How does RHESSI make images?
An important observational goal of
RHESSI is to make sharp images of solar
flares in X-rays and gamma-rays at energies from 3 keV to 15 MeV. Over much of this energy
range, there is no known material that can effectively reflect or refract X-rays.
How do we make sharp images if we cannot use lenses or mirrors?
The answer is to selectively block the X-ray photons. If this is done in
a way that depends on which direction the photons are coming from,
then we can get the information needed to make an image.
In practice we rapidly block and unblock incoming photons and use the
pattern of rapid time-variations in the observed signal to tell us the exact
direction to the X-ray source(s), their size, shape, strength, etc - in
short, all the information needed to make an image.
The device that does this is called a 'modulation collimator,'
an invention attributed to
Such a collimator consists of a pair of widely spaced grids located in
front of a good-sized X-ray detector (needed for sensitivity).
The grids have large numbers of parallel slits and slats made
from a heavy material (tungsten
that is effective at stopping X-rays. The detector, located behind the
grids, tells us the exact arrival time and energy of those X-rays that
succeeded in getting through both sets of slits.
Of course, it doesn't know about the X-rays
that got stopped along the way.
This is illustrated in Figure 1.
Figure 1: An illustration of how the grids (slats seen end-on in
red) block the X-rays seen by the detector (blue rectangle) below the
grids. The plot at the bottom plots the number of detected X-rays
Click the plot to see what happens as the incident angle is changed with time.
Note: The animation may play slowly the first time through.
In the figure, the slats in the top grid cast an X-ray shadow onto
the rear grid where a fraction between 0 or 100% of the
remaining X-rays will reach the detector. This fraction depends on whether
the shadow falls on the slits or the slats in the rear grid. To go from
one extreme to the other requires a only a very small change in angle and
so provides the basis for making very sharp images. The change
in angle (in radians) is just equal to the ratio of the slit-to-slat distance to the
separation of the grids. If two grids like those in Figure 2
are mounted 5 feet apart (as they are on RHESSI)
that angle is only 2.3 arcseconds, or about 1/850th of the diameter of the
Figure 2: A photo of one of RHESSI's grids. This one is made by stacking
about 60 sheets of molybdenum to make a single
1 mm thick grid with 9 cm across. There are
2646 slats here; they are too fine to
see in the photo (where they go from bottom left to upper right).
However they can be seen as the horizontal bars in the inset.
Each slat is separated from the next by 1/30th of a millimeter,
about the thickness of a human hair.
The movie shows that if we were able to change the incident direction of the X-rays,
the number of detected X-rays could be made to vary quite rapidly, giving a distinctive modulated
signal that can be measured. But how do we change the direction from which the X-rays come?
That's the easy part. The
collimator (grids and detector) are
mounted on a rotating spacecraft. (RHESSI is pointed towards the Sun and
spins at about 15 rpm.)
From the point of view of someone (or something) fixed on the spacecraft,
the stars, sunspots and
anything else in the sky (like X-ray stars or
for example) appear to move
in a circle about the center of the Sun as the spacecraft rotates.
(It's the same idea someone standing on the rotating Earth seeing
the stars slowly move in a circle about the north pole. For RHESSI, it takes 4 seconds to go around the circle
instead of 24 hours for the Earth. Looking
along the slats as in Figure 1,
the incident direction of the X-rays appears to move back and forth and so
we a get a rapidly modulated signal (called a modulation pattern).
How do modulation patterns like those in Figure 1 tell us source
characteristics such as strength, location,
size, shape, etc that we need to make an image?
That can be understood by seeing how the modulation pattern changes when
the source is changed in various ways. Below we reproduce the original plot in Figure 1
along with the solar source which would produce the modulation.
The following plots show what the modulation pattern looks like if we make one change at a time in the source.
Click on the plot to compare it to the original case
If the source were weaker, then the pattern just gets lower in amplitude
but otherwise doesn't change its shape.
If the source were located further from the axis of rotation, then there
must be more cycles
during each 4s rotation.
If the source were located the same distance from the axis of rotation
but at a different
angle compared to North, then the pattern is shifted in time, but otherwise stays the same.
If the source were larger in diameter but still put out the same number of
then the average number of detected X-rays would stay the same, but the
pattern gets smeared out and the variations get smaller.
Now that we've seen how each characteristic of the source (size, strength,
location, etc) has a distinctive effect on the measured modulation pattern,
we get to the tricky part. In practice we have to work backwords!
Instead of taking a known source and deducing what modulation pattern it
would give, we must
start with an observed modulation pattern and figure out
what the original source looked like.
Using the examples as a guide, this can be fairly straightforward if there
only one source and it has a simple shape.
Real solar flares aren't so cooperative, however - there are often several
sources at a time, some of which
might have more complicated shapes and all of which combine together to
give just one observed modulation pattern.
It's a nice mathematical puzzle to work
backwards and figure out the image that would give observed modulation
patterns that look like this.
How the RHESSI software solves this problem to generate images routinely
will be the topic of a future nugget. Stay tuned.
Gordon Hurford is a scientist at the Space Sciences Laboratory.