Jim Nelson
scholastic sledgehammer
Reged: 05/10/05
Posts: 852
Loc: SE Michigan
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It just is wrong to say that the XF looses 38% of the light and the Radian 75% of the light of an Ortho.
Read the post again...
That's not what the post says. The post says these values, derived from drawings, are "clearly not realistic."
Edited by Jim Nelson (05/03/06 02:53 PM)
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Amalia
Reged: 10/16/04
Posts: 5165
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Please, just wait a little, gentlemen, I have the answer ready,
I just need to convert the pictures, maybe half an hour or so, ok? 
Amalia
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blandp11
Carpal Tunnel
Reged: 04/19/05
Posts: 1963
Loc: Glen Ridge, NJ USA
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I seem to then agree with the post, since I reversed the meaning!
Philip
Quote:
That's not what the post says. The post says these values, derived from drawings, are "clearly not realistic."
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Mostly refractors
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Amalia
Reged: 10/16/04
Posts: 5165
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Hi Stephonon!
I appreciate your critical and very polite post! 
Let me first thank you -- because to be criticized means to be taken seriously.
And since the moment I discovered your post this morning at school --
you *really* transformed my day into a thriller... 
Now, one thing after the other. Please allow me to quote you:
Quote:
Please do not take this post the wrong way, it is only in the interest
of better understanding and communication.
I appreciate your kind words. As I have many questions: We do both share
this your wish.
Quote:
I guess the message is that what is a huge difference to one person
may only be a small one for another and vice versa. And it would seem that
sketches do not work for conveying these differences, because a person
with more sensitive eyes (and brain) is likely to produce different sketches to
someone with less experience or poorer eyesight {snip}
I really wonder about this, too. Experience and sensitivity are surely major
factors. But also the *will* to drive for hours and to observe at the darkest
possible sites. And I think even *joy* may be involved, yes, really, because
I am sure that galaxies shine brighter for people who love them.
A little bit naive, what?
Quote:
{snip} but the numbers confirm my suspicions that your sketches
greatly exaggerate the differences in brightness/contrast you saw. I believe
this is probably due to the acute sensitivity you must have developed through
experience with observing faint objects.
Assuming 100% transmission for sketch corresponding to the Pentax ortho,
the total light intensity for sketches corresponding to the other two eyepieces
would give transmissions of
62% for the XF,
25% for the Radian,
which are clearly not realistic. Even if the differences were not entirely due to
transmission but other factors, such as lower contrast due to light scatter (e.g.
the Radian's sky background was brighter, drowning out detail), that would still
represent an unrealistic scenario.
This really kept me very very busy. Thank you for this, as it was a great
opportunity to learn on.
WHERE HAPPENED A MISTAKE?
After many many "maybes", here one incertitude which remained:
The sketches you see in CloudyNights are *not* the sketches I sent. Let me be
clear: I really appreciate all the work CN's computer experts did for hours to
make it possible to post my review. It was hard for them, as they had to work
a lot on it (it was a Macintosh AppleWorks file and the conversion did not work
well).
Here is the picture I sent (and this is maybe *a cause of an error*
because the picture in the review got "stretched"):
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Amalia
Reged: 10/16/04
Posts: 5165
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And it comes even worse... 
The picture I sent was not even the same as the original one I computed...
The original is a Photoshop-file and I converted it into a "Save for Web"-GIF.
And I think the original shows the Radian even worse situated. I have remarked
this, but then I thought there are so many TV-fans on CN, the GIF version must be
already hard enough (and of course I did not know how my review would be received).
Here a screenshot, showing both documents,
up is the original big file ("M104 v2.psd" with 1.23M)
down is the converted smaller file ("M104 v2.gif" with 52.6k)
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Amalia
Reged: 10/16/04
Posts: 5165
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Ok. Now let's approach this your critic on a mathematical way. Allow me to add
that this is a slippery way for me, I hope I make no mistakes. I base my
calculations on Mike Hosea's post of the 29.4.2006 in the eyepiece forum:
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Amalia
Reged: 10/16/04
Posts: 5165
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(based on a very useful hypothesis set up by Mike: click here to understand better.
Hmm... so this shows that both eyepieces could be underrated by my sketch.
This shows also that 60% (59.11) would still mean a very high quality eyepiece
with only 0.375% reflectivity per air-glass surface!
Now... one could add other informations, as: the reflections I have seen in the lenses.
