•

# Confused by maximum FOV calculations, field stop, vignetting

19 replies to this topic

### #1 Andy-di-Notte

Andy-di-Notte

Mariner 2

• topic starter
• Posts: 266
• Joined: 26 Jun 2009
• Loc: The Netherlands

Posted 30 April 2020 - 04:51 AM

I have a bunch of questions and just can't avoid writing a long post, sorry. Hopefully someone that can clear this up for me will have the patience to read through it: thanks in advance.

Iâ€™m confused by different bits of information Iâ€™ve read regarding calculating the maximum FOV obtainable in a telescope and Iâ€™m not exactly sure what field stop to look for when searching for eyepieces that will offer the maximum field of view in both my two telescopes:

C8: F/10, F.L. 2032mm
ED80: F/7.5, F.L. 600mm

At the moment I have a T2 diagonal (32mm opening) with a 2 inch (50mm) visual back, and use a  24mm Hyperion with a field stop of 28mm for my widest views.

CALCULATION WITH FIELD STOP:

I was under the impression that to calculate the maximum field of view, you would simply need to use the following formula:

( Eyepiece field stop / Telescope focal length ) X 57.3

Using the field stop size of the eyepiece is pretty straightforward unless the field stop of the eyepiece is larger than any other opening between the eyepiece and the telescope.

If I understood correctly you need to take also into consideration not only the field stop of the eyepiece, but also the maximum opening of the rear of the telescope, such as the rear cell and the visual back in a SCT, or the focusing tube in a refractor, and also of other accessories that are in between the eyepiece and the telescope, such as the diagonalâ€™s nosepiece, any adapters in the light path, and also f.e. the maximum opening in the nosepiece of a binoviewer.

This is where it becomes unclear to me. It seems you canâ€™t just replace the size of the field stop of the eyepiece with any other smaller opening  in the light path.

People then mostly speak of an (approximate) amount of vignetting instead.

CALCULATION EXAMPLES:

If I have a T2 diagonal (with a 32mm max. opening) on a C8 telescope and use a 24mm Hyperion with a field stop of 28mm, then the calculation is straightforward:

True field of view = (28/2032) x 57.3 = 0.79 degrees

If I would use the same diagonal with a 50mm 2 inch GSO that has a field stop of 46mm then I could use this number instead:

True field of view = (46/2032) x 57.3 = 1.3 degrees

However, the maximum opening of the rear cell in my C8 is 37.5mm and that of the diagonal is 32mm.

QUESTIONS:

So how would I calculate the FOV correctly in this case? Using the smallest opening in the light path, which is the 32mm of the diagonal?

And which field stop amount would I use if I would have a 2 inch (50mm) diagonal? The smallest opening then would be the C8â€™s 37.5mm rear cell?

And last but not least, what role does vignetting play in this calculation?

Edited by Andy-di-Notte, 30 April 2020 - 05:00 AM.

### #2 Jon Isaacs

Jon Isaacs

ISS

• Posts: 92,696
• Joined: 16 Jun 2004
• Loc: San Diego and Boulevard, CA

Posted 30 April 2020 - 05:28 AM

And last but not least, what role does vignetting play in this calculation?

Andy:

Your questions are very good ones and show a great deal of thinking.

In short: it is all about vignetting and there are no simple calculations when there are multiple stops both in focus and out of focus in the system.

For a single out of focus stop that is otherwise fully illuminated, one can try to use a Newtonian secondary illumination calculator like Mel Bartels but I'm not sure how valid it is for such short distances.

Using Mel's calculator and assuming the 32 mm stop is at the front of the diagonal 100 mm from the focal plane, I get 2.5 magnitudes Vignetting at the edge of a 40 mm field stop

I think an actual solution for a complex system would have be based on ray tracing.

Further complicating the situation is the insensitivity of the eye to to Vignetting. It's there, a camera sees it, the eye doesn't.

Jon

• Andy-di-Notte likes this

### #3 Ernest_SPB

Ernest_SPB

Surveyor 1

• Posts: 1,531
• Joined: 13 Nov 2010
• Loc: St.-Petersburg, Russia

Posted 30 April 2020 - 06:05 AM

It is easy.

See attached drawing.

When stop placed not in focal plane it named vignetting stop (VS).

