well that copy and paste didn't work as intended. could some assist me as how to cut and paste from excel and keep formatting in a post

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

### #101

Posted 21 March 2015 - 11:03 AM

### #102

Posted 21 March 2015 - 11:45 AM

well that copy and paste didn't work as intended. could some assist me as how to cut and paste from excel and keep formatting in a post

Make a PDF of the spreadsheet, use snapshot tool, paste into Paint, and you have an image.

**Edited by SpooPoker, 21 March 2015 - 11:46 AM.**

### #103

Posted 21 March 2015 - 03:17 PM

Thanks Spoopoker kind of novice question how then do I then post the image here

### #104

Posted 21 March 2015 - 07:39 PM

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.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".

No, they were Russian built.

### #106

Posted 22 March 2015 - 07:54 AM

Yep, more or less agree with this table. My nexstar 5i does feel like a 95mm refractor on planets. or maybe even a 90mm.. Don't get me wrong, I love the gps of it. the looks of it, weight of it, and the versatility of it, but on planets it does not compare to refractors of equivalent aperture.

### #107

Posted 22 March 2015 - 08:29 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.

Remember, though, that Jim's Rule of Three Sevens is for light grasp, not for effective resolving power, perceived contrast or anything else. Jupiter is not the first object I would choose in a comparison of light grasp.

Mike

**Edited by Sarkikos, 22 March 2015 - 10:14 AM.**

### #108

Posted 22 March 2015 - 08:41 AM

While rule helps in selecting a scope of similar apertures (say within two inches), there are other things that are more pertinent and critical than that...I called object based equipment. I would not nitpicking to death about the merits of one from the other, when both may not be the right tool for certain objects. 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...

I think that would depend heavily on the DSOs and double stars observed. 4-6" fast refractors would be the right tool for large DSO and Milky Way vistas. Most any telescope would be appropriate for double stars up to their resolving power, with an edge to refractors for pinpoint images, and to reflectors (Newts and Cats) and APOs for color rendition.

Mike

### #109

Posted 22 March 2015 - 10:07 AM

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.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".

No, they were Russian built.

So was mine. With a 25% CO. The math isn't hard. The 7" Russian Maks operate akin to a 144-146mm "perfect" refractor after you calculate the reflection, transmission and obstruction losses.

It would be quite hard for a perfect 144-146mm scope to go noticeably deeper than a 140mm one visually. It's even tough to differentiate a 2mm difference among 3" scopes; 6 or 7mm at 5.5" is even less of a difference percentage-wise.

- Jim

### #110

Posted 23 March 2015 - 12:49 PM

One of the possibilities for a complement to my refractor is a long focus (F15) 180mm Mak-Cass, so I'm interested in the last few posts. Here is my estimation of the fraction of light showing up at the focal point for a Mak-Cass System like the ones from Intes-Micro.

Assumptions:

1) The I-M Mak-Cass has an actual aperture of 180mm, their primary mirrors are sized to catch all of the light coming in from a celestial object and bent by the corrector meniscus

2) The meniscus passes all of the light incident to it, its transmissivity is 1. This is "non-conservative" but I'm guessing that it's pretty close.

3) Each mirror has a reflectivity of 90% or 0.9. For an I-M, I'm guessing that this is a lower bound. Hopefully, there is some margin in here to offset assuming a perfect meniscus.

4) Define variables:

tm = transmissivity of the meniscus = 1 per Assumption 2

dco = diameter of the central terms relative to the diameter of the primary. For a F15 Mak-Cass, set dco = 25% = 0.25

fco = fraction of light making it past the central obstruction = 1 - (dco)^2 = 1 - (0.25)^2 = 1 - 0.0625 = 0.9375

rp = reflectivity of the primary mirror = 0.9 per Assumption 3

rs = reflectivity of the secondary mirror = 0.9 per Assumption 3

ft = fraction of the light from a celestial object incident to the Ma-Cas making it to the focus

ft = tm X fco X rp X rs

de = effective diameter of the objective for a Mak-Cass = SQRT(ft) = SQRT (tm X fco X rp X rs)

Per Assumption 3, rs = rp and per Assumption 1 tm = 1 so de = rp X SQRT (dco) = 0.9 X SQRT(0.9375) = 0.9 X 0.968 = 0.871

If the Mak-Cass objective has a diameter of 180mm, the effective diameter comes out to 0.871 X 180 = 157 mm

**Edited by Mark Costello, 23 March 2015 - 12:52 PM.**

### #111

Posted 23 March 2015 - 01:08 PM

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,

Acceptable chromatic aberration for an achromat is found with a focal ratio of > 5* aperture in inches. So, a 40" refractor would have to have a focal ratio of at least f/200 (yielding a focal length of 8000", or about 666 feet).