Or the certainly important fact that my sketches are human made
pictures, drawn at subfreezing temperatures, and postprocessed at home
with my computer. They certainly are not to be taken as a 100% truth. And
I have one more idea -- but later more about this.
But these calculations were not useless, you will soon see why. Just remember: 60%.
Well, I think the solution is much easier: I have tried to check your calculations
using Photoshop.
Look, since the "ortho sketch" is to be taken as 100%, for the SMC XF I went
down 38% with the brightness, to 62% -- and for the Radian to 25%, as you
calculated:
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Amalia
Reged: 10/16/04
Posts: 5165
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What happens when I change the *contrast* to the values you calculated:
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Amalia
Reged: 10/16/04
Posts: 5165
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And now I change the game: To find the "real" contrast difference I
use the ortho sketch as 100%, copy-paste it twice, and try to set
down the contrast until I get the approx. same result as in
my original GIF-sketch, so to be able to read in Photoshop how much
the difference is:
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Amalia
Reged: 10/16/04
Posts: 5165
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You see the *very much approximate* results:
ortho sketch: 100% contrast
XF sketch: 86% contrast
Radian sketch: around 60% (comparing only the brightness of the cores -- the
outer part of the galaxy is different because this is a sketch against a paste-copy thing).
Ok, this last picture was kind of a game, as I don't really think a sketch can
be used to get contrast-measured. There are too many human factors involved in this.
But still, you surely remember my calculations: A 4-groups eyepiece with 0.375%
reflectivity loss at 8 air-glass surface could result in a (highly theoretical)
60% contrast -- compared to a 2-groups eyepiece with only 0.25% reflectivity.
The calculations and this last improvised Photoshop measurement shows that this is
very possible.
So, please understand that my sketch *is* realistic.
(Even if you don't like it. Sorry! )
And it also shows that it is *possible* that this is realistic for an
eyepiece.
Now, I suspect another influence, too: Is it possible that the colour
of the glass influences the contrast on DSOs, especially galaxies?
After doing my review I highly suspect, yes, it does.
Being interested in communication about this I ask you:
Do you observe DSOs at really dark sites?
Do you own quality eyepieces with the same amount of air-glass surfaces which
differ in the colour of the glasses?
Would you like to communicate with me about this?
Thank you for reading! Thank you, Stephonon! I feel very good about your question,
as I am very sure that many more doubted about my sketches -- Thanks for asking!
Amalia
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Stephonon
Carpal Tunnel
Reged: 07/28/05
Posts: 1873
Loc: Melbourne, Australia
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Thanks for your thorough response, Amalia. Lots to discuss. You'll hear from me soon.
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Steve H --- Dobs: Saxon/SW 10" f/4.7, GSO 8" f/6, custom truss 8" f/4 | Intes MK-65 (6" Mak) + EQ | binos: Pentax PCF 8x40, AOE 10x50MX Ultra, AOE 12x60.
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Stephonon
Carpal Tunnel
Reged: 07/28/05
Posts: 1873
Loc: Melbourne, Australia
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I best break this up into several installments. Here is the first
On the calculations
Mike's spreadsheet contains some serious errors, and I would not recommend you take those numbers and calculations seriously. But well done to Mike for documenting what the spreadsheet does, otherwise it would have been hard to work out how the results are calculated. Now before people jump at my throat, please read on as I try to explain.
There are at least three problems I can see. The first two are critical the third one not so in this case.
1) Definition of contrast. Contrast is defined here as proportional the contrast ratio: the ratio between the brightest and darkest parts of an image, and 100% contrast is defined to correspond to a contrast ratio of 100:1. Clearly then, we can have 200% contrast for an image with contrast ratio of 200:1, or 10000% contrast for 10000:1 etc etc. So the 100% level is rather arbitrary, certainly not maximum. (In fact there is clearly no theoretical maximum.) If you ever watched a movie on a 100:1 contrast ratio screen you would know that this level of contrast is very poor, and all detail in the darker parts of the image is completely drowned out. There is also an issue with contrast < 1%, but I will not go into it here (those who wish to ponder can ).
2) Definition of "dark". Column F defines the intensity in the darkest area of the obect as 1/100 times the intensity in the brightest area. This factor of 1/100 is completely arbitrary, and comes from nothing other than our common use of the base 10 number system, and the use of the percentage scale. If we were Babylonians it would probably be 1/60. But there is no reason why it couldn't be 1/200 instead, or 1/1000, or whatever you like. And then you would get a completely different result from the calculation!
