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ronharper
Pooh-Bah
Reged: 02/14/06
Posts: 1007
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Something kind of hit me about Porro prisms the other day. See if this makes sense.
A basic property of a reflecting surface is that if the surface is rotated through a small angle, a reflected ray is rotated through twice that angle.
In a Porro prism, there are two such reflecting surfaces 90 degrees apart, intended to send out an image-reversed ray opposite to the incident direction. If the Prism is off from exact alignment (in the plane of double reflection) by a small angle A, then the first reflected ray is deviated by 2A. The same angle-doubling effect happens again at the second reflection, so the output beam is deviated by 4A from the correct direction. A Porro binocular has yet another prism to get the light through, perpendicular to the first. The refractions upon enter and leaving the glass might cancel, I'm not sure, but at any rate would be very tiny, since the angle of incidence is nearly perpendicular at those surfaces.
It is no surprise to me then, that a prism holding/adjusting mechanism that can be adjusted with anything less than a 3/8" allen wrench may not be very robust against bumps and shakes. But, apparently, some of the Mariner and Kunming-8 type porros are turning out to be quite rugged, so maybe adjustable prisms can work pretty well.
If the methods are available to do so in manufacture, it's probably best to set the prisms correctly in the first place, clamp (and glue?) it as securely as possible, and use eccentricly mounted objectives to tweak the optical axis orientation.
I have read, however, that the most commonly used roof prism, the Schmidt-Pechan, sends out its inverted beam in a direction that is not sensitive to prism orientation! This sounds rather miraculous. But I am familiar with something called an "optical corner" that has this property, so I guess it could be so.
Could some of you optics gurus confirm or deny this property of the Schmidt-Pechan? If true, it would seem to contribute to an extremely rugged binocular, and maybe mitigate some of the expense of building roof prism models.
Ron
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pcad
Carpal Tunnel
Reged: 01/17/05
Posts: 1501
Loc: Connecticut
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Hi Ron,
I don't qualify as an optical guru, but you're right about the SP prisms being insensitive to rotation around their optical axis. It would depend on how accurately the Schmidt roof prism and the Pechan prism are made and assembled. If all is correct the incoming axis is the same as the outgoing axis with no offset.
The tolerances are much smaller for the Schmidt prism since there are 4 internal reflections and a roof prism and edge to worry about. The Pechan prism is simpler and I belive has only two internal reflections, one of which requires a reflective coating. The image from the Schmidt prism is fully corrected but the axis is 45 degrees off. The Pechan prism re-directs the axis so it is in line and coincident to the incoming axis.
One reason SP prisms are so popular is that a good chunk of the optical path is in the prism with all those reflections.
The inexpensive SP prisms I've seen are held together in a snap together plastic housing. I've seen some housings with small adj screws built in also, and I think I've seen one with some glue.
The other major roof prism, the Abbe-Konig, has parallel axis' with a small offset. These, like the porros, can't be rotated freely. In higher quality binos the SP prisms may be fixed in position also, but i'm not sure about it.
Peter
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Peter
Telescopes 25 - 318 mm
Binoculars 15 - 88 mm
Microscope 50x - 1000x
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Gordon Rayner
professor emeritus
Reged: 03/24/07
Posts: 506
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What is the "plane of double reflection"? This is an interesting problem. Can you clarify the geometry of which you speak? I am not certain, but if I correctly understand what you are trying to hypothesize, I doubt it. Consider the autocollimation Porro prisms in the Davidson Optronics'
catalog, for example. Or, hold a Porro prism and watch the reflection of your pupil as you rotate the prism as I guess you intend. The reflection of the pupil is invariant. But if you tilt the prism around the axis joining the centers of the entry and exit faces, the reflected ray is deviated by twice the tilt angle. That is the principle of checking the flatness of a surface plate(usually granite, used for layout and measuredment in metrology and machine shop environments) with an autocollimating Porro prism on a sled, using an autocollimating telescope to send /receive a beam to/from the prism. The setup is invariant if the prism happens to rotate around an axis perpendicular to the surface plate.
There is some relevant material concerning errors in Porro prisms ( not in the way they are mounted) in Hanna in ATM III(Willmann-Bell) and how it relates to collimation of the optical axes of each barrel to each other( and to the hinge).
Does what you mean relate to the eccentric field problem noted in some prism tilt collimating binoculars, which was brought to our attention by tireless ED. Z ? Eccentric fields seem likely to be an indication that prism plate tilting had to be taken beyond the bounds of propriety to compensate for excessive errors in the design or fabrication of the mechanisms and/or optics, in order to render the two optical axes and the hinge axis somewhere near mutual parallelism, or perhaps just to get the optical axes parallel at one interpupillary distance. I have done my share of prism plate tilt shimming, and it is never required on an undamaged( but requiring internal cleaning) WW II B&L USN ( all Rochester)Mk. 28, for example.
Have you seen the interesting combination of a beamsplitting cube with the cube corner(trihedral reflector) you mention? Those combinations are fun to play with, and speed orientation of an autocollimationg telescope to its reflector. Leitz(Opto-Metric Tools(defunct)) sold one as the "Mandler prism". I have sketched some binocular collimators using such prism combinations. Surveyors use arrays of cube corners as retroreflectors insensitive to rotations .
