Projection of Astronomical Images onto a CCD
Here we look at various ways in which an image can be projected onto the CCD
surface, and how the effective Fratio of the telescope can be increased/decreased.
Prime Focus
This is the
simplest method and can give the best results. The image is projected directly
onto the surface of the CCD by the telescope objective lens or mirror.
The light gathering power will be a function of the square of the diameter of
the objective, D^{2}, so the bigger the objective the brighter
the image.
The effective focal ratio F = L/D will be as specified for the
telescope. The size of the image d projected onto the CCD is given by
d=Lsinθ.
For example, if a planet of angular diameter θ =
20arcseconds is projected onto a CCD using a telescope of focal length
L=2000mm (e.g. my LX200) then the image of the planet will be of diameter
d=0.194mm.
A Toucam Pro webcam has pixels 0.0056mm square, so the planet will span
0.194/0.0056 = 35 pixels. This will give a small but useful image on your
computer screen.
Another way of looking at it is to say that the L=2000mm telescope
will project 1arcsecond of sky onto 1.75pixels. Given typical seeing conditions
this may well be enough to obtain as much detail as possible. If you are sitting
on top of a mountain with near perfect seeing then you may benefit from some
additional magnification.
Given that a Toucam Pro has a CCD of 640x480 pixels then the total field of
view will be 366x274arcseconds or 6.1x4.6 arcminutes.
Barlow Projection
However,
sometimes a bit more magnification is desirable and a Barlow lens can be added.
A Barlow is a
lens of negative focal length placed between the telescope objective and the
CCD. Normally used with an eyepiece, Barlow lenses are specified as giving a
certain amount of magnification (x2 or x3 etc). When used to project onto a CCD
they can give other values of magnification.
The image projected onto the CCD is bigger than it would be without the Barlow by a
factor M:
M = 1+ d/F_{b}
Where M is magnification, d is distance from the Barlow lens to the
focussed image and F_{b} is the focal length of the Barlow lens.
Barlows often do not have their focal length marked on them, but an
approximation can be obtained by estimating the distance from the Barlow lens to
the field stop of an eyepiece fitted normally to the Barlow.
M factors up to twice the specified power of the Barlow may be obtained before distortions begin to
appear (spherical aberration, vignetting). Alternatively you can stack 2 Barlows
one after the other to obtain additional magnification.
Given our 20arcsecond diameter planet, and a magnification factor of M=2,
the planet will now span 70 pixels of a Toucam Pro (or 3.5pixels per arcsecond).
This will normally be more than enough to capture the maximum detail possible.
The field of view will of course be half that obtained without the Barlow.
Remember also that the same amount of light is now being spread over 4 times as
many pixels so the image will be fainter or you will have to increase exposure.
Eyepiece Projection
An
alternative method of increasing the Fratio of the telescope is to use eyepiece
projection. The eyepiece is placed a little further from the prime focus than would
be normal for visual operation. In the diagram:
1/f_{e} = 1/BC + 1/CD
where f_{e} is the focal length of the eyepiece and
magnification M is:
M = CD/BC
You may need a special tube or 'eyepiece projection kit' to hold the eyepiece
and CCD in the right positions.
Eyepiece projection can be used to obtain magnifications of several times,
but may suffer from spherical aberration.
Focal Reducer
In many situations
the Fratio is too high and field of view too small for the object to be imaged.
This it particularly true of many deep sky objects. In this case a focal reducer can be used. This is a lens of positive focal
length placed before the normal prime focus. It causes the image to be formed at
a shorter distance than prime focus.
Focal reducers, like Barlows, are designed to achieve a specified
magnification, in this case M<1, but in theory M can be varied depending
on the placement of the CCD.
For a focal reducer magnification M is:
M = 1 d/f_{r}
This means that placing the CCD a bit further away than normal could achieve
a further reduction in Fratio. However, focal reducers generally do not work
very well far from their design point.
Eyepiece and Camera
If the CCD has a nonremovable lens (such as many digital cameras) then you can try this approach.
The telescope and
eyepiece are set up and focussed as for normal visual operation. The camera,
focussed at infinity, is placed directly behind the eyepiece to capture the
image as seen by the eye.
In practice this is quite difficult to set up and you will need to have
an adapter to hold the camera firmly in front of the eyepiece. Best results
are obtained using cameras that can be remote controlled from a computer.
This avoids the vibration caused by pressing the exposure button on the
camera. Alternatively set the camera to delayed exposure.
The field of
view obtained by this technique will be the same as that visible
through the eyepiece. Sometimes the full field of view is not correctly
reproduced and it is worth experimenting with different eyepieces and settings
of the camera's "zoom" lens to get the best results.
