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# Comparing refractors to Newtonians to Catadioptric scopes - Curiosity

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### #1 aeajr

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Posted 06 March 2018 - 11:17 PM

This is strictly about curiosity.  Nothing is being bought.

I have read many times that refractors can be smaller than Newtonians or Cats yet have comparable effective aperture because there is central obstruction with the Newts and the Cats.   Makes sense, but how much is the differential?

For example I have seen a 4" refractor/102 mm   equated to a 5" Newt, Mak or SCT.   But when I look at the specs of the central obstructions they are typically less than 10% in area.  So 10% of 127 mm ( 5") would be 12.7 mm so that 127 would be approx equivalent to about a 114 mm refractor.

If I do it a little differently, 127 X 127 = 16,129   Approximately 90% of that would be 14,516.  SqRt of that is 120 mm, a bit over 4.5"

If that is right than a 4" refractor would be about equivalent to a 4.5" Newtonian, Mak or SCT, giving the refractor about a 1/2" edge at this size.

So, someone walk me through the math or show me the logic as to why that doesn't work.   Or explain what other factor comes into play that I am ignoring.

This is not about my wanting to buy anything.   This is just my desire to understand more about how things work and how they are measured.  We often ignore this difference in our conversations but I would like to get a bit better understanding.

### #2 Starkid2u

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Posted 07 March 2018 - 12:50 AM

Ya know, it's amazing what can come across your mind when you're trapped indoors during the off-season....LOL! You're somethin' else, Ed!

STARKID2U

### #3 Migwan

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Posted 07 March 2018 - 12:51 AM

A=pi r^2

4" scope has an area of 12.56sq" (2 x 2 x 3.14) or 8,103sq mm  (50.8 x 50.8 x 3.14)

5" scope A = 2.5 x 2.5 x 3.14 = 19.625 sq "

With 10% CO  19.625 x .9 =  17.6625 sq "

Sorry, I used 25.4 mm per inch.  Still.

For  a 4.5" scope  2..25 x 2.25 x 3.14 = 15.89625 sq "

It would take a little more than a 4.5" refractor to equal the aperture of a 5" Newt with a 10% CO

17.6625 / 3.14 = 5.625   So the Sq Root of that would be the size refractor your looking for if splitting hairs.

jd

Edited by Migwan, 07 March 2018 - 12:52 AM.

### #4 Migwan

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Posted 07 March 2018 - 12:59 AM

Here's a question.  Does the spider count toward the Central Obstruction?  I would think so.

jd

### #5 beggarly

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Posted 07 March 2018 - 02:02 AM

Aberrator simulates the effects of central obstructions.

http://aberrator.ast....net/index.html

### #6 siriusandthepup

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Posted 07 March 2018 - 02:15 AM

If only it were a mere comparison of areas we would not have all the fun and lively discussions on these forums.

The fly in the ointment, as they say, is the loss of contrast caused by the included obstruction. That reduces planetary detail. Yes you have a brighter image, but low contrast detail washes out. Wanna see what I'm talking about? Reach over and turn the brightness up on your computer monitor and turn the contrast down. Hmm...Not so nice is it?

Also don't forget that you have to take into consideration that the aluminum coatings are not 100% reflective. Usually more like 88-90% per surface unless you have enhanced coatings. In a Newt you have two so a typical light through put is on the order of 0.90 x 0.90 = 0.81.

81%

Refractors have a similar consideration for light transmission. An uncoated objective reflects roughly 4% per surface so call it 0.96 transmission, with 4 surfaces in an un-oiled  achromat  (and neglecting that the calculation is actually compounded) 0.96 x 0.96 x 0.96 x 0.96 = 0.85

85%

But, most refractors have some AR (anti-reflective) coatings which improve the overall transmission.

And so on and so forth. Big Yawn.

