1. UNIVERSITY of CALIFORNIA
SANTA CRUZ
STREAMLINING ASTRONOMY: A DEPLOYABLE TERTIARY
MIRROR FOR KECK 1
A thesis submitted in partial satisfaction of the
requirements for the degree of
BACHELOR OF SCIENCE
in
PHYSICS (ASTROPHYSICS)
by
Alex Tripsas
10 June 2016
The thesis of Alex Tripsas is approved by:
Professor J. Xavier Prochaska
Advisor
Professor Adriane Steinacker
Theses Coordinator
Professor Robert P. Johnson
Chair, Department of Physics
3. Abstract
Streamlining Astronomy: A Deployable Tertiary Mirror for Keck 1
by
Alex Tripsas
The twin Keck telescopes in Hawaii have been an extremely important tool in astronomy. With the
emergence of Time Domain Astronomy (TDA) and its increasing relevance, it is important to have
Keck’s array of instruments ready at any time necessary. The Keck 1 Deployable Tertiary Mirror
(K1DM3) will be the first automated deployable tertiary. K1DM3 will provide a 4.7 arcminute
field of view (FOV) to Nasmyth and Bent Cassegrain focus instruments. When necessary K1DM3
will be able to switch focus from Nasmyth to Cassegrain in under 5 minutes and vice versa. Since
repeatability is an issue, 4 sets of canoe-sphere kinematic couplings will be used to provide sub-
micron repeatability upon mirror deployment.
5. v
List of Figures
1.1 A replica of the telescope used by Galileo in his observations of the Jovian moons. . 2
1.2 Above is a diagram of the Keck telescope showing the two different foci of the telescope. 4
1.3 Above is a drawing of the different light paths that a telescope might use. Keck’s two
main foci are the Cassegrain and Nasmyth foci. . . . . . . . . . . . . . . . . . . . . . 4
2.1 Above is a solidworks model of the current K1DM3 module. . . . . . . . . . . . . . . 6
2.2 Above is a solidworks model of the K1DM3 module in the tertiary tower with the
mirror in its retracted position. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Above is a photo of the pneumatic actuator prototype. The brass colored piece will be
attached to the rotating inner drum, then when in position, the silver part containing
the pneumatic piston will come into contact with the brass receiver providing air to
the clamps. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.4 Above is a representation of the mirror in its retracted phase while inside the non-
vignetting envelope represented by the gray polygon shape. . . . . . . . . . . . . . . 8
2.5 A representation of how much smaller the K1DM3 mirror is compared to the current
M3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.1 A Solidworks model of the kinematic testbed. . . . . . . . . . . . . . . . . . . . . . . 12
3.2 A sketch of how the canoe sphere kinematics fit into the v-blocks. Notice that there is
only contact on the angled portions of the blocks. This ensures that there is nothing
over constrained in the system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.3 A cutaway section of an LVDT with a wiring diagram. . . . . . . . . . . . . . . . . . 13
3.4 Data from one of the LVDT calibrations. . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.5 A photo of the small kinematic testbed. Three canoe-spheres and three spheres. The
three spheres each went into a cone, v-groove, and a flat surface. The three canoe-
spheres each went into a v-groove block. The white strips are actually pieces of glass
epoxied onto the metal cylinder in order to give the LVDTs a smooth surface to make
contact on. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.6 Repeatability data from the canoe-sphere test on the small testbed. With the excep-
tion of a few outliers, most of the time the position came back to the same spot to
within 0.05 microns. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.7 This is a photo of the new test bed in its deployed phase seated in the kinematics. On
top there are weights to simulate the weight of the mirror. On the swingplate, there
are a series of I-beams to add stiffness to the plate. The actuator can be partially
seen here. The actuator runs the length of the swingplate and is attached at the end
between the I-Beams. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.8 A photo of the testbed in its retracted phase. Not the spring below the raised plate,
this is the shock absorber to prevent damaging the kinematics in case of a crash. . . 17
6. vi
3.9 Above is the data from our new repeatability testing of 5 minutes of the test bed in
the kinematics over a 24 hour period. For the most part we are seeing very repeatable
deployments. However, as can be seen in this graph, there are the occasional “ex-
cursions” and drifting in the system. This is currently a problem being looked into
but so far the main culprit is temperature variations in conjuncture with the different
materials on the test bed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.10 Above is a picture of the kinematic coupling that was dented as noted by the red circle. 18
3.11 Above is a photo of one of the clamps on the large scale testbed. . . . . . . . . . . . 20
3.12 Above is part of the data from the clamping test. The test had the testbed clamped
for a given length of time and unclamped for the same period of time. . . . . . . . . 20
3.13 This is photo of how we were able to rotate the testbed. The testbed was attached
to a large bearing. While the testbed was taking data, myself and the assistance of
another shop member(Jim Ward) we rotated roughly 15 degrees every 5 minutes or
so to sweep from 0-45 degrees back to zero. . . . . . . . . . . . . . . . . . . . . . . . 22
3.14 Above is the data collected from the rotation test on May 26th 2016. The black line
here is the rotation angle and as we can see there is deflection when rotated, however
our main concern was that the couplings could come back to the same spot. When
looking that the data we noticed that the position comes back to within a tenth of a
micron. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
7. vii
To my friends and family who have supported me through out this stressful time.
