Path: newsfd02.forthnet.gr!HSNX.atgi.net!headwall.stanford.edu!newshub.sdsu.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: 29 Aug 2004 23:30:39 -0700 Organization: http://groups.google.com Lines: 377 Message-ID: References: <1093598175.922815@athnrd02> <1093633886.990864@athnrd02> <1093641120.500668@athnrd02> <1093642681.105451@athnrd02> NNTP-Posting-Host: 216.190.205.196 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1093847439 8637 127.0.0.1 (30 Aug 2004 06:30:39 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Mon, 30 Aug 2004 06:30:39 +0000 (UTC) Xref: newsfd02.forthnet.gr sci.astro.amateur:518684 Ioannis wrote in message news:<1093642681.105451@athnrd02>... > The calculations still show that I should see M33, for example, 0.42 > times less bright in the 20x100 binos than in the 11x80, whereas in > reality I see it about 2-3 times as bright in the larger pair. > Why the apparent discrepancy? Ioannis, Table 6 in this long explanation will help you order the perceived _unit brightness_ seen in telescopes and binoculars applying differing aperature _and_ magnification. This is a long follow-up explanation to my prior post for those wanting more background regarding the general equation for the relative brightness of the telescopic image - RB = ( D_obj^2 * theta_transmission factor) / (D_exit_pupil)^2 * M^2 Eq. 1.0 The amount of light collected by the telescopic, its _light grasp_, is the ratio of the area of the objective divided by the area of the human eye pupil, or about 7.62 mm at its maximal dilated pupil. Using the basic forumla for the area of a circle - A= (D/2)^2 * pi gives - G=((D_obj^2/4)*pi* theta_transmission factor )/( D_exit_pupil^2/4 * pi) Eq. 2.0 Ignore the transmission factor for now, by making it equal to 1 or 100%), giving: G = ( (D_obj^2/4 * pi) ) / ( D_exit_pupil^2/4 * pi ) Eq. 2.1 or by cancelling, simply - G = D_obj^2 / D_exit_pupil^2 Eq. 2.2 This light grasp brightness can be perceived by removing the eyepiece from a Newtonian reflector and observing the brightness of the image of the full Moon as seen in the primary mirror. Here you are comparing the relative brightness of the object as seen by the naked eye (the full Moon in this case), with its unmagnified light-grasp brightness as seen in the primary mirror. But this is not the brightness of the telescopic, or magnified, image seen in the eyepiece. When viewing an extended object, the radius of the area of light collected is increased from the smaller true field to the larger apparent field. For example, the greater amount of light gathered by the objective (its light grasp), looking at let's say 100 arcsecond true field, and is magnified and spread out over the 30 degree field seen in the eyepiece. This dilutes the brightness of the light collected by the objective. This effect can be seen by pointing a Newtonian reflector at the Moon. Remove the eyepiece and look at the brightness of the image in primary mirror. Insert the eyepiece, focus and compare the brightness of the telescopic, or magnified, image, to the light grasp brightness. So the _brightness of the telescopic image_ seen in the eyepiece is given by: B_tel = ( (D_obj/M)^2/4 * pi ) / ( D_exit_pupil^2/4 * pi ) Eq. 3.0 which simplifies to: B_tel = D_obj^2 / ( D_exit_pupil^2 * M^2) Eq. 3.1 The _relative brightness of the telescopic image_ is the ratio of the telescopic image brightness, given by Eq. 3.1, above, to the brightness of the naked eye image. RB = ( D_obj^2 ) / (D_exit_pupil)^2 * M^2 Eq. 4.0 Putting the transmission factor back in we get: RB = ( D_obj^2 * theta_transmission