[Laser] Trihedral prism source?

[James Whitfield]

Jim Moss,


Thank you for taking the time to try to explain how you built a 
retro-reflector with 12X12 mirror panels.

I must confess that it took much longer that I would have expected to follow 
your explaination.  Only part of which can be explained by me being "under 
the weather".  On the whole, I am quite sure that I could use a lot more 
practice "thinking" about ideas like this and I am sure others would 
appreciate it if I spent less time blathering.  However, it seems not to be 
in my nature...........

To the specifics of what you said, I still have more than a bit of 
puzzlement.  Part of me says that it should not have worked.  That it did, 
suggests to me that either I still do not understand how you fit it together 
( another confirmation that pictures can tell a lot more than words ) or 
that my "analysis" of the problem has lead me to over-complicate the 
reality.

Jim, I know that I have intruded into your time and activity more than is 
fair, so I will make the following statements as "thinking out loud" or 
general comments to the other on the list.  While I am not asking for 
response from you, I would certainly welcome your thoughts.

Simply put, I think that the "design" of the three mirror system is 
under-constrained, and therefore should not have resulted in an acceptable 
solution.  As I understand, you mounted a hinge on each of two adjacent 
sides of a mirror, then attached another mirror on each of the hinges.  The 
assembly is then folded so that the two added mirrors travers from parallel 
to the original mirror to positions approximating right angles to it.  The 
remainder of the description seems to be a description of a fine adjustment 
mechanism for the relative angles.  If there was a missing element for my 
understanding, it would seem to be how to attach the fine adjustment to the 
assembly.  Be that as it may, how it should be attached has no bearing on 
the conclusion that two adjustments are not sufficient to align the 
assembly.

The problem expressed in geometry terms is the need for square segments of 
three independent planes to be arranged in space so that a ray may strike 
one of the squares, be reflected on to a second, then a third so that the 
reflection from the third square will then be parallel to, and in opposite 
direction to, the original.

The first square can be placed arbitrarily in space.  The second square has 
restrictions on its placement.  The planes of the first and second squares 
may not be parallel, therefore they will intersect, which will define a 
line.  The "real world" equivalent of the intersect line is the hinge that 
joins mirror one and two.  Using the concept of the intersect line as the 
hinge, one can "adjust the angle" between the two planes.  As a practical 
matter, the hinge does not lie within the mirrors, so the intersect line 
does not pass through either of the squares.  Also, note that while one may 
presume the intersect line will be nearly parallel to one edge of each of 
the two squares, it is not guaranteed by the requirements stated, and 
further it cannot be "adjusted" by the mechanisms provided.  Note also that 
in the "real world" the hinge lines cannot be guaranteed to be even in the 
plane of the mirrors, or parallel to it.  That said, the presumption is 
construction will be close to that condition; there will be error, just not 
a "large" error.

One can however "adjust the angle" such that the two planes are at right 
angles.  More specifically, by selecting a point on the intersect line, one 
can define a line in each plane such that each of the two lines are 
perpendicular to the intersect line.  The angle to be adjusted is then the 
angle between the two perpendicular lines.  The desired condition is that 
angle to be a right angle.  In the case of the mirror assembly, it will not 
be possible to  measure that angle directly.  Rather, one may adjust the 
system and only observe the resulting reflection of a light beam to see if 
it is in the right place.

OK, so we have modeled two mirrors and an angle adjustment.  It is necessary 
to add a third mirror and its angle adjustment.  The problem I have is that 
the result is a device that cannot "adjust" for any error in the resulting 
angle between the second and third mirror.

So, I ask of the readers of the list, am I just applying too much theory and 
not enough practicality?  Will the system work?  Is there enough "slop" in 
the reflections of a trihedral mirror assembly that one does not need the 
third adjustment that I see as necessary?  Do the beams that we would 
encounter in typical communications work expand so much that minor 
construction errors in the angle between the two hinges are masked?


Thank you.

James
 n5gui




----- Original Message ----- 
From: "Jim Moss" <n9jim-6 at pacbell.net>
To: "Free Space LASER Communications" <laser at mailman.qth.net>
Sent: Tuesday, March 10, 2009 8:44 PM
Subject: Re: [Laser] Trihedral prism source?


>
> James,
> The arrangement of the 3 mirrors involves 2 hinges
> Consider 3 mirrors arranged in an L configuration, see this crude 
> text-gram.
> Each mirror was mounted on a wood frame.
>
> [ ][ ]
>
> [ ]
>
> Put hinges on the adjacent sides.
> If folded upward, they will form a corner cube.
> The corner that the 2 lifted sides intersect is where the adjustments are 
> made.
>
> Mount a piece of 90 deg angle aluminum and an aluminum flat strip that 
> will be parallel to each other in each axis/plane. Mount them so that they 
> are about 1 inch apart when the surfaces of the mirror are at about 90 
> degrees.
> I L
> A 1.25 inch screw will go between these 2 parallel plates. A single 4-40 
> screw & 3 nuts are used to adjust & hold the plates.
>
> Arrangement:
> Screw head - plate - nut1 - adjustment space - nut2 - L plate - nut3
>
> Nut1 holds the screw head to plate firmly.  Nut2 and nut3 are used to 
> push/pull the L plate and hold it in position.
> Assuming 1 foot mirrors (1 foot from hinge to adjustment screw), one 
> revolution of the nut will adjust the surface angles about 0.12 degrees. 
> (from memory)
> arctan (1/40 divided by 12) = angle
>
> Do the same thing for the other axis/plane.
> The fit will be tight, but there will still be some fine control.
>
> Does this explain it well enough to get the idea?
> Jim