From: Milton Aupperle <milton@outcastsoft.com>

Date: September 25, 2008 12:01:39 PM MDT

To: Astro_IIDC@yahoogroups.com

Subject: Re: [Astro_IIDC] calculating in arc seconds etc....


Hi Mark;


The usual way is this:


Field of View Width  in Arc Minutes = (CCD Width in mm /  Focal lenght in mm) * (57.3 * 60.00);

Field of View Height  in Arc Minutes = (CCD Height in mm /  Focal lenght in mm) * (57.3 * 60.00);


Calculating the CCD Width / height is sort of tricky because the width of the CCD on the CCD Spec sheet usually includes extra readout pixels around the edges and also includes the gaps between CCD pixel elements. We don't know what the actual Gap between pixel cells is and it's usually assumed that the gap is include din the pixel cell size.


What I use to calculate the mm width and height of the CCD is:


CCD Width in mm = (Number of Horizontal Imaging Pixels) * (Pixel Size in Microns / 1000);

CCD Height in mm = (Number of Vertical Imaging Pixels) * (Pixel Size in Microns / 1000);


So for a TIS  640x480 Mono or Color Camera 1/4" diagonal CCD with 5.6 micron pixel size:


CCD Width in mm = (640) * (5.6 / 1000) = 3.584 mm wide

CCD Height in mm = (480) * (5.6 / 1000) = 2.69 mm high


With a 1000 mm focal length, the field of view is:


Field of View Width  in Arc Minutes = (3.584 /  1000) * 3438.0 = 12.32 arc minutes Wide

Field of View Height  in Arc Minutes = (2.69 /  1000) * 3438.0 = 9.25 arc minutes High


For a PGR Flea 640x480 1/3" diagonal Color Mono CCD camera and the same 1000 mm focal length , the pixel size is 7.4 microns:


CCD Width in mm = (640) * (7.4 / 1000) = 4.736 mm wide

CCD Height in mm = (480) * (5=7.4 / 1000) = 3.55 mm high

Field of View Width  in Arc Minutes = (4.736 /  1000) * 3438.0 = 16.28 arc minutes Wide

Field of View Height  in Arc Minutes = (3.55 /  1000) * 3438.0 = 12.21 arc minutes High


For my PGR Grashopper which is 1384 x 1036 2/3" Diagonal Color Mono CCD Camera and the same 1000 mm focal length, the pixel size is  6.45 microns:


CCD Width in mm = (1384) * (6.45 / 1000) = 8.927 mm wide

CCD Height in mm = (1036) * (6.45 / 1000) = 6.682 mm high

Field of View Width  in Arc Minutes = (8.927 /  1000) * 3438.0 = 30.69 arc minutes Wide

Field of View Height  in Arc Minutes = (6.682 /  1000) * 3438.0 = 22.97 arc minutes High


However there are some other complications too:


1) If your using a Focal Reducer or Barlow, the distance to the camera's CCD will change the expected focal length and you don't know what the true focal length is.

2) If your using an SCT / MAK scope with built in focuser, the field of view will change as you change focus, because focussing moves the mirror and that changes the focal length.


In Case 1, the only way to calculate the true pixel size in arc seconds is to measure the distance of two known object on screen. For northern hemisphere, I like widely spaced double stars like Mizar in the Big Dipper, which has a distance of 708 Arc seconds between the two bright stars components. If my on screen pixel distance was say 900 pixels between them, then each pixel is 1.27 arc seconds (900 / 708) and a TIS 640x480 CCD's width of view is 1.27* 640 = 812.8 arc seconds or 13.54 minutes of arc (812.8 / 60.00). Since you know the arc seconds per pixel, you can work the calculations above backwards and calculate out what your true focal length is. I do this all the time with my Focal Reducer to determine what my "real" focal length was.


Case 2 bit me in the butt when I was imaging this summer with separate LRGB images, because my RGB filters focus at a different point than my unfiltered Luma was. Re-Focussing for the thickness of the filter with an SCT caused the focal length to change, and the Luma pixels are not at the same scale as the R G B images are and the stars were 3 pixels off at the bottom corner than the RGB images are. so the image has to be re-scaled.


HTH..


Milton Aupperle


On 25-Sep-08, at 11:15 AM, Mark Gaffney wrote:


Hi, does anyone know of a link to an online calculator for details involving given scope &

CCD...image scale, FOV,resolution etc. Preferably one that lists TIS & PGR cameras? Mark.