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Immediate Objective
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To create one high-resolution, 2'×2' white-light hologram
showing the structure of a fully developed r-mode wave as it
is "crashing" onto the surface a rapidly rotating neutron
star by September 1, 2001.
The structure that I would most like to view is illustrated here by
frame number 290 from the accompanying
384-frame,
quicktime movie. (As
displayed along the right-hand side of this page, the time-sequence
runs from the top, toward the bottom.
Clicking on any one of these images will load the relevant original
640 × 480 resolution tiff image
from which the quicktime movie was created. Two higher resolution
tiff images of Frame 290 are also available, as indicated.)
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Background
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The three-dimensional neutron star model that will be imaged
comes from a fully nonlinear, gravitational hydrodynamics simulation
that was completed recently by Lee Lindblom (Caltech), Joel Tohline
(LSU), and Michele Vallisneri (Caltech) in an attempt to better understand
what types of dynamical astrophysical events will give rise to
measurable sources of gravitational radiation, as predicted
by Einstein's general theory of relativity. Understanding the
emission from such sources is particularly important at this time
because an instrument
(LIGO) is being constructed
which, for the
first time in history, is likely to be able to detect gravitational
waves. A brief physical description of the Lindblom, Tohline, and
Vallisneri simulation can be found by clicking
here; the more technical description
can be found in the February 12, 2001 issue of Physical Review
Letters (vol. 86, pp. 1152-1155).
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How was each 640 × 480 tiff image created?
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At each time step during the hydrodynamic simulation, we have
a three-dimensional data array that specifies what the mass
density of the fluid is at all points in space. (The r-mode
simulation was conducted on a cylindrical coordinate mesh with
a grid resolution of 66 radial × 130 vertical ×
128 azimuthal zones.) The data in this "rho" array is written
out to disk in binary format using the following fortran90
statements:
program single
implicit none
integer, parameter :: jmax=66, kmax=130, lmax=128
real, dimension(jmax,kmax,lmax) :: rho
character(8) :: outfile
open(unit=12,file=outfile,status='unknown', &
form='unformatted')
write(12) rho
close(12)
end program single
The specific 4,392,968 Byte binary data file of this type that was used to generate
the image shown here as Frame 290 can be
downloaded
by clicking here.
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We feed this 3-D density data array into a program (we call it "polyr")
that uses a "marching cubes" algorithm to locate points (vertices)
on any isodensity surface. "polyr" is also used to specify how these
vertices are to be connected to one another (usually three at a time)
in order to define polygons (usually triangles) that completely cover
and thereby define the specified isodensity surface.
"polyr" then writes out (in ascii format) an "sdl" file that specifies
all of the vertices and polygons on the selected isodensity surface.
Here are the "sdl" files (and their corresponding isodensity surface
values) that were generated by "poly" in order to create the 4 nested
surfaces shown here in Frame 290:
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These four "sdl" files, along with a standard "template" sdl file,
are then fed into a program called "renderit," which utilizes a
sophisticated ray-tracing algorithm to light and color the surfaces
and produce the TIFF image. "renderit" is a commercial program
developed and marketed in the past by
Alias|Wavefront.
(Their newer rendering utilities are now being marketed in a package named
"Maya.")
The "template" sdl file specifies a variety of parameters, such as: the
camera's viewing position relative to the center of the star;
the desired pixel resolution of the TIFF image;
the color and degree of transparency of each isodensity surface;
and the position of various light sources.
The (ascii-formatted) template file that we supplied to "renderit"
in order to generate all of the movie frames shown here can be
downloaded by
clicking here.
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How Will a Hologram be Created?
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It is my understanding that, in order to create a high-resolution
2'×2' white-light hologram
with both horizontal and vertical
parallax, Zebra Imaging needs as many as
300 × 300 (that is, 90,000)
different TIFF images, each with a 300 × 300 pixel resolution.
In order to create a hologram with only horizontal parallax, all
you need is 300 different
TIFF images, each with a 300 × 300 pixel resolution.
Each TIFF image is constructed from the same physical object
(in this case, the object that appears in Frame 290), but each
image should show the object from a slightly different camera
position/orientation.
- If I construct the TIFF images
I could potentially create all of the TIFF images that are required
for the hologram. What I would do is simply "render" the same four
surfaces (defined by the 4 sdl files described above) over and over,
from 300 (or 90,000) different camera positions/angles. In order to
do this properly, the Zebra Imaging technical staff would need to
explain to me precisely how to specify the camera position/angle for
each image (i.e., explain what numbers need to be changed in the
"template" sdl file discussed above).
I estimate that creating
300 images (for a hologram with no vertical parallax) would take
me roughly two days; creating 90,000 images (for full vertical and
horizontal parallax) is out of the question for me right now;
creating, say, 10 different "strips" of 300 images each (in order to
gain some vertical parallax) would take me roughly one month.
- If Zebra Imaging constructs the TIFF images
If the TIFF images are constructed by the technical staff at Zebra
Imaging, then all you should need from me is the 4.3 MB raw data set
that specifies how the star's mass density is distributed throughout
our cylindrical computational grid, along with some suggestions
of which isodensity surfaces would be most interesting to render.
You should be able to download
and read this raw data set from the information given above; I would
suggest creating four nested isodensity surfaces using the four "specified
density levels" itemized in the table, above.
I'm curious to see how you would render this data in preparation for
the hologram. In addition to rendering four nested surfaces, as my
group has done, it might also be interesting to have one quadrant (or
one eighth) of the star "cut away" so that more of the star's
interior structure could be displayed.
Please send me some example TIFF images and/or give me
a call (225-578-6851) so that we can arrive at a result that improves
on what my group already has done in the sample TIFF images shown here.
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Proposal
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I would like to do one of the following:
- Create one "static" hologram from the model shown here as
Frame 290, with no vertical parallax.
- Create one "static" hologram from the model shown here as
Frame 290, but with 5 to 10 different "strips" in order to provide
a certain degree of vertical parallax.
- Create one hologram in which the vertical parallax is used to
illustrate a modest amount of time-evolution. In this case, the
hologram would be divided into 5-10 vertical viewing zones, and
for each zone a different raw data set would be used. (If Zebra
Imaging does the rendering, then I would have to give you these
additional data sets from other points in time in the model's
evolution, as illustrated by the separate movie frames shown
here.)
I'm not sure which of these is the best to do right now.
I need
advice from Zebra Imaging before selecting a particular path to
follow.
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Frame 121
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Frame 161
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Frame 211
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Frame 246
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Frame 311
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Frame 336
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