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Pages: 1 | 2 | 3 | 4 | (show all) drollere Pooh-Bah Reged: 02/02/10 Loc: sebastopol, california "airy disk" diameter changes with magnitude       #5040876 - 01/27/12 12:41 PM Edit   Reply   Quote Quick Reply   i'm posting a puzzle that i cannot explain and that has not been explained to me clearly by anyone else. standard optical theory says that the visual or linear radius of a star diffraction artifact -- central spot or "airy disk" and one or more diffraction rings -- is entirely and solely dependent on aperture or focal ratio: AD = 1.22lambda/aperture. but the visual fact is that the central spot changes diameter with stellar magnitude. the size variation is visible up to some limiting (light grasp dependent) upper magnitude where the disk outline is obscured by optical flare and down to some limiting (light grasp dependent) lower magnitude where the artifact degrades into a tiny fuzzy spot (when imaged on the fovea). i can understand an explanation for the visual diameter of the central spot that involves the luminance threshold of the eye: as the star becomes fainter the threshold is raised vertically across the gaussian profile, where it cuts the central maxima at a higher luminance and smaller diameter (nearer the peak central maximum). however, for most visual magnitudes above the "fuzzy spot" lower limit, the smaller disk also will display a diffraction ring. this ring is smaller in diameter than the diameter predicted by diffraction theory. worse, if we explain the smaller central disk by a raised luminance threshold in the eye, all diffraction rings would be below that threshold and invisible. this smaller diameter ring is something i can't explain. the diagram below (gamma andromedae) was made at around 600x magnification with a 10" f/20 royce dall kirkham, using photoshop on a laptop computer with a black background and dimmed controls. it corresponds reasonably well to the visual facts of size and hue, although atmospheric effects were disregarded and the luminance contrast is sharply truncated by your monitor gamut. it might be that the companion (v.mag. 5.0) shows the "real" central disk and the disk of the brighter primary (v.mag. 2.3) is merged with the first and second rings. but i have seen this difference in the disk size vary continuously across the range v.mag. 2 to 9, and it is quite easy to see the difference in the magnitude of a closely spaced nearly matched pair of stars as a slight difference in the relative disk diameters. the disk does not make discrete "quantum" changes in diameter at it merges with successively wider discrete rings. why is the disk of the fainter star smaller, and why does it have a smaller diffraction ring? Post Extras:       David Knisely Postmaster Reged: 04/19/04 Loc: southeastern Nebraska Re: "airy disk" diameter changes with magnitude [Re: drollere]       #5040980 - 01/27/12 01:31 PM Edit   Reply   Quote Quick Reply   Visually, I have never noticed that much of a difference in the diameter of the first ring between bright and faint stars. Two things are happening here. First, the distance between the center of the diffraction pattern and the middle of the first dark ring between the visible "spurious" disk and the first bright ring is not only dependent on the aperture, but on the wavelength of light being used. The smaller the wavelength, the smaller the diffraction pattern tends to be. With a blue star, you are getting more blue wavelengths, so its pattern may be slightly smaller in size than with the more yellow primary star. In fact, if we use, say 5700 angstroms for the yellow star and 4400 angstroms for the blue star, the yellow star's pattern is about 30% larger than the blue star's pattern. The rest of the effect is just seeing fewer photons in the fainter blue star, making its spurious disk appear smaller than the brighter yellow star. In your image, the brightness of the yellow star may be obscuring the first diffraction ring, making it merge with the bright central maximum. Try using a much shorter exposure for the yellow star and a longer one for the blue star and then see if the patterns are closer to the same size. Clear skies to you. Post Extras:       Astrojensen Post Laureate Reged: 10/05/08 Loc: Bornholm, Denmark Re: "airy disk" diameter changes with magnitude [Re: David Knisely]       #5041058 - 01/27/12 02:28 PM Edit   Reply   Quote Quick Reply   Quote: In your image, the brightness of the yellow star may be obscuring the first diffraction ring, making it merge with the bright central maximum. Try using a much shorter exposure for the yellow star and a longer one for the blue star and then see if the patterns are closer to the same size. I find this comment very amusing, as it is clearly a drawing (and mentioned as being such) and not a webcam image! Clear skies! Thomas, Denmark Post Extras:       drollere Pooh-Bah Reged: 02/02/10 Loc: sebastopol, california Re: "airy disk" diameter changes with magnitude [Re: Astrojensen]       #5041110 - 01/27/12 02:54 PM Edit   Reply   Quote Quick Reply   Quote: Quote: Try using a much shorter exposure for the yellow star and a longer one for the blue star and then see if the patterns are closer to the same size. I find this comment very amusing, as it is clearly a drawing (and mentioned as being such) and not a webcam image! and to eliminate any ambiguity, the difference in the