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Telescope upgrade


james_screech
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I currently use an ED70 (f6) scope with an ASI1600MM-C camera for photometry of variable stars and I’m looking to upgrade the scope. Before I purchase a new scope I want to estimate the change to my exposures before a given magnitude of star will saturate.

Now theoretically a star is a point source and therefor only the aperture should effect the brightness in which case the calculation is based on the increase in area of the primary. However due to seeing and diffraction effects, stars are not actually points but have their light spread over several pixels so they become extended objects. Therefore their brightness should be related to the focal ratio of the scope. So a 200mm f6 scope will give me no gain, just a reduced field of view. Is this correct? If the star brightness is related to the focal ratio how can I estimate the effect of different focal ratio scopes?

 

James

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No, brightness is not related to the focal ratio, only to aperture, the sheer amount of light that enters the telescope. Indeed, star images are not points, they're disks that are bloated to various degrees depending on seeing.

In theory, with scopes in the vacuum of space, a larger diameter will produce a brighter and smaller diffraction spot. But in the air the spot will be more or less bloated because of turbulence. The focal ratio difference between a 70mm f/6 and a 70mm f/12 will not change the spot size because it is dictated by interference, and it's always the same for a given aperture. Otherwise we could cheat and have tremendous resolution with minuscule telescopes but we can't.

 

Edited by Ben the Ignorant
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5 minutes ago, Ben the Ignorant said:

No, brightness is not related to the focal ratio, only to aperture, the sheer amount of light that enters the telescope. Indeed, star images are not points, they're disks that are bloated to various degrees depending on seeing.

In theory, with scopes in the vacuum of space, a larger diameter will produce a brighter and smaller diffraction spot. But in the air the spot will be more or less bloated because of turbulence. The focal ratio difference between a 70mm f/6 and a 70mm f/12 will not change the spot size because it is dictated by interference, and it's always the same for a given aperture. Otherwise we could cheat and have tremendous resolution with minuscule telescopes but we can't.

 

But surely the seeing will make the star a particular size in arc seconds (for me typically 2.5" to 3" looking at recent images), a longer focal length will mean that this is spread over more pixels on the camera, so the number of photons in each pixel will drop. 

 

James

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Nope, at prime focus a longer focal length does make extended objects larger on the sensor but at prime focus point sources are affected by diffraction and interference, which keep the spot size always the same for a given aperture. This is a quantum physics effect, so it's counterintuitive but it's true.

Adding barlows or doing eyepiece projection changes the game but you do photometry at prime focus, right?

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Yes, I'm at prime focus, but I don't see the difference between imaging a 3" diameter planet say or 3" star. If (keeping the primary diameter the same) you double the focal length the diameter in pixels on the sensor will be double, seeing is a physical effect not quantum. Don't get me wrong I hope you are right, it's just I don't see how.

 

James

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Your question about brightness related to diameter has been answered, and you can ignore finer quantum effects in your photometry measurements, but it can be discussed for the sake of curiosity. 

When you say 3" star versus 3" planet (like Neptune) that's after their light has entered the scope. While Neptune has a real 3" span in the sky, a star spans around 0.001". It's a point source while Neptune is an extended source.

After the star's light enters the scope it is submitted to diffraction and interference effects that create a 3" spot, but the spot would be twice as small in a telescope with twice the diameter. Neptune, however, would sill be a 3" image because extended light sources and point sources don't behave the same.

The Neptune image would be the same size, but more detailed because each point in it would be diffracted into a spot twice as small in width. Bigger scopes have better resolution, in other words. YouTube has plenty of good quantum physics initiation videos for those interested. Check The Science Asylum, Physics Girl, Veritasium, Fermilab among others. Quantum physics is strange but worth knowing, and math is not required for basics. 

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42 minutes ago, Ben the Ignorant said:

Your question about brightness related to diameter has been answered, and you can ignore finer quantum effects in your photometry measurements, but it can be discussed for the sake of curiosity. 

When you say 3" star versus 3" planet (like Neptune) that's after their light has entered the scope. While Neptune has a real 3" span in the sky, a star spans around 0.001". It's a point source while Neptune is an extended source.

After the star's light enters the scope it is submitted to diffraction and interference effects that create a 3" spot, but the spot would be twice as small in a telescope with twice the diameter. Neptune, however, would sill be a 3" image because extended light sources and point sources don't behave the same.