factor) / (D_exit_pupil)^2 * M^2 Eq. 4.1 But again, we'll ignore the transmission factor for now, set it to 1 or 100%, giving simply: RB = ( D_obj^2 ) / (D_exit_pupil)^2 * M^2 Eq. 4.2 To see this effect, compare the brightness of the full Moon as seen with the naked eye, to its brightness as seen in the eyepiece. Repeating the light grasp and relative brightness comparisions on the full Moon, note that: Light_grasp_brightness > Brightness_naked_eye > Brightness_magnified_telescopic or G > B_naked_eye > B_tel Eq. 5.0 In Equation 4.1 above, we have the variable of magnification, or M. But magnification can be expressed in terms of a uniform scale, the magnification per aperature inch, times the aperature of the telescope in question. David Knisely, often posts a Usenet summary of useful magnifications based on based magnification per aperature inch: ================= Table 2 - Knisely's Useful Magnifications LOW POWER (3.7 to 9.9x per inch of aperture)(6.9mm to 2.6mm exit pupil) MEDIUM POWER (10x to 17.9x per inch of aperture)(2.5mm to 1.4mm exit pupil) HIGH POWER (18x to 29.9x per inch of aperture)(1.4mm to 0.8mm exit pupil) VERY HIGH POWER (30x to 41.9x per inch of aperture)(0.8mm to 0.6mm exit pupil) EXTREME POWER (42x to 75x per inch)(0.6mm to 0.3mm exit pupil) EMPTY MAGNIFICATION (100x per inch and above) From D. Knisely, 5/14/2004 sci.astro.amateur Usenet post, Thread "Eyepiece advice, again". ================= Sidgwick's Amateur Astronomer's Handbook (1971 3ed.) at pages 29-30 has a similar table, which is expanded here at Table 3: ================= Table 3 - Magnitudes per aperature inch M_ap_inch times D_obj = M Mai D M 3.3 D 3.3D Maximum eye pupil size; minimum useful magnification 3.4 D 3.4D Maximum eye pupil size approx. per Sidgwick 3.5 D 3.5D 3.7 D 3.7D 3.9 D 3.9D 4.1 D 4.1D 4.3 D 4.3D 4.5 D 4.5D 4.8 D 4.8D 5.1 D 5.1D 5.5 D 5.5D 5.9 D 5.9D 6.3 D 6.3D 6.9 D 6.9D 7.5 D 7.5D 8.3 D 8.3D 9.3 D 9.3D 10.5 D 10.5D 12.1 D 12.1D 14.3 D 14.3D 17.4 D 17.4D 22.2 D 22.2D 30.8 D 30.8D 33.3 D 33.3D - Minimum exit pencil from eyepiece perceivable by 50.0 D 50.0D human eye; maximum useful magnification 66.7 D 66.7D ================= Substituting in the magnitudes per aperature inch into Eq. 4.2, we get: gamma = Magnitudes per aperature inch Eq. 6.0 RB = ( D_obj^2 ) / (D_exit_pupil)^2 * ( gamma * D )^2 Eq. 6.1 This simplifies to: RB = ( D_obj^2 ) / ( D_exit_pupil^2 * gamma^2 * D_obj^2 ) Eq. 6.2 RB = 1 / ( D_exit_pupil^2 * gamma^2 ) Eq. 6.3 The maximum exit pupil size (7.620mm;0.30in) is a constant. So Equation 6.2 further simplifies to: RB = ( (25.4^2) / 7.620^2 ) * ( 1 / gamma^2 ) Eq. 6.4 11.1 / gamma^2 Eq. 6.5 or, in inches: RB = ( 1/ 0.3^2 ) * ( 1 / gamma^2 ) Eq. 6.6 11.1 / gamma^2 Eq. 6.7 Again, where gamma is the magnitudes per aperature inch. We now have a method of expressing the relative brightness of the telescopic image as a function of magnitudes of aperature per inch. We usually do not think of magnification in terms of magnification per aperature inch. Rather at a particular scope, we think in terms of the magnification being used. Therefore, the following table shows the magnification applied (lines of constant magnification) and not magnification per aperature inch. ================= Table 5 Relative telescopic brightness (eyepiece brightness / naked eye brightness) and magnification Object size D_obj_in 1 3 3.5 4 4.75 6 8 10 12 D_obj_mm 25.4 76.2 88.9 101.6 120.7 152.4 203.2 254.0 304.8 Magnification applied 6 0.31 8.32 13.22 19.73 33.03 66.58 157.82 308.24 532.64 8 0.17 4.68 7.43 11.10 18.58 37.45 88.77 173.39 299.61 