How much does it limit FOV can be easily calculated from VS diameter (D), distance from the stop to focal plane L and F-number (FN) of the scope.

100% illuminated FOV has diameter = D - L/FN

FOV diameter with 50% illuminated edge = D

FOV diameter with 0% illuminated edge = D + L/FN

* it is in approximation of telecentric off-axial light beams (exit pupil on infinity) - quite good approximation in many cases

for example: in scope with F-number = 10, VS with diameter 32 mm and distance from VS to focal plane 70 mm we have

FOV100% = 32 - 70/10 = 25 mm

FOV50% = 32 mm

FOV0% = 32 + 70/10 = 39 mm

#### Attached Thumbnails

Edited by Ernest_SPB, 30 April 2020 - 06:13 AM.

• Jon Isaacs, Ohmless and howardcano like this

### #4 Jon Isaacs

Jon Isaacs

ISS

• Posts: 92,696
• Joined: 16 Jun 2004
• Loc: San Diego and Boulevard, CA

Posted 30 April 2020 - 08:06 AM

How much does it limit FOV can be easily calculated from VS diameter (D), distance from the stop to focal plane L and F-number (FN) of the scope.

How do handle multiple stops that occur in the optical path.

An 8 inch SCT has a baffle tube that vignettes the image as well as this diagonal closer to the focal plane?

Jon

### #5 Andy-di-Notte

Andy-di-Notte

Mariner 2

• topic starter
• Posts: 266
• Joined: 26 Jun 2009
• Loc: The Netherlands

Posted 30 April 2020 - 02:38 PM

Thanks for the feedback.

It is easy.

See attached drawing.

When stop placed not in focal plane it named vignetting stop (VS).

How much does it limit FOV can be easily calculated from VS diameter (D), distance from the stop to focal plane L and F-number (FN) of the scope.

100% illuminated FOV has diameter = D - L/FN

FOV diameter with 50% illuminated edge = D

FOV diameter with 0% illuminated edge = D + L/FN

* it is in approximation of telecentric off-axial light beams (exit pupil on infinity) - quite good approximation in many cases

for example: in scope with F-number = 10, VS with diameter 32 mm and distance from VS to focal plane 70 mm we have

FOV100% = 32 - 70/10 = 25 mm

FOV50% = 32 mm

FOV0% = 32 + 70/10 = 39 mm

Sorry, I'm not sure I understand this Ernest.

You speak of the field of view expressed as a diameter, and not in degrees.

Should I use those diameters you have calculated instead of the field stop in the calculation of the true field of view?

If I try to relate your explanation to my example , the T2 diagonal's 32mm opening is the vignetting stop which will lead to a reduction of the field of view.

If I use a GSO eypeice with a 46mm field stop, and the results from your calculations:

Only 25mm of the 46mm field stop is illuminated 100%, then at 32mm it will be illuminated only 50%, and beyond 39mm there is no image at all.

If so then:

The true FOV will be (39/2032)X57,3 = 1.1 degrees. Of which only (25/2032)x57.3= 0.7 degrees is fully illuminated.

Is this correct?

Edited by Andy-di-Notte, 30 April 2020 - 02:40 PM.

### #6 Ernest_SPB

Ernest_SPB

Surveyor 1

• Posts: 1,531
• Joined: 13 Nov 2010
• Loc: St.-Petersburg, Russia

Posted 01 May 2020 - 12:05 AM

How do handle multiple stops that occur in the optical path.

An 8 inch SCT has a baffle tube that vignettes the image as well as this diagonal closer to the focal plane?

In terms of FOV100%/50%/0% diameters - the same way (see attached drawing).

Calculate them for each VS and select minimal values:

FOV100% = min(FOV100%),

FOV50% = min(FOV50%)

FOV0% = min(FOV0%)

By the way FOV for intermediate value of vignetting (like V% = 25% or 75%) is calculated with just a bit more complex formula.

FOV(V%) = D + (1-V%/50%)*L/FN

Effect from a number VS is calculated as above.

You speak of the field of view expressed as a diameter, and not in degrees.

Input FOV for eyepiece can be represented in linear form (diameter of it's effective FS). To convert it into AFOV use known formula: AFOV = 57.3*FOV/FL (deg.), where FL - focal length of the eyepiece.

