Knight, J. Brent

NASA Technical Reports Server

AMTD - Advanced Mirror Technology 
Development
In Mechanical Stability
SPIE August 2015
J. Brent Knight
NASA/MSFC/ES22
https://ntrs.nasa.gov/search.jsp?R=20150019515 2019-08-31T06:11:05+00:00Z
Agenda
• Advanced Mirror Technology Development (AMTD)
• Arnold Mirror Modeler
• Objective
• Optical System Stability Big Picture
• Mechanical Stability
• A 4 m segmented mirror case study
• Dynamic Disturbances
• Vibration Isolation
• Summary
NASA/MSFC/ES22/J. Brent Knight
NASA/MSFC/ES22/J. Brent Knight
AMTD
• Efforts associated with this presentation are performed as part of the Advanced Mirror 
Technology Development (AMTD) program
• Larger aperture space telescopes are required to answer our most compelling science questions.
• AMTD’s objective is to mature to TRL-6 critical technologies needed to produce 4-m or larger flight-
qualified UVOIR mirrors by 2018 so that a viable mission can be considered by the 2020 Decadal 
Review. 
•To accomplish our objective, we: 
• Use a science-driven systems engineering approach.
• Mature technologies required to enable highest priority science AND result in a high-performance low-
cost low-risk system.
Arnold Mirror Modeler
• From the engineering analysis perspective, a key element of AMTD is the development of the 
Arnold Mirror Modeler (AMM)
• Interested parties are referred to presentations by Mr. Bill Arnold
• The purpose of this talk is not to discuss the AMM per se but it is certainly worth introducing that 
here
• The AMM is an analysis tool that very quickly (few minutes) creates a Finite Element Model of a 
circular or hexagonal mirror of any size.
• Literally, 10’s of FEM’s of large mirrors can be created and run to predict a stress field or modes, for example, 
in only hours
• Structural design parameters such as mirror thickness or rib thickness can be varied extremely quickly to asses 
the impact/sensitivities of those parameters
• It was originally created to quickly assess mirrors for 
launch environments
• FEMs created with the AMM are now being utilized
in efforts to evolve quick turnaround optical 
performance (mechanical & thermal stability) 
analysis tools
NASA/MSFC/ES22/J. Brent Knight
• The objective of this presentation is to outline a path to provide the 
science communities future required level of optical performance relative 
to Mechanical Stability (MS) using a 4 m mirror case study
• 10 pm RMS over 10 minutes
• The pertinent parameters to achieve that end are
• Structural dynamics
• Mirror, Mirror support structure & Spacecraft 
• Mode shapes, frequencies, damping, etc.
• Dynamic disturbances
• Vibration Isolation System
• Radiation Pressure
• With the exception of radiation pressure the source
of perturbations to MS  are man made
• Therefore, the potential to design them out exists
NASA/MSFC/ES22/J. Brent Knight
Objective
Radiation
Pressure
Thermal
Snap
TCS
Mechanisms
RWA
Optical System Stability Big Picture
NASA/MSFC/ES22/J. Brent Knight
• Optical System Stability (OSS) is a measure of how 
motionless the system is.
• Sources of motion include structural deformations due to 
thermal gradients and motion, flexible (structural 
deformation) or rigid, due to structural dynamics
• Thermal extremes in space are known
• Dynamic/vibratory environments are not known
• They are a function of the mechanical systems on board the space 
craft and the spacecraft structure itself
• Reaction wheels
• Thermal control systems
• Thermal snap …
• The absence of clear bounds on the Dynamic Disturbances adds 
a level of complexity to pertinent engineering
Mirror vibratory mode shape 
Mirror Thermal Gradient 
• Dynamic Disturbances
• Once all dynamic disturbances are identified for a given spacecraft/telescope 
system they have to be modeled for use as inputs to structural dynamic 
analyses
• Some modeled in the frequency domain and some in the time domain
• Some in the frequency domain may be modeled with an enveloping power spectral 
density and some as discrete tones 
• The latter could be numerically represented by a time domain signal in a transient analysis or 
by a frequency and amplitude in a frequency response analysis
• Initially, very early in a future space telescope program, equipment 
specifications and judgment may be used to get initial estimates of dynamic 
disturbances
• Or, use measured data from previous programs such as JWST
