From: Mark Gaffney <markgaffney@mac.com>

Date: September 25, 2008 3:27:12 PM MDT

To: Astro_IIDC@yahoogroups.com

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


Hi Milton, Thanks for all the detailed info! That must have taken you a while to compile! I basically found the widget & input the info from the site about my current camera (which I think you sent me, TIS having updated their site since mine was bought) as to chip description (there`s a link there)-pixel width & height/chip width & height (for which I`ve input the number of effective pixels) & the new scope`s FL, got a reading & gone to bed! I had no idea you`d be working at it for ages afterward. I hope the info you created will be of use to others as well. I thought the focus would change FOV but wasn`t sure how to calculate for it. Today I was going to try the same for the PGR camera I`m looking at. Thanks! Mark.

On 26/09/2008, at 4:01 AM, Milton Aupperle wrote:


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.





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