Download Transmitter Point-Ahead using Dual Risley Prisms: Theory and

Transmitter Point-Ahead using Dual
Risley 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?
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Unlike conventional SLR, the eyesafe SLR2000/NGSLR system
operates with transmitted pulse energies three orders of magnitude
smaller (~60 mJ) 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 NGSLR
Conventional SLR
 Direct transmitter (green cone) at
where target will be one transit
time later to maximize signal
return.
 Open up receiver FOV (yellow
cone) to capture return signal
from previous fire.
 Minimize false alarms via
detection threshold.


Eyesafe SLR2000/NGSLR
 Direct receiver FOV (telescope) to where
satellite was one transit time earlier and use
Quadrant Detector to correct receiver
pointing.
 Direct transmitter (green cone) at where
target will be one transit time later via Dual
Risley Prisms to maximize signal return.
 Reduce receiver FOV (yellow cone) to
minimize noise during daylight operations .
 Transmit and Receive FOV’s no longer
overlap.
Conventional SLR
SLR2000/NGSLR
NGSLR Transceiver Block Diagram
0.085 m
QUAD
Mirror
0.080 m
0.070 m
0.070 m
d1
0.130 m
0.250 m
Working
Distance
0.229 m
Star Camera
Retro
Location
0.350 m
d2
Wall
0.105 m
3 X Telescope
CCD f = -0.1 m f =0.3 m Telescope
1
2
Pit Mirror
Splitter
s2'
s3
d2
P2
d2
p2
Faraday
Isolator/
0.200 m
Half Wave 0.099 m
Plate
0 = 67.4o
0.4 m
P1
Compensator
Block
P3
Translation
Stage
p3
d3
(out of page)
0.051 m
NORTH
( = 0o)
0.213 m
“Zero”
Wedge
Day/Night
Filters
d1
p1 f = 0.108 m
1
d1
5.4X
Beam
Reducer
f2 = -0.02 m
p1
3-element
Telephoto
Lens
f=0. 85 m
Risley
Prisms
Special
Optics
2x-8x
Beam
Expander
Computercontrolled
Diaphragm/
Spatial Filter
(Min. Range : 0.5
to 6 mm diameter)
d1
p1
Quadrant
Ranging
Detector
0.04 m
f = .025 m
Laser
Transmitter
0.088 m
CCD
Camera
0.025 m
Vector out of page
Vector into page
Point-Ahead Procedures
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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 bAE and 
Elevation
cos


Azimuth
From Orbital Predictions
 = azimuth offset between transmit and receive vectors
 = elevation offset between transmit and receive vectors
2
 cos  2   2
tan b AE
bAE
2



 cos 
Definition of Coude -Parameter

The Coude -Parameter takes into account the axis
rotations introduced by the Coude mount and is
given by:
   0   

2
     22.5
o
where
 = satellite azimuth
 = satellite elevation
0 = system specific azimuthal bias = 67.5o for NGSLR
Bias Free Risley Command Angles
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Deflection by an individual prism
is in the direction of the thickest
part of the wedge.
The magnitude of the deflection is
given by
  (n  1) w  15.6arc min

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 bAE+ 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 pointahead angle magnitude.
y
Desired
wedge 2
direction
bAE+
Final Beam Direction
Projected into bench
x-y plane
(bAE +)
and Magnitude
(mt)
mt


a
bAE+
Desired
wedge 1
direction

a
x

bAE+
6a =-(bAE++/2)+/2
=/2-bAE-+/2
5a =bAE+-/2+/2
5a+6a==acos(1-(mt2/22)
Physical Explanation
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 (azel) axes at the telescope.
Third term (bAE): 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, .
 
c
5
 
c
6

2

2
   b AE 
   b AE 

2

2
 mt  2 
  a cos 1 
2 
2 

Risley Command Angles with Biases
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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, 5a and 6a,
according to
 5c   5a  b1
 6c   6a  b 2
y
Desired
wedge 2
direction
Stepper
Motor 2
“Home”
 c
b2
Final Beam Direction
Projected into bench
x-y plane
(bxy = +5a-6a)
and Magnitude
(mt)
mt
Desired
wedge 1
direction


a
bxy

 a
 c
b1
Stepper
Motor 1
“Home”
x
 = satellite point-ahead angle
mt = 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-axis
b1 = bias angle between positive bench x-axis and servo 1 home position
b2 = bias angle between negative bench x-axis and servo 2 home position
5c = 5a -b1 = commanded direction of wedge 1 deflection
6c = 6a -b2 = commanded direction of wedge 2 deflection
bxy = actual angle of deflection relative to positive bench x-axis.
Experimental Validation
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The deflected beam from the Risleys was projected onto
the wall and measured for several values of  and bAE.
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.
300
7.5
Experimental Validation at Wall
and Telescope Aperture
200
5
100
2.5
0
0
6 6.46.87.27.6 8 8.48.89.29.610
Wall
Telescope Aperture
400
15
Bench Y-axis, arcsec
200
0
F
F
H
JJ
100
200
300
400
I
400 300 200 100 0 100 200 300 400
Bench X-axis, arcsec
Elevation Axis, arcsec
G
300
100
6 6.46.87.27.6 8 8.48.89.29.610
FF
10
5
0
I
J
5
i 
10
15
G
J
H
15
10 5
0
5 10
Azimuth Axis, arcsec
10
15
10
10
10
0
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 bAE 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 mt =28.21.
a
Star Camera Experiments
320
X0
scale  86.45
300
 exp  0.011
Yexp i
Ycali
b exp  6.905 deg
Y0
280
b 1  13.302 deg
b 2  6.398 deg
Wedge Angle
Difference
Biases
260
X0  434.333
Y0  278.667
240
380
400
420
440
460
480
Star Camera
Origin
Xexp i , Xcali
•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, b1 and b2.
•It also indicated that the wedge angles differed by about 1.1%.
Summary
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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.