#### Attached Thumbnails

Edited by Ernest_SPB, 01 May 2020 - 12:26 AM.

• Jon Isaacs likes this

### #7 Andy-di-Notte

Andy-di-Notte

Mariner 2

• topic starter
• Posts: 266
• Joined: 26 Jun 2009
• Loc: The Netherlands

Posted 02 May 2020 - 06:35 AM

Thanks again for the response Ernest. I assume you mean to say that the way I used those diameters in my previous post is not correct.

I have to admit then, that I still don't understand how I can use this information to calculate the field stop I need to look for when searching for eyepieces that will offer the maximum field of view in my telescopes.

Andy:

Your questions are very good ones and show a great deal of thinking.

In short: it is all about vignetting and there are no simple calculations when there are multiple stops both in focus and out of focus in the system.

...

Perhaps you are right Jon, and thanks for the compliment by the way, although I might not be doing it honour: apparantly I'm just not smart enough to understand Ernest's explanation and there is indeed no calculation simple enough for me and what I'm looking for.

I think I'll just forget about understanding the underlying science and just rephrase my question in a more basic form and post it again:

"which eyepieces will give me the maximum field of view in a ED80 and a C8, with a T2 diagonal", and then I'll just look up what the field stops are...

### #8 Ernest_SPB

Ernest_SPB

Surveyor 1

• Posts: 1,531
• Joined: 13 Nov 2010
• Loc: St.-Petersburg, Russia

Posted 02 May 2020 - 11:19 AM

I have to admit then, that I still don't understand how I can use this information to calculate the field stop I need to look for when searching for eyepieces that will offer the maximum field of view in my telescopes.

For every eyepiece you can calculate effective diameter of its FS: FSD = FL*AFOV/57.3 - comparing the value with available FOV calculated as above.

E.g.

FOV100% = 32 - 70/10 = 25 mm

FOV50% = 32 mm

FOV0% = 32 + 70/10 = 39 mm

Acceptable FSD somewhere between 32 and 39, let's take 35 mm (strong vignetting, but tolerable). Let's see for some 82 degree eyepiece with focal length... FL = 35*57.3/82 = 24 mm. So 24 mm 82 -degree eyepiece will be enough. Note that FL = 57.3*FSD/AFOV - just another representation of the same formula.

Edited by Ernest_SPB, 02 May 2020 - 11:20 AM.

• Andy-di-Notte likes this

### #9 Andy-di-Notte

Andy-di-Notte

Mariner 2

• topic starter
• Posts: 266
• Joined: 26 Jun 2009
• Loc: The Netherlands

Posted 02 May 2020 - 01:37 PM

Ahh thanks, I begin to see the light at the end of the tunnel!

You do need to decide in advance how much vignetting you find acceptable and what size field stop will generate it. But at least now I know, according to these calculations, that in this situation any field stop diameter up till 39mm is acceptable.

It would be nice to have some kind of visual representation to see the effect of this level of vignetting. I cannot imagine what this would look like. F.e. a 35mm size field stop vs. a  37 or 39mm field stop.

So if I consider eyepieces with a 68 degree AFOV, such as the Baader Hyperions, I'd be able to use a 35*57.3/68 = 29mm version.

Baader actually has a 31mm Hyperion, which will have a 31*68/57.3 = 36.8 mm effective field stop. This still falls into the acceptable range between 32 and 39mm.

Edited by Andy-di-Notte, 02 May 2020 - 02:19 PM.

### #10 Andy-di-Notte

Andy-di-Notte

Mariner 2

• topic starter
• Posts: 266
• Joined: 26 Jun 2009
• Loc: The Netherlands

Posted 03 May 2020 - 02:25 PM

How do you measure the distance from the vignetting stop to the focal plane? I know where the stop is, but where is the focal plane actually?

### #11 dan_h

dan_h

Gemini

• Posts: 3,109
• Joined: 10 Dec 2007

Posted 03 May 2020 - 03:51 PM

How do you measure the distance from the vignetting stop to the focal plane? I know where the stop is, but where is the focal plane actually?

The focal plane will be at the eyepiece field stop when the eyepiece has been brought to focus. It can be a little hard to determine on some widefield eyepieces where the field stop is internal but with simple Plossls, Orthos, Kellners, etc, you should be able to see the field stop in the barrel.

