RE: Focus indication

[Tom Droege <tdroege@veriomail.com>]

Rob,

Yep, the difference in x and y is a measure of the tracking.  One of the 
problems for the Mark IV is adjusting the RA tracking rate.  There is a 
built in DAC to adjust it.  One would like to be able to tweak the RA drive 
rate.  The way the chip is mounted, the RA shows up in y.

My present scheme takes an image with six different RA rates.  I then try 
to look at the image and detect which rate is best.  Very hard to judge.  I 
would like to see the y fwhm measured to .05 (a wild guess) pixel or 
so.  This would allow fine tuning the RA drive.

OK, someone of an analytical bent can analyze this problem.

The full range of the VCO DAC is +/- 6%.   It is an 8 bit device so one bit 
is about .05%  This should allow setting the RA drive rate to one part in 
2000.  This means that if we are within one bit of the right value we 
should be able to make a 2000 second exposure with a widening of the y fwhm 
of one pixel.

A practical exposure is 100 seconds for tests.  This then requires a 0.05 
fwhm measurement to set the RA DAC to the correct bit.

At my location, a 400 second exposure gets me about 20,000 counts of sky 
background.  I think this is about as long an exposure as I want to take.

Note that when the rate is off, the measurement does not tell you which way 
it is off.  The fwhm is larger whether the rate is high or low.  Arne 
probably has some trick for this.  ;^)  My solution has been to take a 
series of measurements and plot them.  Then I look for the minimum.

For doing software, this means that the program that measures fwhm needs to 
feedback parameters to the operating program that is trying to determine 
the proper RA drive rate.

While I have provided a means to make adjustments, I have done about as 
well using the radius of the arm, the lead screw and a measurement of the 
stepping rate.  In other words, I am yet to do a successful experiment 
where I used the DAC to vary the VCO rate to find a best rate.  I have so 
far done as well just using the Counter/Timer to set the pulse rate.  But 
then I tried doing it by eye from a multiple exposure.  Note to do this 
properly, I think you want to get the mean of 100 stars or some such.

Also the present VCO design is pretty stable (this was not true for the 
Mark III).  I have tried to measure the change with temperature, but I have 
not been able to make much sense of the measurements.  This is probably 
because I have put the Counter/TImer in the same environment.  Thus I get a 
combined temperature effect.  A proper experiment would put the Mark IV in 
an oven and the Counter/Timer in the air conditioned room.  NASA would do 
it this way.

Tom Droege

At 04:35 PM 8/1/01 -0600, you wrote:

>Thanks Michael,
>
>I wasn't considering the first method since I had gone to great lengths (~15
>lines of code :-) ) to calculate the centroid.  I didn't immediately want to
>throw away those hard 10ths of a pixel.  But, I noticed on a at least one
>star, the centroid shifted more that a pixel away from my max value, so
>assuming that was correct, the centroid is still useful.
>
>Would there be any intrinsic value in presenting FWHMx and FWHMy?
>Presumably, there would only be a significant difference during scope setup,
>when it might not be aligned.  I could possibly use the FWHM x,y to filter
>out bad/non stars, provided the majority were symmetrical.
>
>Thanks,
>Rob
>
> > -----Original Message-----
> > From: Stupendous Man [mailto:richmond@a188-l009.rit.edu]
> > Sent: Wednesday, August 01, 2001 3:40 PM
> > To: Creager, Robert S; tass@listserv.wwa.com
> > Cc: mwrsps@rit.edu
> > Subject: RE: Focus indication
> >
> >
> >
> >   Rob asked:
> >
> > > I have the centroid, but am unsure on the interpolation
> > from the centroid to
> > > calculate the FWHM.  Theoretically, I believe I should fit
> > a gaussian to the
> > > marginal sums (x and y, from star pixels only).  Is this
> > the only way, the
> > > wrong way, or is there a simpler way?  Strongly looking for
> > the simpler
> > > way...
> >
> >   Simple way:
> >
> >          - round centroid to integer (row, col)
> >          - define "peak value" as the value of pixel at (row, col)
> >                      (after subtracting background)
> >          - walk down rows in the negative direction until you reach
> >                      a pixel with half the peak.
> >                      Call this distance in pixels "d1"
> >          - walk up rows in the positive direction until you reach
> >                      a pixel with half the peak
> >                      Call this distance in pixels "d2"
> >          - walk down cols in the negative direction until you reach
> >                      a pixel with half the peak.
> >                      Call this distance in pixels "d3"
> >          - walk up cols in the positive direction until you reach
> >                      a pixel with half the peak
> >                      Call this distance in pixels "d4"
> >
> >          - calculate
> >                      FWHM = (d1 + d2 + d3 + d4) / 2
> >
> >   Complicated way:
> >
> >          - form the marginal sums in the row and column direction
> >          - fit a gaussian to the 1-D marginal sum in row direction
> >                      Set "d1" = 2.35*sigma of gaussian
> >          - fit a gaussian to the 1-D marginal sum in col direction
> >                      Set "d2" = 2.35*sigma of gaussian
> >
> >          - calculate
> >                      FWHM = (d1 + d2) / 2
> >
> >
> >   The first way is really easy and really fast.  Don't forget to
> > subtract the background from all pixels before starting, though.
> >
> >                                                 Michael Richmond
> >