Imaging applications of Statistical Optics Monday Radio Astronomy Michelson Stellar Interferometry Coherence Imaging Rotational Shear Interferometer (RSI) Wednesday Optical Coherence Tomography (OCT) 03/14/05 wk7-a-1
Radio Telescope (Very Large Array, VLA) 03/14/05 wk7-a- www.nrao.edu 7 Antennae (parabolic dishes, diameter 5m, weight 30t each) Y radius ranges between 1km and 36km wavelengths 90cm 7mm resolution 00-1.5arcsec in smallest configuration; 6 to 0.05 arcsec in largest configuration signals are multiplied and correlated at central station to obtain µ( x, y). van Cittert-Zernicke theorem is used to invert the observations and obtain the source I(ξ,η), e.g. a constellation of galaxies
VLA images The center of the Milky Way from www.aoc.nrao.edu 03/14/05 wk7-a-3
VLA images from www.aoc.nrao.edu 03/14/05 wk7-a-4 The galaxy M81 is a spiral galaxy about 11 million light-years from Earth. It is about 50,000 light-years across. This VLA image was made using data taken during three of the VLA's four standard configurations for a total of more than 60 hours of observing time. The spiral structure is clearly shown in this image, which shows the relative intensity of emission from neutral atomic hydrogen gas. In this pseudocolor image, red indicates strong radio emission and blue weaker emission.
from www.aoc.nrao.edu 03/14/05 wk7-a-5 This pair of images illustrates the need to study celestial objects at different wavelengths in order to get "the whole picture" of what is happening with those objects. At left, you see a visible-light image of the M81 Group of galaxies. This image largely shows light coming from stars in the galaxies. At right, a radio image, made with the VLA, shows the hydrogen gas, including streamers of gas connecting the galaxies. From the radio image, it becomes apparent that this is an interacting group of galaxies, not isolated objects.
Michelson Stellar Interferometer Optical version of the van Cittert-Zernicke theorem Since multiplication cannot be performed directly, it is done through interference (Young s interferometer) Extreme requirements on mechanical and thermal stability (better than λ/100 between the two arms) Alternative: intensity interferometer (or Hanbury Brown Twiss interferometer) 03/14/05 wk7-a-6 from www.physics.usyd.edu.au/astron/susi
Coherence Imaging 03/14/05 wk7-a-7 J. Rosen and A. Yariv, Opt. Lett 1:1101, 1996.
Coherence Imaging x 1 + x ˆ x = x = x 1 x 03/14/05 wk7-a-8 J. Rosen and A. Yariv, Opt. Lett 1:1101, 1996.
Coherence Imaging ( ) ( ) ( ) ( ) min 1 1 1 1 ˆ 1 ˆ r r r q y y x x r y y x x r = + = + + + = Coordinate Transform: J. Rosen and A. Yariv, Opt. Lett 1:1101, 1996. 03/14/05 wk7-a-9
Coherence Imaging 03/14/05 wk7-a-10 D. Marks et al, Appl. Opt. 38:133, 1999.
Coherence Imaging in projective coordinates z = R sp z s 03/14/05 wk7-a-11 D. Marks et al, Appl. Opt. 38:133, 1999.
Coherence Imaging in projective coordinates I ( x, y, z ) ( z ) I3D 03/14/05 wk7-a-1 D. Marks et al, Appl. Opt. 38:133, 1999.
The Rotational Shear Interferometer folding mirror beam splitter folding mirror sensor array dither translation stage input aperture 03/14/05 wk7-a-13 rotating object by David J. Brady, Duke University www.fitzpatrick.duke.edu/disp/
What does the RSI measure? Input field Arm Special case: θ=90 o To Camera Arm 1 Input field 03/14/05 wk7-a-14 Folding prism at Arm 1 Folding prism at Arm (θ=90 o ) Arms 1 & combined at camera plane
Intensity on the RSI Sensor Plane The field on arm 1 is: ( ) = ( θ + θ θ θ) E1 x, y Eo xcos ysin, xsin ycos θ The field on arm is: ( ) = ( θ θ θ θ) E x, y Eo xcos ysin, xsin ycos s (, ) I x y = E + E 1 03/14/05 wk7-a-15 * * 1 1 = E + E + E E + E E = I + I + 1 1 ( x ysin θ, y xsin θ, xˆ xcos θ x, yˆ y xcos θ, τ δ / c) Γ = = = + = = +Γ * o o by David J. Brady, Duke University www.fitzpatrick.duke.edu/disp/
Coherence imaging using the RSI Re [ Γ ( x, y, xˆ, yˆ, τ )] dc k l i j + Interference on CCD τ S( x, y, xˆ, yˆ, v) k l i j J ( xk, yl, xˆ i, yˆ j ) ν = ν 0 ν [ Γ ( x, y, xˆ, yˆ, τ )] dc Re 0 i j + 4-D Fourier transform relationship [ x', y', ' ] Γ( x, y, q, τ ) S z,ν 03/14/05 wk7-a-16 by David J. Brady, Duke University www.fitzpatrick.duke.edu/disp/
EXPERIMENTAL RESULTS: 3-D3 -D spatial / 1-D spectral RSI reconstruction Experimental Setup Color Composite Image Red (590-650 nm) by David J. Brady, Duke University www.fitzpatrick.duke.edu/disp/ 03/14/05 wk7-a-17 Green (50-570 nm) Blue (430-500 nm)
Example RSI Images point sources Experimental Mutual Intensity 03/14/05 wk7-a-18 by David J. Brady, Duke University www.fitzpatrick.duke.edu/disp/
Experimental RSI implementation (University of Illinois) Princeton Instruments camera shutter camera cooling fan mirror tilt flex stages platform linear bearings long-travel platform ( ) Aerotech stage 03/14/05 wk7-a-19 by David J. Brady, Duke University www.fitzpatrick.duke.edu/disp/
Close-up view of the Interferometer Section of the RSI shutter input aperture magnetic coupling 90º shearing mirror 90º dither mirror beamsplitter mirror support flexure stage 03/14/05 wk7-a-0 by David J. Brady, Duke University www.fitzpatrick.duke.edu/disp/
Mobile RSI (University of Illinois and Distant Focus Corporation) 03/14/05 wk7-a-1 by David J. Brady, Duke University www.fitzpatrick.duke.edu/disp/