8. viii
Acknowledgements
I want to thank Xavier Prochaska for all the opportunities he has given me throughout my academic
career as well as the staff at UCO/Lick for all the have taught me.
9. 1
1 Background
Telescopes are the main instrument for the field of astronomy. In fact they have been the
only tools up until the recent observation of gravitational waves with LIGO [5]. Before telescopes
the only way to study the stars was to rely on one’s eyesight. Throughout the ages, man has tried
to peer deeper and deeper into the heavens to understand it. In order to do so, we have had to
apply the technology of the time and further develop our technology in order to probe deeper into
our universe to satisfy our curiosity about the universe that we live in.
The first recorded mention of a telescope was in 1608, where an optometrist by the name
of Hans Lippershey put for a patent for an instrument “for seeing things far away as if they were
nearby”[1]. However, Hans failed to receive his patent due to the large amount of other spectacle-
makers making the same claim shortly after. His design was simply putting two lenses at a certain
distance away from one another to magnify an image.
The following year, Galileo Galilei made his first prototype telescope capable of achieving
3x zoom. Galileo started crafting telescopes at first for the Italian Navy in order to aid their detection
of enemy ships. As his business grew, Galileo started pointing his telescope towards the night sky.
In doing this, Galileo opened up a whole new universe to the world with his observations of the
Galilean moons of Jupiter and the crescent shape of Venus’ reflection[2]. Figure1.1 shows a replica
of the telescope Galileo used.
10. 2
Figure 1.1: A replica of the telescope used by Galileo in his observations of the Jovian moons.
Now in 2016 we are yet again using technology in order to further expand our knowledge of
the universe. Recently there has been a field in astronomy that has become quite prominent, time
domain astronomy (TDA). Time domain astronomy consists or two different observations modes,
first Target of Opportunity (ToO) observations and Cadence Observations. ToO observations are
essentially events that we know occur, however we cannot predict these events in advance. Some
common examples include gamma-ray bursts (GRBs), fast radio bursts (FRBs), supernovae, and
recently gravitational wave (GW) events plus many more. In order to prepare for a ToO event, we
must have a telescope that can quickly start taking data on said event. Some of these events, such
as GRBs can last anywhere between a few minutes to a few days [6]. Cadence observing concerns
phenomenon that deals on a longer time scale. These are observations that deal with events that
can range from days to months. These can be observations of stars orbiting our galactic center,
planets orbiting distant stars, and other orbiting objects. Typically these observations only need a
few exposures per night which leaves a whole night open for other observations.
In order to accommodate this new realm of observational astronomy the folks at UCO/Lick
11. 3
proposed the Keck 1 Deployable Tertiary Mirror (K1DM3). The twin 10-meter Keck telescopes,
located on top of Mauna Kea in Hawai’i, are two of the biggest telescopes currently in operation.
