Calculating the focal length of a Schmidt-Cassegrain scope

[StuartT]

My LX-90 tube (plus focuser) is 46cm long. Given the optics of the SCT design, I struggle to see how it can have a focal length of 2m (as it claims). Is the focal length not just the distance between the primary mirror and the focus? 

 

 

 

Edited March 7, 2021 by StuartT

[Mr Spock]

The primary will have a focal length somewhere around f2.5 or 500 mm. The secondary is convex and interrupts this light cone, so effectively increases the distance by around 4x - which is where f10 comes from. That diagram isn't to scale.

[andrew s]

@Mr Spock is correct, for a compound instrument you work out the effective focal length by projecting back the light cone until its diameter reaches that of the aperture stop. The focal length is the the distance along the optic axis from there to the focus. Obviously this can be well outside the length of the telescope. 

Regards Andrew 

PS the effective focal length varies as the main mirror moves to achieve focus. 

Edited March 7, 2021 by andrew s

[StuartT]

Aha! Thanks my wise friends 👍

[vlaiv]

You are probably confused by magnifying secondary mirror. It is not flat like in newtonian - it has curve and that curve does similar thing to a barlow lens - it diverges light rays coming in from primary mirror and amplifies primary mirror focal length.

[StuartT]

Just now, vlaiv said:

You are probably confused by magnifying secondary mirror. It is not flat like in newtonian - it has curve and that curve does similar thing to a barlow lens - it diverges light rays coming in from primary mirror and amplifies primary mirror focal length.

you are correct. I was assuming the secondary mirror was flat. Thanks

[Louis D]

The primary is about an f/2 concave, thus the very short tube.  The secondary is about an f/5 convex, thus the magnification to a combined f/10 system focal ratio.  Both mirrors are spherical.

To correct spherical aberration, the corrector plate is aspherical.  The resultant system also has low astigmatism.

An SCT has uncorrected field curvature and coma in its standard commercial form.  That's why there are various correctors for them for photography that are placed near the rear port.

[Owmuchonomy]

51 minutes ago, Louis D said:

The primary is about an f/2 concave, thus the very short tube.  The secondary is about an f/5 convex, thus the magnification to a combined f/10 system focal ratio.  Both mirrors are spherical.

To correct spherical aberration, the corrector plate is aspherical.  The resultant system also has low astigmatism.

An SCT has uncorrected field curvature and coma in its standard commercial form.  That's why there are various correctors for them for photography that are placed near the rear port.

Excellent description and succinct.

[StuartT]

1 hour ago, Louis D said:

An SCT has uncorrected field curvature and coma in its standard commercial form.  That's why there are various correctors for them for photography that are placed near the rear port.

I must admit you've lost me a bit there... 😔

[vlaiv]

3 minutes ago, StuartT said:

I must admit you've lost me a bit there... 😔

Maybe a bit too much information. Telescopes suffer different type of aberrations that cause image to be less than perfect.

Field curvature is inherent in almost all telescope designs and represents the fact that focal plane is actually not a plane but rather curved surface. Sometimes this reflects by inability to have both center of the field and edges in focus at the same time (or center of the image and edges when taking a picture thru a telescope). Either center is in focus and edges blurry or vice verse - edges are in focus and center is blurry.

This happens with very wide field observation or imaging (2" long FL eyepieces or large sensors).

Coma is another type of aberration that is inherent in parabolic newtonian telescopes - but sometimes happens in other designs as well - like in SCTs.

Both of these were mentioned by @Louis D as a contrast to the fact that both primary and secondary mirrors are spherical - and spherical surfaces tend to introduce spherical aberration  - but in case of SCT this is corrected by front corrector. In the end SCT does not suffer from spherical aberration (by design - in ideal case) but does suffer from field curvature (as do other telescope designs) and from coma (similar to newtonians).

 

[Louis D]

1 hour ago, StuartT said:

I must admit you've lost me a bit there... 😔

Sorry, but I think @vlaiv covered it pretty well.