How does RHESSI make images?
From RHESSI Wiki
|1st Author:||Gordon Hurford|
|2nd Author:||Steven Christe|
|Published:||29 August 2005|
|Next Nugget:||Small is steep|
|Previous Nugget:||RHESSI and quasi-periodic pulsations|
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 |M. Oda. 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 or molybdenum) 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 against time. 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 Sun!
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 gamma-ray bursters, 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 X-rays, then the average number of detected X-rays would stay the same, but the modulation 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 is 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.
Biographical note: Gordon Hurford is a scientist at the Space Sciences Laboratory.