With the next generation of telescopes coming around the corner it is important not only to optimize
the viewing of the telescope, but also keep it competitive in the future. What K1DM3 plans to offer
is a tertiary mirror that can provide a large enough Field of View (FoV) to the Nasmyth and Bent
Cassegrain instruments on Keck 1 (Figure 1.2) while still being able to have the mirror fold into a
position where it can let light go through to the Cassegrain instruments. The three different foci
on the Keck Telescope are Nasmyth, Cassegrain, and Bent Cassegrain. Cassegrain focus is where
the light focuses at a point behind the primary mirror (M1) with the use of a secondary mirror.
The advantage here is that there there is little light compensation required due to the fact that the
instrument at that focus is pointing where the telescope is pointing. Nasmyth Focus is a modification
to the Cassegrain focus with the addition of a tertiary mirror (M3) that passes light through an
open bearing to the instrument. The advantage to Nasmyth focus is that you can have very large,
very heavy instruments which is becoming increasingly more needed with larger telescopes. The
third focus on the Keck telescope is the Bent Cassegrain focus. This is actually more similar to the
Nasmyth focus in that this requires a tertiary mirror, however the beam is pointed off the rotation
axis of the telescope. Light paths for these foci can be seen in Figure1.3 and on the telescope in
Figure 1.2. In the following sections I will go over the design of the K1DM3 module.
12. 4
Figure 1.2: Above is a diagram of the Keck telescope showing the two different foci of the telescope.
Figure 1.3: Above is a drawing of the different light paths that a telescope might use. Keck’s two
main foci are the Cassegrain and Nasmyth foci.
13. 5
2 Instrument Design
The Keck 1 Deployable Tertiary Mirror (K1DM3) goal is to accommodate new fields in
astronomy. In order to accomplish this the team at UCO/Lick came up with a retractable mirror
that needed to adhere to the following requirements:
1. The mirror will be sized to provide an unvignetted 4.7 arcminute diameter field of view (FOV)
to the Nasmyth focus.
2. The K1DM3 module will not vignette the Cassegrain instruments FOV when the mirror is
fully retracted.
3. The mirror will not vignette the primary or secondary mirror in the mirror’s fully retracted
phase.
4. The K1DM3 module shall be designed for installation in the Keck 1 tertiary tower using the
same defining points provided for the existing Keck 1 tertiary mirror module.
Plus many more requirements that are not needed for the purposes of this document. The current
culmination of these requirements can be seen in Figure 2.1. However, one of the major requirements
of this project was to ensure that the mirror deployment system could be extremely repeatable. Re-
peatable in this case meaning that the mirror, after retracting and coming back into its mounts,
would come back to the same position each time. The level of precision that is required for deploy-
ments are on the micron level. The main reason for this requirement was to factor in the resolution
of future Adaptive Optics (AO) systems where if for some reason K1DM3 needed to cycle through
14. 6
retraction and deployment, the AO system did not need to be recalibrated. In order to achieve this,
the team needed to use a series of kinematic mounts. Kinematic couplings are defined as precision-
machined mechanical contacts used to precisely locate components with respect to each other [4].
These couplings are the key to achieving the repeatability we need.
Figure 2.1: Above is a solidworks model of the current K1DM3 module.
However, there are a lot of other design elements that goes into this instrument. Figure
2.1 shows a small part of what has gone into this instrument so far. However, for the rest of this
section I will show what else went into the design of K1DM3. First, in order to properly actuate
the mirror in and out of position, we decided on two linear actuators (Exlar model GSX40-0601)
both providing up to 850 N-m of torque. These actuators will be attached to the upper ring gear
of the and connected to the “swing arm” of the mirror support structure. These two actuators
are responsible for retracting the mirror out of the light path from the secondary mirror of Keck 1
(Figure 2.2).
15. 7
Figure 2.2: Above is a solidworks model of the K1DM3 module in the tertiary tower with the mirror
in its retracted position.
