- Demonstrate the feasibility in space of X-ray interferometry for astronomical applications.
- Provide an imaging of celestial X-ray sources with resolution of 100 micro-arcseconds, 5000 times better than the Chandra observatory.
The first step in utilizing X-ray interferometry for astronomical purposes is to design a mission where the baseline allows the optics to be contained within a single spacecraft. This will be a necessary first step to demonstrating both the technology required for the full up MAXIM (where the baseline is hundreds of meters) and the science that can be achieved with an X-ray interferometer. A baseline of 1.4 m is well within the envelope of current spacecraft and achieves an impressive resolution of 100 microarc seconds, an advance of 5,000 over current capabilities (For comparison, to achieve the same resolution in the radio at 6 cm wavelength would require 120,000 kilometers).
|Table 1: Performance Requirements
|Field of View
||0.5-2 + 6 keV
|Spectral Resolution (E/dE)
Absorption in the interstellar medium causes most of the most interesting targets to be obscured below 0.5 keV, so the telescope must operate between 0.5. To obtain a reasonable band pass we set an upper threshold of at least 2 keV (effectively covering the ROSAT and Einstein bands). We know from previous missions like Einstein and ROSAT, that 100 cm2 supports excellent work on a large variety of objects. We do not expect or need to move to new targets hourly. A new target every few days would allow the mission to return a spectacular set of about one hundred unique images per year. Thus modest collecting area and leisurely target acquisition are acceptable.
To avoid the potential difficulties of building diffraction limited X-ray optics we have baselined the flat mirror interferometer in the "x" configuration as demonstrated in the laboratory. Table 2 summarizes the characteristics of the interferometer design, while Figure 1 shows the layout of such a system schematically in two dimensions.
This reduces the optics problem to its absolute minimum. Flats are the easiest mirrors to fabricate and to align. The problem is that to achieve adequate fringe magnification the beams must cross at a very low angle as shown in Figure 2. To magnify 1 nm waves to 100 micron fringes requires a cross angle of about 2 arcseconds, which implies that L will be large.
|Figure 1: The basic arrangement of the interferometer involves four flat mirrors in an "x" shaped configuration.|
|Figure 2: The beams from the two apertures must cross at low angle to achieve large fringe width.|
The size of L is in turn driven by the size of d, the spacing between the flats in the beam converger. Our design requirement of 100 cm2 enters here. We will need 32 flat mirrors in a ring to achieve a nice field of view, so each mirror channel should have about 3 cm2 of effective area. Allowing for losses due to the two reflections and the detector, we find the aperture should be 3 cm square. Fitting 32 such mirrors in a ring requires a 30 cm diameter, which we use as the baseline separation in the beam converger.
|Figure 3: Interferometric patterns created by flat mirror pairs in a ring. Two mirrors create lines (fringes), while additional mirrors create more complexity and greater image clarity.|
The effect of bringing 32 flats in a ring into phase coherence is dramatic as shown in Figure 3. The figure is a simulation of the pattern resulting from a monochromatic point source. With two mirrors the detector records the expected sine wave. With four mirrors we find a checkerboard. As the number of mirrors rises, the pattern first becomes complex, and then starts to clear out the region around the central point of constructive interference. We are, effectively, building a diffraction limited telescope out of flat subapertures. As the pointing changes, the bright spot moves around the field of view just as in a telescope. For the 32 mirror case, an excellent image 64 x 64 pixels in extent is achieved without inversion of fringes. For wider fields of view, there is a substantial power to be found in the surrounding rings, that must be removed through image processing.
|Figure 4: Rendering of the two rings of mirrors shown with 8 mirrors per ring.|
An interferometer consists of two rings of flat mirrors. Figure 4 shows a 3-D rendering of the arrays. Only 8 mirrors per ring are shown for clarity, when the interferometer will have 32 per ring. Each mirror will be mounted on precision actuators that will allow in-flight alignment. The mirrors themselves will be 3 cm wide and 90 cm long. They can be as thick as required, because there is no nesting envisioned. The total amount of glass in each interferometer is about the equivalent of a 1m square mirror.
|Table 2. Interferometer Characteristics
|Primary Ring Diameter
|Secondary Ring Diameter
|Distance: Primary to Secondary
|Distance: Secondary to Detector
||3 x 90 cm
|Number of Primary Mirrors
|Number of Secondary Mirrors
|Mirror Quality @ 6328 Angstroms
||Ir + Multilayer
|Resolution @ 0.25 keV
|Resolution @ 1 keV
|Resolution @ 6 keV
|Fringe Width @ 1 keV
|Fringe Width @ 6 keV
|Field of View
||01-2 keV + 6 KeV
The primary ring of the prime interferometer will consist of 32 mirrors with actuators in a ring 1.4 meters in diameter. The resolution of such a ring is given by (l/2D, where D is the diameter of the ring. This supports resolution of 70(as at 1 nm, and 100(as at 0.9keV.
