Rotational Shear Interferometry for Astronomical Imaging

1
Rotational Shear Interferometry for Astronomical
Imaging

• Honors Thesis Defense
• By Bristol James Crawford
• Mentor Prof. Henry Everitt
• Special Thanks to Prof. David Brady
• April 25, 2002

2
Independent Project Goals

• Couple a rotational shear interferometer (RSI) to
  a telescope by matching the numerical apertures
  (NA)
• Image a synthetic binary star made of LEDs with
  small angular separation
• Test the RSI/telescope combination for wavelength
  and distortion sensitivity
• Attach the instrument to the Three College
  Observatory (TCO) 32 telescope

3
Traditional Imaging Limits

• Diffraction Limit
• Ground-based telescope resolution is much lower
  due to atmospheric distortion

M46 Open Cluster with Planetary Nebula
Courtesy of Danford/UNCG

• Interferometry allows data processing to correct
  for atmospheric distortion

4
Interferometers Used in Astronomy

• Speckle Interferometry instantaneous image
  collection freezes atmosphere
• Radio Interferometry radio wavelengths
  relatively unaffected by distortions,
  long-baselines necessary for high resolution
• Michelson Type Shear Interferometry measures
  spatial and temporal coherence of incoming light
  through wavefront shearing

5
The Michelson Interferometer

• Measures temporal coherence of light by
  interfering waves created at different times at
  the source
• Used to calculate the spectrum of a source
• Assume light wave of the form
• Retardation time is given by
• Frequency is unchanged by temporal shift, but the
  phase term changes with time leading to
  interference fringes when the beams recombine

M1
d
M2
M2
BS
Source
Detector
6
The Rotational Shear Interferometer

• Obtained from Michelson by replacing flat mirrors
  with right-angle mirrors
• One mirror is rotated an angle which
  introduces shear
• Measures both spatial and temporal coherence of
  light

7
RSI Theory

• Measures spatial coherence
• by interfering different points
• on the wavefront
• Measures temporal coherence
• by introducing a path delay as in the
  Michelson
• Interference fringes are given by the equation
• for quasi-monochromatic light of wavelength
• There is a degeneracy between wavelength and
  position

Courtesy of Gallicchio
8
The Experimental Setup
Telescope
Source
Filter
RSI
NA Matching Optics
CCD Camera
Flat Mirror
Rail
Alignment Laser
9
Experimental Specifications

• Telescope mirror has diameter of 10, focal
  length of 45
• The numerical aperture for the telescope is given
  by
• , and
  numerical aperture for the RSI is given by
  
• Two lenses are placed on the optical rail at
  distances specified to match the NA of the
  telescope to the RSI
• Sources consisted of an incoherent white fiber
  light, and red/green/yellow quasi-monochromatic
  LEDs
• Image collection and analysis performed on Dell
  desktop computer loaded with Imagekitchen software

10
Image Collection Process

• 32 individual RSI fringe patterns are captured
  using the CCD, each is
• pixels

• Each of the 32 fringe patterns is multiplied by a
  phase factor and added to produce a cumulative
  fringe pattern

• A Fast Fourier Transform (FFT) is performed on
  the cumulative fringe pattern to obtain an image
  of the source

11
Experiments Performed

• A synthetic binary constructed of LEDs was imaged
• Angular separation, wavelength, and shear angle
  were varied in the experiments
• Atmospheric distortion was introduced
• A fiber light with a protractor in front was used
  to test the angular resolution of the
  RSI/telescope combination

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Results Identical Red LEDs
1.
2.
Image A Separation 0.7 cm Ang. Sep. 165.7
arcsec
Image B Separation 1.0 cm Ang. Sep. 237.1
arcsec
5 deg
5 deg
Image C Separation 1.3 cm Ang. Sep. 308.2
arcsec
Image D Separation 1.6 cm Ang. Sep. 379.4
arcsec
15 deg
15 deg

• 1. Two identical red LEDs with separation
  variation, the resulting change in the FFT plot
  is linear with spacing
• 2. Red LEDs at a spacing of 1.0 cm with an
  increase in shear angle from 5 deg to 15 deg

13
Results Wavelength Shift
Two Red
Two Red
Two Red
Red/Green
Red/Green
Red/Green

• The top LED changed from red (658 nm) to green
  (583 nm)
• The FFT point moved radially away from the FFT
  plot center
• The radial shift was exactly proportional to the
  shift

14
Atmospheric Distortion

• Distortion in front of the synthetic binary
  created by hot plate at 150 C, 200 C, 250 C, and
  300 C
• No change in FFT plots due to atmospheric
  turbulence
• Reasons for insensitivity to turbulence
• 1. Low spatial frequency
• 2. No spectral analysis
• In the future the experiment will be conducted
  using a source with high spatial frequency, near
  the resolution limit of the instrument

T150 C
T200 C
T250 C
T300 C
15
Angular Resolution Limit

• A pattern with high spatial frequency was placed
  in front of the fiber light to measure the
  resolution limit
• For the given FFT plot the distance to the source
  was 8.7 m, and the angular separation between
  black lines was .25 mm
• The angular separation is 5.93 arc-seconds
• The angular resolution for a ground-based
  telescope is limited by atmospheric distortion to
  1.25 arc-seconds

16
Photon Counting

• Many sources of photon loss in the RSI/telescope
  instrument
• Altogether, there is a 99.76 loss of photons,
  and only 1 out of every 409 visible light photons
  is used for imaging

17
Conclusion

• An interferometric imaging system for astronomy
  was designed and constructed, complete with NA
  matching
• The RSI/telescope instrument successfully images
  synthetic binary stars with varying angular
  separation, wavelength, and shear angle in
  agreement with theory
• The angular resolution limit is near the
  atmospheric turbulence limited resolution for
  ground-based telescopes
• In the future, photon loss will be
• minimized, NA matching will be
• automated, and the RSI instrument
• will be coupled to the Three College
• Observatory 32 telescope

Courtesy of Danford/UNCG