Instead, remember this ancient rule of thumb: Comparing Newts to typical refractor  - take the Diameter of the Newt Primary and subtract its Secondary diameter to get its contrast equivalent in an unobstructed (refractor). This rule is conservative in that the Newt will perform slightly better than the rule states.

example 10" Newt with 2" sec will perform approx the same as an 8" refractor.

This has been my field experience as well.  All bets are off and none of the calculations mean a darn thing if the optics aren't top notch.

Refractor guys are refractor guys because they desire perfection in their viewing. I understand.

Reflector guys are reflector guys because they desire performance in their viewing.  They don't mind out-sizing the refractors with a slightly larger optic. I understand that also.

Edited by siriusandthepup, 07 March 2018 - 08:41 AM.

### #7 otocycle

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Posted 07 March 2018 - 02:28 AM

A Newtonian has other factors working against it, like tube currents, boundary layer, less stable collimation, etc.

My experience has been that a Mak or Mak-Newt come closer to the performance of an unobstructed apo-refractor, as they have smaller COs and closed optics.  All require adequate cooling.

Math is fun, but it is easy to replicate the impact of a central obstruction by suspending disks of varying % size by thread in front of a refractor's objective.   The loss of contrast and detail is obvious.

### #8 Rustler46

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Posted 07 March 2018 - 02:33 AM

According to a set of two articles in Sky and Telescope (around 1997) entitled "Rules of Thumb for Planetary Telescopes" by an optical engineer (name of Zmek, as I recall):

As far as showing low contrast details in planetary images, all other things being equal, a reflector with central obstruction has performance equal to an unobstructed telescope (refractor) of smaller diameter given by the following formula:

Equivalent Unobstructed Aperture = Reflector Aperture - Secondary Mirror Diameter

For example an 8-inch reflector with 2-inch secondary mirror has performance equal to a 6 inch refractor (8 inches - 2 inches). The articles go on to discuss the effect of other factors that influence the comparison (secondary spider, tube currents, errors in optical figure, etc.). Also of note is the reflector has an open tube with a larger column of air subject to seeing. In other words all other things are not equal.

One point the author made was there is no reason why a reflector cannot produce fine planetary views. It is just a reflector owner must work harder to compensate for the factors affecting the reflector. I'll try to get the exact S&T issue date for these articles. These are the classic comparison of refractor versus reflector, at least as far as planetary viewing.

Edited by Rustler46, 07 March 2018 - 02:35 AM.

### #9 beggarly

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Posted 07 March 2018 - 04:11 AM

1993 7 91 Telescope Making Rules of Thumb for Planetary Scopes -- I "Zmek, William P."

1993 9 83 Telescope Making Rules of Thumb for Planetary Scopes -- II "Zmek, William P."

http://wwwcdn.skyand...ru-Mar-2018.txt

Edited by beggarly, 07 March 2018 - 04:15 AM.

### #10 Redbetter

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Posted 07 March 2018 - 04:28 AM

The differences in overall system transmittance arise from the obstruction, and from the transmission of the mirrors or other optical glass.  This is discussed frequently.

Refractor system transmission is quite high, getting precise values for it is not easy, but is likely north of 95% for any decent one worth comparing.  The prism or mirror diagonal can knock this down some but it remains high.

Celestron has improved their coatings and glass to get fairly good transmission with their SCT's so that the current Starbright XLT coatings claim 83.5% vs. 72% before with the original XLT.  This doesn't include the central obstruction impact.  Mak's will be similar to SCT's in this regard.  Both will likely employ a diagonal.

Newtonian losses are from the transmission losses of the two mirrors (and no extra diagonal) along with the central obstruction.

The % obstruction determines the percentage of light that is thrown in the diffraction rings.  For small % obstruction the impact is not that large and it doesn't change much below 20% by diameter.  It is still not bad at 25% (near typical for an 8 or 10" Dob).  By the time you reach SCT levels of obstruction it is becoming substantial and the residual in outer rings is considerably greater.