In order to keep the mirror in position while the telescope slews to different positions,
K1DM3 will incorporate a pneumatic clamping system. These clamps will hold the mirror assembly
in the kinematics. This is key since the actuators cannot keep the mirror assembly in the kinematic
mounts since it would over constrain the system and no longer be coupled kinematically. Therefore
we use over-center clamps to put (amount?) of pressure on top of the mounts themselves. Air will
be supplied through a custom pneumatic actuator piston that will connect the outer drum to the
inner drum (Figure 2.3). This design was chosen over an electric clamping mechanism due to the
fact that these clamps took up less real estate than electric motors. This was a serious concern for
the team since the envelope in which the mirror does not interfere with M1, M2, and the Cassegrain
instruments is relatively small (Figure 2.4).
16. 8
Figure 2.3: Above is a photo of the pneumatic actuator prototype. The brass colored piece will be
attached to the rotating inner drum, then when in position, the silver part containing the pneumatic
piston will come into contact with the brass receiver providing air to the clamps.
Figure 2.4: Above is a representation of the mirror in its retracted phase while inside the non-
vignetting envelope represented by the gray polygon shape.
17. 9
Arguably the most import piece of the K1DM3 module is the mirror itself. K1DM3’s
mirror will be much smaller than the current M3 on Keck, however it will still provide a full FOV
for the Nasmyth instruments. The current M3 has provides a 20 arcminute FOV compared to the
4.7 arcminute FOV of K1DM3 (Figure 2.5). With this significant change in size and weight of the
mirror it allowed the engineers to come up with a low profile support structure for the mirror as well
as a different bonding approach to the mirror. These mirrors are usually held in place by drilling
holes into the mirror and adhering support rods into them. The approach for the K1DM3 mirror is
to avoid drilling holes into the mirror, which can be a risky procedure, and decided to adhere six
rods inserted into pucks to the back of the glass blank for axial support. For lateral support, there
are an additional three support rods and pucks along the outer edge of the mirror.
Figure 2.5: A representation of how much smaller the K1DM3 mirror is compared to the current
M3.
All of these design elements have had to be tested either in simulation or physical testing.
Serious time and consideration went into putting together these testbeds and over the course of
almost 2 years, these testbeds have provided key results and brought up potential problems in our
18. 10
designs. The next section I will go over the build up and testing of the K1DM3 testbed that I have
been working on for almost the last 2 years.
19. 11
3 Testing and Results
3.1 Small Testbed
One of the major requirements to this project is having the deployable mirror deploy to
a repeatable position each time; repeatable in this case is one the micron level. This is where the
majority of my contributions have been in the K1DM3 project. In order to achieve this, parts need to
be precisions-machined and oriented in a manner that confines all six degrees of freedom of motion.
Kinematic coupling works best when the axis of the three kinematic mounts make an equilateral
triangle. This provides a stable contact area that is less susceptible to external factors.
There are a few different ways to achieve kinematic coupling; first is to have each contacting
member constrain each degree of freedom. This would normally be three spheres, each contacting
a cone (lateral), v-groove (axial), and flat (piston) surfaces. The other option is a new type of
kinematic mount called canoe-sphere mounts. Canoe-spheres are blocks that look like a v-wedge
that fits nicely into a v-groove, however the surface that makes contact is actually a section of a
1-meter sphere. This provides maximum contact area while still acting as a sphere. A rough drawing
of this can be seen in Figure 3.2.
20. 12
Figure 3.1: A Solidworks model of the kinematic testbed.
Figure 3.2: A sketch of how the canoe sphere kinematics fit into the v-blocks. Notice that there is
only contact on the angled portions of the blocks. This ensures that there is nothing over constrained
in the system.
The first goal was to determine which of these kinematic couplings would offer better re-
peatability. What we ended up doing was setting up both types of kinematic couplings on a single
cylinder and tested their repeatability using Linear Variable Differential Transducers (LVDTs)(Figure
3.5). These LVDT’s are accurate to a tenth of a micron and are positioned next to the kinematic
couplings to measure their repeatability(Figure 3.1). LVDTs work by using three solenoidal coils
placed end-to-end around a tube where the center coil is the primary coil while having a ferromagetic
cylinder as the probe. As the probe moves it causes a voltage to be induced in each secondary ac-
21. 13
cording to its position (Figure 3.3). Since LVDTs output voltages, we had to calibrate each LVDT to
output a position. There were a few different ways we calibrated these LVDTs but the most recent
was to use precision blocks on the LVDTs and record the voltages. When we plotted the voltage
versus the displacement cause by the blocks and used the slope of the best fit line as the input gain
to give us real values(Figure 3.4).
