Focal Length

Overview  Polar Align  Focal Length  Focussing  Find & Take  Processing  Color Imaging


The focal length of the telescope determines the field of view (FOV) of the CCD chip and the size of the object you are imaging.  The longer the focal length, the smaller the field of view and the larger the object on the chip. Often you will hear a telescope such as the LX200 described as a 250mm (or 10 inch) f/10 telescope.  The 250mm refers to the aperture of the telescope and the f/10 is the f ratio.  The f ratio is just the telescope focal length divided by the aperture.  So we can deduce that the 250mm f/10 LX200 has a focal length of 2500mm.  For telescopes of the same aperture, the lower the f-ratio the larger the FOV and the smaller the size of the object on the chip. 

 It is very important to adjust your focal length so that the CCD camera can correctly sample the object you want to image.  A correctly sampled image is one which has recorded the finest detail that can be resolved by the telescope and has done so using the minimum number of pixels.  For example, most medium sized telescopes can resolve details as small as 0.5 arcseconds.  To correctly sample this level of detail will require each pixel to cover no more than 0.25 arcseconds of sky.  You could have pixels covering less than 0.25 arcseconds but no more detail will be visible and you will have increased your exposure time.  This is known as oversampling.  If you used pixels covering more than 0.25 arcseconds some detail will be lost.  This is known as undersampling.  In reality, atmospheric turbulence (or seeing) at most locations limits the resolution of any telescope to 3-4 acrcseconds during long exposure imaging.  To correctly sample this level of detail requires each pixel to cover no more than 1.5-2 arcseconds of sky.

The number of arcseconds per mm at the focal point of any telescope is given by the formula 206265/(focal length in mm).  If you know the dimensions of the CCD chip you can then calculate the FOV of the chip. The number of arcseconds of sky covered by each pixel is given by the formula 206*(pixel size in microns)/(focal length in mm).  

The table below shows the FOV in arcminutes and arcseconds/pixel for the MX516 (10 micron pixels) , SBIG ST-7E CCD camera (9 micron pixels), and Canon 10D SLR (7.4 micron pixels) on the LX200 at various f-ratios.

f-ratio MX516 SBIG ST-7E Canon 10D SLR
FOV arcsecs/pixel FOV arcsecs/pixel FOV arcsecs/pixel
f/40 1.7x1.2 0.21 2.4x1.6 0.19 7.7x5.1 0.15
f/20 3.4x2.5 0.41 4.8x3.2 0.37 15.4x10.2 0.30
f/10 6.7x4.9 0.82 9.5x6.3 0.74 30.8x20.4 0.61
f/6.3 10.7x7.9 1.31 15.1x10.0 1.18 49.7x33.1 0.97
f/3.3 20.4x15.0 2.50 28.7x19.2 2.25 94x62.8 1.84

From this table you can easily see that long exposure images of deep sky objects where seeing limits resolution to 3-4 arcseconds are best carried out at f-ratios of either f/6.3 or f/3.3.  For planetary, lunar or solar images, the short exposure durations used (tenths of seconds) can freeze the atmospheric turbulence so that resolutions approaching the limit of the telescope (0.5 arcseconds ) are possible.  For these images a high f-ratio of f/20 or f/40 should be used to ensure that the planet is a reasonable size on the CCD chip and maximum detail is captured.  Increasing the size of the planet on the CCD chip also spreads out the light received.  At f/10 a bright planet such as Jupiter could saturate the pixels even with a minimum duration exposure.

The f-ratio of the LX10 and LX200 can be reduced to f/6.3 and f/3.3 using focal reducers available from Celestron or Meade.  The f-ratio can be increased to f/20 or higher by placing a telenegative (also know as a barlow lens) in front of the camera.  I use a Celestron f/6.3 Focal Reducer, Meade f/3.3 Focal Reducer and Meade 2x Telenegative in my imaging.

As an alternative to reducing the focal length of the telescope to achieve correct sampling you could use the on-chip binning capability provided on the ST-7E.  The ST-7E allows you to create 18 micron and 27 micron pixels by using the 2x2 and 3x3 on-chip binning modes.   The 2x2 binned 18 micron pixels on an f/10 LX200 cover the same arcseconds as the 1x1 binned 9 micron pixels at f/5 and the 3x3 binned 27 micron pixels cover the same arcseconds as the 1x1 binned 9 micron pixels at f/3.3.  The disadvantage to this is that the images produced look very small on the screen.

Most popular deep sky objects will fit within the FOV of the MX516 or ST-7E at f/6.3 or f/3.3.   To image larger objects (e.g. M42 or the Andromeda galaxy) you will need to take images of different parts of the object and create a mosaic.  Alternatively you could use a smaller focal length telescope or camera lens piggybacked on the LX200 OTA.  For wide field images I use a Takahashi FS-60C 60mm apochromatic refractor piggybacked on the LX200.   The FS-60C has a focal length of 355mm at f/5.9.  An f/4.5 focal reducer can also be used with the FS-60C to give a focal length of 270mm.  The FOV table above for the Takahashi FS-60C is:

f-ratio MX516 SBIG ST-7E Canon 10D SLR
FOV arcsecs/pixel FOV arcsecs/pixel FOV arcsecs/pixel
f/5.9 47x35 5.8 66x44 5.2 220x145 4.3
f/4.5 62x46 7.6 87x58 6.8 287x189 5.6

I have also used a Canon 28-130mm zoom lens with the Canon 10D SLR camera piggybacked on the LX200 (this gives a FOV of 46x31 degrees)

For a very good discussion on focal lengths, image sizes and an excellent list of deep sky objects and their sizes visit Doc G's Infosite.