Astrophotography by Rob kantelberg

Calculations

1 Planetary imaging

The modern webcam, unmodified, gives us the possibility to obtain detailed images of the Moon, planets and sun using normal middle class telescopes. The minimum size of details which a telescope can show is depending on a lot of criteria as collimation,obstruction, optical quality, mechanical vibrations atmospheric turbulence etc. etc. but must not be confused by the resolving power of a telescope which can approximately be calculated with the formula :

R=120/D (with R in arc seconds and D in millimeters)
The result from this formula represents the minimum separation of a double star with equal magnitudes, which can be resolved. The size of planetary details which can be imaged with a webcam is depending on many factors like contrast and atmospheric conditions but can be smaller than the stellar resolving power. In order to image the smallest details possible we need to enlarge the focal length of the telescope. This can be done by either a Barlow lens or eyepiece projection.

1.1 Magnification with Barlow lens projection

The real magnification of the Barlow lens is depending of its focal length (F_b) and the distance between the lens and the CCD chip of the webcam (P). The focal length of a Barlow lens is of course fixed but the projection distance (P) is depending on the webcam adapter used and because of that adjustable. After changing P you need to re-focus.

This magnification can be calculated with the formula :

M=P/F_b + 1 (with P and F_b in millimeters)
Standard barlow's like the Meade 2x have a F_b=73mm.

1.2 Magnification with eyepiece projection

Imaging with Barlow’s works fine for low magnifications, less than 5, but if you want to go above you need to use eyepiece projection. The real magnification obtained with an eyepiece depends on the focal length of this eyepiece (F_e) and the distance between the eyepiece and the CCD chip of the webcam (P). Both P and F_e are adjustable which gives you maximum flexibility.

This magnification can be calculated with the formula :

M=P/F_e - 1 (with P and F_e in millimeters)

1.3 Calculating the needed system set-up

With the known magnifications (M), related to the Barlow lenses and the eyepieces you want to use for imaging, and the prime focal length (F_obj) of your telescope we can easily calculate the new system parameters with the formulas:

F_eff=MxF_obj (with F_obj in millimeters)

N_eff=F_eff/D_obj (with F_eff and D_obj in millimeters)

With this parameters, (F_eff and N_eff) and the parameters of the CCD, S (number of pixels) and A(size of the CCD pixels), we can calculate the theoretical resolution (T_r) and the field of view (FOV) as follows:

T_r=206xA/F_eff (with T_r in ”/pixel, A in micrometer and F_eff in millimeters)

FOV=0,0167xSxT_r (S is number of pixels and with FOV in ’)

The best focal ratio for imaging is depending on the used telescope, the used CCD chip, the object to image and the atmospheric conditions. With a turbulent atmosphere you can't push the magnification towards the limits but you can try with a steady and clear atmosphere what your limits are. The final set-up to use should be judged on the spot.

Now we have all the necessary information in order to judge which configuration to use on which, planetary, object.

For planetary imaging I use the unmodified Philips ToUcam 740K which has a Sony ICX098BQ chip inside. The ICX098BQ measures 640x480 pixels and each pixel is 5,6x5,6µm. Find in the table below the configurations I normally use.

150mm Newton Telescope	F_eff	N_eff	Field of view	Theoretical Resolution
Prime focus	940 mm	6,3	13,1’ x 9,8’	1,23”/pixel
2x Barlow lens (F_b= 73 mm, P= 125 mm)	2550 mm	17,0	4,8’ x 3,6’	0,45”/pixel
Projection with 17mm Plössl (F_e= 17 mm, P=82 mm)	3600 mm	24,0	3,4’ x 2,6’	0,32”/pixel
Projection with 17mm Plössl (F_e= 17 mm, P=93 mm)	4200 mm	28,0	2,9’ x 2,2’	0,27”/pixel
Projection with 17mm Plössl (F_e= 17 mm, P=101 mm)	4600 mm	30,6	2,2’ x 2,0’	0,25”/pixel
Projection with 17mm Plössl (F_e= 17 mm, P=127 mm)	6100 mm	40,6	2,0’ x 1,5’	0,19”/pixel

