Theory Of Operation

 

When I wrote this code, I tried to emulate what I did during a normal Couder Mask, Foucault test.  During this conventional test, a series of very defined steps were followed to record the null positions for each zone pair.  Asides from some user interpretation problems, and the amount of time it took to do an accurate test the process was fairly simple.

 

Consequently I went about teaching my computer to do what I did during a Foucault test (Pretty simple yea J, I wish!)

 

So, Lets start with the procedure often taught for a Manual Foucault test

 

  1. First we set the mirror on the test stand
  2. Second we set the platform somewhere near the ROC of the mirror
  3. Then we try and “AIM” the mirror, so the return beam hit the sharp edge of our knife
  4. Finally we put our EYEBALL down by the knife, to see what we see J
  5. Odds are, that either the mirror was fully illuminated, or it was completely dark.
    1. If fully illuminated, we’d cut the knife edge in until we saw a Foucault shadow
    2. If dark, we’d cut the knife edge out, until we saw a Foucault shadow.
    3. In either event, the first thing to happen was often the lateral movement of the knife edge.  Well RTAFT does the same thing J
  6. Back to a manual test.  If we saw a Foucault shadow, we’d probably look at it for a bit to see how smooth it was
  7. After that, odds are we’d walk down range to the mirror, and hang our couder mask on the mirror.
  8. A large portion of the time, the test was conducted starting with zone #1 and working out from there. RTAFT does the same thing
  9. So, were back at the test stand, with our eyeball at the knife edge.  Staring intently at zone #1
    1. Often We’d find that Left and right zone pairs were either:

                                                              i.      Really Bright

                                                            ii.      Really Dim

    1. Again, the first thing to happen was a Lateral knife edge motion, to get a Shade of gray in one of the two hole pairs.
    2. Now the tricky part.  If the hole pairs are not equally the same shade of gray (Very rare on the first look) We move the platform longitudinally towards or away from the mirror!

                                                              i.      But WHICH way to move it?

                                                            ii.      Well, If you KNOW what side the knife edge is on, there is no need to guess, as its simply the following:

1.      If the zone hole opposite the knife is Bright, and the zone hole on the same side of the knife is Dark, Move further away from the mirror!

2.      If the zone hole opposite the knife is Dark, and the zone hole on the same side of the knife is Bright, Move Closer to the mirror!

                                                          iii.      Simple ehh J

    1. Once we get both hole pairs of equal intensity for zone one, we record the position, and start all over again for the next zone!
    2. We keep repeating this for each zone, and for the number of repetitions we think is reasonable for the complete test!
  1.  Of course, its not quite so simple as this, as there are lots of variables, such as:
    1. What shade of gray?
    2. How much do you move the knife Longitudinally when the zones aren’t even?
    3. Is there backlash?  If so, do you always approach a zone pair null from a certain direction?

 

So that’s an overview of the basic Foucault test, and the variables involved.  Before we get any further, let me explain what RTAFT doesn’t and does do J

 

  1. RTAFT doesn’t use a paper couder mask. 
  2. RTAFT doesn’t do a FULL SURFACE Test
  3. RTAFT works with fixed zone radiuses, moving the platform about to find each radius’ null (just like a paper couder mask!)
  4. With a 5 zone “MASK”, RTAFT only tests 10 points on the mirror!
  5. RTAFT does, in effect, a BRUTE FORCE attack for finding zone nulls
  6. Instead RTAFT finds its way to zone 1, gets a null, then finds its way to zone 2, gets a null, and keeps repeating until its out of zones.
  7. The whole process follows a very simple set of rules
    1. Set the shade of gray
    2. Look at the zone under test
    3. Decide which way to move the platform longitudinally to get closer to a null
    4. Repeat step A until zone null found.
    5. Select next zone, repeat Step A until all zones found.

(See its simple! I wish!)

 

 

Shades of Gray

 

As you know, the Foucault test is all about finding equal shades of gray for a zone pair of equal radius from the center of the mirror.  RTAFT does the very same thing!  However, to make this process automatic, I need to make one of the Zone radius sides a “Reference” and the remaining side a “Comparative” measurement. 

 

This “reference” zone is the side of the zone pair OPPOSITE the knife-edge.   So, starting with zone 1, the code does the following:

 

  1. Set the reference side of zone 1 to the “Shade of Gray” level
  2. Compare the two sides of zone 1 and make a decision,
    1. If the reference side is greater than the Comparative side, move away from the mirror and start all over
    2. If the reference side is less than the comparative side, move closer to the mirror and start all over.
    3. If the reference side and comparative side are equal, then this must be the Zone null!

                                                              i.      Record longitudinal position, start working on the next zone

 

The only problem with the above summation is RARELY will both zone pairs be EQUALLY illuminated!  Often they are close, but not perfectly equal!  The result was the code would get stuck in an infinite loop moving a bit forward, then a bit backward.

 

To solve this, I did a little trickery.  I told the code to keep moving towards the mirror, until the zone null was behind the knife-edge some 0.01” or so.  Once that flag is set, the code will start moving slowly away from the mirror, towards the zone null.  At this point 1 of 2 things can happen:

  1. The nulls become perfectly equal! (That’s nice)
  2. The Reference side becomes less than the comparative side, thus we over-shot the target.  However, if the last move was only 0.001”, then what’s the big deal J  I know the null is pretty close to this current position! 

 

BTW, just as an aside.  If you charted the platform motion during an entire mirror test.  The platform would move in a Z shaped plot.   Once zone 1 is found, it slides sideways to set the shade of gray for zone 2, then starts moving towards zone 2.  Once zone 2 is found, it slides sideways to set the shade of gray for zone 3, and so on. 

 

Not very efficient, but it’s the only way I can be certain to have the code find its way to each zone’s null J

 

Well I guess that’s it.  Any questions feel free to ask!

 

Take care,

James Lerch

jlerch@tampabay.rr.com