|Figure 5: Simple model for the effective area of the interferometer. We have included the double reflection off iridium, the efficiency of typical CCD and the transmission of 800 A of aluminum to reject visible light. This does not show the narrow throughput spike at 6keV that can be added by the use of multilayers.|
Note that the resolution is given as (l/2D, not the usual (l/D. The usual formula is appropriate for a filled aperture telescope, where, when the outer edges of the mirror are 180 degrees out of phase, most of the center is still in phase. Also, consider that in an interferometer, an angle change of (l/D will cause a the a full fringe shift, but we can resolve two stars when they are half a fringe out of phase, indicating the resolution is (/2D. Our use of a single ring creates large diffraction rings, but it also doubles the resolution.
The effective area is shown in Figure 5. It reaches 100 cm2 around 0.5 keV and holds a high level to near 1.5 keV. It falls severely near 2 keV. A possible enhancement will be the addition of multi-layers on the mirrors to provide an enhanced collecting area in the 6 keV band (where the iron K line is dominant). The wide field interferometer has an identical set of secondary mirrors to the main interferometer, and its primary mirrors are also the same. However, its primaries are set close together, looking identical to the secondaries around a 30 cm ring. They are pointed out at space instead of at the detector.
Pathfinder concept is shown in Figures 6 through 8. The mission consists of an array of grazing incidence mirrors on a mirror spacecraft, creating X-ray interference fringes that are detected on a second detector spacecraft 450 km away.
|Figure 6: Schematic of Maxim Pathfinder in the two spacecraft configuration.|
|Figure 7: Schematic of optics spacecraft viewed from the end. We show only 8 of the 32 mirrors in the inteferometry array for clarity.|
|Figure 8: The main components on the primary spacecraft are the interferometer mirror rings, the two visible light aspect interferometers, and the laser ranging system. On the other spacecraft are range sensors and the detector.|
Optics Spacecraft: The interferometer will consist of two rings of flat mirrors. Each ring will contain 32 flat mirrors, each fine adjustable to achieve zero null on axis. A laser metrology system will be used to maintain the necessary alignment to 10 nm, with reconstruction to 1 nm. The optics spacecraft that carries the interferometers is about 2.5 meters in diameter and ten meters long. In most respects, such as power and mass, it will be conventional. In the area of pointing stability it must be exceptional. The pointing stability is about 300 micro-arcseconds, with reconstruction of attitude to 30 micro-arcseconds. The pointing information will be generated by two visible light interferometers based on those to be demonstrated on the Space Interferometry Mission (SIM) that will view stars that lie approximately perpendicular to the target line of sight and to each other.
Detector Spacecraft: A quantum calorimeter array for the detector will provide the necessary resolution of E/DE of 100-1000. It will be about 30 mm square with 300 micron or smaller pixels. Energy resolution of 2 eV at 1 keV will allow the fringe coherence to be maintained. The interferometer has a wide field of view, so an array of 3 cm CCDs will surround the quantum calorimeter to increase the field for the observation of extended objects and to centroid on poorly known target positions.
Formation Flying: The detector spacecraft must hold its position in space relative to the telescope spacecraft, to about a tenth of a fringe spacing (1 mm). This can be accomplished using a laser ranging system between spacecraft and microthrusters to offset drifts.
Orbit: Because the two spacecraft need to be stable relative to each other and to the celestial sphere, we must move the mission away from low Earth orbit. Either a drift-away orbit or other deep space orbit would be appropriate.
Some targets will have celestial coordinates accurate to milli-arcsecond level, having been observed by SIM, but many will not. Some targets cannot be observed in the visible, others are too faint or in confused fields. Even if we tried to use this information, building an instrument to re-establish that coordinate system would be difficult. It appears we need a "finder scope".
The approach is to use a modest size Wolter telescope with arcsecond resolution (possibly a Chandra spare shell). This will only 10 or 20 cm2 to function well, as its purpose is to locate the target, given coordinated good only to a few arcseconds. This Wolter can have resolution as large as 5 arcseconds and use the 10 meters of the optics spacecraft as its focal length. Better resolution would be helpful in target acquisition, and it is likely that a Wolter in 0.5 to 1 arcsecond quality range will affordable in this timeframe. The target would be acquired within its field of view based on conventional startracker pointing. Pathfinder would center the target to within one resolution element of the center. Centroiding should then provide pointing to about 0.15 arcseconds.
Because of the relatively large error we have created a large detector array at the focal plane. At 450 km, a 30 cm detector subtends 0.15 arcseconds, enough to find the source. Pathfinder can then complete the pointing. Thus, the detector array is designed for the crucial business of finding our target. However, the interferometer will generate an image, unblurred by aberration across the whole field, so there is a bonus scientific return for a target that has angular extent of a hundred milli-arcseconds instead of just ten.
