PFI Cobra/MC simulator
Peter Mao
purpose
• develop algorithms for fiducial (FF) and
science (SF) fiber identification under
representative operating conditions.
• No attempt is made to account for fiber
collisions or physical interferences.
routines
• make_PFI_bench: complete geometrical
description of the PFI bench (static).
• break_PFI_bench: disables fibers by rail,
connector or individual fibers (random).
• MCsimulator: moves fibers to “home,”
“antihome,” or “random” positions, rotates the
PFI bench and applies a wide-field corrector
(WFC) distortion pattern to the positions.
• find_fiducials: finds the FFs, solves for the
rotation angle and distortion center of the MC
image.
future routines
• move_cobras: takes in the current state of PFI
and returns a MC list of centroids
corresponding to the new state of PFI.
• match_fibers: match non-FF centroids in the
MC image to Cobras.
make_PFI_bench
• includes variability in Cobra and
FF placement, Cobra arm
lengths.
• theta=0 positions are
randomized
break_PFI_bench
• specify number of rail,
connectors and fibers to
“break”
MCsimulator.m
• returns a list of positions
(“centroids”) that would be seen
by an ideal MC looking through the
WFC at PFI.
• In these plots, PA is fixed (but
nonzero), and the distortion center
(marked by “+”) is randomly placed
within 25 mm of the PFI origin.
Hough transform
• calculate the distance (rho) and
angle (theta) of a normal vector
from the origin to a line in 2space.
• colinear line segments cluster in
(theta,rho) space.
Y
rho
theta
X
theta
find_fiducials.m 1/4
•
1.
2.
3.
•
Hough transform:
Identify centroids that have no neighbors closer than 3 mm
(using some nominal pixel scale) – only SF do that.
Identify centroid pairs (after above cut) whose distances lie
between 15 and 16.1 mm (low set by distortion, high set by
pitch + placement error)
Run Hough transform on all pairs.
Can tighten up FF pair identification by running MC image
through inverse WFC correction (assuming distortion center
is at mean fiber location.
• If we can identify at least two of the spines, then we
can solve for the location of the center fiber. (see next
page)
• Presently, if the center FF is missing, the estimated
position from the intersection of the first two Hough
lines is used. A better estimate would use all
information available.
FF spine search region
find_fiducials.m 2/4
• ID the radial spines using angles of the Hough solutions + rotator
information (here encoded in the output of MCsimulation)
• ID the center fiber as the fiber closest to the intersection of the
Hough lines.
• The FF mask (with distortion centered on the PFI origin) is now
lined up with the MC centroids. FF’s are identified by calculating the
distance of the nearest centroid to each FF mask location
find_fiducials.m 3/4
•
•
•
•
Some rejection scheme must be
implemented to match fibers
(centroids) to FFs and detect broken
fibers.
Presently, I’m using median + 1
standard deviation
Some type of clustering algorithm
could also be used to identify the
outliers.
This issue will be left for another
time.
find_fiducials.m 4/4
•
With the FF’s ID’d we can rotate and
translate the MC coordinate system
to align it with the PFI axes
•
•
The location of the mean of all FFs
(using the mask locations for missing
fibers) relative to the origin gives us the
distortion center (DC)
The scaling from mean FF to DC is a
function of the number of lost FFs and
the magnitude of the mean FF position.
MC  PFI coordinate conversion
overview
• The Metrology Camera System (MCS) provides the position feedback for
Cobra motions.
• The MCS image of the backlit fibers will be distorted by the WFC optics.
The distortion will be a function of telescope Altitude angle and
environmental conditions, but NOT rotator angle.
• In this simulation, “measurement error” includes:
– MCS position error (due to seeing and centroiding)
– science fiber homing position error
– fiber home position calibrations error.
• Presumably these errors add in quadrature, so their allocation is outside
the scope of this simulation.
algorithm overview
• Distortion/displacement map requires that ALL fibers be brought to their
home position.
• Axis center locations (found by imaging fibers in motion) are not
sufficiently accurate – we really need the true home positions!
• FF’s must be identified (I don’t have this yet... but I will)
• Using a nominal plate scale for the MCS image, we calculate
– ΔX = XMCS – XPFI
– ΔY = YMCS – YPFI
• Use biharmonic interpolation to make fits to (XMCS, YMCS, ΔX) and (XMCS,
YMCS, ΔY)
• The fit tables and then used to calculate ΔX and ΔY for arbitrary values of
(XMCS,YMCS)
computational time estimates
• sims were run in Matlab on a 2-core PC
• find_fiducials takes ~1 second
• biharmonic fit takes 4.5 sec (only needs to be
done once per pointing)
• biharmonic solution takes 4.5 sec (needs to be
done each time the Cobras are moved).
• baseline, expect time to drop by 1/10 to
1/100.
Interpolation error maps
Log scale for
the zero error
case!!
0 == 1 micron!
FWHM of the
interpolation error
distribution is ~2 x
the measurement
error (better shown
on later slide)
For any realistic
measurement error
(>= 1 um), the
interpolation error is
dwarfed by the
measurement error
scatter plots for no error & 4 micron
measurement error (FWHM)
4 um case is
roughly gaussian
but 0 error case is
NOT Gaussian!
Here, you can
probably eyeball
the fact that the
interpolation error
FWHM is ~ 8
microns for the 4
um measurement
error case
interpolation error cumulative
distributions
interpolation error is
< 1 um for ~98% of
the fibers
magnitude of the
error distribution
scales linearly with
the msmt error
(factors of 2 here).
the 2 um (FWHM)
Gaussian matches
the 1 um msmt
error distribution