For bright targets like the moon you can leave the eyepiece out and project the lunar image onto a white card. The focal plane is where this image comes to a sharp focus.

dan

• Andy-di-Notte likes this

### #12 Andy-di-Notte

Andy-di-Notte

Mariner 2

• topic starter
• Posts: 266
• Joined: 26 Jun 2009
• Loc: The Netherlands

Posted 04 May 2020 - 03:43 PM

Thanks for the info Dan.

You're right, I had a look at some eyepieces and It's indeed tricky to see exactly where the field stop is in some of the ones I have.

I'm only speculating here, but If the focal plane is at the eyepiece field stop I think that the estimated distance of 70mm between the vignetting stop and the focal plane might be too generous.

A 2 inch clicklock eyepiece holder is 36.5mm tall, and the diagonal's stop is just below it, lets say at 38mm from the top. If I assume the field stop of the eyepiece is somewhere inside the eyepiece just above the top of the barrel, then the focal plane would be at about 40mm from the vignetting stop.

According to Ernest's calculations, if  L=40mm instead of 70mm, then the maximum acceptable field stop for the eyepiece would be 32 + (40/10) = 36mm for the C8 and a bit more than 37mm for the ED80.

Not too far from the 35mm Ernest had suggested already.

So it looks like I have a goal, I'm going to try and find an eyepiece with this kind of field stop and have fun testing these numbers in practice.

Thanks again for the explanations, it's nice to learn this kind of stuff ;-)

Edited by Andy-di-Notte, 04 May 2020 - 03:54 PM.

### #13 Eddgie

Eddgie

ISS

• Posts: 27,522
• Joined: 01 Feb 2006

Posted 05 May 2020 - 10:07 AM

First, we have to differentiate between true field and fully illuminated field.  The true field of a C8 can be made a couple of degrees but that does not mean you would want to do it.

We should differentiate between the largest true field and a field that is vignetted to only the degree that the user would find acceptable.

See, even with the factory visual back and diagonal, the field of your telescope is already vignetted. Only a small circle at the center of the field of your eyepiece is fully illuminated (100%) and the moment you move something outside of the field, form there on, it is all vignetted and the further you go away from the center of the field, the worse that vignetting gets.

And this has nothing to do with the rear opening size of the baffle. I could make that rear opening larger, but it would not change the size of the fully illuminated circle because this vignetting is caused by the opening at the front of the baffle. The reason you don't see it is because it is so far away that it is out of focus.

Now the 32mm opening in the front of the diagonal does not reduce the fully illuminated field size (which is nothing to do with the true field size, only the size of the unvignetted true field) because at the point where it passes through the opening, the cone that produces the fully illuminated field would be narrower than 32mm.

And here is how you calculate that. Ray traces suggest that the fully illuminated or unvignetted part of the field of the C8 is about 8mm.  Outside of this, the field starts to vignette and continues to loose brightness over whatever size true field you can see.

Now we know that the size of the cone will grow for 1mm in diameter for every multiple of the focal ratio that you move ahead of the focal plane.    For example, if the fully illuminated field was 8mm, and I measured the diameter 10mm in front of the top of the eyepiece holder, it would be 9mm in diameter.

Now in your case, the light path length to the front restriction in the diagonal is the distance from the restriction to the top of the eyepiece holder. The T2 diagonal has a light path from that 32mm opening that is about 31mm in front of the top of the diagonal flange and as I recall, the eyepiece holder is 30mm, so this means you have a light path of 61mm from the restriction to the top of the eyepiece holder.

This means that if your fully illuminated circle is 8mm at the focal plane, it will be 6.1mm larger at the point where it passes through the opening at the front of the diagonal, so where it passes through that opening, it will be 14.1mm, so the 32mm opening will not further reduce your fully illuminated field size.

Now the rear baffle size does not affect the size of the fully illuminated field, but what it does affect is the point at which illumination falloff becomes more severe.   If you could measure the illumination of your 28mm field stop, you would find that at the edge of the field, the illumination would have fallen by about 16% or 17% at the edge of the field.

