Path: newsfd02.forthnet.gr!HSNX.atgi.net!cyclone-sf.pbi.net!216.196.98.144!border2.nntp.dca.giganews.com!nntp.giganews.com!wns13feed!worldnet.att.net!128.230.129.106!news.maxwell.syr.edu!postnews2.google.com!not-for-mail From: canopus56@yahoo.com (Canopus) Newsgroups: sci.astro.amateur Subject: Re: Image Luminosity vs magnification (long explanation) Date: 5 Sep 2004 15:17:02 -0700 Organization: http://groups.google.com Lines: 232 Message-ID: References: <20040830210134.27025.00000073@mb-m13.aol.com> <20040903205554.26941.00000264@mb-m01.aol.com> NNTP-Posting-Host: 216.190.205.215 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1094422623 10688 127.0.0.1 (5 Sep 2004 22:17:03 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Sun, 5 Sep 2004 22:17:03 +0000 (UTC) Xref: newsfd02.forthnet.gr sci.astro.amateur:519792 billferris@aol.comic (Bill Ferris) wrote in message news:<20040903205554.26941.00000264@mb-m01.aol.com>... Bill Ferris wrote in prior messages: My apologies for the delay in responding. Work demands had to take priority for awhile. > G = D_obj^2 / D_exit_pupil^2 Eq. 2.2 > > I'm assuming "G" is the relative light grasp of > an aperture in relation to the light grasp of the human eye. > Is that correct? In your Eq. 2.1, do you mean to use > "exit_pupil" or "eye_pupil?" If you're calculating > the relative light grasp of an aperture > with respect to the eye, then you probably meant "eye_pupil." Yes, Eq. 2.2 is light grasp "G" and exit_pupil refers to the typical maximal dark adapted diameter of the human eye pupil. This is also Eq. 2.2 in Chris Kitchin's _Telescopes and Techniques_ referenced in the long post. > The telescope will have an exit pupil of 25.4-mm, which will > reduce its effective aperture from 254-mm to 70-mm. > This is 10X the diameter of the observer's eye pupil, > which translates to 100X the light-grasp. In relative brightness Table No. 6, the useless low magnifications have not been removed. This omission was intentional for graphing purposes and to make the overall narrative explanation flow better. As magnification decreases, the exit pencil of light from the eyepiece increases in diameter. As the exit pencil exceeds the diameter of the human eye, there is "wasted" light that is projected onto the human eye's iris. Schaefer's 1990 telescopic limiting magnitude model for point-sources captures this relationship algebrically with: F_ep = (D/M*D_eye_pupil)^2 if D_eye_pupil < D/M Eq. 7.1 F_ep = 1.0 if D_eye_pupil > D/M Eq. 7.2 Conversely, the unit brightness that does reach the eyepiece still would be brighter, since D_obj^2 in Eq. 2.2 is larger. An improved table would parse the "useless" low magnifications from Table No.6. Conversely, "useless" high magnifications are parsed from Table No. 6. As magnification increases, the size of the exit pencil from the objective shrinks to the point of not being detectable by the human eye. Those values, below 0.3mm, are parsed from Table No. 6. Knisley's "useful magnification" table lists 0.3mm as the lower boundary of extreme power. See Table 2. The relevant entries are parsed from Table No. 6. The light at these low levels is still being gathered and presumably could be imaged using CCD or film astrophotography. This part of Table No. 6 and the associated figure could be improved graphically, perhaps by adding constraint contours for the limits of useful minimum and maximum magnification for the human eye. Another improvement might be similar constraint contour line for "typical" film and CCD astrophotography. > What do you mean by, "same unit brightness?" I'm trying to reconcile > how these setups might be equivalent. . . . However, in terms > of the perceived appearance of an extended object, the 10-inch > aperture will kick butt--to put it mildly--on the binocs and > 4-inch scope, and should show a richer, more detailed view > than the 8-inch. This is the weakest concept in my post and one that I am still struggling with. Essentially, it is something equivalent to magnitudes per square _apparent_ arcminute (mpsam), that is the magnitude of one or two arcminutes as seen in the apparent field, not the true field. The problem that I ran into was that light grasp, Eq. 2.2 above, is essentially a dimensionless scale. All the units cancel out. Similarly, the relative brightness of an image is simply: RB = G/M Eq. 8.0 which is also dimensionless or is "light-grasp per magnification power". The narrative description needs to be improved and clarified on this point. Maybe the way to improve it is to add a reference object of known brightness in mpsam or magnitudes per square arcsecond (mpsas), like the full Moon. Then Table No. 6 can be expressed in terms of magnitudes. Another possibility is to express Table No. 6 in relative magnitudes. E.g.: m1-m2 = 2.5 log(rb1/rb2) where rb is the relative brightness of each field. But I felt that percentage and log(10) plotting methods were the easist presentation to follow visually. One point that I struggled with as a beginner was the notion that the image in the eyepiece is always dimmer than object as seen directly with the human eye, or Eq. 5 in my long post: G > B_naked_eye > B_tel Eq. 5.0, and for scopes of differing aperature - G > B_naked_eye > B_tel_larger_aperature > B_tel_smaller_aperature