Jump to content

  •  

CNers have asked about a donation box for Cloudy Nights over the years, so here you go. Donation is not required by any means, so please enjoy your stay.

Photo

The "rule" of three 7s...

This topic has been archived. This means that you cannot reply to this topic.
121 replies to this topic

#76 BigC

BigC

    Fly Me to the Moon

  • *****
  • Posts: 5776
  • Joined: 29 Sep 2010

Posted 18 March 2015 - 09:18 AM

Wow!!

Jim's original 777 rule of thumb sure got something started. Personally, it appears to be a close enough approximation of real-world scope performance. For instance my view of Jupiter in 6" achro vs 8" SCT are very  similar to my eye.



#77 daquad

daquad

    Apollo

  • *****
  • Posts: 1304
  • Joined: 14 May 2008

Posted 18 March 2015 - 10:23 AM

 

 

 

Why would the rule of thumb work for both catadioptrics and Dob/Newts?  Sure the latter generally have smaller COs and two fewer surfaces, but they also generally have standard mirror coatings whereas most modern SCTs have highly enhanced coatings on both mirrors and correctors.

 

Well, maybe it has been a while since you bought a Newtonian.

 

My Orion dob (and most of them sold now) have enhanced aluminum coatings on both mirrors.

 

Voyager 1,  How do you know the Orion dobs have enhanced coatings on both mirrors?  The specs for the XT-8/6 plus say enhanced coatings on the primary, but makes no mention of the secondary.  And their special sale 8, 10, and 12 inch dobs say the same thing.  The other dobs, XT's and intelliscopes make no mention of enhanced coatings on the mirrors.   Did you actually talk to someone at Orion who verified enhanced coatings on BOTH mirrors for all their dobs?



#78 daquad

daquad

    Apollo

  • *****
  • Posts: 1304
  • Joined: 14 May 2008

Posted 18 March 2015 - 10:50 AM

 

 

Example:  The C6 has a 36% CO by diameter.  The XLT corrector transmits 99.75% per surface; the XLT primary and secondary transmit 95% each; total system throughput is 89% before reduction for the big secondary.  That's 11% light loss due to coating inefficiencies, wholly apart from the losses due to the large obstruction.  And Dob/Newts using standard coatings are even worse (about 79-80% efficiency).

 

OK....     To compute this example:

 

Throughput:  The throughput is equal to the transmission of the corrector times the two reflectivities times the proportional area of the secondary mirror.

 

TP = 0.9975 x .95 x .95 x (1-.362) = 0.784    

 

For the C-6, about 78.4% of the light entering the scope reaches the eyepiece.  

 

What is the aperture of a perfect scope that will transmit 78.4% of a 6 inch aperture?  

 

The area of a 6 inch scope is 6 x 6 x Pi/4 = 28.3 square inches.   The effective area is 28.3 sq-in x 0.784 = 22.2 square inches.

 

What is the aperture of the scope whose area is 22.2 square inches:  

 

A = 5.317 inches.  You can verify this yourself.. 

 

For the C-6, the ratio between the effective aperture and the actual aperture is not 0.777 but rather 0.886 (5.317/6)  which is 6 inches times the square root of 0.784.  

 

The premise that this thread is founded on is faulty, it may be that the average transmission of a reflector or CAT is about 78% but that does not mean the equivalent effective aperture is 78% of the scope's aperture, it means it is 88% of the scope's aperture.

 

If one wants a rule, the rule of the Crazy 8s seems reasonable.  

 

Jon

 

Jon, you are exactly right.  I've often made the calculations just as you have suggested.  I've even attempted to take into account the obstructive area of the spider vanes in a Newtonian and the absorption of the glass of a corrector plate in a Cat. I think everyone needs to realize the important point you make about taking the square root of the efficiency to get the equivalent aperture.

 

I go another step further and calculate the loss in limiting magnitude.  Either 5 log(equivalent aperture/real aperture) or 2.5 log(efficiency).  For example, if a particular scope is 78% efficient then the magnitude loss relative to a perfect aperture is 2.5 log(.78) = - 0.27.  That is, a loss of 0.27 magnitude. Note that this loss is independent of the naked eye limiting magnitude. 

 

If we look at the limiting magnitude specification touted by most manufactures, it appears to be the same number for a given aperture regardless of the scope design.  As we have seen from this discussion, this cannot be the case.



