Issue
Date
Page / VLT-MAN-ESO-15220-2676
0.99.12
25/01/2002
1 of 3
1Basic Formulae
1.1Converting Pupil Source, Pupil Destination and Delay Line Carriage Position to Radius of Curvature
The ROC is defined as follows[AD 20, section5, equation 3]:
The curvature C=1/Rz .
D’in and D’out are defined as follows[AD 20, section 5, paragraph 3]:
D'in = M2M3 - Din
D'out = M2M3 - Dout
M2M3 is the per-cat’s-eye distance between M2 and M3[AD 20, This is a per-cat's-eye constant; see section 5, figure 1] and D’in and D’out are defined as follows[AD 20, section 4, equations 1 and 2]:
M1M2 is the per-cat’s-eye distance between M1 and M2, f1 and f2 are the per-cat’s-eye focal lengths of M1 and M2 respectively, and Pin and Pout are the pupil-in and pupil-out lengths measured from the M1 vertex. The outstanding unknowns are Pin and Pout. These we deal with in a moment, but first a digression on the subject of OPLs (Optical Path Lengths).
When the delay line carriage is as far to the left as possible, say in position ref, this is the situation:
where OPLce is the point-to-point path length within from entry into the cat’s eye to exit from it, and is a provided constant specific to each Cat’s Eye. The Optical Path Length from reference position to reference position, when the carriage is at position ref is given by:
OPLRR,ref = OPLce
When the delay line is at position pos, the situation is this:
The Optical Path Length from reference position to reference position, when the carriage is at position pos is given by:
OPLRR,pos = 2DLpos + OPLce
Conveniently, the dlcsControl process in the wdline environment maintains another OPL defined by:
OPLDL,pos = OPLRR,pos - OPLRR,ref
Combining these three equations gives:
Now, returning from the digression to the pupil-in and pupil-out lengths; here is the same diagram as show above, but with the pupil-in and pupil-out lengths marked:
where OFSce is a provided constant specific to each Cat’s Eye.
So, it can be seen that the pupil-in and pupil-out lengths are defined as below:
P0In is PIn at OPL-Zero, P0Out is POut at OPL-Zero.
In summary, the information required by the wdline WS server process to derive the required ROC is, for each VCM:
Symbolic name / Source / Typical valuesM1M2 / VCM configuration data / 700.0 mm mean
M2M3 / VCM configuration data / 800.0 mm mean
f1 / VCM configuration data / 900.0 mm mean
f2 / VCM configuration data / 266.7 mm mean
P0In / dlmsw / 10m to 200m
P0Out / dlmsw / 20m
OPLDL,pos / dlprs
Offset / dlprs setup keyword / 0.0001
OFSce / VCM configuration data