From: "Vladimir Galogaza" 
To: "ATM shore" 
Reply-To: "Vladimir Galogaza" 


By using James Burrows DIFFRACT  I simulated Foucault images for given zone
( moving source), with ranges of lateral KE positions ( zone intensities)
and source sizes ( diffraction content). Then I applied to images search
algorithm looking
for centrally symmetrical pixels (on diameter) mutually equal  in intensity thus
determining  nulled zone (as from  M. Peck or Jery). Finally I compared
zone found with "true" zone used
in simulating the images.
                                                         "True" zone 30%
"True" zone 70%                    "True" zone 90%
Lateral KE position (Y mm)       found zone   zone intensity   found zone
zone intensity      found zone  zone intensity
(source 0,050 mm)                         (%)            (0-255)
(%)            (0-255)               (%)           (0-255)
____________________________________________________________________________
______________________________________

        -0,005                                    28                10
70                  20                    91                27
        -0,001                                    27                41
71                 44                     91                45
         0,000                                     27                54
70                  46                    91                50
         0,001                                     27                69
70                  56                     91                57
         0,005                                     28              137
70                 106                    91                93
         0,010                                     33              201
69                 174                    90              135


   Source size (mm)                           "True" zone 30%
"True" zone 70%                   "True" zone 90%
( KE at 0,000 mm)                   found zone zone intensity       found
zone   zone intensity      found zone    zone  intensity
                                                     (%)           (0-255)
(%)             (0-255)                  (%)            (0-255)
____________________________________________________________________________
____________________

       0,000                                        21             83
70                45                          91                48
       0,010                                        24             44
70                38                          91                36
      0,020                                         23             47
71                42                          91                 41
      0,080                                         29             57
70                56                          90                 56
      0,100                                         29             58
70                57                          90                 62


(Help file of Diffract explains approximations made for simulations and its
limitations and meaning of used parameters.)

Central (30%) zone is difficult to find correctly in any case. Intensity
change is small. At least for this method of zone finding, the bigger
gradient of intensity
the better accuracy. Intensity gradient for central zones is the smallest.


Suggestion by Nils Olof that slit should be better than slittless seems to
be supported by latest measurements by James but I see no ( intuitive)
reason for this
assumption nor was any given. Slitless will give more light to the mirror
but for measurement stray light, usually present in abundance, seems to be
no
problem ( Foucault is seldom done in total darkness). Virtual slit should
block ( in theory)  any other light coming from source and behave in the
same way as if the source is slitted. If robo camera sees more light than
coming from virtual slit than this could be demonstrated. Suggestion that
asymmetry in light intensity distribution across the mirror shadow is great
and therefore must influence the robo outcome does not show in my
measurements .
It is not clear to me why should intensity matter at all ( for robo) since
we do not measure intensity distribution but  looking for equally bright
centrally symmetrical
zones. Looking at the graphical presentation of the light intensity
distribution in the Foucault shadow it is very unlikely that false zones
will be produced.
Since computer algorithms are looking for single pixel wide zones any
ambiguity will be clearly revealed. But this is so providing that we
compare centrally symmetrical pixels. Meaning that  errors in determining
mirror center (and edges) are important. With simulated images I used this
was not an important source of errors. But with real stuff as supplied by
James there is more work involved for robo and I guess of great importance
for results. Diffraction is serious problem and while not easily seen with
eye its presence in simulated images with small source is easily detected.

I admire how ingenious James is in finding and performing experiments to
isolate one by one various possible sources of the robo intensity problem.
His work is inspiring lot of thinking about phenomena taken as granted or
even  overlooked.

Vladimir.

PS
From images: "Raw_zoneNrep0.bmp"    (N=1 to 7) I deduced that zones
1-7 correspond to 32%, 48%, 61%, 69%, 79%, 88%, 100%  of the mirror radius
( plus or minus 1). Is that different from what you have James?

--- BBBS/NT v4.00 MP