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
Chart: 1
February 13, 2001
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Interferometer Types (NASA, AirForce)
SIM-2006
Michelson Interferometer
Precision Astrometry
Space Technology 3-2005
Air Force UltraLITE
Michelson Interferometer
Fizeau Interferometer
Earth Observing Telescope
TPF - 2011
NGST - 2007
Michelson Interferometer
Chart: 2
February 13, 2001
A Common Secondary Mirror (MMT, Fizeau)
Primary Mirror = 8 m diameter
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Interferometer Types (Ground)
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
Michelson Interferometer (Visible)
Keck Observatory:
Multiple Mirror Telescope (MMT)
Fizeau Interferometer (Visible, Infrared)
36 hexagonal segments => 10 m overall aperture
Chart: 3
February 13, 2001
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Michelson Interferometer
Michelson Interferometer
S te
llar
wa
vef
Imaging with Michelson Interferometer
ron
t
x
Beamsplitter
Collector
Detector
FT
Object
Collector
Detector
v
y
v
u
+
v
u
y
u
x
-1
"FT "
u-v (Fourier plane)
Reconstructed
image
Baseline orientations:
Optical delay
line
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
Chart: 4
February 13, 2001
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Fizeau Interferometer
Fizeau Interferometer
Detector
Detector
Telescopes
"Beam combiner"
Telescope
1
Sparse aperture
Telescope
2
Fizeau Interferometer
3
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)
Chart: 5
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Comparison (Fizeau, Michelson)
Fi zea u
Int erf er omet er
M iche lson Inte rfe rom ete r
P ro duce a dir ec t im age o f its
targ et ( Ful l Inst an t u- v c over age
pr ov id ed)
W id e ang le(f iel d) of view
im agi ng app lications
Takes a s ub se t o f u- v po ints
obtaine d a peri od o f tim e.
Ast rome try,
N ulling Inter ferom etr y
R api dly Cha ngi ng t arge ts
(Terre st rial, Ea rt h O bjects)
Targ et u nc han ged
(Ast ron omi cal O bjects)
Takes t he c omb ine d sci en ce
ligh t fr om all the ap ert ure s an d
focuses it i nto C CD
U- V re so lu tion dep end s on b oth
the s epara tio n and the s ize of
aper ture s
O ptima l Con fig ura tio n:
G ol ay (m inim um aper ture s ize )
Me as ure s po ints in Fourier
tran sf orm of ima ges => Inver se
FF T ne eded
A ngula r re so lu tion de pend s
solel y on the s epara tion of
aper ture s
The angul ar res ol ution im pro ves
as t he s ep ara tio n incre as es
Chart: 6
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Common Secondary vs Sub Telescope
Common
Secondary Mirror
Array
Phased SubTelescope Arrays
CCD
Beam
Combiner
Common Primary
Sub Telescope Fizeau
Precise Off Axis Configuration
Off Axis Optical Aberration
Less Central Obstruction(Off Axis)
Need Combiner + Phase sensing and
compensater mechanism (complex)
On Axis Suffers Central Obstruction
Hard to change the Configuration
Can employ Off-the-shelf telescopes
AirForce is studying two options for UltraLITE(Golay 6)
Chart: 7
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Optical Arrays
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
Optical Array Configuration
0.25
0.2
Transmissivity Function:
Derivation see separate
handout (Mennesson)
Chart: 8
February 13, 2001
Y - Distance [m]
0.15
0.1
0.05
0
-0.05
-0.1
-0.15
-0.2
-0.25
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-0.3
-0.2
-0.1
0
0.1
X - Distance [m]
0.2
0.3
MIT Space Systems Laboratory
CDIO: Breaking the Paradigm
Optical Array Configuration
Optical Array Configuration
0.3
0.1
0
-0.1
-0.3
0.3
0.2
Y - Distance [m]
Y - Distance [m]
0.2
-0.2
0.4
Physical
Aperture
Layout
Compare
Architectures
with
-0.4 -0.3 -0.2
-0.1
0
0.1
0.2
0.3
0.4
X - Distance [m]
Quantitative
Monolithic 0.6 m telescope
Metrics
0.1
0
-0.1
-0.2
-0.3
-0.4
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1 0.2
X - Distance [m]
0.3
0.4
0.5
Golay-3 0.6 m telescope
PSF
Chart: 9
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Effective Radius of Optical Array
How to find the effective
radius(Reff) of the array?
• Reff =the radius of the array
thought as that of a monolithic
aperture.
