Through movement of the "aperture" a temporal modulation of the signal from the X-ray source of interest is introduced. For this method, a spatial resolution of the detector surface is not required.
A historically interesting way to "modulate the aperture" is to make use of the occultation of an X-ray source by another celestial body, e.g., the moon. As seen from the earth (or from a satellite), the moon scans certain parts of the sky and occults sources that happen to lie in the half degree wide strip of the moons path. By observing an X-ray source while the occultation is taking place, it is possible to measure the source position and in the case of extended sources their angular extent. Historically, important events were the moon occultations of the Crab nebula . The first European X-ray satellite EXOSAT was planned as a moon-occultation satellite and was put into a highly excentric earth orbit to increase the total area of the sky, which was occulted at one time or the other. Ironically, EXOSAT did not perform a single observation of a moon occultation. The 4-day long, highly excentric orbit, however, turned out to be highly useful, as it provided long uninterrupted observations and thereby allowed the performance of long-term timing studies of X-ray sources, especially of active galactic nuclei (AGN). Occultation by the earth has extensively been used by the BATSE experiment onboard the Compton Gamma Ray Observatory (CGRO) to monitor sufficiently strong persistent X-ray sources .
Historically, an important method to "image" the sky by "nonimaging instruments" was to perform scanning observations with flat detectors equipped with slat colli-mators. Of course, in one linear scanning measurement, the position is determined only in one coordinate (the sanning direction), such that at least a second scanning measurement in a different direction is needed, most usefully perpendicular to the first direction. The first All Sky Survey in the X-ray range was performed by Uhuru between 1970 and 1972, using two gas proportional counters with metal collimators defining fields of view of 5° x 10° and 2° x 10° (FWHM), respectively. Positions, flux levels, limited information on source extent, and rough spectra in the 2-6 keV range were measured for 339 sources (4th Uhuru catalog ). Several further satellites repeated such observations with higher sensitivity and extended energy ranges (most successfully HEAO-1, ), before the first truly imaging X-ray telescope was launched in 1978 on board HEAO-2, later called the "Einstein Observatory." The accuracy reachable through such scanning observations is a fraction of the instrumental angular resolution given by the opening angle of the collimator. The exact fraction is determined by the statistical accuracy by which the collimator response is reproduced by the observation.
There is an interesting proposal for a new hard X-ray (15-200 keV) All Sky Survey with greatly increased sensitivity and imaging capability: the Hard X-ray Modulation Telescope (HXMT) (planned in China) is supposed to carry 18 phoswich detectors (286 cm2 each) equipped with rectangular FOV collimators (0.5° x 5° FWHM), the orientation of which cover the entire circle in steps of 10° . The imaging capability of this multiangle scanning collimator instrument will be utilized by the direct demodulation method.
22.214.171.124 ON/OFF Observations
Even though it is not directly connected to the problem of "imaging," we mention here the technique of ON/OFF observations, because of its basic importance for all nonfocussing observational techniques. Assuming the position of the source is known, a series of observations (for a few minutes integration time each) are performed alternating between an orientation directly to the source ("ON") and an orientation to a background position ("OFF") (where the source is clearly outside the collimator response). The source flux and spectrum is found by taking the difference between "ON" and "OFF." The individual ON/OFF pointings are kept so short in time such that the background flux is not appreciably changing between successive pointings. This technique is used by the high energy X-ray timing experiment (HEXTE) onboard the Rossi X-ray Timing Explorer (RXTE) . For weak sources, the optimum strategy is to spend equal time in "ON" and "OFF." Then the sensitivity of such observations can be expressed through the minimum detectable flux, given by with k being the number of standard deviations by which the source is required to be detected above the background. An alternative method is to use a model of the background (found from repeated observations under different conditions) for subtraction. This method is used for the proportional counter array (PCA) on RXTE.
For measurements with higher angular resolution, collimators have been constructed, which consist of two or more planes (parallel to the detector plane) of parallel rods of absorbing material. The optical axis of such a system is perpendicular to the plane of the detector and the grids. A modulation of the incident flux occurs when the optical axis performs a linear scanning movement in the direction perpendicular to the orientation of the absorbing rods. For the case of two grids (see Fig. 5.1), it is easy to see that the overall transmission of the double grid varies regularly between zero (when the light that travels through the open slits of the upper grid is completely blocked by the lower grid) and one-half (when the two grids are aligned such that they form a common shadow). The transmission function (for small scanning angles) is a repeated triangle with wave length given by d/D (the instrumental angular resolution), where d is the width of the rods (and the slits between them) and D is the distance between the two grids. A higher resolution is achieved, when three or more grids are used (e.g., 4 in the A-3 experiment on board HEAO-1, see below). With a special choice of spacing of the grids, a response function can be produced, which avoids the ambiguity of a regularly repeated pattern and achieves a fine angular
surface of max. transmission
rotation axis surface of max. transmission
Fig. 5.1 (a) Principle of the aperture modulation by a double grid. (b) A rotation modulation collimator (RMC) measures a unique modulation curve (lower right) from which a sky image can be reconstructed 
resolution (e.g., 22arcsec ). Again, for two-dimensional measurements, scans in two or more directions are necessary.
A combined measurement of both coordinates and in fact imaging of the complete field of view (FOV) is possible if a double grid collimator as described in the previous section is placed in front of a detector and rotated (with constant angular velocity) around its optical axis. The flux reaching the detector is modulated in time by the variable transmission of the grid collimator. Such a device is called rotation modulation collimator. It was first proposed by Mertz  (see also ). Depending on the position of the source, a unique modulation curve is produced. For more than one source in the FOV, the resulting modulation curve is the superposition of the curves of all individual sources. The image is generated by a cross correlation procedure: The FOV is thought to consist of small image cells (sky pixels), each cell is then filled by the value of the cross correlation integral of the theoretical modulation curve (expected if the source is at the position of this pixel) and the actually observed modulation curve. Existing sources are represented in the image by a central peak and a system of concentric rings. The amplitude of the peak/rings is a measure of the source flux. Multiple sources can easily be imaged simultaneously and the position and flux of each individual source can be determined. Image imperfections like ghost peaks can be avoided by shifting the grid patterns against each other (by d/2) and by placing the rotation axis at the edge of the desired FOV .
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