This document summarizes research conducted on developing an aperture partitioning optic using four articulating mirrors positioned using piezo-ceramic actuators. Testing characterized the open-loop behavior of the actuators and explored methods to detect errors in mirror configuration. It was found that the actuators behaved as expected with hysteresis and creep within tolerable levels. Detecting piston and tilt errors was most effective using an annular intensity mask in the focal plane data, which could then be used to correct the mirror positions. With the piezo behavior characterized and an error detection method identified, the optic device can be used to improve satellite imagery quality.

1. Developing an Aperture
Partitioning Optic
Air Force Research Laboratory
Kourtney Kehr
University of Colorado at Boulder
Mentors: Dr. Brandoch Calef,
Dr. Steven Griffin,
and Dr. Jeremy Bos

2. Background
• An automated aperture partitioning optic with four separate
articulating mirrors is being developed for improving
daylight imagery of satellites.
Aperture
Partitioning
Optic

3. Optic Components
• The mirror positions are adjusted by controlling the
voltages on piezo-ceramic stack actuators
positioned behind each of the mirrors.
Image from PI USA
Mirror 1
Mirror 2
Mirror 4
Mirror 3
Piezo-Ceramic Actuators
Δx
Δx
Δx
θ

4. Objectives
Problem 1
• Determine if the open-
loop behavior of the
piezo-ceramic actuators
under an applied voltage
is adequate for
positioning.
Problem 2
• Determine a way to
detect errors in the
configuration of each
mirror so the mirrors may
then be moved into the
correct position.

5. How Piezo-Ceramics Work
• Inverse piezoelectric effect
• Electrical Energy → Mechanical Energy
• Ferroelectric polarization used to make the ceramic
microscopically piezoelectric
• The aligning of electric dipoles in the direction of the applied strong electric DC field
a) unpolarized,
ferroelectric
ceramic
c) after polingb) during poling

6. Experimental Setup
X-axis
Y-axis
Piezo Stack, PI
Laser Displacement Sensor,
Keyence
Power Supply
High Voltage Amplifier,
Trek
CoCo Signal Analyzer,
Crystal Instruments

7. Hysteresis Loop
• Hysteresis:
the phenomenon in
which the value of a
physical property
lags behind
changes in the
effect causing it.
• Behaved as
expected.
• Adequate for
positioning.

8. Piezo-Ceramic Creep
• The creep of
the piezo over
a 10 minute
period was
observed to be
less than
approximately
0.5 μm, taking
into account the
noise effect on
the data.
*Data collected at a constant voltage input of 0.

9. Problem 2: Moving the Mirrors
• The four articulating mirrors of the annular adjustment optic
will be moved into different configurations to produce images
of the same object with different parts of the pupil.
Δx
Δx
Δx
θ

10. Modeling the Mirrors
One Mirror Two Mirrors
Phase
Matrix (Φ)
Intensity
Matrix (P)
Φ=0
P=0
P=1
Phase
Matrix (Φ)
Intensity
Matrix (P)
P=1
P=0
Φ=0
Φ=0
Φ = (2π/λ)(2x)
Φ = (2π/λ)(2x)

11. Visualizing OPD Variation
One Mirror vs.
Two Mirrors
• Optical Path
Difference (OPD)
variation has no
effect on the
images produced
when one mirror is
used, but does
have an effect
when two mirrors
are modeled. Two Mirrors
One Mirror
OPD=0 OPD=100
OPD=100OPD=0

12. OPD Variation Graphically
Two Mirrors
• Able to
determine the
correct piston
amount from
the focal
plane data.

13. Modeling the Mirrors
Intensity Ring
Phase
Matrix (Φ)
Intensity
Matrix (P)
P=0
Φ=0
Φ=0
P=0
P=1
Φ = (2π/λ)(2x)
2r/d

14. OPD Variation Graphically
Intensity Ring
• Although
piston error
can be seen in
the image
plane with the
full pupil, it is
much more
easily seen by
putting an
annular mask
at the pupil.