NASA/MSFC/ES22/J. Brent Knight
Optical System Stability Big Picture
Optical System Stability Big Picture
• Combining effects of multiple dynamic disturbances to stability
• The effect of each of the known dynamic inputs (reaction wheels, thermal 
control systems, transients….) has to be considered to represent the overall 
effect on optical performance
• In particular, the wave front error associated with each dynamic/vibratory source of 
excitation has to be considered
• Knowing that many, maybe all, of the disturbances can occur simultaneously 
how are they to be handled? 
• Consider their effect individually? This is  non-conservative
• Linear superposition? This is overly conservative
• RSS? Probably the best approach
NASA/MSFC/ES22/J. Brent Knight
𝑤𝑓𝑒𝑡𝑜𝑡−𝑑𝑦𝑛 =  
𝑖=1
𝑛
𝑤𝑓𝑒𝑖
2
n= number of disturbance sources
Optical System Stability Big Picture
NASA/MSFC/ES22/J. Brent Knight
Reaction wheels
CG eccentricity
TCS
mechanisms
Thermal snap
Stick-slip
Active 
Vibration
Control
System
Optical System
Allowable
Dynamic
Input to OS
• Vibration Isolation
• With the order of magnitude of future space telescope Optical System (OS) 
performance requirements being what they are, a cutting edge active vibration 
isolation system will be paramount
• Overall performance presumably better than JWST - pm levels of stability
• Two parameters are needed to define vibration isolation requirements
• The vibratory signature associated with all disturbances at the spacecraft to isolation system 
interface
• The optical system performance requirement based allowable input levels
• It’s worth saying that more isolation or less disturbance can yield the desired 
result
Mechanical Stability
• Knowing the science required mechanical stability, one can 
derive mirror interface requirements for a given mirror 
design 
• Requirement will be in the form of 
a set of Transfer Functions (TF)
NASA/MSFC/ES22/J. Brent Knight
Stability requirement
levied by the science
community
Analytically 
derived mirror
System transfer
functions
Resultant of all
vibratory 
disturbances at 
isolation system
to telescope
interface
≤
*
Simplified Approach
A 4 m Segmented Mirror Case Study
• Analyses done and presented here are relative to the derivation of transfer 
functions represented in block 2
• The dynamics of a mirror’s suspension system are a huge player in the 
overall system performance 
• However, since there are many potential mirror suspension  system designs 
and they would strongly influence results, analyses performed were of the 
mirror only (w/o a suspension system)
NASA/MSFC/ES22/J. Brent Knight
Stability requirement
levied by the science
community
Analytically 
derived mirror
System transfer
functions
Resultant of all
vibratory 
disturbances at 
isolation system
to telescope
interface
≤
*
A 4 m Segmented Mirror Case Study
• An AMM generated FEM of a 4 m was acquired
• Suspension system was removed
• Bonded pads retained
• Suspension system to pad interface was fixed
• Model summary:
NASA/MSFC/ES22/J. Brent Knight
A 4 m Segmented Mirror Case Study
• FEM mass = 1,938 Kg
• Predicted Modes and Modal Effective Mass (MEM)
• Modes up to 250Hz were captured
• MEM is a measure how readily modes are excited by base excitation
• Global modes are considered easily excited by base excitations
• High MEM is indicative of a global mode and low MEM is indicative of a local mode
NASA/MSFC/ES22/J. Brent Knight
X Y Z ɵx ɵy ɵz
1 214 0.04 0.06 0.00 0.38 0.26 0.00
2 214 0.06 0.04 0.00 0.26 0.38 0.00
3 222 0.00 0.00 0.32 0.00 0.00 0.00
4 240 0.00 0.00 0.00 0.00 0.00 0.00
5 240 0.00 0.00 0.00 0.00 0.00 0.00
Modal Effective MassMode
No.
Frequency
(Hz)
A 4 m Segmented Mirror Case Study
• Mode Shapes
NASA/MSFC/ES22/J. Brent Knight
Modes 1 and 2 Mode 3 Modes 4 and 5
Modes 1 – 3 can contribute to the overall RMS WFE but with practically no MEM acting in 4 & 5 it is not likely
that they will be big players in the overall WFE
A 4 m Segmented Mirror Case Study
• For the analysis performed:
• Assumed damping ratio of .03
• The FEM is fixed at the suspension system to pad interface
• All 6 DOF’s are fixed
• Unit input from 1 – 250 Hz
• 1 m/s2
• Results are displacements
• Z direction, optical axis, displacements are assumed to be normal surface 
deformations
• WFE is assumed to be displacements factored by 2 
NASA/MSFC/ES22/J. Brent Knight
𝑊𝐹𝐸𝑒𝑠𝑡 =
1
𝑛
 