### #112

Posted 23 March 2015 - 07:43 PM

One of the possibilities for a complement to my refractor is a long focus (F15) 180mm Mak-Cass, so I'm interested in the last few posts. Here is my estimation of the fraction of light showing up at the focal point for a Mak-Cass System like the ones from Intes-Micro.

....

If the Mak-Cass objective has a diameter of 180mm, the effective diameter comes out to 0.871 X 180 = 157 mm

Or ~1 inch smaller

### #113

Posted 24 March 2015 - 03:33 PM

One of the possibilities for a complement to my refractor is a long focus (F15) 180mm Mak-Cass, so I'm interested in the last few posts. Here is my estimation of the fraction of light showing up at the focal point for a Mak-Cass System like the ones from Intes-Micro.

....

If the Mak-Cass objective has a diameter of 180mm, the effective diameter comes out to 0.871 X 180 = 157 mm

Or ~1 inch smaller

Yes, 'ndeed, just a little under 15/16" to be a little more precise. The interesting thing is that the fraction for comparing a reflector (lumping SCTs and MCTs with Newts) to a perfect refractor (mine ain't quite perfect, just very good ), is that I keep getting closer to 8/9 or even 9/10 instead of 7/9 by accounting for the obstruction and the throughput (reflectivity and for cats transmissivity) of the elements. There could be other things going on like mirrors tarnishing over time, but it seems that just for considering light gathering and reach of DSOs *only*, the size of the reflector required to match a reference class apo is not that much larger....

**Edited by Mark Costello, 24 March 2015 - 03:34 PM.**

### #114

Posted 25 March 2015 - 10:49 PM

I agree, Mark. I've always felt that these discussions mainly center around the planets, moon, and perhaps double stars, where an unobstructed view does indeed seem to have an advantage. But for faint nebulae, everything seems to come down to aperture, and aperture alone. Galaxies look SO much better in larger dobs. Refractors put up nice images, but pretty much get creamed on DSOs. Globulars, hmm, can't say, really, but I think they may fall half way in these two extremes.

Jim, thanks for creating this thread. One thing you have done, however, is point out what a value the dobsonian is over the refractor. I'm considering an 8" dob. Now, according to your formula, I'd have to get something like the Celestron 6" Advanced VX Series for a mere $1300 to get, actually a little less, of the optical punch an 8" dob would deliver. Have you priced 8" dobs lately? Orion's XT Classic is $381 and can be paid out in $127/3 month installments.

Now, for some, the Advanced VX Series mount is worth it, but not for me. I'm with Jon Isaacs and the "at one with the telescope" John Dobson (gods rest his soul) crowd. I like, and prefer, alt-az viewing. On top of this, the dobsonian design is the most wind-resistant configuration I've ever used, and living in West Texas, I've had plenty of experience with that.

I'm not sure what the formula really is. Many here think your 0.777 rule a little too stingy toward reflectors, and for DSOs, I'm pretty sure they're right, but even if relatively accurate for planetary and double star viewing, look at the price difference? And a 6" F/8 achromat has a Sedgwick/Conrady ratio that's not very impressive, so scads of color. And on top of that, the C6"VX setup is quite large at 76 lbs -- more work than I'd be willing to put up with for a quick night out. An 8" dob is a large scope, yes, but setup is, even with collimating the somewhat forgiving F/6 focal ratio, not going to take very long by comparison. At 41-52 lbs depending on vendor, an 8" dob is big but not overwhelming for one person, and much quicker to set up, something critically important to a father with young children around and less time for astronomy than he'd like (or used to have).

So even with the 0.777 equivalency figure, 8" dobs beat all sub 6" refractors out of the gate, and at least hold their own with a 6". And as Geoff Gaherty wrote 12 years ago, "I wonâ€™t go over 5" aperture because of the size and weight of even an f/8 refractor in this size". Estoy de acuerdo. You may have upset some reflector aficionados, but for me, you've only demonstrated why an 8" dob beats the pants off anything reasonable to move around or affordable in the refractor world.

