•

# The "rule" of three 7s...

This topic has been archived.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

### #51 Peter Besenbruch

Peter Besenbruch

Fly Me to the Moon

• Posts: 7,436
• Joined: 21 Aug 2014

Posted 16 March 2015 - 03:11 PM

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.

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.

Edited by Peter Besenbruch, 16 March 2015 - 03:12 PM.

### #52 JonNPR

JonNPR

Apollo

• Posts: 1,469
• Joined: 04 Mar 2013

Posted 16 March 2015 - 03:41 PM

So, all this means we cannot simply measure the actual throughput for these various examples, and empirically decide among the different formulations?

Or are all of these posts about attempts to formulate the different measured throughputs into generalized math in order to predict any given scope construction - and no one formulation seems to accurately predict a broad range of variations?

I apologize for my confusion about the subject.

Jon

### #53 maknewtnut

maknewtnut

Member

• Posts: 1,462
• Joined: 08 Oct 2006

Posted 16 March 2015 - 05:44 PM

Have to disagree with this one Jim. I compared the TEC140 I once owned with a couple of 180mm Maks too. It was not a matter of splitting hairs. The 7.1" scopes reached noticeable deeper than the 5.5".

### #54 DJCalma

DJCalma

Viking 1

• Posts: 521
• Joined: 17 Jan 2013

Posted 16 March 2015 - 06:17 PM

Have to disagree with this one Jim. I compared the TEC140 I once owned with a couple of 180mm Maks too. It was not a matter of splitting hairs. The 7.1" scopes reached noticeable deeper than the 5.5".

This is particularly interesting since it is commonly believed that the 180mm Mak (if in fact it's of the Skyview / Orion variety) operates at an effective aperture of only about 170mm.

### #55 Peter Besenbruch

Peter Besenbruch

Fly Me to the Moon

• Posts: 7,436
• Joined: 21 Aug 2014

Posted 16 March 2015 - 07:40 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.

### #56 faackanders2

faackanders2

Fly Me to the Moon

• Posts: 6,324
• Joined: 28 Mar 2011

Posted 16 March 2015 - 08:23 PM

"I've come up with a proposed rule of thumb - the "Rule of three 7s".  Here's how it works.  To determine (roughly) the how a given obstructed scope (SCT, MCT, Newt, etc.) matches in light grasp/throughput to a refractor in terms of equivalent aperture, multiply the aperture of the obstructed scope by 0.777 to derive the aperture of an "equivalent" refractor.

Examples:

A 90mm MCT would have throughput equivalent to a ~70mm refractor.

A 16" Dob behaves like a ~12" refractor.

An 8" SCT operates like a ~6" refractor.

A C5 works like a 100mm refractor."

I assume this is for sharpness (pinpoint stars, double star separation, OC, & GC) but not aperture brightening (DSO nebula & galaxies).

### #57 Eddgie

Eddgie

ISS

• Posts: 27,200
• Joined: 01 Feb 2006

Posted 16 March 2015 - 08:37 PM

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.

### #58 Stephen Kennedy

Stephen Kennedy

Surveyor 1

• Posts: 1,950
• Joined: 03 Jul 2014

Posted 16 March 2015 - 10:29 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.

One reason that the one meter (40") Yerkes refractor is the largest ever made is that it was calculated that a larger refractor would be thicker and absorb so much light that there would be no gain in light gathering capacity despite the larger surface area of the refractor.

Another thing to consider is that the glass in lens of a refractor not only absorbs light but also reflects back some of the incoming light adding to the light lost to absorption in the lens.

### #59 KirkH

KirkH

Sputnik

• Posts: 27
• Joined: 01 Feb 2010

Posted 17 March 2015 - 02:26 AM

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.

One reason that the one meter (40") Yerkes refractor is the largest ever made is that it was calculated that a larger refractor would be thicker and absorb so much light that there would be no gain in light gathering capacity despite the larger surface area of the refractor.

Another thing to consider is that the glass in lens of a refractor not only absorbs light but also reflects back some of the incoming light adding to the light lost to absorption in the lens.

With all the optics knowledge at our disposal, all state-of-the-art scopes are reflectors. What I'm curious about is the point where it changes. I know my 4" refractor is better than my 5" Mak.

But, going up a step to a 6" Mak compared to a 4" refractor gets more iffy, and iffier still looking thru an 8" Cat compared to any 5" refractor. Is that the magical point of change? I think it occurs somewhere around there.

After 3-6" refractors, there are only reflectors. Everything else is an outlier.

