ZEBRA IMAGING
of the Nonlinear r-mode in a Rotating Neutron Star

Joel E. Tohline
Department of Physics and Astronomy, Louisiana State University
June 1, 2001

Immediate Objective
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.)

Background
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).
How was each 640 × 480 tiff image created?
  1. 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.

  2. 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:

    Specified Density Level sdl file
    [click on file name to download]
    r/rmax = 0.8 shell_1.sdl
    r/rmax = 0.1 shell_2.sdl
    r/rmax = 0.005 shell_3.sdl
    r/rmax = 0.0001 shell_4.sdl

  3. 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.

How Will a Hologram be Created?
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.

  1. 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.

  2. 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.

Proposal
I would like to do one of the following:
  1. Create one "static" hologram from the model shown here as Frame 290, with no vertical parallax.

  2. 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.

  3. 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.

Frame 121
Frame 161
Frame 211
Frame 246
Frame 290
TIFF at 1280 × 960
TIFF at 2560 × 1920
Frame 311
Frame 336
Actually, it occurs to me that the macroscopic dimensions of the hologram must be 60 cm × 60 cm because each TIFF image is shrunk down to 2 mm on a side, and 300 × 2 mm = 60 cm. But 60 cm × 60 cm = 23.622 inches × 23.622 inches, which is almost 2'×2'.