The Neptune image would be the same size, but more detailed because each point in it would be diffracted into a spot twice as small in width. Bigger scopes have better resolution, in other words. YouTube has plenty of good quantum physics initiation videos for those interested. Check The Science Asylum, Physics Girl, Veritasium, Fermilab among others. Quantum physics is strange but worth knowing, and math is not required for basics. 

Atmospheric seeing effects the star light before it enters the telescope not after. I agree that diffraction effects due to the primary size are purely in the telescope most of the seeing distortion happens in the 10's km of atmosphere before the light enters the telescope and not in the last few mm in the tube (assuming the tube as at ambient temperature).

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59 minutes ago, james_screech said:

Atmospheric seeing effects the star light before it enters the telescope not after. I agree that diffraction effects due to the primary size are purely in the telescope most of the seeing distortion happens in the 10's km of atmosphere before the light enters the telescope and not in the last few mm in the tube (assuming the tube as at ambient temperature).

Your seeing is the same regardless of the telescope.  Whether that is 1cm or a 1m telescope.  Hence the light is spread over the same area because of seeing.  The difference generally is that the larger telescope generally has a longer focal length.  For a given CCD the flux is then distributed over more pixels.  If you set up the 1m telescope with the same focal length as the 1cm then the flux would be distributed over the same area on the CCD. The only difference then is the 1m is capturing a lot more photons from the star - hence the flux will be higher.  Usually though the 1m telescope does have a longer focal length.  You can simply bin your pixels (although it's not quite the same but we'll ignore the technical differences) to an extent that flux is distributed across the same number of pixels (post binned).  However you never want you flux to be more than 50% of your full well depth anyway as you can start to lose linearity enough to mess up low level differences.  For the brightest stars some astronomers deliberately defocus their stars - which is in effect just worse seeing.

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3 hours ago, Whirlwind said:

Your seeing is the same regardless of the telescope.  Whether that is 1cm or a 1m telescope.  Hence the light is spread over the same area because of seeing.  The difference generally is that the larger telescope generally has a longer focal length.  For a given CCD the flux is then distributed over more pixels.  If you set up the 1m telescope with the same focal length as the 1cm then the flux would be distributed over the same area on the CCD. The only difference then is the 1m is capturing a lot more photons from the star - hence the flux will be higher.  Usually though the 1m telescope does have a longer focal length.  You can simply bin your pixels (although it's not quite the same but we'll ignore the technical differences) to an extent that flux is distributed across the same number of pixels (post binned).  However you never want you flux to be more than 50% of your full well depth anyway as you can start to lose linearity enough to mess up low level differences.  For the brightest stars some astronomers deliberately defocus their stars - which is in effect just worse seeing.

Exactly my point, the longer focal length spreads the extra light over more pixels, so assuming no binning, the star’s brightness on the sensor is proportional to the focal ratio and not the primary diameter. Unless the pixel size is large enough that all the light falls on a single pixel, which is not the case in my system.

James

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I know nothing about practical photometry but have used a variety of apochromatic refractors for deep sky imaging. My first thought conerns colour correction because, in strict truth, the apochromatic refractor does not exist. Not surprizingly, blue-violet is the rogue area. I'd have expected the photometric measurement of hot blue stars to require high order colour correction at the short wavelength end? Will this level of correction be consitently available in apos? 

In a nutshell wouldn't you be better off with a naturally apochromatic reflector?

Olly

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A reflector would not make much difference as I use a photometric V filter that lets mainly green light through and block most red and blue light. The only advantage of a reflector would be that for a given appature it would be cheaper, also if focal ratio is the key as I suspect they tend to have lower f numbers.

James

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21 hours ago, james_screech said:

Exactly my point, the longer focal length spreads the extra light over more pixels, so assuming no binning, the star’s brightness on the sensor is proportional to the focal ratio and not the primary diameter. Unless the pixel size is large enough that all the light falls on a single pixel, which is not the case in my system.

James

No that's not correct.  The flux from the star is still higher.  All that it is happening is that it is spread out over more pixels.  That can allow you to capture more flux before you hit the non-linear regime of the CCD or it saturates.  If your thinking was correct why are professional astronomers building ever bigger telescopes rather than ever faster telescopes.  For example lets assume you compare a 1m and 2m telescope

The collection area of the 2m telescope is 4 times larger.  

Lets say the 1m telescope collects 30,000 photons in a second.  The 2m telescope would therefore collect 120,000 photons in a second.  On the 1m telescope this falls on one pixel.  The pixel can accommodate 60,000 photons before it saturates.  