3) Combining reflections from multiple surfaces. One cannot simply sum the reflectivities of multiple surfaces to get the combined reflectivity (try 4 surfaces with 30% reflectivity to see why), although this is a valid approximation when there are a small number of surfaces and/or the reflectivity is small, which is the case here.
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Steve H --- Dobs: Saxon/SW 10" f/4.7, GSO 8" f/6, custom truss 8" f/4 | Intes MK-65 (6" Mak) + EQ | binos: Pentax PCF 8x40, AOE 10x50MX Ultra, AOE 12x60.
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Stephonon
Carpal Tunnel
Reged: 07/28/05
Posts: 1873
Loc: Melbourne, Australia
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Self-consistent definition of contrast
FYI a bit more on contrast (as a bit of an aside). The usual accepted definition of contrast in scientific imaging, and in imaging processing in general, is the ratio:
Contrast = (Imax - Imin) / (Imax + Imin)
where Imax = maximum light intensity, Imin = minimum light intensity in image (or more precisely, region of interest). Notice that this ratio is very different from the "contrast ratio" which is simply Imax/Imin.
Minimum contrast is 0 and maximum contrast is 1. (Multiply by 100 if you like to think in % scale.) Contrast = 0 corresponds to Imax = Imin, so a uniformly illuminated completely featurless field. Contrast = 1 = 100% is perfection and corresponds to Imax/Imin = infinity (unattainable, like perfection ), i.e., either Imin = 0 or perfect black, or Imax = infinity or brighter than the brightest. Also note that with the above definition you cannot have better than 1 (= 100%, perfect) contrast. Some practical values:
Contrast Ratio --- Contrast
1:1 --- 0.00
1:2 --- 0.33
1:4 --- 0.60
1:10 --- 0.81
1:100 --- 0.98
1:1000 --- 0.998
It might be worth noting that contrast values indicated by image processing software only give you some arbirtrary scale to work with and help visualise what you are doing but that is all. In the Gimp, contrast can be adjusted from -127 to 127 from a reference level of 0. Maybe Photoshop works from 0-100 with ref level at 50. I haven't used it for a while so I cannot remember.
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Steve H --- Dobs: Saxon/SW 10" f/4.7, GSO 8" f/6, custom truss 8" f/4 | Intes MK-65 (6" Mak) + EQ | binos: Pentax PCF 8x40, AOE 10x50MX Ultra, AOE 12x60.
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Stephonon
Carpal Tunnel
Reged: 07/28/05
Posts: 1873
Loc: Melbourne, Australia
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Okay, now back to the sketches.
Sketches with "reduced contrast"
Amalia, the images labelled with varying degrees of reduced contrast in your posts above depict more than just contrast changes. When you reduce contrast, everything should shift towards medium grey, so the darker regions should become brighter and the brighter regions dimmer. All I am seeing is everything becoming dimmer, so you must have reduced the brightness as well (or maybe the software automatically does it, pulling black level back to zero pixel value).
Original sketches
The brightness change in going from the ortho to either the XF or the Radian sketch is not uniform over the entire image, which is why you could not reproduce the Radian and XF sketches by simply reducing the brightness in photoshop by the 62% and 25% that I quoted in my earlier post. These figures correspond to the total brightness (total light intensity) change in the images, and most of the decrease in the Radian and XF sketches is due to the decreased brightness in the dimmer parts of the ortho sketch, not in the bright centre. So in fact, over the bulk of the galaxy you have the most contrast in the Radian sketch because it goes all the way down to pitch black where the others only go to grey! More on this in a moment.
Comparison of XF and Radian sketches with ortho sketch
The peak intensities do not change quite as much as the total: Taking the ortho sketch as reference at 100%, the peak intensity in the XF sketch is 80% and in the Radian 55%.
What the Radian sketch shows compared to the ortho sketch is a reduction in brightness and an increase in contrast. It is like when you turn the contrast up too high on your TV. The darks go too dark and you stop seeing faint detail.
The XF sketch shows this too (decrease in brightness and increase in contrast) but to a lesser extent.