Now if you used a 2" diagonal, with a 130mm light path (including visual back) we see from the above chart that at 46mm with a 130mm flange to field stop distance, the field will be vignetted to about 63% or so at the edge of the field. The very outermost part of the field would show enough of a sharp transition to see, but it would not be glaring.

Now that is with a 2" diagonal.

What will the 32mm openening do?  Well, here we have to figure out if the off axis light cone is has gotten small enough to clear the 32mm opening. First, let's go back to the 100mm spacing.

Here, the light cone would be illuminated to about 68%.   We can work forward to see how big it gets as we get closer to the 32mm opening.  We know that it is 46mm at about 68% illumination here, so we know that as we go further forward it will get bigger and we know from our earlier example, it will be 6.1mm larger when it gets to your 32mm opening, so it has expanded from 46mm to 52.1mm.  We also know that it only started at about 68% and now we see that it will not fit through the hole, so the chart above would show the falloff that we now see as happening at 46mm mm would be occurring over an image circle about 32mm in diameter and that this falloff would be about 60% (because the circle is wider in proportion to the opening than it was at the rear baffle.).

Now because the source of the vignetting is much closer to the focal plane and the vignetting increase is quite severe, this would not escape detection. You would see very sharp vignetting in the very outer part of the field of view.

So, essentially you would get something like this:

But that is not the true field limit! That is just the part of the field where the vignetting starts to be more noticeable as you transit from the part of the field with mild vignetting to the part where the vignetting becomes more severe.

So, you scope is always vignetted. With a 2" diagonal, you would see about 63% illumination at the edge of the 2" eyepiece, but because it is very close to the field stop and because the drop is still not wide and sharp enough to see the transition, this would still be usable and the use of this kind of eyepiece in the C8 is pretty common and most report that vignetting is not really an issue.

In the case of the 32mm opening that is 61mm in front of the field stop, the situation is much worse.  The transition from about 75% illumination to maybe 40% illumination occurs over a wider area and you would see a distinct vignetted circle at the edge of your field of view..

But this is not the size of the true field. This is just the amount of illumination at the edge of the true field.  As the above diagram shows, there is still plenty of light there, but things are dimmed by 60% or more.

The maximum true field one could get and have the telescope work at full aperture wold be 1.97 degrees (as we see in the plot above, we could attain that with a focal reducer and a 2" eyepiece if the diagonal box was mounted directly to the focal reducer with no 2" nose piece of visual back).  Now the field would be 100% only at the center and the vignetting would be a very smooth transition form the glow of sky to jet black of fully aperture aperture loss.

But it would be an almost 2 degree true field, just not one that is working very well.

So, your diagonal is not may not be suitable with the eyepiece you want to use. (Never say never... )

The 35mm Panoptic might be OK, but my advice is to upgrade to a 2" diagonal.

Now I could have saved us both a lot of time and maybe you skipped this, but the goal was to help you understand how vignetting works and how to make this kind of analysis in the future if there are other applications (like binoviewers) where it can be important.

The practical true field of the C8 is pretty much exactly what you get if you use a 2" diagonal and and an eyepiece with a 46mm field stop.  The practical true field of your scope using your diagonal would probably be with something like a 31mm Hyperinn Aspheric used with the 2" barrel.  Maybe a 35mm Panoptic, but I think the vignetting would be much more noticable than in the 31mm Ashpheric.  But you see, at this point it starts to get subjective because it depends on how much how wide and sharp the the vignetting is and that is really a personal call.

Edited by Eddgie, 05 May 2020 - 10:47 AM.

### #14 Eddgie

Eddgie

ISS

• Posts: 27,522
• Joined: 01 Feb 2006

Posted 05 May 2020 - 10:13 AM

And as extreme as the option of using a focal reducer and a 2" diagonal attached directly to it, there are people that actually do this and will say that it works well for them.  They want a wide field of view at any cost. If you are under very dark skies, it gets much harder to see complete illumination falloff because the perceived brightness difference between the center of the field and the edge of the field can be subtle is skies are very dark. Under bright skies though, it is like looking through the hole in a black dougnut.

Now I don't know why someone would want a wide field that was reduced in brightness to less than one could get with a cheap 4" acromat over most of it, but there are people that have used the above configuration and loved it.

