AFoV vs. TFoV

[rwilkey]

Chris Lord and I have been in correspondence recently, you may know him from his landmark paper 'Evolution of the Astronomical Eyepiece (1996) found here:

http://brayebrookobservatory.org/BrayObsWebSite/BOOKS/EVOLUTIONofEYEPIECES.pdf

Also:

http://www.brayebrookobservatory.org/BrayObsWebSite/HOMEPAGE/forum/Smyth-Barlow lenses.html#A Chronological History of Smyth & Barlow Lenses

 

For the past 6 months or so I've been ray-tracing eyepiece designs using an affordable Windows XP programme called dbOptic. I've gone through most of the designs mentioned in my Monograph and some of the more recent market introductions.

 

One aspect of UWA & HWA designs is angular magnification distortion.

 

I used raytrace data supplied by Vladimir Sacek to raytrace the 10mm Ethos in dbOptic V3.3.5beta (I've been testing Thomas Settimi's updates).

 

I'll add the results to my Imaginarium Telescopium article that can be downloaded from my Logbook page, next week.

 

Whereas the AFoV at the exit pupil is 110°, the geometric AFoV is 70°. The coefficient of distortion I've yet to evaluate but it's roughly 0.3, which is high.

 

The point I'm driving at is, it's the geometric AFoV that governs the real FoV, rather than the visual AFoV. Given that 110/70=1.571, for this HWA design, the actual FoV calculater is not going to produce the right answer.

I do mention this in my Monograph but without raytraces for every design and focal lengths in the design series, it's impossible to list distortion coefficients (the value doesn't scale with focal length or remain constant).

I do however provide a chart and a description of how to evaluate the distortion co-efficient. Knowing that, and the AFoV you can read off the geometric AFoV.

When you do this it becomes clear that HWA eyepieces aren't the way to obtain a wider actual FoV.

Admittedly there's the wow factor, which can be quantified by the product of EFL & AFoV. That floating in space sensation delivers the illusion of a very wide real FoV.

But what counts in the end is the aperture of the field stop and the diameter of the exit pupil. For the widest real FoV what you should aim for is a 6mm or 7mm exit pupil and for a 2-inch push fit eyepiece a 47mm field stop. Regardless of the AFoV that's what delivers the widest real FoV.

The point you need to get across is how distortion appears to widen the apparent field of view without actually widening the geometric field of view. And the real field of view is the geometric field of view divided by the magnification, not the apparent field of view.

The other point is that a hypothetical perfect telescope married to a hypothetical perfect eyepiece will in all circumstances not result in a perfect image. It's not possible to correct all the aberrations, field curvatures and distortions.

The third point is, even if you did manage to match the perfect eyepiece to the perfect telescope the eye wouldn't produce a perfect image, even if you had perfect eyesight because the eyeball introduces its own aberrations and distortion. The retina's Ganglion cells & the visual cortex sort out the resulting mess. Which is why no two observers perceive the same image, in the same telescope-eyepiece-eye system in the same way.

 If you want to get the best out of your telescope use a Monocentric eyepiece that gives a 1mm - 2mm exit pupil.

If you want a wide real field of view use a big low power Erflé derivative. Avoid neg-pos eyepieces. Minimize air-glass surfaces. Don't use Barlow's or Telecentric amplifiers or eyepieces with a Smyth converter.

 

Here is a reproduction of a ray-trace of the 10mm Ethos (page 87):

 

Follow the maxim, KISS, keep it simple stupid.

Here is a link to Chris's Imaginarium Telescopium where the above trace is discussed.

 

http://www.brayebrookobservatory.org/BrayObsWebSite/HOMEPAGE/PageMill_Resources/IMAGINARIUM .pdf

Thanks to Chris Lord for allowing me to reproduce our email messages, a subject he is still working on!

Well, over to you guys, I found this both helpful and fascinating, what do you think?

 

[Charic]

Thats a bucketload of information, far more technical than most, but informative.

I'm still short of info based on my own favoured ED60's, and the only root info I have is that they were based of the AT Paradigm.

[RT65CB-SWL]

Very informative. Thank you for sharing.

[Ricochet]

2 hours ago, rwilkey said:

Whereas the AFoV at the exit pupil is 110°, the geometric AFoV is 70°. The coefficient of distortion I've yet to evaluate but it's roughly 0.3, which is high.

That's a massive difference. Has anyone with the eyepiece measured the field of view to confirm it? 

[Louis D]

I don't have any Ethos or other 100+ degree eyepieces, but my ES-92s come in right at 93/94 degrees by both flashlight projection and by measuring the actual TFOV on a distant yard stick and back calculating the effective apparent field of view (eAFOV).  The eAFOV is the AFOV needed to calculate the TFOV from the magnification factor.  It automatically compensates for all distortions present in the field of view.

Here are some mismatching AFOV/eAFOV eyepieces from my collection:

The 12mm and 17mm Naglers have 85 degree AFOVs and 81/82 degree eAFOVs.

The 27mm Panoptic has a 69 degree AFOV and a 65 degree eAFOV.

The 40mm Meade 5000 SWA has a 71 degree AFOV and a 65 degree eAFOV.

The 30mm 80 degree Widescan III clone has a 77 degree AFOV and an 84 degree eAFOV.  Yes, it actually shows a wider TFOV than the 30mm ES-82 at the same power (82/81 AFOV/eAFOV).  How?  By compressing the edge (barrel distortion).

The 30mm APM UFF is 73/70 AFOV/eAFOV.

The 23mm aspheric 62 Svbony/Vite is 58/65 AFOV/eAFOV.

The 13mm, 17mm, and 22mm AstroTech AF70 are all 70 AFOV and 75/76/74 eAFOV, respectively.

