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Astrophotography and Sketching >> Solar System Imaging & Processing

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azure1961p
Postmaster

Reged: 01/17/09

Loc: USA
How many pixels to arc second?
#5625001 - 01/15/13 07:19 PM

For planetary imaging with a Dbk21au04 how many pixels to arc seconds do I shoot for with an 1821mm (f/9) system barlowed for extra focal length?
Is there a millimeter focal length formula to arrive at how much a pixel or arc second covers and how would I arrive at it?

Pete

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zAmbonii
Carpal Tunnel

Reged: 01/19/08

Loc: Ypsilanti, MI
Re: How many pixels to arc second? [Re: azure1961p]
#5625034 - 01/15/13 07:32 PM

I just let ccdcalc do the math for me

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RedLionNJ
professor emeritus

Reged: 12/29/09

Loc: Red Lion, NJ, USA
Re: How many pixels to arc second? [Re: zAmbonii]
#5625058 - 01/15/13 07:45 PM

Quote:

I just let ccdcalc do the math for me

Ditto here. And I'm pretty sure the optimal f-ratio has been expounded on ad infinitum in other threads, but the consensus seems to be somewhere between f20 and f28 for a monochrome camera.

So if you're starting with f9 on a scope where the primary doesn't move for focusing, you could apply a 2.5x or a 3x barlow. I'd download CCDCalc and plug in your instruments' numbers, but you'll likely find the image scale comes out to somewhere in the region of 0.1-0.3 arcsec per pixel.

Grant

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azure1961p
Postmaster

Reged: 01/17/09

Loc: USA
Re: How many pixels to arc second? [Re: RedLionNJ]
#5625130 - 01/15/13 08:28 PM

Thanks guys. It truly is important for me to have true knowledge of the pixel image scale. Ill do what you suggested and again, gratis.

Pete

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DesertRat
Post Laureate

Reged: 06/18/06

Loc: Valley of the Sun
Re: How many pixels to arc second? [Re: azure1961p]
#5625135 - 01/15/13 08:30 PM

Pete,
To calculate scale factor you can use the formula:

S = (206.265 / EFL) * C

where
S - is the pixel sampling in arcsec/pixel
EFL - focal length in millimeters
C - pixel size in microns

So for the your example at f/9 and 5.6u pixels of the DBK21 we have:

S = (206.265 / 1821) * 5.6 --> approx 0.6 arcsec/pixel

Somewhere between f/18 and f/25 would be a good place for high resolution work and that camera. Some Mars imagers like to go higher.

Glenn

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azure1961p
Postmaster

Reged: 01/17/09

Loc: USA
Re: How many pixels to arc second? [Re: DesertRat]
#5625152 - 01/15/13 08:37 PM

Glenn!!

Thanks you nailed it for me. So at this point I look to my Barlow at 2.5x to turn the 0.6" per pixel to make it 0.24" ?

Pere

Edited by azure1961p (01/15/13 08:38 PM)

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DesertRat
Post Laureate

Reged: 06/18/06

Loc: Valley of the Sun
Re: How many pixels to arc second? [Re: azure1961p]
#5625184 - 01/15/13 08:55 PM

Hi Pete, the 2.5X barlow would be fine I think, however with any extension it might be working past 2.5X. Which is ok, just thought I'd mention it.

I get this for a 2.5X:
(206.265 / (1821*2.5)) * 5.6 = 0.254 arcsec/pixel

and this for prime focus:
(206.265 / 1821) * 5.6 = 0.634 arcsec/pixel

Of course thats more precision than called for...

Glenn

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azure1961p
Postmaster

Reged: 01/17/09

Loc: USA
Re: How many pixels to arc second? [Re: DesertRat]
#5625371 - 01/15/13 10:45 PM

Aaahhh so I measure the bottom of the barlow to where the DBK begins and add that length to the 1821mm?? Again greatly appreciated!!
Pete

Edited by azure1961p (01/15/13 10:51 PM)

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KpS
member

Reged: 11/07/09

Loc: Prague, Czech Republic
Re: How many pixels to arc second? [Re: azure1961p]
#5625939 - 01/16/13 10:27 AM

Multiplication factor written on Barlow is only a nominal value. The actual number depends on the distance of the chip. The only way to reliably find EFL is a measurement of the image. For example WinJupos provide image resolution in arcsec/pixel. Then, using Glenn's formula we obtain EFL.

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DesertRat
Post Laureate

Reged: 06/18/06

Loc: Valley of the Sun
Re: How many pixels to arc second? [Re: KpS]
#5626150 - 01/16/13 12:54 PM

Yes, Karel is correct. To calculate the true magnification a barlow provides, you would need its negative focal length, which the manufacturer seldom provides (it can be measured however). From that and the distance between the image plane and the barlow you could calculate the effective focal length using the barlow formulas.

Since even the primary focal length may not be known accurately its easier to just calculate the effective focal length of the whole imaging system using the formulas below:

To calculate the focal ratio (FR) or effective focal length (EFL) from an image of an
object (or binary star) of known size and measured image size in pixels we have the formulas:

FR = (206.265 * C / (D / S)) / A = 206.265*(C*S)/(D*A) = EFL / A

hence

EFL = (206.265*C*S) / D

where
FR - focal ratio
EFL- focal length in millimeters
C - size of ccd pixels in microns
D - size of object in arc-seconds
S - size of object in pixels
A - aperture in millimeters

Note that the parentheses in the formulas above are important.

Glenn

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