You also hear stories about people getting larger true fields than this, but that is not really possible and have the scope still work at full aperture.  But you can get a 1.9 degree true field out of a C8.  It is just a horribly inefficient one though and only a tiny tiny tiny tiny tiny point at the center of the field is working at full aperture.  The vignetting falloff though is almost completely linear, and this just tricks you into thinking it is not that bad. It is horrible though, but again, some want a wider field at any cost and will say it works well.

Shout out to Ken Hutchinson.  The chart in the previous post was his work. The cut and paste was mine.  What can I say, it was a lazy way to do something pretty.

Edited by Eddgie, 05 May 2020 - 10:26 AM.

### #15 Andy-di-Notte

Andy-di-Notte

Mariner 2

• topic starter
• Posts: 266
• Joined: 26 Jun 2009
• Loc: The Netherlands

Posted 05 May 2020 - 03:34 PM

Eddgie, wow. Thank you for putting so much time into giving me such a detailed answer to my questions.

I just finished studying your post, and it's going to take me some time to fully digest it. I'll have to read it a few times more. It's an interesting read and as John pointed out earlier, I realize now the explanation goes indeed a little further than a simple calculation :-)

And yes, it will definitely come in handy for future calculations, f.e. with the binoviewer which I also enjoy a lot.

I was already considering looking for an eypepiece with a field stop of about 36/38mm.  If I understood correctly this would be still give me an acceptable amount of vignetting with my setup. Considering the advice I've received, I don't think I'll be looking for anything wider than that.

To be honest my main aim as far as wide fields is concerned, is to use it with the ED80 which should get me to 3.6 deg. FOV. which is plenty.

But of course I would also use it with the C8 for just above 1 degree FOV, just enough to squeeze in more of the double cluster f.e.  That's less than a reducer would get me, but at least I can use the eyepiece in both the telescopes.

However I love using the C8 with a bino, and then wide fields are out of the question :-)

I just upgraded my visual back and diagonal for a stronger setup for the binoviewer+hyperions, so I don't really want to consider a 2 inch diagonal for the time being.

As far as the eyepiece is concerned there are a few possibilities even with my limited budget:

CN favorites like Televue, Pentax, etc. are unfortunately out of my budget range. Or even ES, except for the 62 degree series.

The 31mm Hyperion Aspheric is more in my range, but it gets quite a lot of bad reviews. I love my Hyperions though, so I might be less sensitive to edge aberrations. Or perhaps it's due to my lack of experience with wide views.

I hear the 32mm SW Panaview seems to be a good budget widefield.

Or the 32mm 70deg Agena/Orion Q70 SWA

Here in Europe we have TS around the corner with their own clones such as this: https://www.teleskop...ent-Design.html

And I hear some good things about the 30mm APM Flat Field with a 38mm field stop.

I'd be happy to hear any other suggestions if you have any!

Edited by Andy-di-Notte, 05 May 2020 - 03:51 PM.

### #16 Jon Isaacs

Jon Isaacs

ISS

• Posts: 92,696
• Joined: 16 Jun 2004
• Loc: San Diego and Boulevard, CA

Posted 05 May 2020 - 03:42 PM

A 2 inch clicklock eyepiece holder is 36.5mm tall, and the diagonal's stop is just below it, lets say at 38mm from the top. If I assume the field stop of the eyepiece is somewhere inside the eyepiece just above the top of the barrel, then the focal plane would be at about 40mm from the vignetting stop.

Andi:

You need to consider the stop that is the furthest from the diagonal. In the case of the C-8,  the 38 mm rear port needs to be considered.

Jon

### #17 Andy-di-Notte

Andy-di-Notte

Mariner 2

• topic starter
• Posts: 266
• Joined: 26 Jun 2009
• Loc: The Netherlands

Posted 05 May 2020 - 04:00 PM

Andi:

You need to consider the stop that is the furthest from the diagonal. In the case of the C-8,  the 38 mm rear port needs to be considered.

Jon

I actually initially thought that the worst vignetting was caused by the smaller openings near the focal plane. That's why I was calculating the distance between the diagonal opening closest to the eyepiece and not the other opening on the telescope side. I didn't consider (the obvious fact) that the light cone gets wider as you get further away from the focal plane.

Regarding the rear cell opening, I guess we would have to calculate the size of the light cone at that point. That's not going to happen now, I'm going to sleep on all this information first

Thanks for chiming in again .

