# How many pixels to arc second?

Started by
azure1961p
, Jan 15 2013 07:19 PM

9 replies to this topic

### #1

Posted 15 January 2013 - 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?

Thanks in advance.

Pete

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?

Thanks in advance.

Pete

### #3

Posted 15 January 2013 - 07:45 PM

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

### #4

Posted 15 January 2013 - 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

Pete

### #5

Posted 15 January 2013 - 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

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

### #6

Posted 15 January 2013 - 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

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

### #7

Posted 15 January 2013 - 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

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

### #8

Posted 15 January 2013 - 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

Pete

### #9

Posted 16 January 2013 - 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.

### #10

Posted 16 January 2013 - 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

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