disk size appears in spectrally matched binaries of slightly different magnitudes ... castor for example. alternately, using "red" = 650 and "blue" = 450, the wavelength induced difference in disk sizes would be around 50%, but the diagrammed (observed) difference is on the order of 100% or more (in this case). that line of reasoning is dubious, however, since stars are not monochromatic lights, so the calculation would have to integrate across the entire spectrum. and (after interstellar, atmospheric, telescopic and ocular filtering of the light) the observed spectral profiles of stars actually differ by very little ... certainly not by as much as 50%. this link is to drawings by sissy haas, who similarly records the disk and ring difference in two examples (upper left). http://resources.metapress.com/pdf-preview.axd?code=p321408314n71021&size=largest Post Extras:       Jon Isaacs Postmaster Reged: 06/16/04 Loc: San Diego and Boulevard, CA Re: "airy disk" diameter changes with magnitude [Re: drollere]       #5041158 - 01/27/12 03:26 PM Edit   Reply   Quote Quick Reply   Quote: why is the disk of the fainter star smaller, and why does it have a smaller diffraction ring? This is an interesting question, one I have tried to address a time or two on different forums. It is a fundamental question: Why do bright stars appear larger than fainter stars? Lots of reasons... Jon Post Extras:       drollere Pooh-Bah Reged: 02/02/10 Loc: sebastopol, california Re: "airy disk" diameter changes with magnitude [Re: Jon Isaacs]       #5041196 - 01/27/12 03:45 PM Edit   Reply   Quote Quick Reply   Quote: It is a fundamental question: Why do bright stars appear larger than fainter stars? for the "disk" size, certainly optical flare ("bloom") and gamut clipping at the high end of the response range will get you most of the way. those explanations can't address changes in the diameter of the diffraction rings, which by optical theory must be immutable for a given aperture. Post Extras:       blb Post Laureate Reged: 11/25/05 Loc: Piedmont NC Re: "airy disk" diameter changes with magnitude [Re: Jon Isaacs]       #5041248 - 01/27/12 04:11 PM Edit   Reply   Quote Quick Reply   Quote: Quote: why is the disk of the fainter star smaller, and why does it have a smaller diffraction ring? This is an interesting question, one I have tried to address a time or two on different forums. It is a fundamental question: Why do bright stars appear larger than fainter stars? Lots of reasons... Jon Lots of reasons...? I would love to hear a few of them. Post Extras:       EdZ Professor EdZ Reged: 02/15/02 Loc: Cumberland, R I , USA42N71.4W Re: "airy disk" diameter changes with magnitude [Re: drollere]       #5041264 - 01/27/12 04:21 PM Edit   Reply   Quote Quick Reply   the answers were given above, but I'll just repeat it a slightly different way, to separate the main issues. to start, the Airy disk diameter doesn't change with magnitude. It changes only with variations in aperture or wavelength. The central visible disk diameter does change with magnitude. For two stars of equal brightness, as seen thru the same scope aperture, since Airy disk is entirely dependant on wavelength and red is longer than blue, a red star will have a larger Airy disk than a blue star. The ratio of dimension to the various rings remains constant, but the linear measure to like rings will be longer in the red star. The color of a star will have an impact on the perceived magnitude. For two stars of equal magnitude, a red star will appear fainter, a blue star will appear brighter. The observer would suspect the blue stars to be brighter. Since blue is perceived as brighter than red, the blue star may present a central disk that appears slightly larger than it's wavelength might indicate, if compared to an equal brightness star of other color. Still, it doesn't appear as large as the red star. For stars of different brightness, the effect of magnitude is to vary the size of only the central visible disk. The Airy disk remains as determined above previously, with the predominant difference dependant on wavelength and also with the ratio of dimension to the various rings remaining constant, but the linear measure to like rings longer in the red star. The central visible disk of the bright star grows obviously in apparent size, however, while the mimimum of the Airy disk remains at the same position. Also the apparent difference in magnitude between the growing central visible disk and the first ring may get overwhelmed and I can easily suspect they could potentially become coincident. The visual affects of magnitude and color to me always seem readily apparent. edz Post Extras:       blb Post Laureate Reged: 11/25/05 Loc: Piedmont NC Re: "airy disk" diameter changes with magnitude [Re: EdZ]       #5041500 - 01/27/12 06:45 PM Edit   Reply   Quote Quick Reply   Quote: to start, the Airy disk diameter doesn't change with magnitude... The central visible disk diameter does change with magnitude. Quote: For stars of different brightness, the effect of magnitude is to vary the size of only the central visible disk. The Airy disk remains as determined above previously, with the predominant difference dependant on wavelength and also with the ratio of dimension to the various rings remaining constant, but the linear measure to like rings longer in the red star. Are you saying the Airy Disk is that central visible