• UV coverage plot
u=±
x2 − x1
λ
v=±
y2 − y1
λ
x,y is any point within aperture
• Ruv : the maximum radius of
uv plot without any holes
• Reff = 0.5Ruv
• Fill Factor: the array’s total
collecting area over the area of a
filled aperture with the same uv
coverage(the same Reff)
Chart: 10
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Golay Configurations
•
•
•
Optimum Golay is
Deff-dependent
Labor moves
Golay benefits to
larger Deff
Golay’s sacrifice
Encircled Energy
EE=83.5%
Chart: 11
February 13, 2001
EE=26.4%
EE=9.3%
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EE=3.6%
EE=2.2%
MIT Space Systems Laboratory
Technological Trends
•
•
•
•
•
•
•
•
Chart: 12
February 13, 2001
Lightweight (Low-Area-Density) Optics - 15kg/m2
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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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)
Chart: 13
February 13, 2001
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Optical Sensitivity
•
Sensitivity of Phased Telescope Array (Effective Collecting Area)
R: the reflectance
N
N: the number of reflections
Aeff = Ageo R
•
1
2 types may be viable concept
for quasi-monochromatic
applications; however, phased
telescope arrays will suffer
substantial sensitivity losses for
broadband spectral applications
0.9
E ffec tive Collec ting A rea
0.8
Com m on S econdary
0.7
N=2
0.6
0.5
P has e S ubTeles c ope
A Region: UV
B Region: Visible (Color)
C Region: Quasi-Monochromatic
N=6
0.4
N= 8
0.3
0.2
A
0.1
0
0.65
Chart: 14
February 13, 2001
0.7
0.75
B
0.85
0.8
RE FLE CTA NCE R
C
0.9
0.95
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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)
Chart: 15
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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
Modulation= I max − I min
1
0.8
0.6
I max + I min
0.4
Object
Intensity
Of Object
0.2
0
TextEnd
-0.2
-0.4
FFT(I object)
-0.6
-0.8
-1
0
5
10
15
20
25
30
35
40
45
50
*
OTF=FFT(PSF)
1
0.9
0.8
0.7
Optical
Array
0.6
0.5
0.4
FFT(I image)
0.3
0.2
1
0.1
0
-10
0.8
-4
-2
0
2
0.2
0
-0.2
Intensity
Of Image
-0.4
-0.6
-0.8
-1
0
Chart: 16
February 13, 2001
-6
4
6
8
10
PSF of Optical Array
0.6
0.4
Image
-8
5
10
15
20
25
30
35
40
45
InvFFT
Real Image
MTF=abs(OTF)
50
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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)
Chart: 17
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Fine Optical Pointing and Phasing:
Single Aperture
•
Light
Rays
Secondary
Mirror
Primary
Mirror
•
Fast
Steering
Mirror
Chart: 18
February 13, 2001
Lens
Camera
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-ofsight (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
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Beam Combiner
CCD
Phase(Piston Error) Contributor:
1.
2.
Fig.10, Cassegrain Type beam combiner
(above) and refractive lense combiner
3.
Lateral Pupil Geometry Error (Pupil Mapping
Error)
=>the elimination of this error : golden rule of
separated telescope ( significant in wide field of
view telescope)
Piston Error: part of piston error is induced by
pupil geometry e
Tilt Error : Measured separately from piston
error. X-Tilt Error, Y-Tilt Error
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
Chart: 19
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Lateral Pupil Geometry Error
a
Physical Meaning:
a
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
P = ε sin(aM )
p
Correct Pupil Geometry
Incorrect Pupil Geometry
Pg
Pg = ε sin(
ψ
M
)
ε :lateral pupil
ψ
Chart: 20
February 13, 2001
geometry error
Difficult to measure lateral
pupil geometry =>
abstract optical quantity
Use the relationship and
Kalman filter to estimate
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ε
MIT Space Systems Laboratory
Optical Tolerance
γ
Tilt induced
piston error
Total Piston Error
r
p
m p = pt + ( p g + p)
= r sin(γ ) + [ε sin(
Pt = r sin(γ )
ψ
M
) + p]
P :the optical
path difference
between beams
Errors
Tolerance
Piston
1/10 of wavelength = 55 nm
Tilt
1/10 of λ, r=0.5m => 110 nrad
Lateral pupil
Geometry Error
FOV=4km,h=500km,piston error55nm
=>1µm
Alignment Error
(Image Rotation)
<1/10 of Airy Disk Diameter
(0.1)(2.44λ ) => 33
∆Φ <
µrad
FOVHalfAngle D
Chart: 21
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Beam Combining Layout
OPDA
Scraper(Scan) Mirror
Retro Mirror
CCD
Sensor System (Interferometer)
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
Chart: 22
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Sensor System Optics(Example from AFRL)
Direction to Scraper Mirror
Motor
Polarizing
Beam Splitter
Field Scan Mirror (ψ)
Beam Expander
Filter
Beam Splitter
Argon Laser
Piston
Sensing
Line Scan
Camera
: Lateral Effective
Photo detector(LEP)
Tilt
Sensing
Chart: 23
February 13, 2001
Line Scan
Camera
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: Split Polarizer
: Microscope Lens
MIT Space Systems Laboratory
Fine Optical Pointing and Phasing:
Multiple Aperture
Light
Rays
Light
Rays
Secondary
Mirror
•
•
Secondary
Mirror
Primary
Mirror
Fold
Mirrors
Fast
Steering
Mirror
Fast
Steering
Mirror
Lens
Camera
Chart: 24
February 13, 2001
Beam
Combiner
Optical
Delay
Line
16.684 Space Systems Product Development
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
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
Chart: 25
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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
Chart: 26
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