During the early phases of the mission, the relative alignment of the instruments will need to be calibrated and adjusted so that the acquisition of targets can proceed smoothly. There is no chance that the relative alignment of the instruments will survive launch, so in-flight co-alignment will be needed.
Target acquisition can take place in the X-ray, but maintaining the pointing of the main spacecraft cannot be done in the X-ray. Two visible light interferometers --- one for pitch and one for yaw will provide the necessary attitude information. The interferometers will resemble those on SIM in that they will feature two apertures about 10 meters apart, feeding telescopes that create a white light null fringe. SIM will be able to achieve 4 micro-arcsecond information, so the Pathfinder requirements are directly achievable using the SIM approach.
The Pathfinder targets are scattered around the sky and bright reference stars are required at any arbitrary pointing position. SIM, through the use of an optical delay line, is able to work with stars in a fifteen degree square of sky. Unlike SIM, however, the Pathfinder does not need astrometry, but only needs drift information relative to the null, greatly simplifying operations.
One might question that a visible light interferometer, with its big, floppy photons, would be able to steer an X-ray interferometer. There are two reasons why this works. First, the baseline of the visible interferometer is longer by a factor of five. Visible light across 10 meters gives fringes that are separated by 10 milli-arcseconds. Second, and more importantly, the aspect stars are bright. The null fringe can be centroided to one part in 300, to achieve the sensitivity needed at the 30micro-arcsecond level. SIM expects to centroid another factor of 8, all the way to 4 micro-arcseconds.
The detector is located on a separate spacecraft that can be as far as 450 km from the mirrors, and yet it must be held properly in place. This will be accomplished with the use of precision thrusters reacting to error signals from a pair of laser ranging devices.
|Figure 9: The lateral position of the detector can be measured by sensing the optical path difference between two lasers.|
The beam exiting the converger mirrors at the back of the optics spacecraft is extremely slow, meaning that the depth of field is very large, meters or more. Thus we do not need to control the detector spacecraft particularly well in the focal direction or in orientation.
Arcminute class stability is sufficient for the image on the detector. The difficult direction is lateral drift. Here it is necessary to hold the spacecraft in alignment to a small fraction of a fringe. Since the fringes will be no finer than 100 microns, the knowledge needed will never exceed 10 microns, and position 3 mm. Figure 10 illustrates two lasers 2 meters apart at the back end of the Telescope spacecraft, shining at the detector craft. As the detector drifts to the side, the pathlengths from the two lasers will start to diverge by an amount:
opd = (D/L) * e
where e is the size of the lateral drift. Noting that e/L must be held to about 30 micro-arcseconds, and D is about 2 meters, then the opd must be detectable at the 0.3 nm level, or (l/2000. Laser ranging systems can currently reach 2 pico-meters, so this is achievable.
When the drift is detected, micro-thrusters must be used to correct the error. Such a system is under development for the ST-3 mission. Similarly, LISA will need formation flying and large spacecraft separations monitored by lasers, so Pathfinder should have an excellent technical base to draw upon.
The lengths of the paths that the X-rays travel are sensitive to errors in position and angle in the mirrors. They have to be held to a fraction of an X-ray wavelength, which means 100 picometers. The geometry of grazing incidence, however, relaxes the required tolerances. Figure 10 shows an analysis of the position tolerance for a flat mirror reflecting a plane wave at grazing incidence. In the direction of the mirror normal the position tolerance is relaxed by a factor of 1/sinq ( relative to a normal incidence reflection. In the direction of the ray travel, the relaxation is by a factor of 1/sin2q(, which is easier yet. For 1 nm radiation, we typically use a 2 degree graze angle, which, when inserted into the formula implies that the mirror must be held to about 1.5 nm relative to the mirror on the other side of the interferometer if the fringe is to be held to one tenth of a wavelength. This is the tightest tolerance.
|Figure 10: Position tolerance at grazing incidence.|
Figure 11 shows an analysis of the angular tolerance for each mirror in the interferometer. Its tightest tolerance is for an angular deviation in the in-plane direction. The figure demonstrates that each mirror should be held to one tenth of its own diffraction limit.. For Pathfinder each mirror must be aligned and held to about one milli-arcsecond if it is to hold the tenth fringe requirement.
|Figure 11: Angle tolerance at grazing incidence.|
A feasibility study for the MAXIM Pathfinder was undertaken at the Goddard Space Flight Center in August 1999. Figure 12 shows the resulting preliminary mission design. The IMDC study showed that the basic mission design outlined here is feasible. The detector and optics spacecraft can be launched together on a Delta IV class rocket. The feasibility study highlighted several technology challenges for further studies, including the station keeping. Further mission design studies are underway.
||Figure 12: A preliminary design concept for the MAXIM Pathfinder produced by the GSFC IMDC.