Figure 3.3: A cutaway section of an LVDT with a wiring diagram.
22. 14
Figure 3.4: Data from one of the LVDT calibrations.
The test was a simple one, simply lift the cylinder off of the kinematic mounts and then
set it back down onto its kinematics. We would find the difference of the values between each lift
to find which kinematic coupling offered the best repeatability. Before we looked at the data, the
discussion was that the canoe-sphere kinematics would be preferable due their symmetric shape.
Spheres in cone-V-flat configuration are more susceptible to a varying gravitational vector. However
the concern for the canoe-spheres was that the material had a higher coefficient of friction which
corresponds to worse repeatability. However when we collected data on the small testbed, we noticed
that the canoe-spheres out performed the other kinematics as seen in Figure 3.6.
23. 15
Figure 3.5: A photo of the small kinematic testbed. Three canoe-spheres and three spheres. The
three spheres each went into a cone, v-groove, and a flat surface. The three canoe-spheres each went
into a v-groove block. The white strips are actually pieces of glass epoxied onto the metal cylinder
in order to give the LVDTs a smooth surface to make contact on.
Figure 3.6: Repeatability data from the canoe-sphere test on the small testbed. With the exception
of a few outliers, most of the time the position came back to the same spot to within 0.05 microns.
24. 16
3.2 Large Testbed
After we established what kinematic mounts performed the best (the canoe-sphere, v-block
combination) we moved on to design an actuating testbed. This testbed included one of the two
Exlar linear actuators as well as the De-Sta-Co over-center pneumatic clamps. This testbed was
designed to give initial tests of the mirror support structure’s repeatability as well as how well the
clamps worked on the system. The new test bed can be seen in Figures 3.7 3.8
Figure 3.7: This is a photo of the new test bed in its deployed phase seated in the kinematics. On
top there are weights to simulate the weight of the mirror. On the swingplate, there are a series of
I-beams to add stiffness to the plate. The actuator can be partially seen here. The actuator runs
the length of the swingplate and is attached at the end between the I-Beams.
25. 17
Figure 3.8: A photo of the testbed in its retracted phase. Not the spring below the raised plate, this
is the shock absorber to prevent damaging the kinematics in case of a crash.
3.2.1 Cycle Test
There were a few tests that were performed on this testbed, first was a cycle of the actu-
ator motion where the pseudo-swing arm would retract out of the kinematics, settle back into the
kinematics, engage the clamps and then read the LVDTs position. We learned a few things from
this test, first we learned that we were repeatable on the micron level after each deployment. Second
occurred during a malfunction in the middle of a test, the actuator lost power and the approximately
100 kg of weight crashed down onto the kinematics causing the kinematics to be dented(Figure 3.10).
After this incident, shock absorbers have been added to the testbed as well as the final module in
order to accommodate a possible failure of the actuators. After this crash, new kinematic couplings
were ordered. The new couplings had a new coating to that had a lower coefficient of friction. When
we re-ran the tests, we noticed improved repeatability as seen in Figure 3.9. Figure 3.9 shows three
different measurements, each of the three LVDTs as well as an ambient temperature reading. The
26. 18
most interesting part of this figure is the large deviation towards the tail end of the data. Currently
there is no explanation as to what caused this large rise and fall in our data.
0 100 200 300 400 500 600 700
Time (min)
5
4
3
2
1
0
1
2
3
Position(µm) LVDT1
LVDT2
LVDT3
20.0
20.5
21.0
21.5
22.0
22.5
23.0
23.5
24.0
Temperature(◦
C)
Cycle Test (Simultaneous clamping): 25 May 2016
Figure 3.9: Above is the data from our new repeatability testing of 5 minutes of the test bed in the
kinematics over a 24 hour period. For the most part we are seeing very repeatable deployments.
However, as can be seen in this graph, there are the occasional “excursions” and drifting in the
system. This is currently a problem being looked into but so far the main culprit is temperature
variations in conjuncture with the different materials on the test bed.
