[ATM] Dumb Question about interferometers

[Scott Rychnovsky <srychnov@chem.ps.uci.edu>]

I am starting to plan out an interferometer based on one of Peter 
Ceravolo's reference elements and the recommended laser, etc.  My 
question is about the beamsplitter.  Normally one uses a 50/50 
beamsplitter, but is this important?  Could it be 60/40 or 10/90? 
Part of my confusion is that I don't really understand how it all 
works.

In the recommended setup, the laser goes through a spreading lens 
(GRIN) and then hits the beam splitter.  Half of the beam reflects 
and is discarded.  The other half (50%?, 40%?, 90%?) travels through 
the beamsplitter and them goes through the reference element.  4% of 
this beam is reflected back along the axis.  the transmitted beam 
(96%) hits the uncoated test optic and another 4% is reflected back 
along the path.  If I understand it, these reflected beams are the 
only important ones in the interferometer.  They hit the beamsplitter 
and are partially reflected out of the interferometer and to the 
detector.  Interference between the reflected reference element beam 
and the reflected test optic beam leads to the fringe pattern, and 
all the other beams are just discarded.

OK, here is the question:

The intensity of the reference beam reflection is given by refbeam = 
BS-T X 4% ref-R X BS-R.

The intensity of the test optic reflection is given by testbeam = 
BS-T X 96% X test-R X 96% X BS-R.

I have not thrown in every transmission number in the system, but did 
add another 96%  (X2) to for the test beam because it goes through 
the reference front surface twice.

At the end all I need is for the two beams to have similar 
intensities so they interfere effectively.

The beamsplitter transmission and reflection each show up once for 
both beams.  For a 50/50 BS that adds a factor of 0.25 to the 
intensity.  For a 33/67 beamsplitter it adds a factor of 0.22 to the 
intensity.  For an 8/92 beamsplitter it adds a factor of 0.074 to the 
intensity.  Certainly a BS value close to 50/50 would be desirable, 
but it does not look at all critical.  My conclusion is that a good 
quality beamsplitter is more important than the precise R/T numbers.

What do you think of this argument?  Am I missing anything?

Here is my feeble attempt at ACSII artwork:

               detector
                  ||
                  ||
                 \||    ref beam  |               |
                  \<--------------|<__test beam___|
Laser ---->-------\------------->|-------------->|
                    \             |               |
                     \            |               |
                   BS             ref          test       


Scott
-- 
Scott Rychnovsky
srychnov@chem.ps.uci.edu
ATM Page: http://tlepage.home.mindspring.com/
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