I have tried to approximate your XF and Radian sketches by altering the brightness and contrast of the ortho sketch. We already know that the maximum brightness should be 80% of ortho for the XF and 55% for Radian, which takes the guesswork out of brightness. For a given contrast level, one just decreases the brightness until the peak level is consistent with the sketch being mimicked. The end result is that the original XF and Radian sketches are best approximated with:
orhto -> XF: +15 contrast, 80% peak intensity
ortho -> Radian: +30 contrast, 55% peak intensity,
where contrast is indicated on a scale from -127 to 127, where 0 is the original image, -127 turns all pixels the medium grey, and at +127 every pixel becomes either black or white with no greys.
See attached image. (As well as the above operations, the contrast of the entire composite image of six Sombreros was stretched to max pixel = white, which makes no difference to the relative intensities, just makes the whole image easier to see on a monitor.)
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Steve H --- Dobs: Saxon/SW 10" f/4.7, GSO 8" f/6, custom truss 8" f/4 | Intes MK-65 (6" Mak) + EQ | binos: Pentax PCF 8x40, AOE 10x50MX Ultra, AOE 12x60.
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Stephonon
Carpal Tunnel
Reged: 07/28/05
Posts: 1873
Loc: Melbourne, Australia
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@ Amalia:
Quote:
And I think even *joy* may be involved, yes, really, because
I am sure that galaxies shine brighter for people who love them.
Ah, but of course!
Quote:
After many many "maybes", here one incertitude which remained:
The sketches you see in CloudyNights are *not* the sketches I sent.
Don't worry, they are the same as what you sent (I checked your screenshot). They have just had the brightness increased ("stretched"), but uniformly so, which makes no difference other than make them easier to see. The numbers remain the same. Total relative brightness figures are the same for both sets of pictures, 100%, 62% and 25%. Peak realative brightnesses are the same too: 100%, 80% and 55%. (As already discussed.)
Quote:
Being interested in communication about this I ask you:
Do you observe DSOs at really dark sites?
Yes. I'm a bit of a mountain observer like yourself, but our mountains are more like hills compared to yours. (1300-1400m above sea level.)
Quote:
Do you own quality eyepieces with the same amount of air-glass surfaces which differ in the colour of the glasses?
Would you like to communicate with me about this?
Yes and yes. Coloured widefields include Stratus and T6 Nagler. Not so coloured ones are Pentax XWs and the 8.5mm XF. Light transmission of my "coloured" glass is significantly less. I also have the 17mm T4 Nagler but I am not so sure about this one because I haven't used it much yet. But it seems to have better transmission than the T6.
OTOH Simpler EPs (4 elements) I have HD orthos in colour neutral territory, and Televue plossls, which are a bit reddish, but their transmission is at least as good as the HD orthos. So redder does not always mean dimmer.
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Steve H --- Dobs: Saxon/SW 10" f/4.7, GSO 8" f/6, custom truss 8" f/4 | Intes MK-65 (6" Mak) + EQ | binos: Pentax PCF 8x40, AOE 10x50MX Ultra, AOE 12x60.
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Starman1
Vendor (EyepiecesEtc.com)
Reged: 06/24/03
Posts: 17639
Loc: Los Angeles
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At this point, I think thanks are in order for Stephonon's discussion of brightness and contrast. The understanding I have is dramatically improved. It represents yet another reason why I think the word contrast is often misused by the astronomical community, where descriptions are concerned.
But the reason I post is to talk about the light transmission of eyepieces.
I am concerned that people believe that light transmission is a large part of what is or isn't visible through an eyepiece, and I believe it is not. There are many reasons why an image in an eyepiece with more elements may be worse on axis, but transmission is probably not one of them.
Here are some examples of fully multi-coated eyepieces (perfect coatings, perfect baffling, etc):
Transmission:
Plossl, Orthoscopic, multi-coated, 4 air-to-glass surfaces:
98.0%
T6 Naglers, others, multi-coated, 8 air-to-glass surfaces:
96.0%
Widefields with 10 air-to-glass surfaces:
95.1%
The difference between the worst and best transmission is 3%. No test ever done indicates any human can detect a brightness difference of 3%, in darkness or light.
Actual measurements of eyepieces show lesser figures for transmission, but most tests still show small percentages of differences in eyepieces with fully multi-coated surfaces--at least within the range of "there, but not detectable".
So what accounts for the differences we see?