Edited by Andy-di-Notte, 05 May 2020 - 04:03 PM.

### #18 Eddgie

Eddgie

ISS

• Posts: 27,522
• Joined: 01 Feb 2006

Posted 06 May 2020 - 03:39 PM

I actually initially thought that the worst vignetting was caused by the smaller openings near the focal plane. That's why I was calculating the distance between the diagonal opening closest to the eyepiece and not the other opening on the telescope side. I didn't consider (the obvious fact) that the light cone gets wider as you get further away from the focal plane.

Regarding the rear cell opening, I guess we would have to calculate the size of the light cone at that point. That's not going to happen now, I'm going to sleep on all this information first

Thanks for chiming in again .

This diagram explains what is happening.   The top diagram shows the rays that form the fully illuminated circle.

Because of the baffle, the off axis rays are partially cut off outside of that fully illuminated circle and that is shown on the top diagram. This is what makes the fully illuminated field size.

The bottom diagram shows what happens at the point where the off axis light that is still reaching the focal plane travels at an angle that continues to widen past the baffle opening but notice that the rays on the opposite side are not able to travel to the focal plane any longer so that side is "opaqued" (zero rays are coming through from this side of the aperture) No rays rays entering from top side of the field in the bottom diagram, so the field is only getting the rays coming in at an angle from the other side of the field, so in other words, 50% illumination in this case (diffraction actually makes it a bit more than this but let's ignore this for now to keep it simple.  Ray traces do not factor in diffraction because it is not needed to understand the major behavior and this would only be a minor modification).

These drawings are also from Ken, but the Red is from me and I did not try to be in scale here. I am only using his diagrams to illustrate how off axis illumination works and how a restriction will affect it. The red represents on side of the circular restriction and it is the same lenght to the same grid line, but as can be seen, the rays are further from the edge of the field the closer they get to the focal plane and some are running into the 32mm restriction..

Now, using the enlarged drawing, imagine that you put a 32mm opening 60mm in front of the focal plane the rear of the telescope and the focal plane  Some of those rays that can reach the focal plane now, would be intercepted and this would create more vignetting than would be present without the 32mm opening..   How much added vignetting will occur depend on the distance between the field stop and the restriction.   If you move the 32mm opening closer to the focal plane (the middle line in the enlarged drawing and let's say this is 30mm in front of the focal plane), you loose more of the off axis rays.  The vignetting then is worse the closer it gets to the focal plane.

Now what happens if you continue to move it to the focal plane?  As it gets very close to the focal plane, it becomes an out of focus field stop.  The light is almost completely opaged because the angle that a ray would have to come in at is  impossible so here, you are seeing a bit of diffraction and the out of focus field stop, but mostly, the restriction now becomes the field stop for the system, the apparent field of the eyepiece is made smaller (assuming the restriction is smaller than the field stop in the eyepiece) and the true field is now calculated using the new field stop size.

Now, back to the top picture.. If I moved the restriction far enough toward the objective, it would eventually get to the point where the diameter of the restriction becomes the same size as the converging light cone for the fully illuminated field and any further movement toward the primary cuts off the outside rays and the aperture is reduced.

We can calculate that.  If the fully illumined circle is 8mm, then to get to a point where it was 32mm wide, we would have to move the restriction pretty far forward. to get it to be 32mm wide, I would have to position the restriction 240mm in front of the focal plane.   Now this would be way way way inside the baffle.

But lets see where the fully illuminated circle comes from..  Let's say I put a 38mm restriction in the light cone. To get the cone that wide would need it to be 30mm wider than it is at the focal plane, so that would be 300mm.

Well, guess how big the front of the baffle is in a C8!!!!.  Remember, we are starting 100mm behind the telescope, so we need an additional 200mm of spacing, or about  8 inches.  Now that is about (and these are rough approximations) how far the length of the baffle tube in the C8!  So, that is why the fully illuminated field is only about 8mm (as per the ray trace in my previous post).  The 38mm baffle opening is about 300mm in front of the focal plane, and that is the size the light cone starts at and in 300mm, at the rage of 1mm of convergence for every multiple of the focal ratio,  it will have shrunk (and intensified) to 8mm at the focal plane.

Again these numbers may not be exact, but they are generally pretty close aproximations.