It's easy to buy a \$300 8" dob and have the mirror redone or replace it with a Royce 3 lb that would put any 5" refractor to shame - no way that .777 formula would make a lick of sense.

I see your meaning, Jim, it helps as an overview for common small scopes, but that's it.

### #60 Edd Weninger

Edd Weninger

Apollo

• Posts: 1,103
• Joined: 16 Feb 2014

Posted 17 March 2015 - 02:43 AM

Amazing !!  Three pages attempting to derive an approximation.

Folks, we've had personal computers and programs like Excel for over forty years.  The first time I wanted to know these numbers I built a spread sheet to do the math.  No need for approximating.

Cheers,

### #61 sqrlman

sqrlman

Vostok 1

• Posts: 181
• Joined: 02 Jan 2008

Posted 17 March 2015 - 06:19 AM

I have compared a C8 with Starbright coatings to an AP 155 EDF. Both scopes were made around 1997. The C8 was brighter. Anyone could see this at a glance. This "rule" is nonsense.

Steve

Edited by sqrlman, 17 March 2015 - 06:20 AM.

### #62 GlennLeDrew

GlennLeDrew

Hubble

• Posts: 15,850
• Joined: 17 Jun 2008

Posted 17 March 2015 - 06:27 AM

The main unknown for us 'garage tinkerers' is the throughput, or transmission efficiency. Much beetling of brows arises over the assumed value. Why wonder? Measure!

If you have an evenly illuminated wall, for example, point the scope at it and photograph a larger exit pupil. Then without changing any (fully manual) camera settings whatsoever, including focus, photograph the wall. Measure the two brightnesses and compute the transmission efficiency.

I leave out here the details, but that's the method we can easily enough employ with readily available equipment. My only further comment. This test utilizes the invariance of an extended fulx's surface brightness as it transits an optical system, as described by the principle of etendue. No matter the aperture or exit pupil diameter, the latter will exhibit a surface brightness equal to that of the target directly seen, less instrument transmission losses.

When an outfit like Celestron supplies a transmission value for a telescope, I strongly suspect it's the 'dimensionless' efficiency which does not account for any obstruction. The test I outlined above determines this same factor; the fraction of photons passed by glass only. Which is our great unknown, the diameters of primary and obstructor being known and/or directly measureable with a ruler. Once the 'dimensionless' transmission efficiency is determined, then the obstruction's relative area is subtracted therefrom to derive the system efficiency.

As for a rule of thumb, I'd suggest a nice, 'round' 0.8. It's at least simpler to calculate in one's noggin using 4/5.

### #63 figurate

figurate

Apollo

• Posts: 1,149
• Joined: 09 Feb 2013

Posted 17 March 2015 - 07:54 AM

Works for me.

Fred

### #64 jrbarnett

jrbarnett

Eyepiece Hooligan

• topic starter
• Posts: 30,343
• Joined: 28 Feb 2006

Posted 17 March 2015 - 06:08 PM

The point is simply that I'd rather trust the empirical evidence of what is actually observed through the eyepiece than a mathematical formula, void of any empirical evidence whatsoever.

So are you saying that the math me & Jon used for computing light loss due to

obstruction and coating reflectance have no empirical basis? These have

been used for decades, maybe centuries, precisely because they agree

with measurements.

Also, visual observations are subjective and prone to confirmation bias.

Photoelectric data would be preferable.

I'm sure nobody who is debating the math on this issue would dare suggest that their .777 or .88 theory is based on "well established science & engineering." What annoys me is when someone sets up a straw man argument and then proceeds to knock it down.

No the whole point is that they are not, they are just numbers pulled out of a...hat.

When you do the actual calculation with established methods, they don't agree.

And it has to be done on a case-by-case basis, because obstruction and

reflectance varies. There is no one-size-fits-all relationship.

No I think he's saying that these mathematical models are woefully incomplete at even modeling throughput much less any other aspect of telescope design performance.  That is, there are many other variable affecting whether light entering manages to leave than aperture, obstruction, reflectivity and transmission.  If "0.777" agrees with what he's seeing at the eyepiece, then for amateur astronomers, who are not opticians or scientists, but rather device users using devices primarily for aesthetics, it's useful to him.

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.

So as a "rule of thumb" it's fine and no more arbitrary than your model using your assumptions regarding coatings.

- Jim

Edited by jrbarnett, 17 March 2015 - 06:23 PM.

### #65 austin.grant

austin.grant

Apollo

• Posts: 1,457
• Joined: 18 Oct 2010

Posted 17 March 2015 - 06:26 PM

I think the "Three 7's" rule works perfectly, because that's exactly what I'd have to hit at the casino to be able to afford a refractor that even approaches the light gathering ability and resolution of my 16" reflector!

