We made computer simulations to compare the quality of images from
direct demodulation with that from cross-correlation deconvolution and
other methods for the same simulated RMC data. The following
normalized cross-correlation function was used in our calculations
To estimate the background, we calculated
then found the bin with maximum s(i) and subtracted the contribution
of the apparent discrete source at point i from the data. The
background data
was obtained by repeating the above procedure until the maximum value
of s(i) was less than a given threshold. The background b can be found by
solving Eq. (10) iteratively. In the iterations, a continual
constraint was used, i.e. the difference between two neighbouring bins
should not be greater than a certain value.
In the simulations, we used an RMC telescope structured as in Fig. 1 (click here) with
strip width a=1.0 cm, the separation of the two grids H=95 cm, the
total active area of the detector 1000 cm2 and
FOV
.
To avoid "ghost'' peaks in the image, we set up a 0.5 cm offset between
the grids in the two planes.
The background is assumed to be 0.09 counts cm-2 s-1
and the observation time is 24 hours.
We first supposed that only a single point source exists in the FOV at the
position 
(see Fig. 3 (click here)a) with a flux of
ph cm-2 s-1.
The rotating period was divided into 400 units (m=400).
A Monte Carlo sample of observed data of the RMC
telescope was produced. The cross-correlation map and CLEAN
cross-correlation map from the simulated data are shown in Figs. 3 (click here)b
and c respectively. For the same simulated data, we did image analysis by
the direct demodulation method and got the result shown in Fig. 3 (click here)d.
From the direct demodulation map, we find the position of the point source at
and flux
ph cm-2 s-1, which is
consistent with the assumed values. The errors of the position and counts
are the standard deviations of values of the quantities measured for images
from twenty Monte Carlo samples.
Figure 3: Images from the simulated data of a single point source observed by a
RMC system with height H=95 cm, strip width a=1.0 cm and
FOV=
.
a) Object. b) Cross-correlation map. c) CLEAN cross-correlation map.
d) Image from direct demodulation
It is clear from comparing Fig. 3 (click here)d with Fig. 3 (click here)b that
the direct demodulation technique can significantly improve the angular
resolution. The FWHM of the point-source image in Fig. 3 (click here)d from DDM is
, much smaller than that in Fig. 3 (click here)b from CCM, 
.
The cross-correlation maps, Fig. 3 (click here)b and c, show severe sidelobes around the image of the point source. The image derived by using the direct demodulation technique with the same simulated data, Fig. 3 (click here)d, has a much clearer background.
Figure 4: Discriminating two nearby sources. a) Object scene.
b) Cross-correlation map. c) CLEAN cross-correlation map.
d) Image from direct demodulation. e) Image from Richardson-Lucy
iterations
For further comparing the angular resolution ability of the two methods,
we set up two point sources placed at and
with fluxes
ph cm-2 s-1 and ph cm-2 s-1,
respectively.
The results of image analyses by CCM, CLEAN CCM and DDM
are shown in Figs. 4 (click here)b, c and d, respectively. From Fig. 4 (click here)d, one can see
that the direct demodulation technique can clearly discriminate the two point
sources with a separation smaller than the intrinsic resolution of the
telescope, while the cross-correlation and the CLEAN cross-correlation
cannot. Figure 4 (click here)d gives two point sources sited at
and
with fluxes
ph cm-2 s-1 and
ph cm-2 s-1, respectively.
We also tried the Richardson-Lucy algorithm (Richardson 1972;
Lucy 1974)
and got an image shown
in Fig. 4 (click here)e, in which many false sources appear and from which the fluxes
of the two sources are 
ph cm-2 s-1 and
ph cm-2 s-1, much less than the assumed values.
It is difficult to give correct source locations and intensities
in the case of multi-source imaging
with a single RMC and the cross-correlation deconvolution.
Simultaneous imaging for both point and extended
sources is also difficult by a single RMC.
Figure 5 (click here)a shows an object scene with two point sources and an extended
source. The fluxes of the two point sources are assumed to be
and 
ph cm-2 s-1,
respectively, and the total flux
of the extended source 
ph cm-2 s-1.
The background, the observational duration and the RMC system configuration
are assumed to be the same as that in subsection 3.1.
Figure 5 (click here)b shows the cross-correlation map from the simulated data and
Fig. 5 (click here)c the CLEAN cross-correlation map, from which only the
strong point source can be identified. For the same simulated data,
we made a direct demodulation reconstruction and got the result shown in
Fig. 5 (click here)d. Besides the strong point source, an image of the weak
point source and structure of the extended source can also be seen from
Fig. 5d. The fluxes estimated from Fig. 5 (click here)d are 
and
ph cm-2 s-1 for the two point sources and
ph cm-2 s-1 for the extended source,
respectively.
Figure 5: Imaging for point and extended sources by a single RMC
with strip width a=1.0 cm, height H=95 cm and FOV=.
a) The object scene. b) Cross-correlation deconvolution.
c) CLEAN
cross-correlation. d) Direct demodulation reconstruction