𝑖=1
𝑛𝑓
 
𝑗=1
𝑛𝑔
(2𝑧𝑖𝑗)2
ng= on the surface of the mirror FRM
Z  = displacement in the z direction
nf= number of frequencies considered
n  = nf * ng
A 4 m Segmented Mirror Case Study
• Frequency Response Analysis 
was performed using the 4 m 
case study FEM
• The WFE TF results order of 
magnitude are deceptive
• This is not the predicted WFE
• Results are TF’s that would be 
factored by a known 
disturbance level
• TF is an estimated WFE per unit 
(1 m/s2) input per frequency
NASA/MSFC/ES22/J. Brent Knight
A 4 m Segmented Mirror Case Study
• The RMS of the WFE TF’s is on the order 
of 7 *10-3 across the frequency range
• The region in which the mirror has 
modes (captured in this analysis), 
210 Hz ≤ f ≤ 250 Hz
has an RMS on the order of 7.3 *10-6
• So those modal responses contribute 
little to the overall potential response
NASA/MSFC/ES22/J. Brent Knight
• Obviously, those frequencies at which 
there are no dynamic disturbances would be factored by 0 when computing
the WFE 
• Potential misconception
• Minimizing the effects of structural modes of vibration is paramount 
• But that alone will likely not be enough to meet future performance 
requirements
• The point to make is that in the complete absence of vibratory modes, forced 
vibratory motion will always be there
• The magnitude of this is perceived as significant relative to the need for pm level stability
• Of course, everything is significant relative to pm requirements
• Example:
NASA/MSFC/ES22/J. Brent Knight
A 4 m Segmented Mirror Case Study
Cantilever beam
Input base
Excitation
1 g @ 50 Hz
First mode is @ 80 Hz
The beams natural frequency of 80 Hz will not couple 
with the 50 Hz excitation so resonance (amplified response)
will not occur
But the beam still exhibits the 50 Hz forced motion
So, to reiterate, to limit concerns to modal responses will likely 
not suffice
A 4 m Segmented Mirror Case Study
• How would one go from here, with the set of transfer functions to predict 
the WFE?
• In an existing program disturbance/vibration data associated with all known 
disturbance sources (RWA, compressors, mechanism,…) would be in hand (or in 
work)
• Those disturbances modeled in the frequency domain would be used to factor the 
transfer function and output the actual WFE due to that disturbance
• WFE from all sources would have to be combined and the cumulative result 
compared to the science levied requirement
NASA/MSFC/ES22/J. Brent Knight
Frequency 
Domain
Disturbance
(m/s2)/Hz
* =
WFE for that 
Disturbance
Over the
spectrum 
Dynamic Disturbances
• In the proposal phase of a program, or very early in a program, 
existing disturbance data from the current in service programs would 
be a great first cut
• For feasibility studies and proposal efforts for a proposed post JWST program, 
for example, use the JWST disturbance data 
• It is assumed that since the new program wouldn’t manifest until years after JWST
• Seemingly, RWA technologies, for example, would have advanced by that time so 
assuming that those disturbance levels are conservative is reasonable
NASA/MSFC/ES22/J. Brent Knight
Samples of JWST Disturbance Data
Vibration Isolation
• With future performance requirements being in the in Pico meters, a state 
of the art vibration isolation system will be paramount
• How much isolation is needed?
• While a given vibration system can advertise that they can isolate to some level or 
provide a level of reduction, one cannot know how much isolation they will need in a 
future system without knowing the net disturbance level
• Example of isolation system transmissibility
• Transmissibility is output/input
• w/o the input disturbances one cannot know
how much reduction is needed
NASA/MSFC/ES22/J. Brent Knight
From reference 2 
d𝑖𝑠𝑡𝑢𝑟𝑏𝑎𝑛𝑐𝑒 ∗ 𝑇𝑟𝑎𝑛𝑠𝑚𝑖𝑠𝑠𝑖𝑏𝑖𝑙𝑖𝑡𝑦 = 𝑜𝑢𝑡𝑝𝑢𝑡 ≤ 𝑠𝑡𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑚𝑒𝑛𝑡
• In early efforts to lay out a future space telescope program, a tool such as the 
AMM will add enormous efficiency
• The effect of all dynamic disturbances can not be assessed w/o a first cut at 
the disturbance levels
• One cannot know how much vibration isolation will be needed w/o the above
• So again, a first cut at the dynamic disturbances has to be included in the assessment
• Perhaps start with the resultant (loosely stated) of all JWST disturbances
• With the exception of radiation pressure, perturbations to MS  are man made
• Therefore the potential to design them out exists
• It is likely not adequate to simply focus on controlling the modes of the 
structures in question since forced vibrations will be an input
• To mitigate this, disturbance levels at all frequencies need to be minimized
NASA/MSFC/ES22/J. Brent Knight
Summary Points


AMTD -Advanced Mirror Technology Development in Mechanical Stability

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