#79 jrbarnett

jrbarnett

    Eyepiece Hooligan

  • *****
  • topic starter
  • Posts: 30072
  • Joined: 28 Feb 2006

Posted 18 March 2015 - 10:55 AM

 

 

Incidentally, my number (0.777) wasn't pulled out of a hat as I've already explained.  It is, however, based on different assumptions about mirror reflectivity and coatings effectiveness than those that Jon used in his example.  It is also seemingly closer to "reality", perhaps by accident.  That is, it may be based on pessimistic estimates of AR coating efficacy and mirror coating reflectivity, but coincidentally such pessimism may be warranted by other factors not accounted for by the model (mirror coating deterioration, internal vignetting in catadioptrics, spider vanes and light lost from the focused image due to scatter from things in the light path, etc.

 

Actually, when I computed your example of the C-6, I used the numbers for the reflectivities that you provided for the Starbright XLT coatings, you chose to use the reflectivity for the standard coatings... 

 

But in any event, I will say this:  There is a great variation in the performance of telescopes.  A well thought out reflector can be an amazing performer and very efficient, a well thought out refractor can be an amazing performer.  Poorer quality examples of both exist.  

 

But if one wants a rule of thumb, one digit is sufficient, the rule of .7, the rule of .8, the rule of .9, whatever.   .777, totally unrealistic. I suggest a better set of rule would be a fraction... 1/2, 2/3, 3/4, 4/5, 5/6, 6/7...7/8... 1

 

Take your pick, it'll apply to some scope.  

 

Jon

 

As I explained earlier, I based my calculations on data for the Synta MCTs.  Those do not use the Starbright XLT coatings group, but rather standard primary coatings and multicoated correctors.

 

But point taken; reflectivity and transmission numbers will vary widely.  So I'll revise the rule of three 7s - "Your obstructed scope will be equal to or better than a refractor of 0.777 times its aperture in terms of equivalent light gathering."  It's a floor.  

 

:grin:

 

- Jim



#80 Jon_Doh

Jon_Doh

    Vanguard

  • -----
  • Posts: 2337
  • Joined: 16 Sep 2011

Posted 18 March 2015 - 02:06 PM

Wow!!

Jim's original 777 rule of thumb sure got something started. Personally, it appears to be a close enough approximation of real-world scope performance. For instance my view of Jupiter in 6" achro vs 8" SCT are very  similar to my eye.

Everything in a 6 inch achro looked about the same as an 8 inch SCT in side by side tests I did one night except for globs and they looked better in the SCT.  

 

Good rule of thumb to remember when needing to make a comparison of different types of scopes.  .777 is easy to remember.  At least the formula didn't turn out to be .666  ;)



#81 junomike

junomike

    Hubble

  • *****
  • Moderators
  • Posts: 16991
  • Joined: 07 Sep 2009

Posted 18 March 2015 - 02:22 PM

I can't find a refractor to compare my 50" dob with.

Here!

 

Mike



#82 etsleds

etsleds

    Viking 1

  • *****
  • Posts: 559
  • Joined: 14 Nov 2009

Posted 18 March 2015 - 03:34 PM

I think we sort of miss the point of rule of thumb...

 

0.8x or 0.9x or take an inch or two, it's meant to be useful when quickly thinking about things.



#83 austin.grant

austin.grant

    Vendor - Modified DSLR Cameras

  • *****
  • Vendors
  • Posts: 1435
  • Joined: 18 Oct 2010

Posted 18 March 2015 - 05:11 PM

I think we sort of miss the point of rule of thumb...

 

0.8x or 0.9x or take an inch or two, it's meant to be useful when quickly thinking about things.

 

Or, perhaps we try too hard to create a rule of thumb when there needn't be one. Sometimes, the answer is just too complex to simplify into a one size fits all statement. 



#84 jrbarnett

jrbarnett

    Eyepiece Hooligan

  • *****
  • topic starter
  • Posts: 30072
  • Joined: 28 Feb 2006

Posted 18 March 2015 - 06:14 PM

 

 

 

I was wondering about the effects of absorption. I remember reading somewhere that as refractors increase in size, absorption becomes an issue, so much so that at 12" the absorption of a 12" refractor roughly matches the low transmission of standard coatings.  If this is true, the equations posted need another fudge factor.


I said that back on page one.

 

First, I'm still on page one. Second, I was hoping for more specificity. If absorption is indeed that bad in a 12" refractor, then perhaps some kind of accommodation needs to be made.

 

 

FPL53 transmission in the visible range of 420 nm to 700 nm is 99.7%, in the peak visual range of 550 nm to 600 nm is 99.9% for 10mm thickness. The mating elements would be similar. So light loss due to absorption in refractors is there, but it takes a lot of glass to become significant. AP's 175 has a measured transmission at peak visual wavelength of over 97% (includes glass absorption and coating efficiency at six air-glass surfaces).

