail. Detectable - above the lower limit (however small) of visibility Seeing - excellent Collimation - perfect Optics - diffraction limited Magnification - highest usable 40X/in Contrast - black on well illuminated white Planets - all lined up in a row. IOW, best case scenario, optimal gear and conditions. Thankx. Errol www.pasnola.org |
#2
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Detecting a dark spot -
On Mar 10, 7:17 pm, "Starboard" wrote:
Detecting a dark spot - How would someone go about calculating the theoretical limit of the smallest dark spot detectable (naked eye) for any given diameter aperture? Not resolving two spots (as in using Dawes limits/Rayleigh criterion ), but detecting one spot. Errol, It has become sort of a rule of thumb that a point source of about 0.1 of the Dawe's Limit can be detected. I say "about" because you are dealing with information input that is subject to a fistful of variables. Case in point: During the 2003 Mars opposition I was judging my resolution by those two fingerlike projections that extend from the Mare Cimmerium out into the Cerberus region. I call them the "Cimmerium Dactyls" and CCD images take them down very well. I had them pretty well resolved one evening when a pocket of still air drifted across my FOV and for about five seconds I could see three craters *inside* of the boundaries of the dactyls. It was shocking. It was one of those "moments" you read about in S & T that introjects itself into the memory and stays with you. The price was about 250 hrs of observation for those five seconds. Was it worth it? Yeah. (Did 152 drawings for the 2003 opposition) Anyway there's nothing to compare with a moment of perfect seeing and I feel like the rule of thumb is justified: 0.1 x Dawes Limit (about) Ben, 90.126 n 35.539 PS: Those weren't "floaters" either - they faded out just as the boundaries of the dactyls did. (10" @ 400x) |
#3
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Detecting a dark spot -
Well, from the book AMATEUR ASTRONOMER'S HANDBOOK (J.B. Sidgwick)
OBSERVATIONAL EXAMPLES OF RESOLUTION OF CERTAIN EXTENDED DETAIL (from AMATEUR ASTRONOMER'S HANDBOOK, by J.B. Sidgwick, p.49-50) ("r" is Dawes Limit = 4.56/D in arc seconds with D the aperture in inches) (NOTE: those specifically interested in the minimum aperture necessary to resolve the Cassini and Encke divisions from their adjacent ring edges should pay close attention to "C" below.) A. BLACK SPOT ON A WHITE BACKGROUND: i. W.H. Pickering, while testing his 10 inch reflector under good seeing conditions in Jamaica, found that a circular spot became visible if its angular diameter exceeded 0.20" arc (r/2.3). ii. Experiments by W.H. Steavenson showed that r/3 is a fair average figure. iii. The naked-eye visiblity of sunspots whose diameter is less than r is well known. B. SINGLE DARK LINE ON A WHITE BACKGROUND: i. Cassini Division, width of about 0.5" arc was discovered with about a 2.5 inch aperture (r/3.5). ii. Experiments by W.H. Steavenson yielded about r/5 as an average figure. iii. During testing of an 11 inch refractor at Harvard, a human hair was visible against a light-toned ground at a distance of nearly 1/4 of a mile where it subtended 0.029" arc (r/14). iv. W.H. Pickering glimsed a dark line 0.03" wide with his 10 inch (r/15). C. PARALLEL LINES ON A LIGHT BACKGROUND: i. W.H. Pickering: minimum separation for resolution with a 10 inch reflector was 0.63" arc (1.4r). ii. A similar performance was given by the Arequipa 15 inch, which resolved a pair of parallel lines when their separation was increased past 0.42" arc (1.4r), in good seeing; slight atmospheric deterioration immediately raised the threshold to about 2r. At less than 0.42" arc, the lines appeared as a grey band of width about 1.5 times their separation. iii. Resolution of the lines at 12" arc with a 0.4 inch Object Glass (1.1r). Clear skies to you. -- David W. Knisely Prairie Astronomy Club: http://www.prairieastronomyclub.org Hyde Memorial Observatory: http://www.hydeobservatory.info/ ********************************************** * Attend the 14th Annual NEBRASKA STAR PARTY * * July 15th-20th, 2007, Merritt Reservoir * * http://www.NebraskaStarParty.org * ********************************************** |
#4
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Detecting a dark spot -
How would someone go about calculating the theoretical limit of the
smallest dark spot detectable (naked eye) for any given diameter aperture? Not resolving two spots (as in using Dawes limits/Rayleigh criterion ), but detecting one spot. Errol It has become sort of a rule of thumb that a point source of about 0.1 of the Dawe's Limit can be detected. I say "about" because you are dealing with information input that is subject to a fistful of variables. Ben Thanks Ben. Night before last, two friends and I brought some scope stuff to a local school having a science camp (approx 100 kids and 30 adults). My scope (12" Dob) stayed fixed on Saturn at 400X for 3 1/2 hours (very labor intensive). Seeing and transparency were excellent. Everyone who looked at Saturn was in total shock and awe as usual. The most common comment of the night was, "is that real?" Anyway, so we're talking about Saturn and one of my friends says he's seen Encke in a three inch refractor. I told him I thought that he should go have his eyes checked, have his head checked, and to keep his delusions to himself when in public. I was thinking that it should be pretty much impossible to see Encke in a three inch scope. Then I got to thinking that I was basing my guess off of Dawes limit; which, in hind sight, was not correct - as *detecting* a feature is not the same as *resolving* two features from one another. However, it appears that even using the adjusted formula, it is still impossible to do with 3 incher. Case in point: During the 2003 Mars opposition I was judging my resolution by those two fingerlike projections that extend from the Mare Cimmerium out into the Cerberus region. I call them the "Cimmerium Dactyls" and CCD images take them down very well. I had them pretty well resolved one evening when a pocket of still air drifted across my FOV and for about five seconds I could see three craters *inside* of the boundaries of the dactyls. Ben Amazing. Thanks again. Errol |
#5
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Detecting a dark spot -
David Knisely wrote:
Well, from the book AMATEUR ASTRONOMER'S HANDBOOK (J.B. Sidgwick) .... OBSERVATIONAL EXAMPLES OF RESOLUTION OF CERTAIN EXTENDED DETAIL David, Thanks for the data. Errol |
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