**Edited by CollinofAlabama, 26 March 2015 - 09:27 PM.**

### #115

Posted 26 March 2015 - 05:53 AM

Quality does affect deep sky too from what I've seen. Maybe the effect is not as dramatic as on planets, but better mirrors are able to focus light better on an object where badly figured mirrors and coatings tend to scatter light a bit more.

Dust and miscollimination also tends to make things worse. I remember this when looking at the andromeda galaxy in various telescopes.

### #116

Posted 27 March 2015 - 11:05 AM

Quality does affect deep sky too from what I've seen. Maybe the effect is not as dramatic as on planets, but better mirrors are able to focus light better on an object where badly figured mirrors and coatings tend to scatter light a bit more.

Dust and miscollimination also tends to make things worse. I remember this when looking at the andromeda galaxy in various telescopes.

I agree. On bright galaxies in particular refractors maintain their contrast advantage. I can trace the dust lanes in M31 and the mottling in the rim of edge on galaxies like the Needle Galaxy with a much smaller refractor than I can obstructed scope. The smaller refractors lose in brightness but not in detail seen so long as the target is bright enough to be viewed in the refractor. For dim galaxies, sure you have no choice. See it with a sloppy lower contrast obstructed instrument or don't view it at all.

- Jim

### #117

Posted 28 March 2015 - 12:36 PM

Jim,

To be honest, I haven't had a whole lot of experience with larger refractors. Amongst our current group of Club members and geographically associated astro dudes (and, rarely, one dudette), they're mostly all large dob owners. Ironically, I'm the most likely member to show up with my Kunming F/7 102ED or Celestron 102GT amongst the various dobs or Cats. I've also experienced the buyer's remorse of having a lowly Orion 120ST spanking my 102mm ED scope for low power sweeps of the Scorpius star clusters/Sagittarian Star Clouds.

In times past, we had a Club member, God rest his soul, who went through a series of refractors. Don Fritz was quite an astronomer, who liked buying and selling scopes and trying and changing things out. He was a progressive retired farmer, and quite the self-trained optician (two EE sons who ended up working for TI who have retired and become consultants). During his many phases, he went through a refractor series, and owned an Orion 120mm ED at one point. Just so happens I had just bought a Meade 8" LightBridge (remember when they made those?) We compared the two on Saturn one night. There was NO contest, the GSO 8" gave a brighter, more 3D, clearer, overall better image. They were both good, of course, but we both agreed the 8" dob's vista was altogether better. That's exactly what you'd expect given your 0.777 formula, with a GSO 197mm dob performing as well as a clear aperture 153mm apo. I'm sure a multi-thousand dollar 6" apo would have done better than the 120mm ED, too. Don went back to dobs, and had a self-built 10" dob when he passed on All Saint's Day 2013.

I've never seen the mottling in the Crab Nebula in anything less than a 10" dob. Not saying on an especially clear evening one wouldn't see this in a 6" apo (or 8" dob, for that matter), but I've never seen the clear, crab shell-like mottling in M1 with less than a 10" dob. In fact, from our *dark* sky site closest to the City, I've never seen this in any scope, and many times in a 10" from either of our two darker sky sites I've not seen this. But occasionally, when the sky is very clear, I have seen this at these two sites even with a 10" dob. Some more experiential testimony "from the field", as it were.

Since an 8" dob can perform planetary at least as well as a 6" apo, look at the value difference? It's not even close. For folks who want the most performance for their buck, get a dob. For people with more money than God and can handle huge, heavy, expensive mounts, get an apo. According to your formula, you'll need a 190mm apo behemoth to match the performance of a 10" dob. I understand the refractor mystique, and love them, myself, but the facts are the facts.

I should note that I'm talking strictly about visual astronomy. For AP, well, that's a different story, and I simply have to say I know nothing of this. I have seen 80mm ED scopes do amazing things via a CCD, so I defer that argument for others to debate, having no dog in that fight. But for naked eyeball astronomy, folks, it's your money -- caveat emptor.