The smallest visible details you can image needs at least two CCD pixels. This means that the maximum resolution you can reach, after ideal processing, will be two times the theoretical resolution. For example with my 6 inch Newton at F=3600mm (see table) under good skies it should be possible to capture Moon details of 0,64” (appr. 1,2km at mean distance to earth). My experience is that, with my equipment under reasonable skies, I easily can resolve 2km feathers on the Moon at F=3600mm. This means that, for objects with a lot of contrast like the Moon and planets, we can apply to the following :

2xT_r < Resolution < 4xT_r

Below two examples to illustrate this.
Moon details come from the Virtual Moon Atlas (http://www.astrosurf.com/avl/UK_index.html)

Rima Gay-Lussac, visible on the Copernicus image of May 10th 2003 (F=3600mm)


Rima Gay-Lussac (dimensions: 40x2km) Distance Moon : 369.718km Image scale : 1km=0,56”=1,8T_r		Rima Gay-Lussac on pixel level (3-4 pixels wide)

Rimae Mersenius, visible on the Gassendi image March 14th 2003 (F=3600mm)


Rimae Mersenius (dimensions: 230x2km) Distance Moon : 371.525km Image scale : 1km=0,56”=1,8T_r		Rimae Mersenius on pixel level (3-4 pixels wide)

In paragraph 4 you can download a focal lenght calculator for your own use.

2 Wide field imaging

In order to reach a "wide field" with a webcam you need to use lenses with a short to medium focal length. The normal fish-eye and standard can be used for this. These configurations are mostly used for imaging conjunctions, constellations and the Milky way. Due to the objects involved in conjunction images (Moon and planets) you can easily use an unmodified webcam but if you want to image constellations, the Milky way or conjunctions involving planetoids you need to use a modified webcam.
You can find a lot of info about webcam modification on the QCUIAG website.

For determining the FOV of these lenses you can use the flowing formula:

FOV=0,057xSxA/F (S is number of pixels and with FOV in °, A in µm, F in mm)

A Philips ToUcam 740K which has a Sony ICX098BQ chip inside (S=640x480 pixels and A=5,6µm) would give:

Used lens	Field of view
F=16mm	12,8° x 9,6°
F=35mm	5,9° x 4,4°
F=50mm	4,1° x 3,1°
F=135mm	1,5° x 1,1°

3 Deepsky imaging

With deepsky imaging the goal is to image separate objects in the sky, from small like M57 to big like M31. For this you need a telescope in prime focus for the smaller objects and the same telescope in combination with a teleconverter or even a telelens for the more extensive objects in the sky. Furthermore you need a modified webcam in order to make long exposures (>1 second).

3.1 Deepsky imaging in prime focus

Deepsky imaging in prime focus of a telescope is like imaging with a very big telelens. The main difference will be the smaller FOV. This FOV can be used for small objects like planetary nebulae, most globular star cluster and galaxies.

If you want to image the more extensive objects like reflection nebulae, emission nebulae and open star clusters you need to use a focal reducer in order to be able to have the necessary FOV to image this object.

3.2 Deepsky imaging with a focal reducer

The real magnification of the focal reducer lens is depending of its focal length (F_r) and the distance between the lens and the CCD chip of the webcam (P). The focal length of a focal reducer lens is of course fixed but the projection distance (P) is depending on the webcam adapter used and because of that adjustable. After changing P you need to re-focus.

This magnification can be calculated with the formula :

M=1 - P/F_r (with P and F_r in millimeters)
Standard focal reducers like the Meade F/6,3 have a F_r=285mm.
With this magnification you can calculate the resulting FOV as shown in paragraph 1.3.

In paragraph 4 you can download a focal length calculator for your own use.

4 Download

Download here your own focal length calculator. You can either download the zip file (6Kb) or the Excel file (27Kb).
Included are a Barlow lens, an eyepiece projection and a focal reducer calculator.
Standard they are filled in with the examples used on this page, you just can fill in your own data.

Download focal length calculator (zipped file)

Download focal length calculator (excel file)

© Copyright Rob Kantelberg