15. Full Circle Mask vs. Annular
Full Circle Intensity Mask Annular Intensity Mask
• There is a larger variation seen graphically when an annular
intensity mask is used, rather than a full circle mask at the pupil.

16. Conclusions and Future Work
Problem 1
• The piezo-ceramic actuators
behaved according to a hysteresis
loop as expected.
• The hysteresis loop can now be
characterized, and from this
characterization, control voltages
for each desired displacement can
be obtained.
Problem 2
• It was observed that the piston
and tilt error can be measured in
the focal plane data best with an
annular intensity mask.
• The errors measured in the focal
plane data can then be corrected
by adjusting the actuators.
With the behavior of the piezo ceramic actuators determined and a
method found for detecting error in the mirror configurations the
optic device can be used effectively and efficiently to improve the
quality of daylight imagery of satellites.

17. Acknowledgements
Akamai is led and managed by the Institute for Scientist & Engineer Educators at the University of California Santa
Cruz, in partnership with the University of Hawai‘i Institute for Astronomy. Funding for the 2015 Akamai Internship and
Mentor Program is provided by: Thirty Meter Telescope International Observatory, THINK Fund at the Hawaii
Community Foundation, University of Hawai‘i System, University of Hawai‘i at Hilo, National Science Foundation
(AST#1347767), and National Solar Observatory.
Dr. Brandoch Calef,
Dr. Steven Griffin,
Dr. Jeremy Bos,
and
Christopher Shurilla

18. BackupMaterial

19. Hysteresis Loops
• The frequency
and wave
shape of the
voltage input
had little effect
on the
hysteresis
loop.
Sine Wave Voltage Input, 0.25 Hz frequency Triangle Wave Voltage Input, 0.25 Hz frequency
Sine Wave Voltage Input, 0.5 Hz frequency Triangle Wave Voltage Input, 0.5 Hz frequency

20. Visualizing OPD Variation
Two Mirrors
• OPD (Optical
Path Difference)
variation and
radius has an
effect on the
image when two
mirrors are used.
r=8, OPD=0 r=8, OPD=100
r=32, OPD=0
r=16, OPD=0 r=16, OPD=100
r=32, OPD=100
r=64, OPD=0
r=64, OPD=100

21. Visualizing OPD Variation
Intensity Ring
• The width of
the intensity
ring as well
as the OPD
does affect
the image
produced.
d=10, OPD=0
d=8, OPD=0
d=6, OPD=0 d=6, OPD=100
d=8, OPD=100
d=10, OPD=100
d=4,
OPD=0
d=4,
OPD=100
d=2,
OPD=100
d=2,
OPD=0

22. Visualizing OPD Variation
Full Circle
Intensity vs.
Intensity Ring
• OPD variation has
a greater effect on
the images
produced when an
annular mask is
used instead of a
full circle for the
intensity.
Annular Intensity Mask
Full Circle Intensity Mask
OPD=0 OPD=100
OPD=100OPD=0

23. OPD Variation Graphically
Intensity Ring
• The width of
the intensity
ring as well
as the OPD
does affect
the image
produced.

24. OPD Variation

25. Tilt Variation

26. Modeling the Mirrors
One Intensity Square Two Intensity Squares
Phase
Matrix (Φ)
Intensity
Matrix (P)
P=1
P=0
Φ=0
Φ=0
P=1
Outer Mirror
Inner Mirror
Phase
Matrix (Φ)
Intensity
Matrix (P)
P=1
P=0
Φ=0
Φ=0
P=1
Outer Mirror
Inner Mirror
Φ = (2π/λ)(2x) Φ = (2π/λ)(2x)

27. OPD Variation Graphically
One Intensity
Square
• OPD variation
does have an
effect on the
images
produced
when an
intensity
square is
used.

28. OPD Variation Graphically
Two Intensity
Squares
• OPD variation
does have an
effect on the
images
produced
when two
intensity
squares are
used.