Re: John!!!

[P3D William Carter <wc@xxxxxxxxxxxxxxxxxxx>]

Mr. Bill writes:
>Since the cone of light from a lens is a projection of the aperture...   and 
>since this cone reverses at the focal point...

So, by marking the aperture in some way, we can distinguish between 
foreground and background image points. 

Mr. Bill queries:
>Some shifts along this Z-axis may be to small to be resolved.  What is 
>that distance? What sort of depth resolution can we expect? How does 
>that compare to more well known systems?

The Formula:
The formula proffered is a simple trig. attempt at a solution to these 
questions. The idea was to define, via Rayleigh, what a lens could resolve. 
Then to use that information to determine discretely resolvable steps along 
the Z-axis. 

The resolution of a lens (Rayleigh) expressed as an angle theta:

Theta = 1.22 X lambda /a ( answer in radians )

where: lambda = wavelength (about 5.6 x10 -5 cm for white light)               
                   a = diameter of lens aperture

The Z-axis resolution of a lens, expressed as a distance Z:

                               D (squared) x tan theta / 2
                      Z = --------------------------------------------
                                   (a/2 - D tan theta /2)

If a lens can just resolve two points (:), these two points could be side by 
side, or laying along the Z-axis. We know by Rayleigh how far apart these 
points need to be in order to be seen as distinct in two space. My formula 
describes how far apart these points need to be along the Z-axis, their 
separation in three space.

Another Formula:
A lens is one part of a system. Before any "real world" results can be 
anticipated, the whole system must be taken into account.

The formula for determining the Resolution in a system is:

                                      R1 x R2
                  R(total) = ----------------------
                                      R1 + R2

Now we're at a point where we can reasonably anticipate certain real world 
results from the system as it has been described.

Z-axis Resolution vs. Binocular Separation:
These two different approaches predict vastly different results.
The dual lens system is well documented, well understood and quite 
predictable. 
Resolution plays a minor roll in dual lens 3-D. 
As an anecdotal example, I am reminded of seeing a demonstration by our 
own, illustrious, John O. Merritt. He had taken a series of slides to 
demonstrate the advantage of 3-D in robotic applications. Specifically for 
mobile platforms. Land forms and hazards not distinguishable in 2-D where 
easily observed in 3-D. Then he refocused the projectors so that little was 
recognizable. But, although objects remained unrecognizable, the land 
forms, hazards etc. where all still quite clear in 3-D.

Resolution is the back bone of SL3-D. 
The above example would have exhibited quite differently had John used 
SL3-D pairs. 
In fact the results from looking through a lens, looking at a stereo pair 
taken through the same lens, but viewed in cheap viewers, or looking 
through one of Dr. T's older realist red buttons will all give significantly 
different results (I've never actually used a realist, but I have a good 
projector setup). 

What led to this model? How "much" is "different"? When's lunch?
(End part deux)

                                


-- 
                     mailto:wc@xxxxxxxxxxxx
    37deg 39.09'N x 122deg 29.56'W x 90'MLLW







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