Sparse Aperture Imaging

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Sparse Aperture Imaging
Matthew P Dierking Air Force Research Laboratory
Sensors Directorate Electro-Optical Combat ID
Branch
Nicholas J Miller Bradley D Duncan LOCI Universit
y of Dayton (Ohio)
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Sparse Aperture Imaging

• Objective
• Resolution metrics (PSF and MTF)
• Designing optimized sparse arrays
• Inter-aperture phase aberrations
• Imaging experiment
• Future work
• Conclusions

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Why construct sparse aperture imaging arrays?

• The resolution of a conventional,
  diffraction-limited optical imaging system is
  determined by its aperture diameter.
• Can we synthesize a large effective aperture
  (yielding higher resolution) from multiple,
  strategically located sub-apertures? YES.
• We will construct a sparse aperture array from
  identical, unit-diameter, diffraction-limited
  circular apertures.

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Sparse aperture array with resolution equivalent
to a single, large aperture
Sparse aperture figure of merit, fill factor
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Sparse Aperture Imaging

• Objective
• Resolution metrics (PSF and MTF)
• Designing optimized sparse arrays
• Inter-aperture phase aberrations
• Imaging experiment
• Future work
• Conclusions

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PSF resolution metrics

• FWHM of central peak
• Peak-to-Integrated-Side- Lobe-Ratio, PISLR

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MTF resolution metrics
raxx

• Spatial frequency cutoff
• Mid-frequency MTF level

rmin
We define, Deff rmin(lf)
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Sparse Aperture Imaging

• Objective
• Resolution metrics (PSF and MTF)
• Designing optimized sparse arrays
• Inter-aperture phase aberrations
• Imaging experiment
• Future work
• Conclusions

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Optimized two-dimensional arraysGolay described
point arrays having compact nonredundant
autocorrelations



Autocorrelation
Point array
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PSF and MTF of a Golay-3 array



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PSF and MTF of a Golay-6 array



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PSF and MTF of a Golay-9 array



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PSF and MTF of a Golay-12 array



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Golay-9 array Optimization by expansion factor
Expansion factor s/D
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Golay-9 array 1.0 expansion factor
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Golay-9 array 1.1 expansion factor
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Golay-9 array 1.2 expansion factor
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Golay-9 array 1.3 expansion factor
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Golay-9 array 1.4 expansion factor
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Golay-9 array 1.5 expansion factor
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Golay-9 array 1.6 expansion factor
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Golay-9 array 1.7 expansion factor
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Golay-9 array Optimization by expansion factor


Expansion factor considered optimized when
MTFmin 0.03 in passband
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Quality measures of optimized N sub-aperture
Golay arrays

Selected as optimal sparse aperture array
Recall our figure of merit,
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Sparse Aperture Imaging

• Objective
• Resolution metrics (PSF and MTF)
• Designing optimized sparse arrays
• Inter-aperture phase aberrations
• Imaging experiment
• Future work
• Conclusions

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Golay-9 array Piston added to a single
sub-aperture
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Golay-9 array 0l/10 piston applied to single
sub-aperture
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Golay-9 array 1l/10 piston applied to single
sub-aperture
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Golay-9 array 2l/10 piston applied to single
sub-aperture
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Golay-9 array 3l/10 piston applied to single
sub-aperture
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Golay-9 array 4l/10 piston applied to single
sub-aperture
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Golay-9 array 5l/10 piston applied to single
sub-aperture
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Golay-9 array 6l/10 piston applied to single
sub-aperture
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Golay-9 array 7l/10 piston applied to single
sub-aperture
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Golay-9 array 8l/10 piston applied to single
sub-aperture
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Golay-9 array 9l/10 piston applied to single
sub-aperture
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Golay-9 array 10l/10 piston applied to single
sub-aperture
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Golay-9 array Tilt aberrations on a single
sub-aperture
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Golay-9 array 0l/5 tilt applied to single
sub-aperture
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Golay-9 array l/5 tilt applied to single
sub-aperture
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Golay-9 array 2l/5 tilt applied to single
sub-aperture
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Golay-9 array 3l/5 tilt applied to single
sub-aperture
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Golay-9 array 4l/5 tilt applied to single
sub-aperture
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Golay-9 array 5l/5 tilt applied to single
sub-aperture
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Golay-9 array 6l/5 tilt applied to single
sub-aperture
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Golay-9 array 7l/5 tilt applied to single
sub-aperture
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Golay-9 array 8l/5 tilt applied to single
sub-aperture
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Golay-9 array 9l/5 tilt applied to single
sub-aperture
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Golay-9 array 10l/5 tilt applied to single
sub-aperture
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Sparse Aperture Imaging

• Objective
• Resolution metrics (PSF and MTF)
• Designing optimized sparse arrays
• Inter-aperture phase aberrations
• Imaging experiment
• Future work
• Conclusions

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Incoherently imaging a resolution target with a
Golay aperture array

Golay pupil masks
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ISO 12233 resolution target Transmissive chrome
on glass chart Chart dimensions 15.2 by 11.4 mm

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Horizontal and vertical MTFs of single aperture


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Horizontal and vertical MTFs of Golay-3 array



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Horizontal and vertical MTFs of Golay-6 array




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Horizontal and vertical MTFs of Golay-9 array





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Horizontal and vertical MTFs of Golay-12 array





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MTF attenuation means reduced contrast compared
to filled apertures

• MTF is a measure of contrast transference. We
  observed that, , for a
  sparse aperture imaging system which means
  reduced contrast at middle spatial frequencies.
• Therefore, a practical sparse aperture imaging
  system should employ a post-detection restoration
  filter, such as a least squares Wiener filter, to
  improve image contrast.

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Golay-1 raw and Wiener restored images





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Golay-9 raw and Wiener restored images





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Future work

• Instead of using the large imaging lens to
  combine optical beams prior to detection, use a
  coherent detection method to directly measure
  both the focal plane intensity and phase at each
  sub-aperture.

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Synthesis of sub-aperture field by a single
imaging lens (a) Post-detection synthesis of
intensity images by virtual lens (b)

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Conclusions

• Optical sparse aperture imaging was theoretically
  shown to enhance resolution over a single
  monolithic aperture of equal total area.
• The enhanced resolution was verified by
  calculation of MTF from experimental edge images.
• The resolution gain of a sparse aperture imaging
  system comes at a cost -- loss of contrast and
  reduced SNR. We successfully applied a
  restoration filter to recover lost contrast.
• Sparse arrays require accurate phasing of the
  multiple sub-apertures.