10 0.11 3.00 4.76 7.10 11.89 23.97 56.82 110.97 191.75 20 0.03 0.75 1.19 1.78 2.97 5.99 14.20 27.74 47.94 30 0.01 0.33 0.53 0.79 1.32 2.66 6.31 12.33 21.31 40 0.01 0.19 0.30 0.44 0.74 1.50 3.55 6.94 11.98 50 0.00 0.12 0.19 0.28 0.48 0.96 2.27 4.44 7.67 60 0.00 0.08 0.13 0.20 0.33 0.67 1.58 3.08 5.33 70 0.00 0.06 0.10 0.14 0.24 0.49 1.16 2.26 3.91 80 0.00 0.05 0.07 0.11 0.19 0.37 0.89 1.73 3.00 90 0.00 0.04 0.06 0.09 0.15 0.30 0.70 1.37 2.37 100 0.00 0.03 0.05 0.07 0.12 0.24 0.57 1.11 1.92 110 0.00 0.02 0.04 0.06 0.10 0.20 0.47 0.92 1.58 120 0.00 0.02 0.03 0.05 0.08 0.17 0.39 0.77 1.33 130 0.00 0.02 0.03 0.04 0.07 0.14 0.34 0.66 1.13 140 0.00 0.02 0.02 0.04 0.06 0.12 0.29 0.57 0.98 150 0.00 0.01 0.02 0.03 0.05 0.11 0.25 0.49 0.85 ================= Table 5 shows the brightness of the image of an object seen in the eyepiece as compared to the brightness of the object as seen with the naked eye. For simplicity, Table 5 (and Table 6, below) omit the effect of transmission factors of various scopes, i.e. - about 95% for refractors and 70% for reflectors. Table 5 would be hard to plot as its relative brightnesses range between a high of 532 to a low of 0.01. It is easier to plot in terms of the percent of the brightest image, the 12" telescope used at the lowest magnification being the reference value of 100%: ================= Table 6 Relative telescopic brightness and magnification expressed as percent of brightest image (the 12" telescope) Object size D_obj_in 1 3 3.5 4 4.75 6 8 10 12 D_obj_mm 25.4 76.2 88.9 101.6 120.7 152.4 203.2 254.0 304.8 Magnification applied 6 0.06% 1.56% 2.48% 3.70% 6.20% 12.50% 29.63% 57.87% 100% 8 0.03% 0.88% 1.40% 2.08% 3.49% 7.03% 16.67% 32.55% 56.25% 10 0.02% 0.56% 0.89% 1.33% 2.23% 4.50% 10.67% 20.83% 36.00% 20 0.01% 0.14% 0.22% 0.33% 0.56% 1.13% 2.67% 5.21% 9.00% 30 0.00% 0.06% 0.10% 0.15% 0.25% 0.50% 1.19% 2.31% 4.00% 40 0.00% 0.04% 0.06% 0.08% 0.14% 0.28% 0.67% 1.30% 2.25% 50 0.00% 0.02% 0.04% 0.05% 0.09% 0.18% 0.43% 0.83% 1.44% 60 0.00% 0.02% 0.02% 0.04% 0.06% 0.13% 0.3% 0.58% 1.00% 70 0.00% 0.01% 0.02% 0.03% 0.05% 0.09% 0.22% 0.43% 0.73% 80 0.00% 0.01% 0.01% 0.02% 0.03% 0.07% 0.17% 0.33% 0.56% 90 0.00% 0.01% 0.01% 0.02% 0.03% 0.06% 0.13% 0.26% 0.44% 100 0.00% 0.01% 0.01% 0.01% 0.02% 0.05% 0.11% 0.21% 0.36% 110 0.00% 0.00% 0.01% 0.01% 0.02% 0.04% 0.09% 0.17% 0.30% 120 0.00% 0.00% 0.01% 0.01% 0.02% 0.03% 0.07% 0.14% 0.25% 130 0.00% 0.00% 0.01% 0.01% 0.01% 0.03% 0.06% 0.12% 0.21% 140 0.00% 0.00% 0.00% 0.01% 0.01% 0.02% 0.05% 0.11% 0.18% 150 0.00% 0.00% 0.00% 0.01% 0.01% 0.02% 0.05% 0.09% 0.16% ================= A graphic of this table can be found at: http://members.csolutions.net/fisherka/astronote/astromath/RelativeBrightness/RelativeBrightnessMagnificationPercentChart.gif (The project directory is at: http://members.csolutions.net/fisherka/astronote/astromath/RelativeBrightness/ The above graphic can be "surfed to" via this link.) Two implications of Tables 5 and 6 and the foregoing chart, confirming general experience, is that small telescopes cannot be used with much magnification to view faint objects before the image dims and the object can no longer be seen. Larger telescopes can be used at relatively higher magnifications on faint objects before the image dims below visibility. For example, in Table 6, an 8-power 25mm binocular, a NexStar 4 at 40 power, might be expected to produce images of comparable brightness as an 8" telescope used at 120 power. My personal test was to compare the _unit brightness_ of image produced by a 10x50 binocular, a 20x70 binocular, a 6" newtonian at 40x and 100x