 

Plate glass, OTOH, has relatively high absorption due to impurities, especially in the green. Not sure what SCT manufacturers use these days but when they used plate glass for the corrector there was about a 0.5% loss in transmission due to absorption alone.

 

They use water white glass now rather than soda lime plate.

 

- Jim



#85 Star_Shooter

Star_Shooter

    Vostok 1

  • -----
  • Posts: 111
  • Joined: 13 Jan 2009

Posted 18 March 2015 - 06:34 PM

APOs usually have better baffle system and provide better contrast than SCT/Dobs. This should give them a slight advantage in perceived brightness. It is hard to calculate the effect mathematically though.



#86 etsleds

etsleds

    Viking 1

  • *****
  • Posts: 559
  • Joined: 14 Nov 2009

Posted 18 March 2015 - 11:27 PM

Getting a precise number is indeed more complicated, as well as essentially fruitless if you're smart about using your rules of thumb.  It's fun playing with the gear, but for goodness sake I'm an apo guy yet the list of reflectors I listed are what's come through my house in the past 3 years :)

 

The basic light grasp and central obstruction arguments aren't rocket science.  Agreed that the other factors like figure, thermal performance, scatter control, mechanical handling for me differentiate far more than a few percent or mm's either way.  There are good values (depending on what your values are), but there aren't a whole lot of real surprises in scope performance.

 

 

I think we sort of miss the point of rule of thumb...

 

0.8x or 0.9x or take an inch or two, it's meant to be useful when quickly thinking about things.

 

Or, perhaps we try too hard to create a rule of thumb when there needn't be one. Sometimes, the answer is just too complex to simplify into a one size fits all statement. 

 


Edited by etsleds, 18 March 2015 - 11:46 PM.


#87 Kon Dealer

Kon Dealer

    Viking 1

  • -----
  • Posts: 975
  • Joined: 05 Jan 2011

Posted 19 March 2015 - 04:28 AM

As an empirical scientist, I much prefer to work with real data.

Has anyone tried these various 'scopes with a standard light source and a photometer and actually measure througput?



#88 mogur

mogur

    Gemini

  • *****
  • Posts: 3468
  • Joined: 29 Jul 2011

Posted 19 March 2015 - 07:23 AM

 

 

I can't find a refractor to compare my 50" dob with.

Here!

 

Mike

 

 

I live 60 miles from Yerkes, and actually got to look through the 40" a couple of times.

 

Deep sky objects are impressive. But Jupiter had tons of CA, a big blue-violet halo.

 

 

That's odd. At f/18 one would think CA to be almost non-existant. One of these days I gotta get down there to see for myself. It's only about 50 miles away.



#89 alnitak22

alnitak22

    Gemini

  • *****
  • Posts: 3306
  • Joined: 12 Feb 2011

Posted 19 March 2015 - 07:49 AM

As an empirical scientist, I much prefer to work with real data.

Has anyone tried these various 'scopes with a standard light source and a photometer and actually measure througput?

Oh please....this is CN, remember? Here's a summation of a rule of thumb seen over and over on CN fora..."My personal experience in my own unique observing situation, trumps any scientific evidence." 



#90 Mark Costello

Mark Costello

    Soyuz

  • *****
  • Posts: 3551
  • Joined: 08 Mar 2005

Posted 19 March 2015 - 09:34 AM

 

 

 

I can't find a refractor to compare my 50" dob with.

Here!

 

Mike

 

 

I live 60 miles from Yerkes, and actually got to look through the 40" a couple of times.

 

Deep sky objects are impressive. But Jupiter had tons of CA, a big blue-violet halo.

 

 

That's odd. At f/18 one would think CA to be almost non-existant. One of these days I gotta get down there to see for myself. It's only about 50 miles away.

 

 

Hi, mogur.  The level of CA also depends on the achromat's diameter, the bigger it is, the more intense the CA is.  It might not be noticeable on a 3"F18 but a 40"F18 is a different story.  Best Regards,



#91 EricR

EricR

    Messenger

  • *****
  • Posts: 477
  • Joined: 10 Jun 2008

Posted 19 March 2015 - 11:27 AM

Tested the rule at .795 awhile back,,, 22" against 17.5",,, views FELT EXACTLY THE SAME!

Oh wait, they were both obstructed.

Oh yeah, it was completely clouded over.

Forgot to mention we had resorted to heavy drinking due to the cloud cover so I was pretty far gone and my observation notes are completely illegible.

 

Seriously, I really like the idea of a very rough/general rule of thumb (as the OP proposed), even though I have a math background. (A degree or two in math depending on what you count, a B.A and a ... 'eh hum A.A.).

 

The "digital camera and software" measurement presented earlier seems ideal if anyone has the motivation.

