16.684 Space Systems Product Development
Chart: 1
February 13, 2001
MIT Space Systems Laboratory
Introduction to Optics
part II
Overview Lecture
Space Systems Engineering
presented by: Prof. David Miller
prepared by: Olivier de Weck
Revised and augmented by: Soon-Jo Chung
16.684 Space Systems Product Development
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February 13, 2001
MIT Space Systems Laboratory
Interferometer Types (NASA, AirForce)
Space Technology 3-2005 Air Force UltraLITESIM-2006
Michelson Interferometer
Precision Astrometry
Michelson Interferometer Fizeau Interferometer
Earth Observing Telescope
TPF - 2011
NGST - 2007
Michelson Interferometer
A Common Secondary Mirror (MMT, Fizeau)
Primary Mirror = 8 m diameter
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February 13, 2001
MIT Space Systems Laboratory
Interferometer Types (Ground)
Michelson Interferometer (Visible)
Keck Interferometer-2006
Michelson Interferometer (Infrared)
Twin 10 m Keck Telescopes and four 1.8 m outriggers
Baseline 85m
Palomar Testbed Interferometer
Michelson Interferometer (Infrared)
Testbed for Keck and SIM
Mark III Interferometer
Keck Observatory:
Multiple Mirror Telescope (MMT)
Fizeau Interferometer (Visible, Infrared)
36 hexagonal segments => 10 m overall aperture
16.684 Space Systems Product Development
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February 13, 2001
MIT Space Systems Laboratory
Michelson Interferometer
Independent Light Collectors feed light to a common beam
combiner. Get interfered fringes => Inverse Fourier Transform
(CLEAN,MEM)
Suitable for Astronomical Objects:
Unchanged over a long period of time
Beamsplitter
Collector
Collector
Michelson Interferometer
S
t
e
l
l
a
r
w
a
v
e
f
r
o
n
t
Detector
Detector
Optical delay
line
Object
Imaging with Michelson Interferometer
FT
"FT
-1
"
Baseline orientations:
+
y
x
yvvv
uu u x
u-v (Fourier plane) Reconstructed
image
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February 13, 2001
MIT Space Systems Laboratory
Fizeau Interferometer
Gives a direct image of a target from a large combined primary
mirror, and a wide field of view (Imaging applications in space
and MMT)
Suitable for Wide Angle Astrometry
And for rapidly changing targets (Terrestrial, Earth Objects)
1 2 3
Telescope
Telescopes
Fizeau Interferometer
Fizeau Interferometer
DetectorDetector
Sparse aperture
Telescope
"Beam combiner"
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February 13, 2001
MIT Space Systems Laboratory
Comparison (Fizeau, Michelson)
Fi zea u
Int erfer omet er
Miche lson Inte rfe romete r
Pro duce a dir ec t im age o f its
targ et ( Full Instan t u- v c over age
pr ov ided)
Takes a sub se t o f u- v po ints
obtaine d a peri od o f tim e.
