Re: stereo with a scanning electron microscope

[T3D John W Roberts <roberts@xxxxxxxxxxxxxxxxx>]

John B. writes:
>Dr. T asserts that it is OK to use a tilt table in an SEM to 
>generate a stereo pair because the views are as seen from 
>infinity but magnified (sort of parallel rays from object to 
>image plane.)  I feel he's correct but I can't quite get there.  
>Anyone want to help?
 
then Ted replies:
>Subject: SEM 3d/toe in
>As a practical matter, i agree with George that stage tilt is the standard 
>method of creating 3d SEM pairs.  At least that is what one is taught as the 
>proper method.  I was taught to use 6 degrees of tilt. In the textbooks of 
>SEM that i have seen (sorry-don't have them here) there was no particular 
>justification given for the technique--or even much discussion.

>...
>As a practical matter, i think the degree of translation possible in small 
>(micro range) SEM specimens is too limiting for the depiction of depth, and 
>specimen tilt is necessary.

I agree with this, and I've been trying to think of an explanation of why
tilt is *necessary* if there's going to be any chance of 3D at high 
magnification:

Imagine the fields of view of the left and right images as being two parallel
cones, emanating from the left and right points of view and directed toward
the object being observed. The circles (approx) of intersection of these cones
with the object represent what can be seen in the final photo. With no toe-in,
stereo is achieved by displacing the two views side to side, using the 1-in-30
rule or some such, based on the distance from the points of view to the object.
With very low magnification, the two cones are relatively "fat", and the two
fields of view mostly overlap to provide a nice big stereo image.

As magnification goes up, the cones get "skinnier", but the distance from point
of view to object does not change, so the side to side displacement necessary
for good stereo does not scale with the reduction of the size of the fields of
view. [Here's where some math guys need to put in an actual formula.]
Therefore with higher magnification, the two cones (and field of view) 
intersect less, and there's an increasingly small overlap and stereo image.
At a certain point (not sure where, but probably <<100X for an optical
microscope), the two cones are so skinny that the two fields of view no
longer overlap at all, and there's no coherent image pair. If you move the
points of view closer together so the cones *do* overlap, then the stereo
base becomes so small that little or no depth will be perceived. Therefore
if there's going to be any chance of good stereo, there has to be toe-in,
which is accomplished by tilting the stage.

As to why it's possible to get away with toe-in, I think I can see why you
don't get significant keystone distortion, and maybe the geometry folks
can apply that to other types of distortion:

Imagine again the relatively fat cone (field of view) representing 1X
magnification, and suppose the "plane" of the object is not parallel to
the axis of the cone - there's a 6-degree tilt. Then (distance from point
of view to furthest part of plane) divided by (distance from point of view
to closest part of plane) will be a fairly large number, and parts of the
image from the "close" side of the field of view will look significantly
larger than the parts from the "far" side. Now replace this fat cone with
an extremely skinny cone representing the field of view at high
magnification. With the same tilt, the ratio of "far side"/"near side"
distances becomes very close to 1, so keystone distortion becomes
insignificant.

>BTW--i am not sure how long the (sshhhh) secrecy of this list will last, 
>since Alta Vista and ?other search engines seem to point to lots of postings 
>on listgroups, and a search done on our various discussion topics will reveal 
>our existence to the curious.  Meanwhile we can enjoy our secret clubhood.

Isn't that for Usenet newsgroups? Anyway, I expect John will announce the
existence of the list after it's had time to "stabilize".

John R


------------------------------