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Gordon Rayner
professor emeritus
Reged: 03/24/07
Posts: 506
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Pcad: "SP prisms insensitive to rotations around their optical axis". You mean tilts around axes contained in the entry or exit planes, do you not? A porro pair is insensitive to rotations around its optical axis, no? But not insensitive to tilts around the other two axes in an xyz coordinate system.
I am tempted to rummage through some of my stuff and spend away the day playing with prisms.
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ronharper
Pooh-Bah
Reged: 02/14/06
Posts: 1007
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Pcad,
Thanks for the info on the Schmidt Pechan. So, what I read is sort of surprising but true. If I read you right, that sure seems like a good thing for an instrument like a binocular that is subject to rough use. Rather, a great thing, a fantastic thing!
Gordon,
By the "plane of double reflection", I mean the plane in which an axial ray remains as it takes the two reflections on its way through a Porro prism. If the prism is rotated about an axis perpendicular to that plane, that is when I believe the large miscollimation sensitivity arises. For rotations about any other axis, it is harder to understand. I hope this is clear, if verbose. I guess I don't speak the correct lingo. It is hard for a duffer like me to communicate with someone with your experience, but thank you for your response. I would be interested to hear the result of your experiments.
Ron
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Gordon Rayner
professor emeritus
Reged: 03/24/07
Posts: 506
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Ron: Thank you for the explanation. Get a Porro and put its side on a table. Rotate it as you describe. You will find that it is insensitive to rotations around an axis perpendicular to the table and to the plane you describe, unless there are gross errors in its manufacture (pyramidal error). I have enjoyed your observing reports. We are fortunate to live at relatively southern locations.
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pcad
Carpal Tunnel
Reged: 01/17/05
Posts: 1501
Loc: Connecticut
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Ron and Gordon,
It's always difficult to describe these things like prisms and optics in layman's terms. So much depends on optical definitions and conventions which some of us know and some don't. I have some training in clinical optics but virtually none in the type of optics that's required to design and build instruments. As far as discussions in these forums go, I'm a layperson doing the best he can.
With the SP prism assembly, looking straight in, perpendicular to the surface of the Schmidt prism, you can rotate the assembly 360 degrees without affecting the image. I noticed this while putting a 8x20 monocular back together. The prism assembly housing rested on a circular ledge with no means of locking the assembly in any particular position. It was either fully seated or not. I tried rotating the prism assembly and found that this had no percievable impact on how the monocular worked. This was also the case in an inexpensive 10x25 binocular that I was fixing.
I have to think about what would happen if a SP prism were to be tilted. I think I know but I'll check later.
With a Porro assembly, if the assembly is rotated around the incoming central ray (for lack of a better term), the image remains corrected, but the exiting central ray shifts position. This can't be allowed to happen in a binocular for obvious reasons.
Given all the reflections in the SP prism and the 4 reflections in the Porro and Abbe-Konig correctors, I'm still impressed that a fully corrected image can be achieved with as little as two reflecting surfaces, such as an Amici roof prism and the EMS system. Not straight through, but corrected none the less.
Peter
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Peter
Telescopes 25 - 318 mm
Binoculars 15 - 88 mm
Microscope 50x - 1000x
Edited by pcad (08/05/08 07:44 PM)
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ronharper
Pooh-Bah
Reged: 02/14/06
Posts: 1007
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Gordon,
I don't know where the miscommunication lies, but your experimental result seems very surprising. My "theory" aside, how could adjustable prisms work at collimation if the output beam didn't care about prism orientation? I am at 36deg N, nothing to brag about in the continental US, but I have some pretty clear air and at 7000-9000 feet can see to the south pretty well sometimes.
Peter,
I believe you mean you were spinning the prism about the optical axis and the light ray that you were observing, right? That is very interesting. But, for the Schmidt Pechan to have the advantage I believe I have read about, a tilt with respect to the light ray should have no, or very little, effect either. I guess if your monocular is back in one piece, this experiment might be impossible. This all makes me want to visit some garage sales for binos to tinker with!
Does anybody follow my basic argument that a rotation of a reflecting surface by a small angle causes a deviation in a reflected ray that is twice as large? Is this right?
Thanks,
Ron
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Gordon Rayner
professor emeritus
Reged: 03/24/07
Posts: 506
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The collimation adjustments are via tilting the Porro pair as a pair on the plate,by tilting the plate. Or, by rotating individual prisms around an axis contained in the plane of the entry and exit faces,which axis is at right angles to the one we have been discussing( but I have not seen a binocular adjusted in this last mentioned way). Get a single Porro prism and experiment with it ,to experience the mentioned effects.
Yes, a mirror or a prism surface acting as an internally reflecting mirror deviates a reflected ray by twice the angle of incidence of the incoming ray on that surface.
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pcad
Carpal Tunnel
Reged: 01/17/05
Posts: 1501
Loc: Connecticut
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Hi Ron,
I found the monocular and removed the SP prism assembly again. As I suspected, tilting the prism bends the light path. I suppose SP binos could be made that use prism tilting to adjust collimation as many Porro binos do, but I'm not aware of any that do. Probably just as well.
Peter
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Peter
Telescopes 25 - 318 mm
Binoculars 15 - 88 mm
Microscope 50x - 1000x
Edited by pcad (08/15/08 10:43 PM)
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ronharper
Pooh-Bah
Reged: 02/14/06
Posts: 1007
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Peter,
Thanks for that effort and the results. I thought I had read otherwise about SPs, and am glad you set straight with an experiment.
OK, so don't drop your roof binos either!
Ron
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