**Edited by CollinofAlabama, 28 March 2015 - 12:41 PM.**

### #118

Posted 28 March 2015 - 08:00 PM

Perhaps the 777 rule works for achromats, but at least to my eyes, due to the increased contrast, the APOs work roughly at a 0.6 rule. E.g. for getting a view as nice as an 8" SCT I would need a 4.8" APO. Anyway, that's my own empiric rule when comparing telescopes - I don't have much experience with achromatic refractors though so I haven't yet personally formulated a ratio - perhaps I will adopt the 777 for now

### #119

Posted 29 March 2015 - 08:03 AM

Mike

**Edited by Sarkikos, 29 March 2015 - 08:04 AM.**

### #120

Posted 30 March 2015 - 07:56 PM

Again, Jim's ROT is for light grasp, not surface detail seen nor perceived contrast. Would a 4.8" APO have light grasp equal to an 8" SCT?

Mike

Not even close. Using Celestron's numbers, the overall system transmission with Starbright XLT is 83.5% without diagonal, assumed to be 99% for a dielectric. The central obstruction is 31% of the primary. So the equivalent perfect aperture is SQRT[(1 - 0.31^2)X0.835]X8 = 6.95". I did not include the 1% loss from the diagonal, since both the refractor and the cat would use one. In addition, the Celestron 8 will have better resolving power. BTW 6.95/8 = 0.868.

The GSO 8" dobs offered by Orion, Astronomics, and Opticsmart have 91% - 94% reflectivity for both mirrors (depending on whose spec sheet you want to embrace) and a 23% central obstruction. The equivalent perfect aperture then becomes SQRT[(1 - 0.23^2)X 0.91^2]X8 = 7.08". An 8" dob on an equatorial mount such as a Losmandy G-8 or an Orion Atlas is an excellent all round scope for deep sky, planetary and imaging (with some mods, perhaps).

Also 7.08/8 = 0.886. So conservatively, I would use 0.85 assuming reflectors with modern enhanced coatings. But even with standard coatings (88% reflectivity) the equivalent perfect aperture for a typical newt with a 25% secondary is SQRT[(1 - 0.25^2)X0.88^2] = 0.852. So a 10" dob should equal or exceed an 8" refractor in terms of light gathering power and an 8" dob with standard coatings (equivalent aperture 0.85X8 = 6.8") should equal or exceed a 6" refractor.

The rule of 0.777 is IMO too conservative for evaluating the light grasp of a reflector relative to that of a refractor. Let us not forget that the refractor with a dielectric diagonal is not a perfect aperture. Lens transmission is 96% and the diagonal is 99%, so the equivalent perfect aperture is SQRT[0.96X0.99)] = 0.974, neglecting absorption losses in the glass. So a 6" refractor using a dialectric diagonal has an equivalent perfect aperture of 0.974X6 = 5.85".

What is the limiting magnitude difference between an 8" newt with standard coatings and a 6" refractor?

5log(6.8/5.85) = 0.327 or about 1/3 magnitude deeper for the newt. The newt can do better than this with enhanced coatings. For the C8: 5log(7.08/5.85) = 0.414 or about 0.4 magnitude.

What about that 4.8" refractor, equivalent aperture 0.974X 4.8 = 4.68? 5log(7.08/4.68) = 0.899 ~ 0.9 magnitude. That is the C8 will go nearly one magnitude deeper than a 4.8 " refractor.

I am a refractor nut, but I realize that for sheer light grasp a reflector is the only way to go and I am now looking into getting a 10" dob.

### #121

Posted 30 March 2015 - 11:26 PM

Again, Jim's ROT is for light grasp, not surface detail seen nor perceived contrast. Would a 4.8" APO have light grasp equal to an 8" SCT?

MikeNot even close. Using Celestron's numbers, the overall system transmission with Starbright XLT is 83.5% without diagonal, assumed to be 99% for a dielectric. The central obstruction is 31% of the primary. So the equivalent perfect aperture is SQRT[(1 - 0.31^2)X0.835]X8 = 6.95". I did not include the 1% loss from the diagonal, since both the refractor and the cat would use one. In addition, the Celestron 8 will have better resolving power. BTW 6.95/8 = 0.868.

The GSO 8" dobs offered by Orion, Astronomics, and Opticsmart have 91% - 94% reflectivity for both mirrors (depending on whose spec sheet you want to embrace) and a 23% central obstruction. The equivalent perfect aperture then becomes SQRT[(1 - 0.23^2)X 0.91^2]X8 = 7.08". An 8" dob on an equatorial mount such as a Losmandy G-8 or an Orion Atlas is an excellent all round scope for deep sky, planetary and imaging (with some mods, perhaps).