Figure 3.10: Above is a picture of the kinematic coupling that was dented as noted by the red circle.
27. 19
3.2.2 Clamping Test
The second test, the arm stayed in the kinematics while the clamps engaged and disengaged.
This was to find out the effects the clamps have on our system. These clamps work by locking into
position over center of the kinematic mounts allowing constant force over the kinematics without
the need of constant air pressure (Figure 3.11). The current version of the testbed has a clamping
force of 330-340 ft-lbs at 80 PSI. When we ran our test, we noticed an interesting behavior as can
be seen in Figure 3.12. As seen in Figure 3.12, there is fairly repeatable actions. The jump in our
data is due to something called Hertzian deformation. This is when a force is applied to two meeting
surfaces and causes the material to compress. Hertizian deformation can be calculated for a sphere
on a flat surface by the following equation:
y = 1.55
P2
E2KD
1/3
(3.1)
Where P is the load in pounds, E is the modulus of elasticity, and KD is the radius of the sphere
making contact, and y is the amount of deformation. The material of the kinematic couplings is
440 C Stainless Steel which means that E = 29 × 106
psi and the load P is the combined weight
of the testbed plus the clamping force. The testbed at each kinematic is roughly 67 lbs while each
clamp adds roughly 330-340 lbs of force. The canoe spheres at each surface are sections of one meter
spheres or 39.4 inches. Therefore when we plug in the numbers we get:
y = 1.55
P2
E2KD
1/3
= 1.55
(400lbs)2
(29 × 106psi) × 39.4in
1/3
= .000262 in ≈ 6 microns (3.2)
When we do the same calculation for the just the weight of the testbed we get ≈ 2 microns, the
difference between these two would suggest that there should be roughly 4 mircon shifts in our data
from just clamping and un-clamped (Figure 3.12). At first we were concerned about the different
directions the LVDT’s were going, however since they are showing repeatable behavior, it was decided
that it did not warrant further investigation.
28. 20
Figure 3.11: Above is a photo of one of the clamps on the large scale testbed.
Figure 3.12: Above is part of the data from the clamping test. The test had the testbed clamped
for a given length of time and unclamped for the same period of time.
29. 21
3.2.3 Rotation Test
Since the Telescope will not be at one position all of the time, we wanted to know how the
testbed acted when we varied the gravity vector. So the test was simply have the testbed seated in
the kinematics while clamped and then rotated the whole testbed to different angles(Figure 3.13).
What we were most concerned about with this test was that after going to a different gravity vector
and returning to the original angle, there would be a difference in the positioning. The test was
performed by manually moving the large rotation bearing to different angles while the test was
running and returning to the starting angle. As we can see in Figure 3.14 the position of the
LVDT’s was repeatable to sub-micron levels. Therefore we concluded that there was no further
testing necessary.
30. 22
Figure 3.13: This is photo of how we were able to rotate the testbed. The testbed was attached
to a large bearing. While the testbed was taking data, myself and the assistance of another shop
member(Jim Ward) we rotated roughly 15 degrees every 5 minutes or so to sweep from 0-45 degrees
back to zero.
31. 23
0 2 4 6 8 10 12 14 16
Time (min)
8
6
4
2
0
2
4
6
8
Position(µm)
LVDT1
LVDT2
LVDT3
0
5
10
15
20
25
30
35
40
Rotation(deg)
Rotation Test: 26 May 2016
Figure 3.14: Above is the data collected from the rotation test on May 26th 2016. The black line
here is the rotation angle and as we can see there is deflection when rotated, however our main
concern was that the couplings could come back to the same spot. When looking that the data we
noticed that the position comes back to within a tenth of a micron.
32. 24
4 Conclusion
With the next generation of large telescopes coming just around the corner, older telescopes
will need to find a way to still be relevant. With the promise of opening up a new field of observational
astronomy , Time Domain Astronomy, K1DM3 is hopefully the first of many efforts to accommodate
this. Because of the success of K1DM3, we are already looking into a deployable tertiary mirror for
Keck 2. This could also potentially be applied to any other telescope with different foci to allow
similar operations to many more telescopes.
33. 25
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