I have done some crude analysis of the encircled energy and effective angular size for ~90% of the energy to be recaptured in various apertures and types.  Ignoring the brightness difference, the contrast difference is becoming comparable somewhere around 6" for a refractor vs. an 8" SCT assuming equal figure and apo/near apo refractor.  An 8" Dob with 25% obstruction starts with a considerably more of its energy in the airy disk than the SCT, so while they are reaching comparable levels of total encircled energy in the diffraction rings, the Dob starts a bit crisper to begin with 72.6% vs. 63.5% in the airy disk.  The SCT still has less than 92% of the energy recovered by the end of the 3rd ring while the Dob is near 94%.  At the same arc second radius, but only the 2nd ring, the 6" refractor is also at about 94%.  Smaller refractors reach that level farther out in proportion to their aperture.

From the above comparisons and looking at the distribution of the rings and even slower recovery by the SCT's, it is understandable why they have substantial resolving power because of their aperture, but also produce softer images visually.  (Some might also be to roughness of surface, figure, etc. but the distribution impact is there.)  This is true comparing to Dobs, and to refractors.

### #11 happylimpet

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Posted 07 March 2018 - 04:52 AM

As said above, the central obstruction received a lot of undeserved flack for reducing contrast over the years, when it was thermal effects that were really causing this. Keep it <=20%, manage your thermal issues (not easy) and your Newt will match an equivalent aperture refractor.

### #12 aeajr

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Posted 07 March 2018 - 05:36 AM

Gentlemen,

All I can say is thank you for taking the time to even consider my question.   The depth of knowledge and understanding of people on this forum is impressive.  The willingness to take the time to explain such things also impressive.

I have read these types of comparative comments in discussions before but never really understood it.  Now I have at least a high level grasp of some of the factors that go into the comparison.

So, if we net this out to rough approximations:

5" Newtonian/SCT/Mak is approximately equal to a 4" refractor of similar quality.

10" Newtonian/SCT/Mak is approximately equal to an 8" refractor of similar quality.

Leaving all the details to the posts above, this is what I am getting.

Close enough?

Edited by aeajr, 07 March 2018 - 05:38 AM.

### #13 sg6

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Posted 07 March 2018 - 05:54 AM

I never bother thinking about the central obstruction. The front corrector tends to diverge the incoming light so I guess that it reduces the light at the mirrors as much or more then the centreal obstruction.

There will I expect be a bigger difference in the reflected percentage more then anything and would I expect exceed the blocking of the central obstruction. The mirror surfaces will not be that good and loss at them will be significant. If 2 mirrors in the system, primary and secondary, and each is good at 95% reflectivity then the final is 90%

Refractors lose at each surface and again if 98% transmisson (good coatings) but a triplet then 88% transmission as the end result. An ED doublet would be 92%. Does anyone consider the loss at the multiple surfaces in an eyepiece? 6 element Paradigm, 2% loss at each surface, so 12 surfaces means you are down at 78% for just the eyepiece.

Also my 105 Mak has an measuered front aperture of 108mm so that gives 5% more area then what is "expected"

It is easy to just accept that a 120mm in any is the "same" as the others. Where they do in my thinking differ is the final image that is rendered..

So my opinion is that it is a bit pointless to consider the aperture comparison that is however so often done.  A 120mm whatever is a 120mm scope.

### #14 caveman_astronomer

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Posted 07 March 2018 - 06:02 AM

In most ways this is a moot point.

Refractors above about a 5-inch are rare or expensive or unwieldy.  Maks aren't much bigger.

There isn't any need to worry about how your 12-inch Newt stacks up against a 12-inch refractor, because you'll probably never have a 12-inch refractor anyway.

### #15 caveman_astronomer

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Posted 07 March 2018 - 06:10 AM

This is strictly about curiosity.  Nothing is being bought.