Edited by austin.grant, 17 March 2015 - 06:27 PM.

### #66 DJCalma

DJCalma

Viking 1

• Posts: 521
• Joined: 17 Jan 2013

Posted 17 March 2015 - 07:11 PM

I think the "Three 7's" rule works perfectly, because that's exactly what I'd have to hit at the casino to be able to afford a refractor that even approaches the light gathering ability and resolution of my 16" reflector!

I was thinking something along those lines, but was afraid to actually post it. However, since you did . . . .

### #67 JonNPR

JonNPR

Apollo

• Posts: 1,469
• Joined: 04 Mar 2013

Posted 17 March 2015 - 07:36 PM

Finally! Glenn used the M word - measure. I've asked twice in this thread with zero responses correcting the error of the question, whether or not measuring throughput, light transmission was possible in order to resolve the myriad angels on the pinhead. The fact that people have used formulas for many many years isn't all that convincing when there are so many disputes about the performance of scopes. Surely the instrumentation exists in 2015 to test each component of the optical chain against standard illuminations.

Are there no Galileos here?!

Jon

### #68 Jon Isaacs

Jon Isaacs

ISS

• Posts: 87,234
• Joined: 16 Jun 2004

Posted 17 March 2015 - 07:46 PM

One simple example would be for DSOs, that 4-6" scopes, no matter what design or coating they have, are simply not quite suitable...likewise for double stars...

It really depends where you observe from for DSOs and which DSOs you chose to observe.  A 5.5" from NELM 7.2 desert is fantastic on brighter members of every class of DSO, showing structure in galaxies, substantially resolving bright globulars, etc.

As for double stars, you are in error IMO.  A 4" to 6" refractor will perform much closer to its theoretical limits than will a 10" or 12" obstructed scope on the vast majority of nights.  Refractors also manage light much better than obstructed designs, improving contrast at a given aperture.  Many, many nights one can pick out "tough" unequal doubles like Sirius with a 3" to 6" refractor, but be unable to do so with 6" and larger obstructed scopes.  Lastly once you factor in atmospherics the number of nights a large refractor (5" or 6") will resolve sub-1 arc second splits will be greater than the number of nights a 10" or 12" light bucket will do the same.

Refractors are the best tools for double stars.  The limit being their high cost per unit of aperture in the 6" range and larger.

- Jim

The suitability of a refractor for double stars depends on the targets chosen as well as the local seeing conditions.  The vast majority of the nights in the northeast are quite different than the vast majority of the nights down my way..  I generally choose a larger reflector because once cooled, they make the close splits easier.  There are certainly splits that are more difficult in a large reflector but for the close splits the aperture is a definite advantage..

YMMV

Jon

### #69 Jon Isaacs

Jon Isaacs

ISS

• Posts: 87,234
• Joined: 16 Jun 2004

Posted 17 March 2015 - 08:01 PM

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

### #70 JonNPR

JonNPR

Apollo

• Posts: 1,469
• Joined: 04 Mar 2013

Posted 17 March 2015 - 09:20 PM

Sorry, EJN. I did miss your reply. My apologies. I guess the measurement approach must have problems that cannot resolve these debates.

Jon

### #71 stevew

stevew

Now I've done it

• Posts: 6,557
• Joined: 03 Mar 2006

Posted 17 March 2015 - 09:39 PM

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......

### #72 austin.grant

austin.grant

Apollo

• Posts: 1,457
• Joined: 18 Oct 2010

Posted 17 March 2015 - 09:45 PM

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......

What are stars? I haven't even seen the one nearest earth in over 10 days. Weather has been absolute garbage around these parts!

### #73 etsleds

etsleds

Viking 1

• Posts: 561
• Joined: 14 Nov 2009

Posted 18 March 2015 - 12:54 AM

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.

### #74 GlennLeDrew

GlennLeDrew

Hubble

• Posts: 15,850
• Joined: 17 Jun 2008

Posted 18 March 2015 - 05:20 AM

To measure a telescope's transmission efficiency to what I think should be a confidence level of about 95%, if not better, one needs only a camera which can operate in full manual mode and software that permits to measure the brightness of some chosen area in the image. No photometers or calibrated references required whatsoever.

### #75 Paul G

Paul G

Cosmos

• Posts: 9,013
• Joined: 08 May 2003

Posted 18 March 2015 - 05:57 AM

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.

## Recent Topics

 Cloudy Nights LLC Cloudy Nights Sponsor: Astronomics