Transmitter Point-Ahead using Dual Risley Prisms: Theory and Experiment John Degnan 1, Jan McGarry...
-
date post
18-Dec-2015 -
Category
Documents
-
view
212 -
download
0
Transcript of Transmitter Point-Ahead using Dual Risley Prisms: Theory and Experiment John Degnan 1, Jan McGarry...
Transmitter Point-Ahead using Dual Transmitter Point-Ahead using Dual Risley Prisms: Theory and ExperimentRisley Prisms: Theory and Experiment
John Degnan1, Jan McGarry2, Thomas Zagwodzki2, Thomas Varghese3
1Sigma Space Corporation, 2NASA/GSFC, 3Cybioms
16th International Workshop on Laser Ranging
Poznan, Poland
October 13-17, 2008
Why Transmitter Point-Ahead?Why Transmitter Point-Ahead?
Unlike conventional SLR, the eyesafe SLR2000/NGSLR system operates with transmitted pulse energies three orders of magnitude smaller (~60 J) and is designed to be autonomous (no operator).
Automated pointing of the telescope/receiver is accomplished using a photon-counting quadrant MCP/PMT detector which seeks a uniform distribution of counts among the quadrants.
In order to concentrate more laser energy on high satellites, the transmit beam divergence is narrowed by a computer-controlled beam expander in the transmit path.
To prevent saturation of the MCP/PMT detector during daylight operations, the receiver FOV must be restricted to roughly + 5 arcsec, which is smaller than the largest anticipated point-ahead angle of 11 arcseconds.
Since the transmit and receive FOV’s no longer overlap as in conventional SLR systems, transmitter point ahead (i.e. separate boresighting of the transmitter and receiver) is required.
Conventional SLR vs Eyesafe NGSLRConventional SLR vs Eyesafe NGSLR
Conventional SLRSLR2000/NGSLR
Conventional SLR
Direct transmitter (green cone) atwhere target will be one transittime later to maximize signalreturn.
Open up receiver FOV (yellowcone) to capture return signalfrom previous fire.
Minimize false alarms viadetection threshold.
Eyesafe SLR2000/NGSLR
Direct receiver FOV (telescope) to wheresatellite was one transit time earlier and useQuadrant Detector to correct receiverpointing.
Direct transmitter (green cone) at wheretarget will be one transit time later via DualRisley Prisms to maximize signal return.
Reduce receiver FOV (yellow cone) tominimize noise during daylight operations .
Transmit and Receive FOV’s no longeroverlap.
NGSLR Transceiver Block DiagramNGSLR Transceiver Block Diagram
CCDCamera
0.4 m
0.088 m5.4XBeam
Reducer
0.04 m
0.025 m
CCDSplitter
QUADMirror
CompensatorBlock
TelescopePit Mirror
FaradayIsolator/
Half WavePlate
0.080 m
0.070 m
P1
0.085 m 0.105 m 0.350 m
0.070 m
“Zero”Wedge
Day/NightFilters
3-elementTelephoto
Lensf=0. 85 m
0.130 m
LaserTransmitter
0.213 m
Risley Prisms
Computer-controlled
Diaphragm/Spatial Filter
(Min. Range : 0.5to 6 mm diameter)
QuadrantRangingDetector
0.200 m0.051 m
3 X Telescope
f1 = -0.1 m
0.099 m
NORTH( = 0o)
0 = 67.4o
f2 =0.3 m
d1
d2
d3(out of page)
f1 = 0.108 m
f2 = -0.02 m
f = .025 m
d1
p1
d1
p1
d1
p1
d2
p2
Vector out of page
Vector into page
p3
s3
d2
s2'
0.250 mWorkingDistance
0.229 m
SpecialOptics2x-8xBeam
Expander
Translation Stage
P3
P2
Wall Star Camera Retro Location
Point-Ahead ProceduresPoint-Ahead Procedures Point-ahead angles, expressed in the azimuth and elevation
axes of the telescope, are obtained from the orbital prediction program.
In determining the appropriate Risley rotation angles, we must properly take into account the complex and time dependent coordinate transformations imposed by the various optical components in the transmit path and the axis rotations of the Coude mount as the pulse travels from the Risleys to the telescope exit aperture.
Finally, we must account for any angular biases between the two servo “home” positions and the actual direction of deflection by the prisms.
Definition of Definition of AE AE and and
Azimuth
Elevation
cos
AE
From Orbital Predictions = azimuth offset between transmit and receive vectors = elevation offset between transmit and receive vectors
costan
cos 22
AE
Definition of Coude Definition of Coude -Parameter-Parameter
The Coude -Parameter takes into account the axis rotations introduced by the Coude mount and is given by:
o5.2220
where = satellite azimuth = satellite elevation0 = system specific azimuthal bias = 67.5o for NGSLR
Bias Free Risley Command AnglesBias Free Risley Command Angles Deflection by an individual prism is in the
direction of the thickest part of the wedge.
