Why Image in the Fourier Domain?
Recent results
from data obtained with the Japanese Yohkoh satellite have indicated that
high spatial and temporal resolution hard X-ray and gamma-ray imaging
spectroscopy can provide definitive answers to fundamental questions
concerning the evolution of solar flares. The High Energy Solar Imager (HESI) has been studied as a Fourier transform
imager with finer spectral and spatial resolution and an energy response that
extends into the gamma-ray domain. More recently, the High Energy Solar
Spectrographic Imager (HESSI) has been
accepted for stage-two studies of the same concept. It builds on the
technological heritage developed with the High Energy Imaging Device (HEIDI) and the High Resolution Gamma-Ray
Spectrometer
(HIREGS) balloon payloads.
Hard X rays and gamma rays cannot be reflected or focused with lenses
or mirrors. Even grazing-incidence reflection, used very effectively
in soft X-ray astronomy, is impossible in the photon-energy domain
above a few keV. What is required is a variation on the pinhole
camera consisting of transparent apertures in material opaque to these
radiations.
Implementation of Fourier Imaging
The Fourier-transform imaging technique employed with HESI is
implemented with a set of twelve Rotation Modulation Collimators
(RMCs). A single RMC consists of two uniform grids, with
identical pitch, made from a high-Z material such as tungsten,
separated by a distance large compared to the slit width of the grids.
The grid pairs are co-aligned forming RMCs within the telescope
assembly, which is pointed to within a small fraction of a degree of
Sun center and rotated. An X-ray detector is situated behind the rear
grid of each RMC and measures the X-ray flux from the source as
modulated by the rotating grid pair as shown in
Figure 1. Note that
this technique imposes no requirement with respect to position
sensitivity on the X-ray detectors. They are required only to measure
the counting rate as a function of time and photon energy. The RMCs
modulate the X-ray flux observed with the detector by alternately
occulting and de-occulting the source, providing that a symmetric
X-ray source is not situated on the rotation axis of the collimators.
If the X-ray source is located on the rotation axis, then no
modulation of the incoming X-ray flux occurs. The fundamental of the
modulated signal from each RMC provides information on one spatial
Fourier component of the source being observed. Together, using
components obtained at all rotation angles, they provide the
information necessary to reconstruct an image of the source.
End-To_End Testing of Fourier Imagers
It is essential, despite the difficulties, to make end-to-end tests of imaging
instruments proposed for space flight. At one point in the development of
Fourier imaging concepts at Goddard, it was thought that Fourier telescopes
such as HEIDI and HESI required a point source at infinity to test their
modulation capabilities. A laser calibration
test was devised which met most of the objectives desired for an
end-to-end test. Although this technique bypassed the diffraction problems of
testing with visible light, it did not provide a test of the high energy
detectors. Quite recently, we have developed a laboratory test using hard
X-rays from a small source at a finite distance from the Fourier telescope. A
schematic design for this test is shown in Figure 2.
The basic idea in this design is that the point source is placed in front
of the front grid at a distance equal to the distance between the front and
rear grids. As shown inFigure 2, the X
rays strike the rear grid at positions with a spatial period twice that of the
grid pitch. The source is then moved laterally while the flux of X rays is
monitored by the detector. Except in the case where the slit/slat ratio
equals unity, the detector signal rises and falls, much as if the source were
at infinity. In Fourier analysis terms, the modulation occurs at the
second harmonic for a source at our finite distance; whereas the
modulation would occur at the fundamental for a source at infinite
distance.
It is worth noting that in the case where
the grid slit/slat ratio = 1, no modulation occurs, because the area of the
rear grids where X rays pass through does not change with source position.
However, if the slit/slat ratio is appreciably different than 1, significant
modulation occurs. Design studies for some Fourier imagers have adopted the
60:40 slit/slat ratio as a suitable choice, independent of considerations of
end-to-end tests. Maximum modulation as a function of slit/slat ratio would
occur if slit/slat = 1:2 or 2:1, but such ratios are undesirable for other
reasons.
We are currently studying various concepts for the source of X rays. One
possibility is a bremmstrahlung X-ray source (such as one which already exists
at Goddard, Code 313), or a radioactive source (of a few hundred micro Curies)
in an appropriate hard X-ray line. Both concepts have advantages and
disadvantages. The bremmstrahlung source is not portable, but it can be
turned on and off, and provides a spectrum which can be measured by the
detectors. The source size in such a machine may be as small as 10 microns,
which makes it possible to analyze collimators with grid pitches of order 30
microns. A radioactive source would be portable, but could not be turned off
(except by a shielding drum). The source size in this case could not be much
smaller than 1 mm, but a sequence of apertures in the form of a gridlet
(see Figure 2) could effectively reduce
the source size, while providing a periodic array of sources. The gridlet
could be the same as a small section of one of the collimator grids, and its
aperture could effectively be reduced by rotating the gridlet by a small
fraction of a degree from nornal incidence, using internal shadowing by the
slit sides.
Considering the likely range of source parameters, telescope
configurations and spatial scales, there appear to be no technological
show-stoppers in designing a suitable end-to-end hard X-ray test along
these lines.