I have read many times that refractors can be smaller than Newtonians or Cats yet have comparable effective aperture because there is central obstruction with the Newts and the Cats.   Makes sense, but how much is the differential?

For example I have seen a 4" refractor/102 mm   equated to a 5" Newt, Mak or SCT.   But when I look at the specs of the central obstructions they are typically less than 10% in area.  So 10% of 127 mm ( 5") would be 12.7 mm so that 127 would be approx equivalent to about a 114 mm refractor.

If I do it a little differently, 127 X 127 = 16,129   Approximately 90% of that would be 14,516.  SqRt of that is 120 mm, a bit over 4.5"

If that is right than a 4" refractor would be about equivalent to a 4.5" Newtonian, Mak or SCT, giving the refractor about a 1/2" edge at this size.

So, someone walk me through the math or show me the logic as to why that doesn't work.   Or explain what other factor comes into play that I am ignoring.

This is not about my wanting to buy anything.   This is just my desire to understand more about how things work and how they are measured.  We often ignore this difference in our conversations but I would like to get a bit better understanding.

To make an approximate comparison in regard to fine, low contrast detail, subtract the diameter of the obstruction from the aperture of the Newtonian to find the diameter of refractor you would need to see that same detail.

The larger Newtonian gathers more light and has higher resolution and that will make all the difference.

### #16 Jon Isaacs

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Posted 07 March 2018 - 06:28 AM

Ed:

In comparing telescope types, one cannot make blanket statements because there are several factors to consider:  resolution, image brightness/light throughput and contrast.  And when considering contrast, there are two types, the fine scale contrast one is concerned about with the planets and bright objects and the deep sky contrast of a nebulae or galaxy.

- Resolution:  Resolution is determined by the aperture alone.  This is because the size of the Airy disk is inversely proportional to the aperture and it is ultimately the size of the Airy disk that determines the resolving power of a telescope. In resolving two stars of equal magnitude, a larger CO can help slightly but with stars of unequal magnitude, the greater energy in the diffraction rings is detrimental.   All the operational issues like thermal equilibrium, optical quality, collimation, these can affect the resolution but these can be managed.  The Dawes Limit is 4.56 inches/D in arc-seconds.  With a 4.56 inch scope, the Dawes limit is 1".  With a 10 inch scope, it's 0.456".

- Light throughput depends on both the transmission/reflectivity of the optics as well as the size of the central obstruction.  Refractive optics are very efficient, overall losses are only a few percent.  In the big scheme of things, a refractor can be considered 100% efficient because the errors in the estimation of the reflectivity of the mirror surfaces will be greater than losses in a reflector.  A few examples:

A Celestron SCT with Starbright XLT coating has a transmission efficiency of 84% across the visual spectrum.  If the CO is 36%, that represents an additional 13% loss so the throughput is 0.84*0.87 = 0.73 = 73%.  The equivalent perfect telescope (refractor) would be the the square root of that so 85%.. multiply the aperture by 0.85.  For a 6 inch SCT, this would be the equivalent of a 5 inch refractor.

A Newtonian with fresh high transmission coatings and a 16% CO:  This would be a best case scenario for any reflector. Coatings can be 95% efficient, the small CO is easily possible with a larger aperture instrument. That would be 0.95*0.95 x (1-0.162) = 0.88 = 88%.  The equivalent refractor would be the square root of that = 94%.

A more typical Newtonian would have a 90% coatings and a 25% CO and so the transmission would be 76%, much closer to the SCT.

- Contrast:  There are really two types of contrast, fine scale planetary contrast and deep sky contrast.

- Fine scale contrast:  The Airy disk consists of a central disk surrounded by a series of diffraction rings.  The central obstruction transfers light away from the central disk to the outer rings.  This has the effect of spreading the light out and reducing the fine scale contrast.  Imagine the pixels on your computer screen were round dots with a series of rings surrounding them.  Each pixel would partially effect those nearby. This is how the central obstruction affects fine scale planetary contrast.

