what is the formula?

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messier 111 Canada
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what is the formula?

#1

Post by messier 111 »


hi all ,
what is the formula to know the percentage of increase in light capture, for say a telescope of 100 mm vs 120 mm.
I hope to make myself understood and also I hope I have chosen the right place to post.
thx .
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Re: what is the formula?

#2

Post by SkyHiker »


It's a combination of focal length F and objective diameter D. The square of the focal ratio F/D (written F/<number>) is inversely proportional to the light flux on the sensor. So, an F/4 objective has a flux (7/4)^2 (about 3) times larger than an F/7 objective, and will be 3 times faster (assuming that we want to have a given number of photons on the sensor).

If you want to look at F and D separately, for a given D the light flux is inversely proportional to the square of F, and for a given F the light flux is proportional to the square of D. For a reflector you would have to correct a bit for the light blockage by the secondary mirror.
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Re: what is the formula?

#3

Post by sdbodin »


As Henk stated, the basic is just a comparison of aperture squared. So in your 120 vs 100mm frac case; it would be 120^2/100^2 or the 120 gathers 1.44 times more photons.

But, remember that one magnitude is 2.51 times more photons, so this is only a fraction of a magnitude.

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Re: what is the formula?

#4

Post by KathyNS »


You need to be more specific about what light where that you want to compare.

If you just want to compare the number of photons entering the front of the scope, that is simple: (A1 / A2) ^ 2. So, the 120mm scope will collect (120/100)^2 = 1.44 times as many photons.

If you want to compare how much light they focus per unit area at the focal plane, then you need to compare the focal ratios. Again you have to square the ratio: (Fr2 / Fr1) ^ 2. An f/4 scope will illuminate the focal plane (8/4)^2 = 4 times as brightly as an f/8 scope.
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Re: what is the formula?

#5

Post by messier 111 »


KathyNS wrote: Wed Dec 28, 2022 8:06 pm You need to be more specific about what light where that you want to compare.

If you just want to compare the number of photons entering the front of the scope, that is simple: (A1 / A1) ^ 2. So, the 120mm scope will collect (120/100)^2 = 1.44 times as many photons.

If you want to compare how much light they focus per unit area at the focal plane, then you need to compare the focal ratios. Again you have to square the ratio: (Fr2 / Fr1) ^ 2. An f/4 scope will illuminate the focal plane (8/4)^2 = 4 times as brightly as an f/8 scope.
when the manufacturers say,
the 120mm picks up 40% more light than the 100mm.
how do they arrive at this calculation?
I LOVE REFRACTORS , :Astronomer1: :sprefac:

REFRACTOR , TS-Optics Doublet SD-APO 125 mm f/7.8 . Lunt 80mm MT Ha Doublet Refractor .

EYEPIECES, Delos , Delite and 26mm Nagler t5 , 2 zoom Svbony 7-21 , Orion Premium Linear BinoViewer .

FILTER , Nebustar 2 tele vue . Apm solar wedge . contrast booster 2 inches .

Mounts , berno mack 3 with telepod , cg-4 motorized , eq6 pro belt drive .

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Re: what is the formula?

#6

Post by sdbodin »


messier 111 wrote: Wed Dec 28, 2022 8:48 pm

when the manufacturers say,
the 120mm picks up 40% more light than the 100mm.
how do they arrive at this calculation?
Simple approximation; the 120mm gathers 1.44 times, e.g.144%, of a 100mm. Subtract the 100% for the 4 incher and round to 40% more light.

Steve
Scopes; Meade 16 LX200, AT80LE, plus bunch just sitting around gathering dust
Cameras; Atik 460ex mono, Zwo ASI1600MC-cool, QHY5L-II color and mono
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Re: what is the formula?

#7

Post by KathyNS »


messier 111 wrote: Wed Dec 28, 2022 8:48 pm when the manufacturers say,
the 120mm picks up 40% more light than the 100mm.
how do they arrive at this calculation?
144% is 44% more than 100%. So the 120mm picks up 44% more light than the 100mm. Rounding it to 40% is reasonable for advertising copy.
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Re: what is the formula?

#8

Post by Gfamily »


messier 111 wrote: Wed Dec 28, 2022 8:48 pm when the manufacturers say,
the 120mm picks up 40% more light than the 100mm.
how do they arrive at this calculation?
The area of a 100mm objective lens (50mm radius) is πx50^2 =7,854sq mm
The area of a 120mm objective lens (60mm radius) is πx60^2 =11,310 sq mm
The second area is 44% larger than the first, so it'll gather 44% more light.
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Re: what is the formula?

#9

Post by messier 111 »


thx to all of you .
I LOVE REFRACTORS , :Astronomer1: :sprefac:

REFRACTOR , TS-Optics Doublet SD-APO 125 mm f/7.8 . Lunt 80mm MT Ha Doublet Refractor .

EYEPIECES, Delos , Delite and 26mm Nagler t5 , 2 zoom Svbony 7-21 , Orion Premium Linear BinoViewer .

FILTER , Nebustar 2 tele vue . Apm solar wedge . contrast booster 2 inches .

Mounts , berno mack 3 with telepod , cg-4 motorized , eq6 pro belt drive .

“Your assumptions are your windows on the world. Scrub them off every once in a while, or the light won't come in.”
― Isaac Asimov

Jean-Yves :flags-canada:
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Re: what is the formula?

#10

Post by sdbodin »


As you may have noticed, area of a circle involves a pi and r^2, but when taking a ratio all that pi stuff cancels out and diameter is just as good and radius, the 2 cancels, also feet, inches, meters, mm, etc are just as good. But if you got a square scope vs a round scope then long hand is required.

Example 5 inch to 4 inch, 25/16 = 1.56, a five is slightly bigger than a 120mm.

BTW, just subtract the secondary area from the full aperture for reflectors, you'll be surprised that the secondary even up to half the primary diameter doesn't block that much light.

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Scopes; Meade 16 LX200, AT80LE, plus bunch just sitting around gathering dust
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Re: what is the formula?

#11

Post by JayTee »


Just food for thought--

There is no website calculator that covers all the math discussed here above. I know because I spent all day looking for one. Now, don't get me wrong, there are calculators that cover a part of what has been discussed, but nothing that allows you to compare one OTA vs another using several ways of comparison.

I throw this out there because I'm an idea guy, not an execution guy!
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Re: what is the formula?

#12

Post by KathyNS »


JayTee wrote: Thu Dec 29, 2022 11:54 pm Just food for thought--

There is no website calculator that covers all the math discussed here above. I know because I spent all day looking for one. Now, don't get me wrong, there are calculators that cover a part of what has been discussed, but nothing that allows you to compare one OTA vs another using several ways of comparison.

I throw this out there because I'm an idea guy, not an execution guy!
There are plenty of spreadsheets downloadable off the internet that will do all the scope calculations.

The calculations involved in this thread involve ratios squared. On a simple 4-function calculator, the calculations are all A ÷ B * =. Or A ÷ B ^ 2 if you have a multi-function calculator. Figuring out which scope's measurement is the numerator and which is the denominator should be intuitive.
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DSO AP: Orion 200mm f/4 Newtonian Astrograph; ATIK 383L+; EFW2 filter wheel; Astrodon Ha,Oiii,LRGB filters; KWIQ/QHY5 guide scope; Planetary AP: Celestron C-11; ZWO ASI120MC; Portable: Celestron C-8 on HEQ5 pro; C-90 on wedge; 20x80 binos; Etc: Canon 350D; Various EPs, etc. Obs: 8' Exploradome; iOptron CEM60 (pier); Helena Observatory (H2O) Astrobin
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