Wide angle(field) of view
im aging app lications
Ast rome try,
Nulling Inter ferom etry
Rapidly Cha nging t arge ts
(Terre strial, Ea rth Objects)
Targ et u nc han ged
(Ast ron omi cal Objects)
Takes t he c omb ine d sci en ce
ligh t from all the ap erture s an d
focuses it into C CD
Me as ure s po ints in Fourier
tran sform of ima ges => Inver se
FFT ne eded
U- V re so lution dep end s on b oth
the separa tion and the size of
aper ture s
Angula r re so lution de pend s
solely on the separa tion of
aper ture s
Optima l Con figura tion:
Golay (m inim um aper ture size )
The angul ar res olution im pro ves
as t he sep ara tion incre as es
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February 13, 2001
MIT Space Systems Laboratory
CCD
Beam
Combiner
Common Secondary vs Sub Telescope
Phased Sub-
Telescope Arrays
Common Primary Sub Telescope Fizeau
Precise Off Axis Configuration
Off Axis Optical Aberration
Need Combiner + Phase sensing and
compensater mechanism (complex)
Less Central Obstruction(Off Axis) On Axis Suffers Central Obstruction
Hard to change the Configuration Can employ Off-the-shelf telescopes
Common
Secondary Mirror
Array
AirForce is studying two options for UltraLITE(Golay 6)
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February 13, 2001
MIT Space Systems Laboratory
Optical Arrays
-0.3 -0.2 -0.1 0 0.1 0.2 0.3
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-0.15
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0
0.05
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0.25
Optical Array Configuration
X - Distance [m]
Y -
D
is
tance
[m]
Instead of using a single aperture use several
and combine their light to form a single image
Aperture positions (uv) are critical -
look at combined PSF / Transmissivity
of the Optical Array
Transmissivity Function:
Derivation see separate
handout (Mennesson)
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February 13, 2001
MIT Space Systems Laboratory
CDIO: Breaking the Paradigm
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0
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Optical Array Configuration
X - Distance [m]
Y
- D
i
s
t
a
n
c
e
[m
]
Golay-3 0.6 m telescope
-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4
-0.3
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0
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Optical Array Configuration
X - Distance [m]
Y
- D
i
s
t
a
n
c
e
[m
]
Physical
Aperture
Layout
Monolithic 0.6 m telescope
Compare
Architectures
with
Quantitative
Metrics
PSF
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February 13, 2001
MIT Space Systems Laboratory
Effective Radius of Optical Array
How to find the effective
radius(Reff) of the array?
? =the radius of the array
thought as that of a monolithic
aperture.
? UV coverage plot
x,y is any point within aperture
? : the maximum radius of
uv plot without any holes
?
? Fill Factor: the array’s total
collecting area over the area of a
filled aperture with the same uv
coverage(the same Reff)
u=±
x
2
? x
1
λ
v=±
y
2
? y
1
λ
R
uv
R
eff
R
eff
= 0.5R
uv
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February 13, 2001
MIT Space Systems Laboratory
Golay Configurations
?Optimum Golayis
D
eff
-dependent
? Labor moves
Golay benefits to
larger D
eff
? Golay’s sacrifice
Encircled Energy
EE=83.5% EE=26.4% EE=9.3% EE=3.6%
EE=2.2%
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February 13, 2001
MIT Space Systems Laboratory
Technological Trends
? Lightweight (Low-Area-Density) Optics - 15kg/m
2
? Deployable Optics
? Adaptive and Active Optics
? Membrane Mirrors and Inflatables
? Ultra-Large Arrays (CCD Mosaics)
? Distributed Optical Arrays
? Space Based Astronomy
? White light interferometry
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February 13, 2001
MIT Space Systems Laboratory
Optical Performance Criteria
? Sensitivity(Effective Collecting Area)
? Point Spread Function(PSF): Frequency used merit
function(Irradiance distribution),Can measure Phase difference, can derive
Resolution,EE, MTF(OTF)
? Encircled Energy: particularly relevant merit function of the
optic performance of an optical system whose purpose is to collect light and
direct it thru the entrance slit of a spectrometer
? Modulation Transfer Function(MTF): For many
imaging applications involving extended objects containing fine structure,
the MTF is a more appropriate performance criterion than PSF. Practical
Cutoff Frequency(Fr) -> Cutoff Frequency(Fc)
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February 13, 2001
MIT Space Systems Laboratory
Optical Sensitivity
0.65 0.7 0.75 0.8 0.85 0.9 0.95 1
0
0.1
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0.5
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0.9
1
N=8
N=6
N=2
Phase SubTelescope
Common Secondary
E
f
f
e
c
t
i
v
e C
o
l
l
ec
t
i
n
g
A
r
e
a
REFLECTANCE R
? Sensitivity of Phased Telescope Array (Effective Collecting Area)
R: the reflectance
N: the number of reflections
?
