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This may be discussed elsewhere, but I thought I could share some results I obtained during the course of trying to photograph YU55 and some other faint objects. The background references are Roggeman and Welsh, "Imaging through turbulence" and David Saint-Jacques' Ph.D dissertation which I downloaded at: http://www.google.com/url?sa=t&rct=...sg=AFQjCNFUNLv0Lq32L73kmxBlwhRbfjZgeg&cad=rja
The dissertation is quite well-written, and clearly explains the nature of the problem (clear air turbulence). One chapter is devoted to 'field tests', and that's where I got a lot of this information.
First, all you need is an image of stars- leave the shutter open as long as you like, but do not over-expose. Here's a crop of my image (2 second exposure time):
[PLAIN]http://img339.imageshack.us/img339/6885/dsc16581.png [Broken]
The image was scaled up 400% (without interpolation), and I performed a linescan across two of the stars to figure out how big the 'Airy disk' is- here it's about 4 pixels FWHM.
Step 1: figure out the angular FOV per pixel. This image was acquired using a 400mm lens, 35mm image format, for a total view angle of q = 2*arctan(d/2f) = 2*arctan (36mm/800mm) = 5.1 degrees. Each pixel thus covers 3 arcsec.
Result #1: My point spread function/ Airy disk diameter is about 6 arcsec, based on the faint star.
Step 2: figure out the entrance pupil diameter. This is the focal length divided by the f-number, and is close to the physical diameter of the front lens element. On my lens, this is 140mm.
Step 3: now calculate the theoretical airy disk diameter- q = 2*arcsin(1.22*l/d), where l is the wavelength of light. I use l = 500 nm (green), giving me q = 1.6 arcsec.
Result #2- my seeing conditions limit what my lens can resolve. This is why I stopped trying to image faint stars/nebulae at 800mm- the only effect is to decrease the amount of light hitting the sensor, meaning I have to leave the shutter open longer, which increases the 'star trails'.
Step 4: calculate the coherence length 'r'. This number is the length over which the incoming wavefront fluctuates by 1 radian, and is a measure of how good the seeing conditions are- the larger 'r' is, the more quiet the upper atmosphere, and the larger the telescope aperture can be. The relevant formula is r = l/q, where q is the angular extent of the star image.
Result #3: r= 17mm for my site, when this image was acquired. For reference, 'normal' seeing conditions for astronomy has q = 1 arcsec and r = 100 mm. This is an important result- r is a measure of the maximum useful entrance pupil diameter. That is, I could operate my lens all the way down to f/4 without affecting the amount of resolvable detail. That is, the real advantage to having a large entrance pupil is the ability to *detect* faint objects, not to resolve them. There is no point to me getting a 12" telescope, for example- a 12" POS shaving mirror would work just as well at my site.
Step 5: calculate 'minimum acquisition time' to prevent star trails: Without any tracking mount, this is given by setting the acquisition time equal to the angular size of a pixel divided by the angular speed of stars- which depends on the declination of the star. For my lens, and looking at the ring nebula (5 arcsec/sec), this comes to about 1 second.
Step 6: calculate the coherence time- this depends on the windspeed, and is a measure of how fast the wavefront varies. The calculation is fairly complex, but as an approximation is given by: t = 2.6*(r/v)(1+8(d/r)^1.7)^0.1). Estimating v = 10 m/s and using the values for d and r, I get t = 1/15 second. This means any acquisition time over 1/15 second will time-average out the temporal variations, leaving only the blurred average image. Shorter acquisition times can be used (IIRC) to perform wavefront deconstruction, and sets the limit on adaptive optics correction schemes.
Final result- For bright objects, I am better off using a lower focal length lens (85mm, 12 arcsec/pixel) as my minimum acquisition time can be much longer (2-3 seconds), and because the seeing conditions are so poor, I do not lose very much resolution.
Edit- for the case where the exposure time is much less than the coherence time (e.g. for very bright objects like the moon, Jupiter, Space Station, etc), the spatial blurring is 'frozen', resulting in an improvement in image quality- the aberration can be considered as a spatially-varying magnification. This means I do gain some improvement by working at 800mm. Also, the technique of 'focus stacking' will work best if the frame rate is high- a generic 30 fps video camera would most likely be ideal for me to use.