If someone has multiple scopes to do the math on (for each scope's specifics), then compare the measured results (camera/software) against the expected (from the math), that would be the most objective post so far.

...so, uh, yeah,,, I'm not up for that. Anyone else motivated enough?

 

Gut feel for me is probably closer to the "crazy 8s" (0.888) that came up earlier but I'll admit to being highly biased towards larger reflector over smaller refractor when it comes right down to it. (As someone else said, for rule of thumb, I'd probably round to less than 1/1000s precision for general discussions).

 

I feel like without an actual measurement (camera/software or something to that effect), your factor will probably end up just "fitting" to whatever the steps are between the instruments you happen to be using. Personally, I'm sure I wouldn't be able to detect a difference of a few percentage points (or even more) just visually.

 

<<<given the length of this thread I decided to not worry about throwing out my own babble that doesn't do much in the way of adding meaning to the discussion, so just went for it>>>


Edited by EricR, 19 March 2015 - 11:34 AM.


#92 Paul G

Paul G

    Cosmos

  • *****
  • Posts: 8532
  • Joined: 08 May 2003

Posted 19 March 2015 - 11:50 AM

 

As an empirical scientist, I much prefer to work with real data.

Has anyone tried these various 'scopes with a standard light source and a photometer and actually measure througput?

Oh please....this is CN, remember? Here's a summation of a rule of thumb seen over and over on CN fora..."My personal experience in my own unique observing situation, trumps any scientific evidence." 

 

+1.  :)



#93 SpooPoker

SpooPoker

    Viking 1

  • *****
  • Posts: 969
  • Joined: 04 Jun 2013

Posted 19 March 2015 - 01:12 PM

What is the mechanism that reveals faint objects or details?  Assuming one is keeping aperture a constant, is contrast not more important than one instrument being able to collect a greater proportion of photons?  I know the extra light helps from increased transmission efficiency, but revealing certain features could well be not so much seeing more photons in totality but actually seeing less photons that are interfere with the background and the object in question.  Basically, I am thinking along the lines of what % of light is good light so to speak - this in context of to-the-limit observations. 

 

You guys all need to stop debating which scope design is equal to another scope design,

and get out under the stars and enjoy the scopes you have...... :lol:  

 

Certainly wise words.  Nonetheless the devil in the details for each instrument design is somewhat interesting - at least in trying to unify a theory for telescopic design and associated unveiling of the universe.  

 

I am glad this thread has not derailed into the "my 4" APO is better than your 8" SCT" which serves no purpose other than folks feeling the need to attack or defend what are ultimately inanimate objects.



#94 Sarkikos

Sarkikos

    ISS

  • *****
  • Posts: 30684
  • Joined: 18 Dec 2007

Posted 19 March 2015 - 01:36 PM

Why do astronomers seem to want to compare equipment and have this A verses B contest?

 

Hmmm.... :thinking:  Maybe so they can come to rational decisions about which scopes they will buy, keep or sell?

 

Mike


Edited by Sarkikos, 19 March 2015 - 01:37 PM.


#95 Paul G

Paul G

    Cosmos

  • *****
  • Posts: 8532
  • Joined: 08 May 2003

Posted 19 March 2015 - 01:41 PM

 

Why do astronomers seem to want to compare equipment and have this A verses B contest?

 

Hmmm.... :thinking:  Maybe so they can come to rational decisions about which scopes they will buy, keep or sell?

 

Mike

 

 

And it's an equipment discussion forum so...



#96 Peter Besenbruch

Peter Besenbruch

    Fly Me to the Moon

  • *****
  • Posts: 7011
  • Joined: 21 Aug 2014

Posted 19 March 2015 - 03:26 PM

 

I live 60 miles from Yerkes, and actually got to look through the 40" a couple of times.

 

Deep sky objects are impressive. But Jupiter had tons of CA, a big blue-violet halo.

 

That's odd. At f/18 one would think CA to be almost non-existant. One of these days I gotta get down there to see for myself. It's only about 50 miles away.

 

Good chromatic aberration control requires an f-ratio of 5 times the diameter in inches. For the 40" Yerkes refractor, that would be f200. For decent control, it's three times the diameter in inches, or f120.



#97 Jon Isaacs

Jon Isaacs

    ISS

  • *****
  • Posts: 79082
  • Joined: 16 Jun 2004

Posted 19 March 2015 - 06:53 PM

 

 

As I explained earlier, I based my calculations on data for the Synta MCTs.  Those do not use the Starbright XLT coatings group, but rather standard primary coatings and multicoated correctors.