If the 2m telescope was designed with the same focal length (and hence faster) as the 1m then that 1 pixel would then lose half of the flux because it saturates.  If instead you spread the flux over 4 pixels by increasing the focal length you then capture all the 120,000 photons.  The 2m still provides a greater flux.  

Simply you sum the flux in an aperture to get the total flux captured (it is not the maximum in any one pixel).  A larger telescope will generate more flux, it just may be spread over more pixels.

 

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On ‎22‎/‎08‎/‎2018 at 19:08, james_screech said:

And if the larger flux is spread over more pixels, in your case 4 times as many then the number of photons per pixel per second will be the same.

However you are talking about undertaking aperture photometry for variable stars. Your aperture is not at a per pixel scale.  To do it correctly you sum the total of all your pixels in the aperture.  It doesn't matter how thinly spread it is, because you want the total flux captured.  You could do it at a per pixel level but instead of 100,000s of counts you are capped at 65000 (assuming 16 bit camera).

Look it another way suppose you took two walls and drew a squares on each one.  On wall A you draw fine squares; on wall B you draw very large squares.  Now you take some paint, one is 1000ml pot and one is 5 ml paintball.  You throw the 1000ml pot at the wall with the fine squares.  You throw the 5ml paintball at the one with large squares.  Wall A still has more paint on it - it doesn't matter that it is spread over more squares.  There may even be less paint in any individual square compared to wall B.  However fundamentally you still have more paint on wall A.  For aperture photometry what you want to do is measure the total paint, not the paint per square.

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11 hours ago, Whirlwind said:

However you are talking about undertaking aperture photometry for variable stars. Your aperture is not at a per pixel scale.  To do it correctly you sum the total of all your pixels in the aperture.  It doesn't matter how thinly spread it is, because you want the total flux captured.  You could do it at a per pixel level but instead of 100,000s of counts you are capped at 65000 (assuming 16 bit camera).

Look it another way suppose you took two walls and drew a squares on each one.  On wall A you draw fine squares; on wall B you draw very large squares.  Now you take some paint, one is 1000ml pot and one is 5 ml paintball.  You throw the 1000ml pot at the wall with the fine squares.  You throw the 5ml paintball at the one with large squares.  Wall A still has more paint on it - it doesn't matter that it is spread over more squares.  There may even be less paint in any individual square compared to wall B.  However fundamentally you still have more paint on wall A.  For aperture photometry what you want to do is measure the total paint, not the paint per square.

That would give me more dynamic range, but in the issue is pixel saturation. I never want to completely fill a pixel as then the measurement will be wrong. With a larger aperture the signal to noise ratio and dynamic range will increase as I'll be capturing more photons. However the saturation point for a pixel will not change if the focal ratio stays the same, the saturation point will be related to the focal ratio. 

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12 hours ago, james_screech said:

That would give me more dynamic range, but in the issue is pixel saturation. I never want to completely fill a pixel as then the measurement will be wrong. With a larger aperture the signal to noise ratio and dynamic range will increase as I'll be capturing more photons. However the saturation point for a pixel will not change if the focal ratio stays the same, the saturation point will be related to the focal ratio. 

That is irrelevant though with regards photometry.  You are correct in saying you don't want to saturate a pixel (you don't want to go above 50% of the full well depth).  However a larger aperture with the same focal ratio means a longer focal length.  A longer focal length means the flux is spread out over more pixels (assuming the same camera).  When you undertake photometry you want to count the flux in all the pixels.  You will get more flux from the a larger aperture, double the radius and you will quadruple the total flux you receive across all pixels the star covers (assuming everything else is perfect which isn't strictly correct).  If you want to undertake photometry you want the largest flux you can get because it increases the signal to noise in the aperture and hence you can see smaller depth transits.  Just because that flux is spread out over more pixels doesn't matter because you are summing the total flux over the whole aperture.  Strictly speaking there are other issues such as increasing noise the more pixels you have but I'll ignore this for the moment).

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So to summaries if the camera does not change:

A larger aperture will give a better signal to noise ratio due to more photons being collected and so the difference between the brightest and faintest stars that can be accurately measured will increase. 

If seeing makes stars extended objects, a smaller focal ratio will make the brightest stars that can be images without saturating pixels, fainter.

Therefore to get accurate photometery of the faintest stars I need a large aperture small focal ratio scope. (I can dream of a C14 with Hyperstar ?).

 

Thank you
James

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