APS Formation Sensor

1
APS Formation Sensor

• Optics
• Dennis Charles Evans
• 15 March 2002

2
Optical Studies

• Optical Design
• Centroid Error Modeling
• Summary
• Back-up Information

3
Optical Characteristics

• Telecentric Design (Modified Aerial Mapping
  Camera)
• Changes in length do not change plate scale
• Aperture 100 mm (selected)
• Optical Speed f/5 (selected for ease of
  fabrication)
• Focal Length 500 mm (result)
• Optical Design Half Angle FOV 5.0 degrees
  (larger angles possible)
• Plate Scale Needed for Point Design
• Based on deployed element distribution
• 5 km at 50 km (source) 50 mm at 500 mm (focal
  plane)
• 40960.013 53.248 mm typical detector
• Half angle 2.9 degrees
• The tracker could handle a wider distributed
  source by using a larger detector or series of
  detectors.
• Glasses Schott SK4, F 5, LF 5
• May have to replace with radiation hard glasses
• Design is internally baffled only
• An external sunshade may be needed for a
  particular instrument

4
Optical Characteristics

• Tolerance Analysis (not done, not expected to be
  a problem)
• Design was selected to be insensitive to changes
  in focus.
• Thermal characteristics similar to CHyMERA.
• Thermal changes in index of refraction change
  focus more than mechanical expansion of lens
  holder.
• A matched lens holder coefficient of expansion
  will not make an thermally insensitive design.
• CHyMERA required near zero CTE (GFRP) because of
  thermal gradients perpendicular to optical axis
  (banana effect)
• Commercial Tilts Decenters acceptable
• Implications
• Proportional Thermal Controller (3 degree C
  range)
• Would like Lenses near ambient and Detector near
  0 ?C
• for simplicity detector housing should be above
  freezing

5
Optical Characteristics

• Ghost images will result from reflections at lens
  and filter surfaces
• Filter ghosts will be centroid aligned with
  beacon image
• Filter ghost will be 0.004 of image or lower
• Lens ghosts will be generally diffuse
• Reference to other designs implies lens ghosts
  will be 0.001 to 0.0001 of image or lower.
• Flat Field Monitoring is provided by illuminating
  a diffuser plate on the back of the closed
  aperture door
• Wavelength filters are needed for resolving
  multiple beacons on same daughter or daughters
  very close together.
• depending on stability, beacons could be turned
  off and on for identification and angular
  separation

6
Telecentric Aerial Photo Lens
SK4 3.57 g/cc
F5 3.47 g/cc
LF5 3.22 g/cc
SK4
F5
SK4
SK4
SK4
LF5
100 mm diameter Telecentric Stop
7
Defocused Spots for Centroiding
8
AutoCAD 3D Model
9
Basic Mounting Internal Baffle Layout
Defining 100 mm diameter Telecentric Stop
Pseudo Stop Aperture
Detector
10
Centroid Error Modeling

• Uniform Defocused Image Model
• Photoelectron Random Normal Statistics

11
Centroiding Model Results

• Electro-Optical system throughput was calculated
  for 0.001 sec cycle.
• 3 x 3 and 9 x 9 pixel centroiding with 40 000
  PE/px, integrated for 10 cycles (0.01 sec),
  results in noise statistics about 5 x better than
  the 0.012 arc-sec error needed.
• For 1000 cycle averaging, the centroid error is
  0.0005 arcsecond equivalent to 0.150 mm at 50
  km, much better than the basic requirement.
• A significant noise margin exists for the point
  design! The margin on noise can be greatly
  improved if needed.
• Noise is reduced most effectively by increasing
  the number of PE/px.
• Well depth is being improved for APS arrays.
  CCD arrays have an order-of-magnitude deeper
  wells at present.