N
geoeff
RAA =
2 types may be viable concept
for quasi-monochromatic
applications; however, phased
telescope arrays will suffer
substantial sensitivity losses for
broadband spectral applications
A Region: UV
B Region: Visible (Color)
C Region: Quasi-Monochromatic
A
B
C
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February 13, 2001
MIT Space Systems Laboratory
PSF,EE (Golay Array –3)
Preliminary Calculation(0.3m GR) => D=2.0m,approx needed !!
For Reff=1m, r=0.5m and Array Radius(L)= 1.m (Golay 3,monochrome)
r=0.3685m and Array Radius(L)= 1.1m (Golay 6,monochrome)
Using Analysis
Tool:
Evaluate
Configuration
Using
?PSF(Point Spread
Function)
?Encircled Energy
?MTF(Modulation
Transfer Function)
?FF(Fill Factor)
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February 13, 2001
MIT Space Systems Laboratory
Modulation Transfer Function
? An image of an extended object is far more complex thant point source(e.g)
astrometry. PSF is not enough! -> MTF of each configuration is necessary
? Both Resolution and Contrast (Modulation) Transfer IMPORTANT
0 5 10 15 20 25 30 35 40 45 50
-1
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1
TextEnd
-10 -8 -6 -4 -2 0 2 4 6 8 10
0
0.1
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1
0 5 10 15 20 25 30 35 40 45 50
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1
Intensity
Of Object
Image
Object
Optical
Array
PSF of Optical Array
Intensity
Of Image
Modulation=
I
max
? I
min
I
max
+ I
min
FFT(I object)
OTF=FFT(PSF)
FFT(I image)
*
Real Image
InvFFT
MTF=abs(OTF)
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February 13, 2001
MIT Space Systems Laboratory
Optical Control and Beam Combining
Optics Control
Actuators
Piezoelectric translators (PZTs)
Fast steering mirrors (Tilt and Tip)
Optical delay lines (or inchworm positioners)
Alignment mirrors
Sensors
Laser interferometers
Quad cells
Charge Coupled Device (CCDs) cameras
Avalanche Photo Diodes (APDs)
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February 13, 2001
MIT Space Systems Laboratory
Fine Optical Pointing and Phasing:
Single Aperture
? Light path
– Light enters spacecraft by reflecting off
primary and then secondary, after which it
is collimated (not converging or diverging
except for diffraction effects)
– Reflects off two-axis (tip and tilt) Fast
Steering Mirror (FSM)
? FSM controls out the low level line-of-
sight (LOS) jitter in the deadband of
the attitude control
– Lens focuses light onto camera
? LOS jitter control using FSM
– Feedforward attitude sensors to command
FSM
– If bright point source in FOV, measure
motion on camera and command FSM to
minimize its motion
Primary
Mirror
Secondary
Mirror
Fast
Steering
Mirror
Light
Rays
CameraLens
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February 13, 2001
MIT Space Systems Laboratory
CCD
Fig.10, Cassegrain Type beam combiner
(above) and refractive lense combiner
Beam Combining Goal:
1. maintain the optical phase difference of each beam to a fraction of a
wavelength
2. align images from telescopes to within a fraction of a resolution
element over the whole field of view
(Additionally) Field of curvatures on the order of wavelength, finer than
required for conventional telescopes
Beam Combiner
Phase(Piston Error) Contributor:
1. Lateral Pupil Geometry Error (Pupil Mapping
Error)
=>the elimination of this error : golden rule of
separated telescope ( significant in wide field of
view telescope)
2. Piston Error: part of piston error is induced by
pupil geometry e
3. Tilt Error : Measured separately from piston
error. X-Tilt Error, Y-Tilt Error
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February 13, 2001
MIT Space Systems Laboratory
Lateral Pupil Geometry Error
Physical Meaning:
If the subapertures of the entrance pupil