Also 7.08/8 = 0.886. So conservatively, I would use 0.85 assuming reflectors with modern enhanced coatings. But even with standard coatings (88% reflectivity) the equivalent perfect aperture for a typical newt with a 25% secondary is SQRT[(1 - 0.25^2)X0.88^2] = 0.852. So a 10" dob should equal or exceed an 8" refractor in terms of light gathering power and an 8" dob with standard coatings (equivalent aperture 0.85X8 = 6.8") should equal or exceed a 6" refractor.

The rule of 0.777 is IMO too conservative for evaluating the light grasp of a reflector relative to that of a refractor. Let us not forget that the refractor with a dielectric diagonal is not a perfect aperture. Lens transmission is 96% and the diagonal is 99%, so the equivalent perfect aperture is SQRT[0.96X0.99)] = 0.974, neglecting absorption losses in the glass. So a 6" refractor using a dialectric diagonal has an equivalent perfect aperture of 0.974X6 = 5.85".

What is the limiting magnitude difference between an 8" newt with standard coatings and a 6" refractor?

5log(6.8/5.85) = 0.327 or about 1/3 magnitude deeper for the newt. The newt can do better than this with enhanced coatings. For the C8: 5log(7.08/5.85) = 0.414 or about 0.4 magnitude.

What about that 4.8" refractor, equivalent aperture 0.974X 4.8 = 4.68? 5log(7.08/4.68) = 0.899 ~ 0.9 magnitude. That is the C8 will go nearly one magnitude deeper than a 4.8 " refractor.

I am a refractor nut, but I realize that for sheer light grasp a reflector is the only way to go and I am now looking into getting a 10" dob.

Celestron's figures cover only mirror reflectivity and corrector transmission. They do NOT account for the area of the central obstruction. FYI.

Also your lens transmission figure for a refractor (96%) is too low. Most refractors use 99.5% or better transmission coatings per surface. An air spaced triplet, therefore, would come in around 97%. An air spaced doublet, around 98%. An oiled triplet, closer to 99%. SCTs, too, use diagonals. You can't factor diagonal losses in for a refractor and not also do the same for an SCT or MCT.

Lastly there are the mystery losses present in reflecting scopes. Scatter from spider arms, vignetting from baffle tubes, lack of baffling reducing contract, coating deterioration on mirrors through time, etc. In practice, I think you'd be lucky to see a reflecting scope reach as deep as a refractor of 77% of its aperture, though I did not model such losses into my original calculations in coming up with three 7s.

Regards,

Jim

### #122

Posted 31 March 2015 - 11:48 AM

Again, Jim's ROT is for light grasp, not surface detail seen nor perceived contrast. Would a 4.8" APO have light grasp equal to an 8" SCT?

MikeNot even close. Using Celestron's numbers, the overall system transmission with Starbright XLT is 83.5% without diagonal, assumed to be 99% for a dielectric. The central obstruction is 31% of the primary. So the equivalent perfect aperture is SQRT[(1 - 0.31^2)X0.835]X8 = 6.95". I did not include the 1% loss from the diagonal, since both the refractor and the cat would use one. In addition, the Celestron 8 will have better resolving power. BTW 6.95/8 = 0.868.

The GSO 8" dobs offered by Orion, Astronomics, and Opticsmart have 91% - 94% reflectivity for both mirrors (depending on whose spec sheet you want to embrace) and a 23% central obstruction. The equivalent perfect aperture then becomes SQRT[(1 - 0.23^2)X 0.91^2]X8 = 7.08". An 8" dob on an equatorial mount such as a Losmandy G-8 or an Orion Atlas is an excellent all round scope for deep sky, planetary and imaging (with some mods, perhaps).

Also 7.08/8 = 0.886. So conservatively, I would use 0.85 assuming reflectors with modern enhanced coatings. But even with standard coatings (88% reflectivity) the equivalent perfect aperture for a typical newt with a 25% secondary is SQRT[(1 - 0.25^2)X0.88^2] = 0.852. So a 10" dob should equal or exceed an 8" refractor in terms of light gathering power and an 8" dob with standard coatings (equivalent aperture 0.85X8 = 6.8") should equal or exceed a 6" refractor.

