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1. Introduction

Imaging is a difficult task in hard X-ray and soft tex2html_wrap_inline982-ray astronomy. For soft X-rays (<5 keV), one can get images with reflecting optics directly. For high energy tex2html_wrap_inline982-rays (>10 MeV), multilayer spark chambers can be used, in which the direction of an incident photon may be determined from the electron-positron pair that it creates. But in hard X-ray and soft tex2html_wrap_inline982-ray range (from tens keV to several MeV), these techniques are no longer useful. Imaging can be achieved only by applying aperture modulation techniques. The scanning modulation collimator with two grids was first put forward by Oda (1965) for imaging X-ray sources without focusing and without a position sensitive detector. Shortly after, it was suggested that a rotating collimator may be better (Mertz 1968). The RMC was first proposed for X-ray astronomy by Schnopper et al. (1968). The RMC technique was successfully used in a number of rocket flights (Schnopper et al. 1970; Cruise & Willmore 1975) and balloon-borne experiments (Staubert et al. 1983; Ubertini et al. 1985; Sood et al. 1996) for hard X-ray imaging. Nishimura et al. (1978) used a balloon-borne wide-field RMC instrument to localise gamma-ray bursts. In the mid-1970s, three satellites equipped with RMC systems, Ariel 5, SAS-3 and Hakucho, were launched. The hard X-ray RMC telescope WATCH is currently operating on the GRANAT satellite (Lund 1985).

Figure 1: Rotating modulation collimators

Figure 2: A typical modulation signature of RMC, which is the expected observed intensity I against rotating angle tex2html_wrap_inline994 for a point source with unit intensity

Figure 1 (click here) illustrates a typical structure of RMC. Two identical and parallel wire grids with absorbing and transmitting strips of equal width a are rotated about their axis. The transmission ratio of photon flux from a source will change with the rotation angle tex2html_wrap_inline994, which results in a temporal-modulated intensity of the photon flux transmitted to the detector. For a point source with coordinates (tex2html_wrap_inline1000) and intensity I0, the intensity received by the detector is
where tex2html_wrap_inline1004 is the modulation function of RMC
where tex2html_wrap_inline1006 is the detection efficiency, tex2html_wrap_inline1008 the integer which satisfies tex2html_wrap_inline1010 and tex2html_wrap_inline1012. There exists a "ghost'' image at tex2html_wrap_inline1014 which can be removed by a certain offset between the grids in the two planes.

The intrinsic angular resolution of the RMC system is

A typical modulation signature of RMC is shown in Fig. 2 (click here).

Compared with other techniques, e.g. coded aperture masks, RMC has a larger field of view and does not require a position-sensitive detector. RMC can be constructed in simple and cost-effective structure, which makes it attractive, particularly in wide-field monitoring.

Since the raw data of RMC is a modulated count rate varying with time, it needs a suitable inversion treatment for the observed data to reconstruct an image of the X-ray sky. The traditional technique to determine the source position is Fourier analysis of the intensity or cross-correlation analysis of the observed intensity function with the modulation function. Images from a traditional inversion technique usually have complicated sidelobes. Their sensitivity and angular resolution are not good enough in many practical cases. Imaging for extended sources is still a difficult problem for the RMC technique. The direct demodulation method (DDM) has been put forward in the early 1990s and proved to be effective in many inversion cases in high-energy astrophysics (Li & Wu 1992, 1993, 1994). We have made a simulation study to apply this technique to analyse RMC data and have gotten results showing significant improvement in the qualities of RMC images. We give a brief description of the direct demodulation method in Sect. 2. The results of applying the direct demodulation technique to analyse simulated RMC data are presented in Sect. 3 and brief discussions in Sect. 4.

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