disk and the two or three rings of light around the central disk? The visible central disk does vary with magnitude but the overal size of the rings of light around the central disk remain the same size no mater what the magnitude of the star is? This is true for all stars except for the variation in color(wavelength), apeture and their effect on the ring size? Post Extras:       EdZ Professor EdZ Reged: 02/15/02 Loc: Cumberland, R I , USA42N71.4W Re: "airy disk" diameter changes with magnitude [Re: blb]       #5041558 - 01/27/12 07:29 PM Edit   Reply   Quote Quick Reply   actually, this doesn't say the rings will be the same size, but does mean the rings radii do not move. The rings could be thicker in a bright star and in fact probably they are thicker. However, the ratio of position to the peak center of each ring or the minimum between each ring remains exactly the same. So the extent (to the 1st minimum) of the Airy disk is still at 1.22 lambda /D and the center of the 1st ring is still at 1.72 lambda and the center of the 2nd ring is still at 2.2? lambda. Changing magnitude does not change the position of the rings, but changes the thickness of the rings. Nothing changes the relative position of the rings. Only changing wavelength changes the linear dimension of the rings (assume scope is constant). I assume you know the Airy disk is to the 1st muinimum at 1.22 lambda and is constant. Yes, the visible disk or central disk varies in size with magnitude, as is well describe above. edz Post Extras:       GlennLeDrew Postmaster Reged: 06/18/08 Loc: Ottawa, Ontario, Canada Re: "airy disk" diameter changes with magnitude [Re: EdZ]       #5041602 - 01/27/12 08:00 PM Edit   Reply   Quote Quick Reply   I attribute this to the fact that the 'disk' is a Gaussian, the width of which is described at some intensity with respect to peak brightness. A more saturated Airy disk will appear as larger because the lower intensity region toward the 'base' of the Gaussian is detected. Your illustration would seem to imply that the size of the diffraction rings scales with the apparent Airy disk diameter. Their size is fixed irrespective of brightness, with the exception, of course, that there is some variation with wavelength (although for non-pure colors, the mix of wavelengths ensures a pretty good approximation to fixed size.) Post Extras:       EdZ Professor EdZ Reged: 02/15/02 Loc: Cumberland, R I , USA42N71.4W Re: "airy disk" diameter changes with magnitude [Re: GlennLeDrew]       #5041626 - 01/27/12 08:19 PM Edit   Reply   Quote Quick Reply   the Gaussain example (also given earlier) is the easiest to visualize the growth to the extent of the central visible disk due to increased magnitude and also the increasing thickness of the brightened rings, while at the same time the positions of the max and mins remain the same. Yes the size of the rings scales with the Airy disk. Lambda and D will always see to that. Just as we have a defined constant of 1.22 to find the extent of the Airy disk (but not so easily the extent of the visible disk) , we have similar constants for the positions of the peaks of each bright ring. Those constants mean that the rings scale with the Airy disk. edz Post Extras:       azure1961p Postmaster Reged: 01/17/09 Loc: USA Re: "airy disk" diameter changes with magnitude [Re: EdZ]       #5041829 - 01/27/12 11:01 PM Edit   Reply   Quote Quick Reply   Bruce, That is an EXCELLENT rendering of the double. Pete Post Extras:       azure1961p Postmaster Reged: 01/17/09 Loc: USA Re: "airy disk" diameter changes with magnitude [Re: azure1961p]       #5041838 - 01/27/12 11:12 PM Edit   Reply   Quote Quick Reply   So if Ive got this right Bruce, the dimmer blue star ought to have this much wider gap between its dimmer/smaller spurious disc and first diffraction ring but instead the entire pattern and whats visible of it looks miniaturized to fit the fainter light? This is a compelling thread and a fav topic. Im just going to observe this one and reserve theory comment. Pete Post Extras:       David Knisely Postmaster Reged: 04/19/04 Loc: southeastern Nebraska Re: "airy disk" diameter changes with magnitude [Re: Astrojensen]       #5042512 - 01/28/12 01:11 PM Edit   Reply   Quote Quick Reply   Quote: Quote: In your image, the brightness of the yellow star may be obscuring the first diffraction ring, making it merge with the bright central maximum. Try using a much shorter exposure for the yellow star and a longer one for the blue star and then see if the patterns are closer to the same size. I find this comment very amusing, as it is clearly a drawing (and mentioned as being such) and not a webcam image! Clear skies! Thomas, Denmark I did miss that (shows what happens when you are trying to respond to a question while having the flu ). In any case, I have never seen a huge difference between the radii of the first minimum of the diffraction pattern of stars of differing brightness. The apparent size of the visible spurious disk does change with the brightness of the star, as the edge is only defined by the visual threshold, but the exact location of the first minimum stays pretty much the same, other than the effect of observing stars of notably different color. Clear skies to you. Post Extras:       David Knisely Postmaster Reged: 04/19/04 Loc: southeastern Nebraska Re: "airy disk" diameter changes with magnitude [Re: David Knisely]       #5043601 - 01/29/12 01:47 AM Attachment (35 downloads) Edit   Reply   Quote Quick Reply   Here is what Gamma Andromeda looked like a number of years ago as the B-C pair was closing to the point of the near-merging of the Airy disks. Post Extras:       blb Post Laureate Reged: 11/25/05 Loc: Piedmont NC Re: "airy disk" diameter changes with magnitude [Re: David Knisely]       #5044112 - 01/29/12 12:26 PM Edit   Reply   Quote Quick Reply   That is a beautiful drawing there David. When I enlarged the drawing by 400% and scaled the rings, I found the brightest first ring on the yellow star was 0.75" in diameter and the close little blue stars were 0.55" in diameter. Is that difference in size due to the differences in the wavelength or color difference between these stars? Or is it the difference in there magnitude? Post Extras:       David Knisely Postmaster Reged: 04/19/04 Loc: southeastern Nebraska Re: "airy disk" diameter changes with magnitude [Re: blb]       #5044230 - 01/29/12 01:35 PM Edit   Reply   Quote Quick Reply   Any difference is due to the limited pixel size I used and my inability to precisely duplicate the exact size of the stars using my paint program. I measured the yellow star's diffraction disk radii from the center to the middle of the first dark ring as 5 pixels and the one of the blue star to 4 pixels, but again, most of this is because I didn't quite get the sizes right (it is, after all, just a drawing). However, that difference does come close to the nearly 30% example I gave earlier, so perhaps it isn't all that bad an attempt. Clear skies to you. Post Extras:       GlennLeDrew Postmaster Reged: 06/18/08 Loc: Ottawa, Ontario, Canada Re: "airy disk" diameter changes with magnitude [Re: David Knisely]       #5045343 - 01/30/12 02:14 AM Edit   Reply   Quote Quick Reply   If the star colors could be sufficiently pure, the diffraction rings would to a good extent scale with wavelength. But given that most stars are more like white light with a bias to (slight) bluishness and orange, the mix of wavelengths blends the contributions of all wavelengths so that the rings have nearer to the same size. It must be noted that only by contrast do the hotter stars appear bluish. To the eye, with its 'built-in filtration', even the hottest stars are essentially white. And so only the cooler (or more reddened) stars will have a significantly non-white aspect. As a result, we can expect the diffraction ring diameters to be defined by characteristic wavelengths in the range ~500-620nm, a variance of no more than 25%. Post Extras:       drollere Pooh-Bah Reged: 02/02/10 Loc: sebastopol, california Re: "airy disk" diameter changes with magnitude [Re: GlennLeDrew]       #5045925 - 01/30/12 01:08 PM Edit   Reply   Quote Quick Reply   Quote: If the star colors could be sufficiently pure, the diffraction rings would to a good extent scale with wavelength. But given that most stars are more like white light with a bias to (slight) bluishness and orange, the mix of wavelengths blends the contributions of all wavelengths so that the rings have nearer to the same size. yes, as i pointed out above. stars are not monochromatic lights, but broadband sources, and integrating over the whole visible profile will produce only very small variations in the gaussian scale. a single "dominant wavelength" (often used as the metameric match for a broadband profile) is being confused with a single wavelength used to simplify a physical calculation. anyone who has experience observing double stars under high magnification and good seeing, and has actually visualized the central disk and the difference between the disk and the surrounding rings has seen that the disk is not always the same size. it varies with magnitude, and one of the more enjoyable visual features of unequal double stars is the contrast in the size of their disks. yes, the wave theory requires the central disk to be "the same size", but unfortunately wave theory does not determine what is seen by the observer -- the eye and the amazing image processing abilities of the brain having quite a bit of influence. the problem with attributing the variations in the size of the central disk to some visual threshold effect, as glenn suggests, is that any visible reduction in the diameter of the disk would require a threshold that was raised above the luminance of the diffraction rings. look at the gaussian profile of a point image; the rings are far below the peak luminance of the central spot. yet knisely and i both observe the fainter companion with both a smaller disk and with a surrounding ring. where i differ with knisely is that i see the ring around the secondary of gamma andromedae as hugging it rather closely. i do not see the large gap he shows. however our two drawings are excellent diagrams of competing hypotheses, and perhaps some of you can refer to gamma andromedae yourself, and compare what you see to the two drawings, and give your impression as to which seem more accurate. remember: high magnification, at least 500x, is helpful to examine the diffraction artifact clearly. the common advice about maximum magnification ("what the seeing will allow," 25 times aperture in inches, etc.) is basically the standard for lunar/planetary observation. with double stars, the magnification limit easily can be double what a good lunar view would require. 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