Focal Reducers, Barlows & Extended Barlows.

On the night of the 19th of November 2005 I was blessed with some exceptional seeing. With Mars so unusually steady in the eyepeice I took the opportunity to image the planet using various image scales. To do this I used a Celestron APO Barlow lens and various extention tubes I had to hand. I also used my Mogg 0.6 focal reducer to complete the test. I was interested in the actual magnification effect over Newtonian focus of the Barlow and various extention tubes and also the usefulness of that extra magnification in obtaining a better image.
Magnifying the image is something of a trade off. Doubling the image size on the CCD increases the number of pixels covering the planet, thus improving the image quality (to a point) but this also means there is a quarter less light per pixel, so noise becomes more of a factor as gain has to increase. The other factor that needs to be taken into account is the resolving power of the telescope itself. The larger the telescope the better the resolution of the telescopes image. Also the shorter the wavelength of light the better the resolution.

For this test I took an image of Mars during some very good seeing. The following table shows some of the parameters of the test...

Diameter of Mars	18.6 arcseconds
ToUcam "pixel" size	5.6痠
Telescope	222mm Mirror, F8
Telescope resolving power*	0.563 arcseconds

*Resolving power calculated by the formula:
Rp=0.25 x (500nm / Mirror Diameter in mm)
where 500nm = roughly the wavelength of green light.

The images above are the processed results if the various tests. All were 3600 frame avi's and all were processed to bring out the best result.

Images 1 to 4 were processed essentially the same way: Registax3 Wavelett 1 at 100%, Gausian Blur - Unsharp Mask - Gausian Blur in Serif PhotoPlus 8.
Images 5 & 6 required much less Wavelett adjustment. 100% ruined the image.

To obtain the size of each Mars image I cropped the image to only contain the planet itself, with no gap at the top, bottom or sides, and took an average of the height and the width measurement of the resulting image.

Image Number	Diameter of Mars in Pixels	Lens and extention(s) in mm	Barlow Extention	Magnification of image at Newtonian Focus	Effective Focal Ratio	Focal Length	Arcseconds per Pixel	Arcseconds per Pixel / resolving power
1	156	b+75+60+37	172mm	x5.57	44.6	9895mm	0.119	4.7
2	135	b+75+60	135mm	x4.82	38.6	8563mm	0.138	4.1
3	103	b+75	75mm	x3.68	29.4	6533mm	0.181	3.1
4	68	barlow (b)	0mm	x2.43	19.4	4313mm	0.274	2.1
5	28	prime	0mm	x1.00	8.0	1776mm	0.664	0.8
6	17	FR -0.6	0mm	x0.61	4.9	1078mm	1.094	0.5

From a comparison of the images I would suggest that Image 2 or image 3 show the most detail. The sampling rate for these images is 4x or 3x the resolution of the telescope, respectively. The accepted minimum good sampling rate to avoid loosing data is 2x the image resolution of the telescope. This test suggests that sampling at a minimum of 3x the telescopes resolution (i.e. at about F30), at least in good seeing conditions, will give better results.
There is however a caveat, Mars is a fairly bright object to image, in the case of a planet like Saturn which is less bright, the extra noise from the additional gain required, may result in a poorer quality image.

Below are all the images again, this time with all shown the same size. When shown this way image number 3 appears to show the most detail.
Images 5 & 6 show just how much information is lost by under sampling.