So, the size and position of the restriction determines how serious the vignetting gets and if the restriction is smaller than the field stop, the closer to the focal plane it gets, the more severe the vignetting is.

The off axis rays that illuminate the field beyond the size of the rear opening in the baffle are the rays coming in from the opposite side of the mirror and the angle that they can come in at is determined not by the size of the front opening (assuming it is a tube and not a cone but by how far in front of the rear opening the front opening is. If I cut the baffle in half, I would greatly increase the size of the true field and the center of the field illumination, but I can't do that or off axis light could fall directly on the focal plane. That is what baffles do.  They prevent unwanted off axis light from falling on the focal plane.

Again, you have to realize that at some point, the rays from the outside of the mirror that would normally go to the opposite side of the focal plane hit the rear opening and are cut off but in the C8, those rays can come in from a pretty wide angle (almost a 2 degree field before 100% of them are intercepted by the baffle wall on the opposite side from where they enter the front of the baffle. If I insert something smaller than the baffle behind the baffle if it gets too close to the focal plane, it will increase the vignetting and the closer it is, the more extreme off axis rays it will block, and the vignetting will get worse.

So, your 32mm opening will not cause your fully illuminated circle to be affected but it will cause your 50% vignetted circle to be reduced in size and past about 32mm, the falloff will be fairly rapid but how bad is too bad is a subjective call.

Edited by Eddgie, 06 May 2020 - 03:52 PM.

### #19 Andy-di-Notte

Andy-di-Notte

Mariner 2

• topic starter
• Posts: 266
• Joined: 26 Jun 2009
• Loc: The Netherlands

Posted 11 May 2020 - 06:00 AM

Thanks for the new lesson on optics Eddgie.

Just managed to get through this and as usual things seem to get more complex the further you dig into the science.

I definitely know more about my C8 now and about that long baffle tube inside the scope and its effect on vignetting.

Ironically I wasn't totally wrong about vignetting increasing closer to the focal plane, but not because I understood how this is applicable to off-axis light rays.

What I find baffling (excuse the pun) is that from your explanation it seems that, as long as the fully illuminated field is unrestricted, the closer to the focal plane the restriction is, the worse the vignetting. While I had previously understood the opposite, looking at the  light cone formed by on-axis light rays.

It's also interesting that you do not use the term "vignetting stop" and rather "restrictions" but as I understand it boils down to the same thing.

One thing I'd add to previous calculations regarding the distance between the 32mm restriction and the focal plane, is that I'd be using a 2 inch eyepiece holder instead of the current 1,25 inch. The height of the Baader 2 inch holder is 36,5mm so that would increase the distance even more creating more vignetting.

As interesting as it is to learn all this stuff, it's still theory though, and actually looking into an eyepiece with a certain field stop is probably the only way to find out how much vignetting one is willing to put up with.

It would be great if someone came up with an interactive site or app to mimic the effect.

If I think of the image I see through my 28mm field stop eyepiece with the T2 diagonal, I just don't notice any vignetting at all! So possibly I'm rather tolerant of it and might even be able to get away with a larger field stop than 38mm.

Edited by Andy-di-Notte, 11 May 2020 - 08:58 AM.

### #20 Andy-di-Notte

Andy-di-Notte

Mariner 2

• topic starter
• Posts: 266
• Joined: 26 Jun 2009
• Loc: The Netherlands

Posted 11 May 2020 - 06:04 AM

Andi:

You need to consider the stop that is the furthest from the diagonal. In the case of the C-8,  the 38 mm rear port needs to be considered.

Jon

Jon, I might as well dare to pretend I know how to answer this:

if I've understood correctly the 38mm opening of the rear cell in the C8 is not really important in this case because the 32mm opening of the T2 diagonal is practically right next to it so the restriction of the light cone is more determined by the diagonal at this point.

Also, although I'm still trying to get my head around this,  the 32mm restriction is not only smaller , but from the above explanations it seems that because it is also closer to the focal plane than the 38mm rear port it therefore cuts more into the off-axis light rays and has a greater effect on vignetting.

Edited by Andy-di-Notte, 11 May 2020 - 07:37 AM.

## Recent Topics

 Cloudy Nights LLC Cloudy Nights Sponsor: Astronomics