--baffling(are the eyepieces well designed? Recent problems with some say this is not guaranteed)
--light scatter from interior surfaces(lens edges, barrel interiors, spacers)
--light scatter from exterior surfaces(kudos to William Optics, here)
--polish on the lenses (with poorer polish, or less accurate surfaces, more lenses equals poorer images)
--quality of coatings(are they dark and well-applied?)
--type of glass used and frequency of light transmission(does the glass itself filter certain frequencies of light?)
--brightness of the image(brighter images also produce brighter light scatter and reflections)
--vignetting(does the full axial ray come through? How wide is the 100% illumination field? Does the eyepiece stop the scope down?)
--Eyepiece design (the ability to reduce peripheral light outside the eyepiece. Ever notice cupping your hands around the eyepiece allows you to see fainter details?)
--Eyepiece design II (is there residual distortion of a type that affects the image quality?)
One thing I think for certain: some of these problems can be avoided by simple tests that can be administered in the shop before the eyepieces are purchased. Others reveal themselves only after testing. But if the issues present themselves in the shop (transmission, tint, etc), then don't buy the eyepieces.
But the point I make here is that I don't believe noticeable transmission differences are due to the number of elements, but the quality of coatings, glass types, and other issues unrelated to the overall number of elements.
Recently (well, a year ago), I tried an experiment: since the Paracorr has 4 elements, and 4 air-to-glass surfaces, and 97-98% transmission, I tried observing M5 on the meridian both with and without it to see if resolution or faintness of stars was affected by it. You know what I'm going to say, don't you? Fainter stars were visible WITH the Paracorr than without, and the cluster was noticeably better resolved WITH the Paracorr than without. The explanation was tightness of focus and the size of the star images--light tranmission and the number of surfaces wasn't relevant. The answer might have been very different at f/10. But it points out that there are more issues with the telescope-eyepiece interaction than a simple analysis of the number of lenses will give you.
So, a reviewer (like Amalia) can report what she sees, and that is probably good enough for us. But to extrapolate to the reasons for what is seen is dangerous unless there are some really defined lab/field tests involved. I applaud her for attempting to do just that. This is a short step down a long road.
--------------------
Don Pensack
www.EyepiecesEtc.com
12.5" Teeter/Zambuto, 5" Maksutov
Sustaining Lifetime IDA member
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Starman1
Vendor (EyepiecesEtc.com)
Reged: 06/24/03
Posts: 17639
Loc: Los Angeles
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Well, I guess coatings may be the culprit.
Here is an article about eyepiece coatings that is VERY germane to this discussion:
http://geogdata.csun.edu/~voltaire/roland/coating.html
Roland Christen does a very good job of explaining why some eyepieces appear very different than others, even when all are "fully multi-coated".
Highly illuminating. 
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Don Pensack
www.EyepiecesEtc.com
12.5" Teeter/Zambuto, 5" Maksutov
Sustaining Lifetime IDA member
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Amalia
Reged: 10/16/04
Posts: 5165
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Hi Stephonon!
Thank you for your intelligent answers!
Quote:
Mike's spreadsheet contains some serious errors, and I would not
recommend you take those numbers and calculations seriously.
I rather think that Mike found out a clever way to explain me some things,
and he adapted his explanations to my "mathematical level"...
Maybe I should not have used his simplified explanations in this context.
But I was so sure to have understood something, for once, and it took me
"only" something more than two or three hours to translate *the thoughts into
the formulas* to create the spreadsheet...  Oh, well... 
Quote:
Maybe Photoshop works from 0-100 with ref level at 50.
I haven't used it for a while so I cannot remember.
Photohop works so: When I open the *Contrast and Brightness" window,
the picture is set on zero, with the possibility to go up to +100 or down to
-100, with a controller for contrast and another for brightness.
Quote:
Sketches with "reduced contrast"
Amalia, the images labelled with varying degrees of reduced contrast in your
posts above depict more than just contrast changes. When you reduce contrast,
everything should shift towards medium grey, so the darker regions should
become brighter and the brighter regions dimmer. All I am seeing is everything
becoming dimmer, so you must have reduced the brightness as well (or maybe
the software automatically does it, pulling black level back to zero pixel value).
I tried this on the PSD and the GIF file right now - Photoshop does exactly as
you say: it dims down everything. Result is black, not grey. There seems to be
a "different philosphy" between our softwares.