The Speers-Waler 5-8mm is 78 AFOV at every setting, but 79/81/82/86 eAFOV at 8mm/7mm/6mm/5mm, respectively.  Obviously, distortion grows with increasing barlow magnification.

I've got more, but most eyepieces match pretty closely between AFOV and eAFOV.

[rwilkey]

17 hours ago, Charic said:

Thats a bucketload of information, far more technical than most, but informative.

I'm still short of info based on my own favoured ED60's, and the only root info I have is that they were based of the AT Paradigm.

If you haven't already seen it, here is a schematic of the AT Paradigm 25mm, along with the WO SPL, which I know you value:

In order: 3mm; 6mm; 12.5mm

Note its similarity to the Plössl, but with a negative (Smyth converter) lens added

 

[Louis D]

3 hours ago, rwilkey said:

If you haven't already seen it, here is a schematic of the AT Paradigm 25mm, along with the WO SPL, which I know you value:

In order: 3mm; 6mm; 12.5mm

Note its similarity to the Plössl, but with a negative (Smyth converter) lens added

 

Not what I expected from the provided diagram (BST Starguider/Paradigm?).  The diagram at left shows a Konig variant (1-2-1) for the positive section when in fact it's a 2-2 Plossl variant.

[rwilkey]

2 hours ago, Louis D said:

Not what I expected from the provided diagram (BST Starguider/Paradigm?).  The diagram at left shows a Konig variant (1-2-1) for the positive section when in fact it's a 2-2 Plossl variant.

Hi Louis D, thanks for your kind comments, I went with the Plössl variant!

[Ricochet]

6 hours ago, Louis D said:

Not what I expected from the provided diagram (BST Starguider/Paradigm?).  The diagram at left shows a Konig variant (1-2-1) for the positive section when in fact it's a 2-2 Plossl variant.

Which Starguider has a Plossl variant section? The 25mm? 

I know the diagram does not apply to the 18 or 25mm eyepieces. 

[Louis D]

2 hours ago, Ricochet said:

Which Starguider has a Plossl variant section? The 25mm? 

I know the diagram does not apply to the 18 or 25mm eyepieces. 

According to @rwilkey's post, here is the diagram:

[rwilkey]

13 hours ago, Louis D said:

According to @rwilkey's post, here is the diagram:

Hi Louis D, that is a much better diagram, thanks for that!

[Louis D]

2 hours ago, rwilkey said:

Hi Louis D, that is a much better diagram, thanks for that!

And that is clearly not a Plossl variant.  As near as I can make out, it uses a relay lens of sorts at the beginning to avoid changing the image scale too much while allowing for some edge correction followed by a Konig variant again.

I'm guessing that the original diagrams are for the 55 degree long eye relief (LER) eyepieces that were popular about a decade ago.  I think they were made by Kunming United Optical.  It's interesting that they took the straight forward approach of essentially barlowing a Plossl.  That's probably what limited the design to 55 degrees rather than 60 degrees or more.

[Louis D]

27 minutes ago, Louis D said:

I think they were made by Kunming United Optical.

Finally found it.  They were made by Long-Perng.  My memory is going fast.  Those eyepieces 14.5mm and shorter are all listed as 7 elements in 4 groups rather than 6 elements in 3 groups as shown in the original diagram.  Did someone actually disassemble the WOs to get those diagrams?

[rwilkey]

32 minutes ago, Louis D said:

And that is clearly not a Plossl variant.  As near as I can make out, it uses a relay lens of sorts at the beginning to avoid changing the image scale too much while allowing for some edge correction followed by a Konig variant again.

I'm guessing that the original diagrams are for the 55 degree long eye relief (LER) eyepieces that were popular about a decade ago.  I think they were made by Kunming United Optical.  It's interesting that they took the straight forward approach of essentially barlowing a Plossl.  That's probably what limited the design to 55 degrees rather than 60 degrees or more.

Hi Louis, I meant that the WO SPL's look like derivatives of the Plössl, as you identify.  I agree that the StarGuider owes some of its design to the König, or a reverse RKE!  König eps are virtually unknown in the UK.  The only time I ever bought one was from the US (eBay) and it performed quite well, if I remember correctly.

[rwilkey]

5 minutes ago, Louis D said:

Finally found it.  They were made by Long-Perng.  My memory is going fast.  Those eyepieces 14.5mm and shorter are all listed as 7 elements in 4 groups rather than 6 elements in 3 groups as shown in the original diagram.  Did someone actually disassemble the WOs to get those diagrams? 

I am not sure whether they were disassembled or X-rayed, I found the picture after searching the internet using the search criteria 'spl eyepiece pics', but it originates here: http://www.davidesigillo.eu/test_6.html

 

[Louis D]

1 hour ago, rwilkey said:

I am not sure whether they were disassembled or X-rayed, I found the picture after searching the internet using the search criteria 'spl eyepiece pics', but it originates here: http://www.davidesigillo.eu/test_6.html

 

Thanks for the link.  It doesn't answer where that person got the diagram from, but the following from google translate explains the missing element:

The optical scheme is that of a 5 element Erfle with the addition of a Barlow doublet at the bottom of the barrel, ie two cemented doublets facing each other with a biconvex lens in the middle in the diagram (2 + 1 + 2) +2 . In the picture you can see that the central biconvex lens does not seem to be colored gray instead of green as the doublets. The lenses have all the side blackening and the opacification of the threads is good.

There's a lens in between the doublets not colored green in the diagram I was missing.  With it, there are 7 elements in 4 groups!  So, the positive group is really a 5 element "super Plossl" or Zeiss Astroplan variant.

[rwilkey]

21 hours ago, Louis D said:

There's a lens in between the doublets not colored green in the diagram I was missing.

Hi Louis, neither did I see it, also thanks for doing the Google translation, I didn't think to do that!