Constant Depth |
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Optimized Depth
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| This example shows the effectiveness
of these optimum design methods. The color contour
plots show the corrected surface deformation due
to gravity for an adaptively controlled mirror whose
depth is constant compared to an adaptively controlled
mirror whose depth is optimally sculpted. The optimum
sculpted mirror design was generated by performing
design optimization in MSC/NASTRAN™ to minimize
the corrected surface error without exceeding the
weight of the constant depth mirror. This resulting
optimum mirror design gives a corrected RMS surface
error which is 24% less than that for the unoptimized
mirror but has the same weight. |
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| Design
optimization
equations in MSC/NASTRAN format may be written
with SigFit for various
useful quantities of optical surface deformations.
These quantities include:
- Rigid Body Motions
- Zernike Coefficients
- Residual Surface
RMS Error
- Residual Surface
P-V Error
The rigid body motions
are written with a node at the origin of
the fitting coordinate system and an RBE3
interpolation element as shown below. SigFit
conveniently computes the proper weighting
coefficients for use on the RBE3 element
based on the model geometry.
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| Zernike
coefficients are written with SPOINTs and
MPC cards. The coefficients for which MPC
equations are written are specified by the
user. Shown below are the four Zernike coefficients
for bias, tilts, and power. |
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| The
equation for residual surface RMS error
is expressed with a DRESP2 entry which references
the displacements of a set of dummy grids
generated by SigFit. These
dummy grids are duplicates of the optical
surface nodes and have constrained axial
displacements which represent the surface
deformation after the Zernike polynomials
that were chosen to be fit are subtracted.
A similar DRESP2 entry is written for surface
P-V error. These entries allow the user
to evaluate surface RMS and surface P-V
errors within the design optimization capability
of MSC/NASTRAN. |
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