I have taken up your idea, (but the original pen sketch is gone long ago, so I have
re-read my descriptions, searched in my memory, but well, this sketch was done in
mid-february, so... hmm). Then I have copy-pasted the "ortho sketch" and played
with contrast and brightness, and maybe this result is "more scientific". There
should be less brightness difference now. I'd actually really like to re-test this under
the sky. Do you like this one better?
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Amalia
Reged: 10/16/04
Posts: 5165
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But this is exactly the point: Does a sketch really have to *be measurably scientific*?
I looked after the translation of "sketch". It is "Skizze", as I already thought to
know, and in my language I understand a Skizze as a "result which does not
pretend to be finished or perfect".
While searching in my memory, I remembered two things about the making
of these skteches:
#1 It was a big problem to show this impression: "With the Radian I can see that
M104 shows a black dust belt -- but I can not see the smaller part of the galaxy".
So I had to introduce a compromise, which was to draw a tiny line, a part of
the smaller half of M104, because else there would have been no impression
of the black dust on the sketch. I have *not* seen this line, though.
#2 One thought came up, and I think this is maybe the most important one, even
more important than any measurability: It is about *time*.
Let's do a little experiment, will you?
Look at this wonderful sketch, well, this masterpiece by Carol L: Click!
Don't read on... watch the sketch, please...
Please, now say how long you watched the sketch...
One, two, or three minutes, maybe?
And this is exactly the point I want to tell you. Let me explain. I have observed
the Crescent Nebula, too. I have a 12" Dobsonian and lots of very good eyepieces.
Carol observed with a SCT 8" (which is more obstructed than my Dob),
and as I think to know, she never mentioned special eyepieces. Now... sadly
enough, I must admit that with all my 4" more I have not been able to see half of
the impressions Carol presents us by her sketch. Amazing, isn't it?
Now what happened? Let's take in consideration that she is a *much* more
experienced observer than me, and a real artist. But the thing which actually
matters, is that she spent hours, or entire nights to do her sketch. I don't
know how long it took her, but she surely observed the Crescent Nebula much
longer than I did. And... she sketched. I have done less than a dozen of sketches,
but when I sketch, I watch differently, more deep. I see more.
From my impressions with 12" I could say: "This sketch of the Crescent Nebula
is waaaay exagerated!" And it is surely is, from a scientific point of view, if
someone would have the idea to measure the contrast, for instance... 
One never sees that much contrast on the Crescent Nebula, no, at least *not me*
with 12" and O III at a really dark site. -- But maybe the most difficult part of
sketching is dealing with contrast to be able to show all these very faint
impressions.
It is because this is about "time". He who watches the sketch does this for less
than a minute. And in this time gets all the impressions of *much more time* of
observing and sketching.
Let me know what you think -- you know, I think I will anyway ask CN for a
change of this picture, as it was not intended to be so big, that definitely
disturbs me: It changes the impression way too much, as so the galaxy seems
to jump out of the screen.
About your second post: More later!
Amalia
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Starman1
Vendor (EyepiecesEtc.com)
Reged: 06/24/03
Posts: 17639
Loc: Los Angeles
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Hmm.
My recorded impression of the Crescent Nebula (with an identical 8"SCT) was:
"Britest section is crescent arc,averted vision shows filled-in pear.Many filaments fill pear shape, making nebula rather large. UHC filter. Center striations appear to be somewhat parallel, as if ripples moving across a pond".
Carol's drawing shows that her night vision was partially damaged by the light she used to draw with, and, perhaps, that she views in a more heavily light polluted site than I do.
My 12.5" shows so much detail I could not draw it, with the crescent part broken up into discrete tendrils wreathed together, and not too dissimilar to the section of the Veil Nebula that contains the bright star 52 Cygni.
Try it again when it is near the zenith, and you will be amazed at the amount of detail.
There have been many times I have looked through the eyepiece of a large telescope and seen a lot of detail in a DSO, only to return to my 8" or 12.5" and notice that now I can see all the same details, only dimmer. It is why I think sketches often will show more than immediately confronts the eye, but less than can be seen with careful study. The tiny, subtle, details that can be seen by the eye often cannot be drawn. It is why even the best sketches display a lot less detail than the eye can see. I suspect Carol's sketch is the same.
What it means is that, unlike a photograph, a sketch cannot be taken too literally to represent exactly what was seen.
--------------------
Don Pensack
www.EyepiecesEtc.com
12.5" Teeter/Zambuto, 5" Maksutov
Sustaining Lifetime IDA member
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