12
Centroiding Noise Model
13
Centroiding Error Sensitivity
14
J40 000PE/px, 9x9, 1 Cycle Average
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J40 000PE/px, 9x9, 3 Cycle Average
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J40 000PE/px, 9x9, 10 Cycle Average
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J40 000PE/px, 9x9, 1000 Cycle Average
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Wide Flux Design Range

• Electro-Optical system throughput was evaluated
  at 0.001 second cycle rate, not 1 second.
• System time constant is likely to be in the
  seconds to minutes range.
• Position requirement of 3 mm at 50 km was 0.012
  arcsecond
• Integration of Centroid for 1000 cycles gives a
  position error of 0.0001 pixel width (1/22 of
  design goal)
• Centroid error is 0.0005 arcsecond equivalent to
  0.150 mm at 50 km.
• Implication
• System has more capability than required
• Could be reduced in size by an order-of-magnitude
  in volume

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Optical Performance Summary

• Thermally stable Telecentric Optical Design
• analytically attractive
• flight proven design concept
• Position error due to photoelectron statistical
  noise is well below the 0.012 arcseconds needed
  for this design
• If 3mm error at 50km is all that is needed, the
  size of the sensor system might be reduced
  significantly, possibly by a factor of 10 in mass.

20
Back-up Information
21
Aerial-02.ZMX Prescription
22
Lens Element Mass

• ELEMENT VOLUME DATA
• Values are only accurate for plane and spherical
  surfaces.
• Element volumes are computed by assuming edges
  are squared up
• to the larger of the front and back radial
  aperture.
• Volume cc Density
  g/cc Mass g
• Element surf 2 to 3 372.375669
  3.570000 1329.381137
• Element surf 4 to 5 1111.283091
  3.570000 3967.280633
• Element surf 6 to 7 670.546997
  3.470000 2326.798080
• Element surf 11 to 12 786.881150
  3.220000 2533.757302
• Element surf 13 to 14 832.146110
  3.570000 2970.761614
• Element surf 15 to 16 249.365462
  3.570000 890.234699
• Total Mass
  14018.213466

23
Photo Electron Noise Modeling

• Photo Electron Noise is related to the square
  root of the signal.
• The square root of the signal is approximately 1
  sigma deviation.
• The noise is modeled as a Normal (Gaussian)
  distribution with a one sigma standard deviation
  equal to the square root of the signal.
• Procedure for generating normal distribution
  noise
• Computer language generates pseudo random number
  from 1 to 1000 and scales to 0.001 to
  1.000
• Function converts number to random normal
  distribution.

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Normal Distribution
25
Random Normal Signal Distribution
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Centroiding Model

• 9 TrackerFocalPlane 40000 Centroid is at
  12,8 39572
• ArrayJI
• A1 A2
• 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0
• 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0
• 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0
• 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0
• 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0
• 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0
• 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0
• 0 0 0 40128 39672 39884 39948 39964 39804 39752
  40060 40300 0 0 0 0 0 0 0 0
• 0 0 0 40128 39844 40032 39504 39880 40380 40004
  40156 39992 0 0 0 0 0 0 0 0
• 0 0 0 40236 39604 39792 39800 40052 39876 40116
  39948 40264 0 0 0 0 0 0 0 0
• 0 0 0 39820 40208 40092 40572 40092 39816 40028
  40124 39808 0 0 0 0 0 0 0 0
• 0 0 0 39976 39960 39892 39944 39572 39844 40252
  40024 40140 0 0 0 0 0 0 0 0
• 0 0 0 39936 40280 40100 39872 40124 40220 39836
  39740 39696 0 0 0 0 0 0 0 0
• 0 0 0 39940 40420 39924 39832 39980 39524 39944
  40144 39880 0 0 0 0 0 0 0 0
• 0 0 0 39936 40168 39976 40228 40040 40104 39840
  40068 39704 0 0 0 0 0 0 0 0
• 0 0 0 40028 39776 40008 40128 39904 40080 39840
  40112 40124 0 0 0 0 0 0 0 0

A1 A2 etc.
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Centroiding Model Numerical Sample
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Centroiding Model Numerical Sample
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A Design with Filter Lens Ghosts
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Typical Reflection Ghosts
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Typical Lens Filter Reflection Ghosts