One can look at this analytically but there are some rules of thumb:  The effect of a central obstruction under 20% in negligible.  Beyond that, there is the "clear aperture approximation". To get the equivalent unobstructed aperture, one subtracts the central obstruction's diameter from the aperture.  An 8 inch scope with a 2 inch CO is the equivalent of a 6 inch unobstructed scope.  In reality, the diffraction effects are related to the area of CO (and the Newtonian's spider) so the effect of a large CO is underestimated.

This is why large aperture planetary scopes are often Newtonians, very small central obstructions are possible.

Deep Sky Contrast:  This is primarily a function of stray light control.  Roland Christen says it very simply:

"There are two kinds of contrast. One needs to define which contrast you mean. If it's planetary contrast, then baffling plays no part. Planetary contrast is strictly a function of how well the optic is figured.  (this would include the CO)

If it's deep sky contrast, then optical perfection plays little or no part, and the main contributer will be how well the tube has been made to exclude stray light (i.e. baffled).

Rolando"

https://www.astromar...&news_id=&page=

In general, refractors are better baffled than reflectors.

- So, as one can see, there is no easy comparison.  And these comparisons assume equal optical quality, that the scopes are collimated and that they are free of thermal issues.

In general, it's my experience that a good refractor is able to work at near 100% efficiency, most of the time.  Newtonians and CATs face thermal issues that mean they will be operating at less than their peak a good part of the time.

Of course the big player is aperture.  If one is looking at a 16 inch Newtonian, even if it is only comparable to a 12 inch refractor, no one owns 12 inch refractors.

Jon

### #17 Jon Isaacs

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Posted 07 March 2018 - 06:33 AM

Refractors lose at each surface and again if 98% transmisson (good coatings) but a triplet then 88% transmission as the end result. An ED doublet would be 92%. Does anyone consider the loss at the multiple surfaces in an eyepiece? 6 element Paradigm, 2% loss at each surface, so 12 surfaces means you are down at 78% for just the eyepiece.

Modern Anti-reflection coatings are much better than that.  Tests show that Type 6 Naglers have a transmission efficiency of about 95% across the visual spectrum.  Astro-Physics triplets are 97% or better across the visual spectrum. A doublet would be better.

Jon

### #18 Starkid2u

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Posted 07 March 2018 - 09:01 AM

A=pi r^2

4" scope has an area of 12.56sq" (2 x 2 x 3.14) or 8,103sq mm  (50.8 x 50.8 x 3.14)

5" scope A = 2.5 x 2.5 x 3.14 = 19.625 sq "

With 10% CO  19.625 x .9 =  17.6625 sq "

Sorry, I used 25.4 mm per inch.  Still.

For  a 4.5" scope  2..25 x 2.25 x 3.14 = 15.89625 sq "

It would take a little more than a 4.5" refractor to equal the aperture of a 5" Newt with a 10% CO

17.6625 / 3.14 = 5.625   So the Sq Root of that would be the size refractor your looking for if splitting hairs.

jd

Nice. Totally beyond my math knowledge, but you know, you don't have to be a Van Gogh to appreciate great art. Same holds true here. Very nice.

STARKID2U

### #19 aeajr

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Posted 07 March 2018 - 09:26 AM

Again, thanks everyone for your posts.

As I stated in the first post, this is strictly curiosity.  Knowledge for its own sake as I have no intention of testing any of it, building my own scopes or working on a new design.  Just trying to understand how things work.

And, as has been mentioned, this really only comes into play when talking about refractors 6" or smaller as anything larger is pretty rare in the hobby market.

Probably the most useful place to consider this is in the 3-5" refractor vs the 4-6" reflector.  After that, as one person said, it becomes moot.   But I still find it interesting.