and the 6" newt's primary mirror. The ordering of brightness generally followed that suggested by Table 6. Another method to plot Table 5 is by the log base 10 of the relative brightness. A graphic plotting by the log of the relative brightness can be found at: http://members.csolutions.net/fisherka/astronote/astromath/RelativeBrightness/RelativeBrightnessMagnificationLogChart.gif If Table 5 is expressed as the percentage of relative brightness, with the reference 100% being the highest relative brightness in each row (the 12" scope), then a constant ratios of brightness are found, as summarized in Table 1, in the prior post, reproduced here: ================= Table 1 Relative telescopic brightness as a percentage of the brightess image within a magnification class Objective size D_obj_in 1 3 3.5 4 4.75 6 8 10 12 D_obj_mm 25.4 76.2 88.9 101.6 120.7 152.4 203.2 254.0 304.8 Relative Brgt 0.06% 1.56% 2.48% 3.70% 6.20% 12.50% 29.63% 57.87% 100% ================= This applies when comparing different aperatures operated at the same magnification. An Excel worksheet generating the charts and tables in this post can be found at: http://members.csolutions.net/fisherka/astronote/astromath/RelativeBrightness/20040828_RelativeBrightness.xls This is amateur work. Any corrections or pointing out things that are flaty wrong are welcomed and appreciated. Enjoy - Canopus (Kurt) References: Kitchin, Chris. 2003. Telescopes and Techniques. Springer. At 35-36. Knisely D. 5/14/2004 sci.astro.amateur Usenet post, Thread "Eyepiece advice, again" Sidgwick, J.B. 1971 (3rd ed). Amateur Astronomer's Handbook. Dover. New York. At 29-30. Resources: Project directory: http://members.csolutions.net/fisherka/astronote/astromath/RelativeBrightness/ Path: newsfd02.forthnet.gr!HSNX.atgi.net!headwall.stanford.edu!newshub.sdsu.edu!postnews2.google.com!not-for-mail From: canopus56@yahoo.com (Canopus) Newsgroups: sci.astro.amateur Subject: Re: Image Luminosity vs magnification Date: 29 Aug 2004 23:21:28 -0700 Organization: http://groups.google.com Lines: 95 Message-ID: References: <1093598175.922815@athnrd02> <1093633886.990864@athnrd02> <1093641120.500668@athnrd02> <1093642681.105451@athnrd02> NNTP-Posting-Host: 216.190.205.196 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1093846888 8189 127.0.0.1 (30 Aug 2004 06:21:28 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Mon, 30 Aug 2004 06:21:28 +0000 (UTC) Xref: newsfd02.forthnet.gr sci.astro.amateur:518683 Ioannis wrote in message news:<1093642681.105451@athnrd02>... > The calculations still show that I should see M33, for example, 0.42 > times less bright in the 20x100 binos than in the 11x80, whereas in > reality I see it about 2-3 times as bright in the larger pair. > Why the apparent discrepancy? What you are trying to do is compare the unit brightness of images seen in telescopes of differing aperature and magnitude. The _relative brightness of the telescopic image_ is the ratio of the telescopic image brightness to the brightness of the naked eye image, given by the general equation - RB =( D_obj^2 * theta_transmission factor) / (D_exit_pupil)^2 * M^2 Eq. 1.0 In summary, expressed using constant lines of magnification applied to telescopes of varying size, the relative brightness of each image in the eyepiece, using the brightess image in the largest scope as a standard is: ================= Table 1 Relative telescopic brightness as a percentage of the brightess image within a magnification class Objective size D_obj_in 1 3 3.5 4 4.75 6 8 10 12 D_obj_mm 25.4 76.2 88.9 101.6 120.7 152.4 203.2 254.0 304.8 