The magnitude of the deflection is given by
where n =1.52 is the refractive index and w = 30 arcmin is the wedge angle
The final deflection is the vector sum of the two individual wedge deflections as in the figure. It makes an angle AE+ with the positive x-axis of the bench. The magnitude is equal to mt where mt is the post-Risley transmitter magnification and is the point-ahead angle magnitude.
min6.15)1( arcwn
x
y
Desiredwedge 1direction
Desiredwedge 2direction
Final Beam DirectionProjected into bench
x-y plane(AE +)
and Magnitude (mt)
a
a
AE+
mt
AE+
AE+
6a =-(AE++/2)+/2
=/2-AE-+/25
a =AE+-/2+/2
5a+6
a==acos(1-(mt2/22)
Physical ExplanationPhysical Explanation
2
2
6
5
21cos
22
22
t
AEc
AEc
ma
First term (/2): Makes the two wedges antiparallel, cancelling out the deflection ( =0), with the individual deflections lying along the bench y-axis.Second term (): Rotates the bench x-y axes into the instantaneous azimuth-elevation (az-el) axes at the telescope.Third term (AE): Rotates the deflection direction to the proper value in the telescope az-el reference system ( still equal to zero).Fourth Term(/2): Provides the final magnitude for properly accounting for the post-Risley beam magnification, mt , and the wedge deflection angle, .
Risley Command Angles with BiasesRisley Command Angles with Biases
The home positions of the servos may be displaced in angle (positive or negative) relative to the bench x-axis leading to “rotational biases” as in the figure.
The command angles, 5c
and 6c, are therefore
adjusted from the actual values, 5
a and 6a,
according to
x
y
Desiredwedge 1direction
Desiredwedge 2direction
Final Beam DirectionProjected into bench
x-y plane(xy =+5
a-6a)
and Magnitude (mt)
2 1
a
a
c
c
StepperMotor 1“Home”
StepperMotor 2“Home”
xy
mt
= satellite point-ahead anglemt = total transmitter magnification beyond Risleys
5a = actual ccw direction of wedge 1 deflection relative to positive bench x-axis
6a =actual cw direction of wedge 2 deflection relative to negative bench x-axis1 = bias angle between positive bench x-axis and servo 1 home position2 = bias angle between negative bench x-axis and servo 2 home position
5c = 5
a -1 = commanded direction of wedge 1 deflection6
c = 6a -2 = commanded direction of wedge 2 deflection
xy = actual angle of deflection relative to positive bench x-axis.266
155
ac
ac
Experimental ValidationExperimental Validation
The deflected beam from the Risleys was projected onto the wall and measured for several values of and AE.
The deflected beam was also viewed at the telescope exit window.
In a separate set of experiments, a retroreflector placed in the transmit path before the 3-power beam expander reflected the laser beam into the star camera which provided arcsecond quality angular measurements.
These experiments were used to:– Check/determine the validity of servo controls and algorithms– Measure the rotational bias angles– Estimate the difference between the two wedge angles.
Experimental Validation at Wall Experimental Validation at Wall and Telescope Apertureand Telescope Aperture
JJ
F
FJJ
F
F
G
G
H
HI
I
These experiments validate the predicted orientation and spread of the spots on the wall and at the telescope aperture. In this particular experiment, was constant at 10 arcsec except for point J ( =0) and AE took on values 0,90,180, and 270o. As expected, the telescope aperture pattern is rotated by = 90o with respect to the wall pattern and the angular deviations are smaller by a factor m t =28.21.
Star Camera ExperimentsStar Camera Experiments
380 400 420 440 460 480240
260
280
300
320
Y0Yexp i
Ycali
X0
Xexpi Xcali
scale 86.45
exp 0.011
exp 6.905deg
1 13.302 deg
2 6.398 deg
X0 434.333
Y0 278.667
•In the above plot, the abscissa and ordinate values correspond to star camera pixel numbers.•Each pixel corresponds to about 0.49 arcsec of movement.•Each individual red square corresponds to the observed location of the retroreflected transmitter spot in the star camera image plane for different point-ahead angles and orientations.•Each blue diamond corresponds to the position predicted by theory.•This experiment provided extremely high angular resolution and provided the numerical values for the rotational biases, 1 and 2.•It also indicated that the wedge angles differed by about 1.1%.
Biases
Star CameraOrigin
Wedge AngleDifference
SummarySummary The development of the point-ahead algorithms was approached
through both theoretical ray analyses and experiment until we achieved agreement.
We are now prepared to implement the automated receiver pointing correction and transmitter point-ahead features needed for reliable daylight ranging.
During the star camera experimentation, we found that the two prisms have slightly different wedge angles (1.1%) so that zero deflection can never be achieved. Ignoring this difference produces a maximum transmitter pointing error of about 1.5 arcsec for small . For larger , the errors are typically sub-arcsecond.
Similar transmitter point-ahead systems and algorithms will be required for future interplanetary laser transponder and communications systems where can take on values of several tens of arcseconds.