### #20 Cotts

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Posted 07 March 2018 - 10:55 AM

As said above, the central obstruction received a lot of undeserved flack for reducing contrast over the years, when it was thermal effects that were really causing this. Keep it <=20%, manage your thermal issues (not easy) and your Newt will match an equivalent aperture refractor.

^^^^^^^^^^THIS X 1000^^^^^^^^^^

My MakNewt 145mm, f/6 with a 17% central obstruction in extensive side-by-side tests on Jupiter and double stars produced views which were literally identical to a 150mm Astro-Physics refractor.  No difference could be seen. By me or a couple of other experienced observers.

Suiter's book states that the contrast transfer effects of a central obstruction of 20% or less on the diffraction pattern of a star at high power cannot be distinguished from that of an unobstructed refractor..

In an unobstructed scope, 83.8% of the light goes into the central spot*. The remaining 16.2% goes into the rings, the great majority in the first ring.   With a 20% obstruction we now have 76.4% in the spot and 23.6% in the rings.   That is a 7.2% difference in light intensity.  Suiter, therefore, posits that the 7.2% reduction in the brightness of the central spot cannot be distinguished by the human eye.  My experience with small C.O. Newts, Mak Newts and Mak Casses agrees.  Small being under 20%.

By the way, a 7.2% reduction in light intensity is equivalent to less than a tenth of a magnitude.  No one can eyeball a 0.1 magnitude difference......

Small central obstructions throw that "subtract the obstruction from the aperture" rule of thumb totally out the window.  It just doesn't apply.

Dave

*data from telescope optics dot net.  Pretty much the best source you can find on every conceivable aspect of the workings of telescopes.

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Posted 07 March 2018 - 11:39 AM

As said above, the central obstruction received a lot of undeserved flack for reducing contrast over the years, when it was thermal effects that were really causing this. Keep it <=20%, manage your thermal issues (not easy) and your Newt will match an equivalent aperture refractor.

The common wisdom on the internet grossly overrates the importance of CO. There is an active thread in the refractor forum where someone 3D printed a 36% CO and put it in front of his Astro-Physics 5" APO and posted photos with and without. Many felt the photo with the obstruction in place was slightly BETTER.

As hilarious as it would be, this doesn't mean you can improve the performance of your \$7000 refractor by obstructing it. It means there's many variables in play and the CO is just another drop in the bucket.

Many similar photos showing negligible difference due to obstruction can be found online from highly respected sources ranging from S&T, Damian Peach, and telescope-optics.net.

### #22 caveman_astronomer

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Posted 09 March 2018 - 05:02 PM

Newtonians DO tend to have COs greater than 20% for practical reasons.  It is more difficult to have a well-designed Newt with obstructions below 20%, unless the scope is both large and of longer focal ratio.

Mathematically, the subtract-the-obstruction rule of thumb is valid, except that very-small-CO Newts can be uncommon and the effects of the small obstruction can be subtle.  In the real-world we are dealing with Newts having 20%+ obstructions and SCTs having 30%+ obstructions.

Large refractors are rare, so the comparisons to make are between Newts and SCTs, not refractors.

### #23 aeajr

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Posted 09 March 2018 - 05:13 PM

I presume you mean 20% by diameter, not area.

Here are the specs for my XT8.  203 mm

Secondary mirror obstruction 47mm
Secondary mirror obstruction by diameter 23%
Secondary mirror obstruction by area 5%

Going back to my original post, I could see that a 5% obstruction, by area, would have little impact on the image.

If I square 203, take 95% of that and then take the sqrt I get 197.9 mm.

Not likely I can tell the difference between 203 mm and 197.9 at the eyepiece.

### #24 rolo

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Posted 09 March 2018 - 05:17 PM

The most    subject in history.

### #25 aeajr

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Posted 09 March 2018 - 05:27 PM

Maybe for you rolo, but this discussion was not started for your benefit.

Some of us are new to this.   Please be patient with those of us who are trying to learn.

Edited by aeajr, 09 March 2018 - 05:30 PM.

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