PFS setup timing model

PFS setup timing model

Peter Mao

WARNING

• This is a toy model. It is intended to promote discussion of PFI setup time trades.

• Assume that all parameters and assumptions made here were pulled from thin air.

Timing diagram (schematic)

close shutter, read out CCDtelescope slew/settle

cobra anti-home, cobra scan to home w/ MC integration

MC readout, calibration, centroiding

calculate distortion map

Cobra moveMC integrate

MC readout, calibration, centroiding

ID centroids, calc SF PFI(x,y)

transfer new targets

iteration sequenceiteration sequence

report final status to OBCP/SOSS

ASIAA

JPL

Caltech

Other

repeatrepeat donedone

Positioning error model• Presently, derived from C.Fisher’s 2008 data on Cobra convergence.• The calibrated (red) curve has a functional dependence:

• d = d010-0.6(n)

• with d = distance in microns, interpreted as the 1 stdev distance in a 2D gaussian distribution.

• and n = iteration• This is used to calculate

– 1. the Cobra move time– 2. the MC integration time– 3. the number of (un)finished fibers

Distance to TargetTarget #56: [1000,1525]

1

10

100

1000

10000

0 1 2 3 4 5 6 7 8 9 10 11 12

Iteration Number

Dis

tanc

e to

Tar

get (

m m)

During Calibration Post-Cal #1 Post-Cal #2 Post-Cal #3

Cobra move time• move time should be a function of the distance error. probably a

linear function.• INPUTS:

– positioning error (d) [microns]– miminum move time (default: 0.01 sec)

• INTERNAL PARAMETERS:– Cobra velocity (5000 microns/sec)

• This should really be sorted out in (θ,ϕ) space, not in cartesian coords.• For initial moves, the angular velocity is 2π rad/sec.• When angular errors are smaller (< 10 deg) cobra moves at π/2 rad/sec.• High velocity is likely only used for the first two iterations.

– Assume Cobras are moved in 5 groups.• FUNCTION

– t = (tmin < d/v) * 5

Cobra move time vs. step #

MC integration time• integration time should scale inversely with required

accuracy• required accuracy should be proportional to distance error

(of the next step)• INPUTS:

– MC allowed position error [function of cobra position error]• using d/10 for now.

– seeing limit [in microns now, but should be in arcsec]– integration time at seeing limit [default = 10 sec]– minimum exposure time (default = 0.1 sec)

• FUNCTION– C = dseeing * tseeing

– dMC = (dseeing < dcobra/10)– tMC = (tmin < C/dMC)

MC integration time vs. step # and positioning error

# finished fibers• Assume that SF locations are Gaussian-

distributed about the desired position, and that the position error, d, is the standard-deviation of that distribution.

• INPUTS– position error [d = d(iteration step)]– number of science fibers– error budget allocation for SF location (dmax)

• Nfibers_on = floor(NSF * (1 – exp(-0.5 * (dmax/d(n))2)• NSF = Nfibers_on + Nfibers_off

Science fiber positioning success vs step #

Sample output• Study of fiber efficiency vs.

MC integration time at seeing limit.

• Based on timing model:– giving up 27 fibers breaks

even if the MC integration time at the seeing limit drops by ~5 seconds.

– up to 5 seconds, the MC integration time is a subdominant factor in observing efficiency.

• Trade can be calculated for any variable in the timing model

dBη = 10 log10(η)η = (# observed)/(max observable)1 Fiducial fiber = 0.8 Science fibers

Loose ends

• Cobra timing models needs to be updated• MC timing model needs input from ASIAA• Setup excecution sequence will evolve during

development• All parameters need to be vetted.