have a D, and separated by S, with
magnification M, the exit pupil must have
dimensions for D/M and separation S/M
a
a
)sin(aMP ε=
p
Correct Pupil Geometry
Incorrect Pupil Geometry
Difficult to measure lateral
pupil geometry =>
abstract optical quantity
Use the relationship and
Kalman filter to estimate
ε
Pg
ψ
)sin(
M
P
g
ψ
ε=
ε
:lateral pupil
geometry error
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February 13, 2001
MIT Space Systems Laboratory
Optical Tolerance
p
γ
r
Tilt induced
piston error
)sin(γrP
t
=
])sin([)sin(
)(
p
M
r
pppm
gtp
++=
++=
ψ
εγ
FOV=4km,h=500km,piston error55nm
=>1μm
Lateral pupil
Geometry Error
<1/10 of Airy Disk Diameter
=> 33
μrad
Alignment Error
(Image Rotation)
1/10 of λ, r=0.5m => 110 nradTilt
1/10 of wavelength = 55 nmPiston
Total Piston Error
P :the optical
path difference
between beams
ToleranceErrors
DFOV
HalfAngle
)44.2)(1.0( λ
<?Φ
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February 13, 2001
MIT Space Systems Laboratory
Beam Combining Layout
OPDA(Optical Path Difference Adjuster) :is driven by
?Piezoelectric translator(PZT) = Fine Control
Translation Range (-12 μm),Resolution(5nm), SlewRate(4.5 μm/s)
Angular Tilt Range(700 μrad),Resolution (200 nrad)
?Burleigh inchworm positioners = Coarse Control
Translation Range(5mm) with a resolution of 0.1 μm
CCD
Retro Mirror
Sensor System (Interferometer)
Scraper(Scan) Mirror
OPDA
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February 13, 2001
MIT Space Systems Laboratory
Sensor System Optics(Example from AFRL)
Polarizing
Beam Splitter
Filter
Beam Splitter
Direction to Scraper Mirror
Line Scan
Camera
Line Scan
Camera
Beam Expander
Argon Laser
Motor
Field Scan Mirror (ψ)
Piston
Sensing
: Lateral Effective
Photo detector(LEP)
: Split Polarizer
Tilt
Sensing
: Microscope Lens
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February 13, 2001
MIT Space Systems Laboratory
Fine Optical Pointing and Phasing:
Multiple Aperture
? Now need to stabilize both absolute
and relative LOS jitter (Differential
Wavefront Tilt)
? Also need to interfere same
wavefront of light at combiner
– Use Optical Delay Lines (ODLs)
? ODLs add and subtract
optical pathlength from the
companion telescope to the
combiner.
? Used to control small
positional mis-alignment
and S/C attitude error
? Typically a multi-stage
device with voice coils and
piezoelectrics
Primary
Mirror
Secondary
Mirror
Fast
Steering
Mirror
Light
Rays
Camera
Lens
Secondary
Mirror
Light
Rays
Fast
Steering
Mirror
Optical
Delay
Line
Fold
Mirrors
Beam
Combiner
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February 13, 2001
MIT Space Systems Laboratory
References
[1] Larson, W.J., Wertz, J.R., “Space Mission Analysis and Design”, Second
Edition, 9.5 Designing Visual and IR Payloads, pp.. 249-274, Microcosm,
Inc,1992
[2] Born Max, Wolf Emil, “Principles of Optics”, Electromagnetic Theory of
propagation interference and diffraction of light, Sixth Edition, Cambridge
University Press, 1998
[3] Hecht E. “Optics”, Addison-Wesley, 1987
[4] Günter Diethmar Roth, “Compendium of Practical Astronomy”, Volume 1,
Instrumentation and Reduction Techniques, Springer Verlag, Berlin, New York,
ISBN 3-540-56273-7, 1994
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February 13, 2001
MIT Space Systems Laboratory
Optical System Design Process
From SMAD Chapter 9
1. Determine Instrument Requirements
2. Choose preliminary aperture
3. Determine target radiance
4. Select detector candidates
5. “Optical Link Budget”, SNR considerations
6. Determine Focal Plane architecture and scanning schemes
7. Select F# and telescope/optical train design
8. Complete preliminary design and check MTF
9. Estimate weight, power and ACS requirements
10. Iterate and document - code optics software module