Eq. 9.0 assuming the scopes are used at the same magnification. Nonetheless, the experience of Eq. 5.0 at the eyepiece can be illustrated by roughly referring the beginner to look at the "unit brightness" or magnitudes per _apparent_ arcminute of each image. The focus of Ioannis' question was that beginners using small aperature scopes focus on the detectability of extended objects, which in small aperatures and under good non-light polluted skies, is principally a function of aperature size and light grasp. He was trying to order his telescopes and binoculars of differing type by the relative brightness that each image produces. That problem is captured in Eq. 9.0 above. While this relationship can be illustrated by using a single telescope, the 6" DOB example discussed in my long post, it would be nice to have some illustrations that use common small aperature telescopes and binoculars available to most beginners to demonstrate Eq. 5.0 and 9.0. I was trying to roughly relate that experience at the eyepiece to the underlying telescope math. By "richness" you are referring to the enhanced ability of human eye to resolve details in the image because, when larger light grasp aperatures are used at higher magnifications, the human eye has more light to work with. For example, at low aperature sizes (<4") color is not visible in most galaxy DSOs or in most globulars. From posts in this newsgroup, I understand in large aperature scopes (>10") the additional light grasp allows for the seeing of color in such objects. But does this effect, the ability to resolve the smallest arcsec sized contrast of an extended object, hold true when two instruments of differing resolution are used that the same magnification? > [T]he visual images in the two binoculars are explained by the 100-mm > aperture binoculars having an effective light-gathering power nearly > twice that of the 80-mm binocs, the larger image scall in the 20X binocs vs. > the 11X optics, and the lower contrast threshold of the larger aperture instrument. and my examples - >For example, in Table 6, the following telescopes roughly might >produce an image of the same unit brightness: > >1) a NexStar 4 at 20x (relative brightness 0.33% in Table 6), >2) an 8" telescope used at 60 power (relative brightness 0.3% in >Table 6), >3) a 10" telescope used at 80 power (relative brightness 0.33% >in Table 6), and maybe a >4) a 10-power 50mm binocular (relative brightness somewhere >between 0.02% and 0.56% in Table 6). Table No. 6 errs and is incorrect in that it does not capture Clark's effect of background contrast. The narrative should be corrected to expressly state that limitation. IMHO, Table No. 6 is probably still sufficient for its intended purpose, to enable beginners to experiment with a few binoculars and scopes lying around the house. My examples and Table No. 6 will only roughly approximate the order the relative brightness of scopes of differing aperature used at differing magnifications. Within each line of constant magnification, I believe the brightness relationship is properly expressed in Table No. 1. Clark's minimum detection magnification also encompasses the effect of background contrast through his contrast index - i.e. brightness of the object / brightness of the background. This effect is not captured in the simplier, basic-telescope-math relative-brightness model in my long post. Background contrast changes with increasing magnification. Clark's model is a much more comprehensive model, but IMHO, is much more mathematically complex. It is more than most beginners armed with a small telescope and binoculars are prepared to bite off. Clark's background contrast effect can be illustrated by taking a single scope, viewing a blank patch of sky or galaxy DSO, and then increasing the magnification. For the target audience, binoculars that Ioannis is working with and small telescopes, maybe _holding magnification constant_ and then comparing differing scopes is a good supplemental approach for beginners. That was the focus of my post. Then do the Clark contrast example, holding aperature constant and changing magnification. Once the physic's effects of aperature and magnification are experienced separately, then their combined effect, captured in Clark's MDM model along with Black's human eye physiology, are easier for beginners to follow. Bill, thanks for taking the time to plow through my post. What happens when you take a 100-mm binocular at 20x and compare it to an 8" Newt or SCT at 20x? > I've put together an Excel table that quantifies the above examples in terms > common to amateur astronomer. If you'd like, I'd be happy to email you this > file. I'd love to look at it Bill. I'm sure you will come up with something that is easier to follow. My large-attachment email is: fisher$%*&^ka@csolutions$%*&^.net (remove the obvious spam retarding string) or for small attachments (<100k), I can also receive attachments at: canopus56@yahoo.com Is your spreadsheet available at your outstanding Cosmic Voyage website? Thanks again - Canopus Clark, R.N. Visual Astronomy of the Deep Sky. Cambridge Univ. Press. 1990. Kitchin, Chris. 2003. Telescopes and Techniques. Springer. At 35-36. Schaefer, B.E. Feb. 1990. Telescopic Limiting Magnitude. PASP 102:212-229.