Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

OP1
STAR
Z
OP2 OP3
Coll 1 Coll 2 Bus Coll 3 Coll 4
RWA
Combiner
OP4
Figure 6-6: Structural model schematic showing optical paths.
the combiner through each collector are all equal to B
2
X
+ R, where R is the distance
from the star to the collector. These paths are shown in in Figure 6-6. However, if
the collectors and/or combiner are perturbed from their nominal positions, the path
lengths are affected as follows:
OP1 = R − Z1 + Xc − X1 + B
2
OP2 = R − Z2 − Xc − X2 +2x3 + B
2
OP3 = R − Z3 + Xc − 2X2 + x3 + B
2
OP4 = R − Z4 − Xc + X4 + B
2
(6.4)
(6.5)
(6.6)
(6.7)
where Zi and Xi are the Z and X coordinates of the i th collector, and Zc and Xc
are the Z and X coordinates of the combiner. The OPDs are then found by simply
subtracting the relevant path lengths:
OPD12 = Z2 − Z1 +2Xc − X1 + X2 − 2X3 (6.8)
OPD13 = Z3 − Z1 − X1 +2X2 − X3 (6.9)
OPD14 = Z4 − Z1 +2Xc − X1 − X4 (6.10)
where OPDij is the optical path difference between the i th and j th collectors. Equa-
tions 6.8 through 6.10 form the optical sensitivity matrix from the instrument position
states to the performance metrics.
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