But point taken; reflectivity and transmission numbers will vary widely.  So I'll revise the rule of three 7s - "Your obstructed scope will be equal to or better than a refractor of 0.777 times its aperture in terms of equivalent light gathering."  It's a floor. 

:grin:

- Jim

 

Jim:

 

But it's not even a lower limit, a reflector can be far worse than 0.777 if the coatings have deteriorated..   There are no easy generalizations...

 

Jon



#98 jrbarnett

jrbarnett

    Eyepiece Hooligan

  • *****
  • topic starter
  • Posts: 30072
  • Joined: 28 Feb 2006

Posted 19 March 2015 - 09:09 PM

I'm in agreement with several that computing by area gives a consistently higher result than 0.777.

 

From published system transmission / reflectivity numbers and measured actual central obstruction on the cats I've owned, what I get for effective diameter multiplier vs a 98% transmission refractor is:

 

TEC 6 (std coatings)      0.87

TEC 6 (enhanced)          0.93

TEC 200 f15.5                0.88

Mewlon 180                    0.92

Mewlon 250                   0.92

C8                                  0.80

Starmaster 14.5             0.94

 

I agree coating quality & age will play a factor - when my TEC6 came back from Yuri with enhanced coatings, it was noticeably brighter, something I had not expected for a 10% increase in specified brightness - I think this means I likely got 20-30% brighter (including the psychological factor of wanting to see the image as brighter after spending the money!).

 

Of course it all gets complicated further when looking at the central obstruction, figure, etc.

 

What's more useful for me and consistent with what I've observed in my own scopes is that a good modern reflector has light grasp approx that of a refractor of 1" smaller aperture and (based on typical MTF discussions) the contrast of a refractor of 2" smaller aperture...generally holds true for the 6-14" range most of us are talking about for reflectors.

Out of curiosity, how does your Starmaster 14.5 with 2.6" secondary transmit 94% when the secondary blocks 3% by area, the IAD standard coated primary with quartz overcoat, when new, reflects just 91% and the secondary reflects 96-97% (numbers from Starmaster's website)?

 

Mirror losses alone, assuming clean new coatings, you're at 0.88 out of the gate, best case, then you factor in the secondary blockage and you're suddenly at 85%, 9% below your figure and 7% above my rule of thumb.

 

- Jim



#99 etsleds

etsleds

    Viking 1

  • *****
  • Posts: 559
  • Joined: 14 Nov 2009

Posted 20 March 2015 - 02:27 AM

Jim, I think you're still missing the square root, or else I wasn't clear these were my multipliers for diameter, not area.  The 0.94 is the diameter multiplier for the SM14.5, the square root of 0.88.

 

I use a simple equation in my spreadsheet, but by your long-hand:

 

Diameter of primary: 368 mm; secondary: 70 mm

Area of primary: 106535 mm^2

Area of secondary: 3846 mm^2

System reflectivity: 90% (which you are arguing is 88%, fine)

Reflector = (106535 - 3846) * 0.9 = 92420 mm^2 effective

 

Working back to the refractor:

 

Refractor transmission: 98% assumed

92420 mm^2 / 0.98 = 94306 mm^2

Diameter of lens = 2 x sqrt (94306 mm^2 / PI) = 347 mm

 

Divide the refractor by the reflector = 347 / 368 = 0.94

 

I agree with age / dust / stuff, likely it's worse than that, especially for an open tube reflector.  But that's still ok for sake of argument, even if I put in a system reflectivity of 80%, I still get a ratio of 0.89.

 

I think crazy 8's is probably a better multiple than lucky 7's and frankly three digits is false (but fun) precision.

 

Then again, I subtract better than I multiply, especially in the dark, so it's easier for me to think of subtracting an inch for light grasp and two inches for contrast.


Edited by etsleds, 21 March 2015 - 01:37 AM.


#100 Curtis Jones

Curtis Jones

    Sputnik

  • -----
  • Posts: 42
  • Joined: 01 Feb 2009

Posted 21 March 2015 - 10:59 AM

Using Jared Willson's article and worksheet,

 

http://www.cloudynig...mparision-r1901

 

I did the calc for my scopes:

 

I would say the triple 7s is pretty much right for SCT for planetary contrast when it comes to light lost among the all the surfaces
but the ratio is a little higher for DSO.

 

As for newtonians, mak-casses and mak-newts the ratio is a little higher in the mid 80s


Edited by Curtis Jones, 21 March 2015 - 11:36 AM.



CNers have asked about a donation box for Cloudy Nights over the years, so here you go. Donation is not required by any means, so please enjoy your stay.


Recent Topics






Cloudy Nights LLC
Cloudy Nights Sponsor: Astronomics