The rule of 0.777 is IMO too conservative for evaluating the light grasp of a reflector relative to that of a refractor. Let us not forget that the refractor with a dielectric diagonal is not a perfect aperture. Lens transmission is 96% and the diagonal is 99%, so the equivalent perfect aperture is SQRT[0.96X0.99)] = 0.974, neglecting absorption losses in the glass. So a 6" refractor using a dialectric diagonal has an equivalent perfect aperture of 0.974X6 = 5.85".

What is the limiting magnitude difference between an 8" newt with standard coatings and a 6" refractor?

5log(6.8/5.85) = 0.327 or about 1/3 magnitude deeper for the newt. The newt can do better than this with enhanced coatings. For the C8: 5log(7.08/5.85) = 0.414 or about 0.4 magnitude.

What about that 4.8" refractor, equivalent aperture 0.974X 4.8 = 4.68? 5log(7.08/4.68) = 0.899 ~ 0.9 magnitude. That is the C8 will go nearly one magnitude deeper than a 4.8 " refractor.

I am a refractor nut, but I realize that for sheer light grasp a reflector is the only way to go and I am now looking into getting a 10" dob.

Celestron's figures cover only mirror reflectivity and corrector transmission. They do NOT account for the area of the central obstruction. FYI.

Also your lens transmission figure for a refractor (96%) is too low. Most refractors use 99.5% or better transmission coatings per surface. An air spaced triplet, therefore, would come in around 97%. An air spaced doublet, around 98%. An oiled triplet, closer to 99%. SCTs, too, use diagonals. You can't factor diagonal losses in for a refractor and not also do the same for an SCT or MCT.

Lastly there are the mystery losses present in reflecting scopes. Scatter from spider arms, vignetting from baffle tubes, lack of baffling reducing contract, coating deterioration on mirrors through time, etc. In practice, I think you'd be lucky to see a reflecting scope reach as deep as a refractor of 77% of its aperture, though I did not model such losses into my original calculations in coming up with three 7s.

Regards,

Jim

Jim, I took the loss due to the C8 central obstruction into account in my calculations. That is what the factor (1 - 0.31^2) is for. So my result for the equivalent perfect aperture for the C8, 6.95", and my correction factor of 0.868 stands as valid.

I did use the wrong equivalent aperture when comparing the magnitude difference between the C8 and the 4.8" refractor. I mistakenly used the equivalent aperture for the 8" newt. I should have used the 6.95" figure for the C8 corrected for the diagonal. SQRT[(1 - 0.31^2)X0.835X0.99]X8 = 6.92", yielding a magnitude difference of 5log(6.92/4.8) = 0.79 or about 0.8 magnitudes, vice the 0.9 that I reported in my previous post. Thanks for catching that.

As for your optimistic transmissions for modern refractors, I refer you to the Astro-Physics web site. The transmission specs quoted there for their newest refractor designs is 97% and that is without a 99% diagonal. I used 96% as a reasonable estimate and I'm sure that is the case for many scopes out there. So my refractor transmission figures also stand. However, if you think they need modification, then here it is: (0.97)X(0.99) = 0.96. And the equivalent aperture is SQRT(0.96) = 0.98 with dielectric diagonal, not much different than my original value of 0.974 for 96% transmission with dielectric diagonal.

your analysis of refractor transmission does not take absorption into account. I don't know what the transmission losses are for modern glasses, but for ordinary crown and flint used in achros, the loss is about 0.7% per cm. assuming the losses are similar for modern glasses, the transmission for a doublet with each element being 2 cm thick is:

[(1 - 0.007)^2]^2 = 0.972, about what Astro-physics quotes on their website. Multiply that by (0.995)^4 for two elements and we have 0.972X(0.995^4) = 0.953. It appears that my use of 0.96 transmission with no diagonal is justified.

The "mystery" losses you speak of are not easily quantified. That is why I reduced my correction factor to 0.85. Granted, coatings deteriorate over time, but let's not add that red herring to the mix. Reasonably cared for reflectors last a long time. As far as light grasp is concerned, vignetting plays a role only at the very edge of the field and in newts, at least, contrast is not a problem for high contrast objects like stars, which is what the original question was concerned with -- light grasp.