From: "James Lerch" 
To: "ATM List" 
Reply-To: "James Lerch" 


----- Original Message -----
From: "Vladimir Galogaza" 
>
> James,
>
> >.  I'll leave the exact standard deviation calculation over
> >the entire set of tests as an exercise for the list ;)
>
> (How nice of you.)
>
> In working on the exercise I stumbled on the following question.
>
> In tables of results you gave 1 zone radius and 4 readings for each zone.
> I checked mean zonal standard deviation ( using R) and it is in full
> agreement
> with your figure (for 7 zone test).
> But final results (surface errors) are calculated from the sets of two pairs
> of measurements ( longitudinal KE position and corresponding zone radius)
> They are two independent (!) variables and you gave 4 measurements for
> respective longitudinal KE positions but one zonal radius for all 4
> measurements.
> If I understand your method well, (not very likely), you should give 4
> longitudinal KE
> positions paired with 4 zonal radii as found by robo. ( Except if all four
> measurements
> always result in  same zonal radius)

Hi Vladimir,

Very good question, and in 'Theory' Robo is always measuring FIXED zone
radiuses, much like the classic method of using a Pin-Stick Foucault test.

However in practice, the real world relationship between Robo's zone radius
and the one actually measured, may deviate based on the following error
prone possibilities: (Btw, I currently 'assume' that these possible errors
will have limited effect on the final result.    Fortunately, we should
know fairly soon
if these assumptions were ill conceived on my part )

#1 The user didn't tell Robo the 'Real' mirror diameter. (For instance, on this
project, I told Robo the mirror was 12.5" in diameter, when in reality
its probably closer to 12.48" or so.   This will effect the pixel
scale, which will
effect the measured zone radius.)

#2 The digital circle that defines the edge of the mirror in the video, is also
THE factor in determining the pixel scale.  If the digital circle is
smaller / larger than the image of the fully illuminated mirror, this will
effect the pixel scale, which will effect the measured zone radius.

#3 Since the camera moves along with the platform, the apparent size of the
mirror in the video changes with longitudinal travel.  The amount of change
is pretty dang small, maybe a pixel or two in a worse case scenario, like a
6" F/4 (or any F/4?).  Once Robo starts an automated test, the pixel
scale is already determined (by the digital circle defining the mirror edge
in the video). During the course of the automated test, the pixel scale is
NOT updated.  I could address this in future revisions, but its another one
of the assumptions I've chosen to live with at the moment..

#4 Periodic motions in the X-Y platform the camera and knife edge ride along,
can also effect the zone radius points that Robo measures against.  For instance
my incredibly crude, mostly wooden, X-Y stage has a visible amount of
periodicy (as seen from the video stream).  Robo attempts to compensate for
this with a tracking routine.  The tracking routine isn't perfect, but it
keeps the digital circle fairly well fixed on the apparent motion of mirror
surface in the video stream.

The above are the Big Four possible errors in zone radius calculations, as I see
it.  While I haven't implemented a method to quantify exactly how much all
the above contributes, I'd "Guess" a zone radius standard
deviation (for this exercise) must be somewhere around 0.08" (2
pixels) and in reality is probably less.

An ambitious soul could attempt to quantify this from the still images collected
during the most recent exercise.  The data is available! :)
(http://lerch.no-ip.com/atm/2ndTry and pick a test result folder to work
on)

In addition, a complete list of possible zonal radius error margining
wouldn't be complete with out the following items as well:

#1 How much does the Diffraction ring around the edge of the mirror effect the
apparent diameter of the mirror in the video stream?

#2 What if the image of the mirror doesn't fit neatly inside the pixel wells of
the CCD in the camera?

#3 What are the effects of the 'STUFF' between the camera's CCD and the Final
BMP image inside the computer, and how will this effect image scale?

#4 The zone radius, in real world units, is solved for using Nils Olof Carlin's
mirror zone math, which uses input from the user (Diameter & Number of
Zones). Robo takes this real world measurement multiplied by the pixel
scale, and rounds
off to the nearest pixel.  This pixel value (and 5 above and 5 below this
location) is what Robo uses to determine the zone intensity.  Since this
procedure does a Rounding function, by definition that is a source of
error.

> Robo is not calculating zonal radii from longitudes, it is measuring them
> ( I think).

Yes!

> So both measurement errors should be known ( reported) because their errors
>  will go into final calculations ( only James knows to what extent)
> and contribute to  final error budget.

Heck, I don't know!  I assume its not enough to be concerned about unless
were looking for that 3rd or 4th decimal point in the strehl, but I really
"DONT KNOW, yet!" 

Here's something else I don't know, HOW are we going to compare the
intereferometry results (with its 36 Zernike Polynomial coefficients) and
its 2D
surface height map with the results we currently have????

> Vladimir.
>
> PS
> Amount of data you put on your "2ndTry" site is terrific.

Thank You!

James

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