Relative Brgt 0.06% 1.56% 2.48% 3.70% 6.20% 12.50% 29.63% 57.87% 100% ================= These percentages apply if you comparing, for example, an 11x80 bino with 10" DOB dropped down to 10 magnification. How do you compare brightnesses of different aperatures and magnifications? Graphics showing the relative brightness of telescopes of various aperatures and magnifications are posted at: http://members.csolutions.net/fisherka/astronote/astromath/RelativeBrightness/RelativeBrightnessMagnificationPercentChart.gif http://members.csolutions.net/fisherka/astronote/astromath/RelativeBrightness/RelativeBrightnessMagnificationLogChart.gif (The project directory is at: http://members.csolutions.net/fisherka/astronote/astromath/RelativeBrightness/ The above files can be "surfed to" via this link.) A more detailed explanation of how these percentages were derived follows in the next long post, for those wanting to read further. One counterintuitive implication of the relative brightness equation (Eq. 1.0) is that the magnified image in the eyepiece is always dimmer - in terms of the brightness of a unit area - than that seen with the naked eye. The brightest image is that seen directly in the primary mirror with an eyepiece. The current full Moon can used to illustrate these effects. First, look at the light grasp brightness. Light grasp brightness can be perceived by removing the eyepiece from a Newtonian reflector and observing the brightness of the image of the full Moon in the primary mirror. Compare this to its naked eye brightness. Next, compare the brightness of the full Moon as seen with the naked eye, to its brightness as seen in the eyepiece. Note that: Light_grasp_brightness > Brightness_naked_eye > Brightness_magnified_telescopic > Why the apparent discrepancy? Again, this is on the basis of unit area brightness. The effect of having the magnified Moon expanded in the 50 degrees of apparent field in the eyepiece (and a correspondingly larger area of your eye's fovea) can lead to the errorenous impression that the magnified image is brighter than the naked eye image. For exploring relative brightness by aperature and magnification using the full Moon, compare the _unit brightness_ of image produced by a 10x50 binocular, a 20x70 binocular, a 6" DOB at 40x and 100x and the 6" the DOB's primary mirror. The ordering of brightness generally follows that suggested by Table 6 in the following detailed post. Again, a more detailed explanation of the relative brightness equation follows in the next long post, for those wanting to read deeper. The post is split into two parts as a courtesy to those who do not want the additional information. Enjoy - Canopus (Kurt) Path: newsfd02.forthnet.gr!jussieu.fr!ciril.fr!fr.ip.ndsoftware.net!proxad.net!postnews2.google.com!not-for-mail From: canopus56@yahoo.com (Canopus) Newsgroups: sci.astro.amateur Subject: Re: Image Luminosity vs magnification (long explanation) Date: 30 Aug 2004 09:33:55 -0700 Organization: http://groups.google.com Lines: 35 Message-ID: References: <1093598175.922815@athnrd02> <1093633886.990864@athnrd02> <1093641120.500668@athnrd02> <1093642681.105451@athnrd02> <1093849144.886794@athnrd02> NNTP-Posting-Host: 168.179.186.155 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1093883635 5362 127.0.0.1 (30 Aug 2004 16:33:55 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Mon, 30 Aug 2004 16:33:55 +0000 (UTC) Xref: newsfd02.forthnet.gr sci.astro.amateur:518728 Ioannis wrote in message news:<1093849144.886794@athnrd02>... > Canopus wrote: A correction to the long explanation: > For example, in Table 6, an 8-power 25mm binocular, a NexStar 4 at 40 > power, might be expected to produce images of comparable brightness as > an 8" telescope used at 120 power. > > > My personal test was to compare the _unit brightness_ of image > produced by a 10x50 binocular, a 20x70 binocular, a 6" newtonian at > 40x and 100x and the 6" newt's primary mirror. The ordering of > brightness generally followed that suggested by Table 6. Should read: 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). My personal test was to compare the _unit brightness_ of image produced by a 10x50 binocular (not on Table 6), a 20x70 binocular (RB=0.14%), a 6" newtonian at 40x (RB=0.28%) and 100x (RB=0.05%) and the 6" newt's primary mirror. The ordering of unit brightness generally followed that suggested by Table 6. - Canopus 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. Από: "Brian Tung" Θέμα: Re: apparent image size Ημερομηνία: Τετάρτη, 17 Μαρτίου 2004 9:41 μμ Tombo wrote: > Forget the analogies Al. The fact is, F20 and F8 are not the same thing. > F- ratio is a ratio of FL to Aperture. An F20 > scope will give a narrow FOV whereas F8 will over double the FOV. FOV is > also dependant on the FL of EP. > > FOV is a linear relation to F ratio. I think that is rather an inappropriate way of putting it. In case it isn't obvious to the original poster, there are two fields of view: true and apparent. True field of view (TFOV) is the size of the actual patch of sky that you can see through the eyepiece and telescope. Apparent field of view (AFOV) is how big that patch of sky *looks* when magnified by the telescope. Thus, AFOV is, roughly, TFOV times the magnification. Neither is in a simple relationship to f/ratio. AFOV is independent of the telescope altogether; you can see that by looking through the eyepiece when it isn't inserted into any telescope. You'll generally see the field stop clearly delineating the AFOV. TFOV, on the other hand, is dependent on the focal length of the telescope and the field stop opening of the eyepiece. To first order, field stop opening TFOV = ------------------------ * 57.3 degrees telescope focal length The 57.3 "magic number" comes from the number of degrees in a radian. (My next Astronomical Games column will explain this formula, among other things.) Strictly speaking, then, TFOV doesn't depend on the telescope's focal ratio, either, or the focal length of the eyepiece. Practically speaking, there may be some dependence on the focal length of the eyepiece, because shorter focal length eyepieces tend to have smaller field stops, and longer focal length eyepieces wider field stops. If a short focal length eyepiece had a very wide field stop, it would probably have too wide an AFOV and be showing significant aberrations near the edge of the field. Conversely, a long focal length eyepiece with a small field stop would be like looking through a soda straw. Nonetheless, it is misleading to say that either FOV depends on the focal ratio of the telescope. To first order, they don't depend on that at all. Yes, there is some dependence between aperture and focal ratio, but that is an inverse relationship--focal ratio tends to fall as aperture increases--and that makes focal length depend less on focal ratio than it would otherwise (if all telescopes had the same aperture, for instance). Brian Tung The Astronomy Corner at http://astro.isi.edu/ Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/ The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/ My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.txt