The dissertation is quite well-written, and clearly explains the nature of the problem (clear air turbulence). One chapter is devoted to 'field tests', and that's where I got a lot of this information.
First, all you need is an image of stars- leave the shutter open as long as you like, but do not over-expose. Here's a crop of my image (2 second exposure time):
[PLAIN]http://img339.imageshack.us/img339/6885/dsc16581.png [Broken]
The image was scaled up 400% (without interpolation), and I performed a linescan across two of the stars to figure out how big the 'Airy disk' is- here it's about 4 pixels FWHM.
Step 1: figure out the angular FOV per pixel. This image was acquired using a 400mm lens, 35mm image format, for a total view angle of q = 2*arctan(d/2f) = 2*arctan (36mm/800mm) = 5.1 degrees. Each pixel thus covers 3 arcsec.
Result #1: My point spread function/ Airy disk diameter is about 6 arcsec, based on the faint star.
Step 2: figure out the entrance pupil diameter. This is the focal length divided by the f-number, and is close to the physical diameter of the front lens element. On my lens, this is 140mm.
Step 3: now calculate the theoretical airy disk diameter- q = 2*arcsin(1.22*l/d), where l is the wavelength of light. I use l = 500 nm (green), giving me q = 1.6 arcsec.
Result #2- my seeing conditions limit what my lens can resolve. This is why I stopped trying to image faint stars/nebulae at 800mm- the only effect is to decrease the amount of light hitting the sensor, meaning I have to leave the shutter open longer, which increases the 'star trails'.
Step 4: calculate the coherence length 'r'. This number is the length over which the incoming wavefront fluctuates by 1 radian, and is a measure of how good the seeing conditions are- the larger 'r' is, the more quiet the upper atmosphere, and the larger the telescope aperture can be. The relevant formula is r = l/q, where q is the angular extent of the star image.
Result #3: r= 17mm for my site, when this image was acquired. For reference, 'normal' seeing conditions for astronomy has q = 1 arcsec and r = 100 mm. This is an important result- r is a measure of the maximum useful entrance pupil diameter. That is, I could operate my lens all the way down to f/4 without affecting the amount of resolvable detail. That is, the real advantage to having a large entrance pupil is the ability to *detect* faint objects, not to resolve them. There is no point to me getting a 12" telescope, for example- a 12" POS shaving mirror would work just as well at my site.
Step 5: calculate 'minimum acquisition time' to prevent star trails: Without any tracking mount, this is given by setting the acquisition time equal to the angular size of a pixel divided by the angular speed of stars- which depends on the declination of the star. For my lens, and looking at the ring nebula (5 arcsec/sec), this comes to about 1 second.
Step 6: calculate the coherence time- this depends on the windspeed, and is a measure of how fast the wavefront varies. The calculation is fairly complex, but as an approximation is given by: t = 2.6*(r/v)(1+8(d/r)^1.7)^0.1). Estimating v = 10 m/s and using the values for d and r, I get t = 1/15 second. This means any acquisition time over 1/15 second will time-average out the temporal variations, leaving only the blurred average image. Shorter acquisition times can be used (IIRC) to perform wavefront deconstruction, and sets the limit on adaptive optics correction schemes.
Final result- For bright objects, I am better off using a lower focal length lens (85mm, 12 arcsec/pixel) as my minimum acquisition time can be much longer (2-3 seconds), and because the seeing conditions are so poor, I do not lose very much resolution.
Edit- for the case where the exposure time is much less than the coherence time (e.g. for very bright objects like the moon, Jupiter, Space Station, etc), the spatial blurring is 'frozen', resulting in an improvement in image quality- the aberration can be considered as a spatially-varying magnification. This means I do gain some improvement by working at 800mm. Also, the technique of 'focus stacking' will work best if the frame rate is high- a generic 30 fps video camera would most likely be ideal for me to use.
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