4 Test 1 - point-like sources

4.1 Input configuration

We address the problem of point-like sources separated by $15\hbox {$^{\prime \prime }$ }$(half-energy width of the on-axis PSF), $30\hbox {$^{\prime \prime }$ }$ and 60 $\hbox{$^{\prime\prime}$ }$with different flux ratios. We include the PSF model and background but do not apply the vignetting effect.

The raw input test image is shown in Fig. 2 (available on line) together with its Gaussian convolution, MR/1 wavelet filtering and WAVDETECT output image. Visually, the Gaussian image is quite noisy, while there are few spurious detections in the WT images.

4.2 Detection rate and positional errors

The number of missing detections and false objects are shown in Table 4.

 

 

Table 4: Test 1. Detection results. The total number of input objects is 36

Method	Missed	False
EMLDETECT	4	13
G+SE ($4\sigma$)	6	1
MR/1+SE	7	1
WAVDETECT	7	21
EWAVELET	6	4
VTPDETECT	12	19

The one sigma input-detect position differences are less than the FWHMof the PSF ( $6\hbox {$^{\prime \prime }$ }$) for all procedures and the maximum occurs for the blended objects, as expected. Note the large number of spurious detections with WAVDETECT, VTPDETECT and EMLDETECT.

Figure 3: Test 1. The three panels of each figure show the results in terms of the ratio of inferred counts SCTS(out) and input counts SCTS(in) as a function of the varying input counts for the three cases of object separations (indicated by $\delta r$). The mean and st.dev. of the corresponding points are also indicated. When there are no detections, the mean and the st.dev. are both zero. Objects with input counts fixed at 100 (squares) are placed beside their corresponding neighbors (circles), rather than being plotted at 100

4.3 Photometric accuracy

The results for the photometry in terms of the inferred to the input counts are shown in Fig. 3.

$\delta r=15\hbox{$^{\prime\prime}$ }$.

Only EMLDETECT detects two of the six fainter objects. None of the other procedures separates the objects and consequently the inferred counts are a blend from both sources;

$\delta r=30\hbox{$^{\prime\prime}$ }$.

The proximity of objects influences the detection and the photometry. EMLDETECT and EWAVELET show the best detection rate results while all the other procedures miss one of the faintest objects;

$\delta r=60\hbox{$^{\prime\prime}$ }$.

We can safely assume that the objects are well separated. The recovery of the properties is informative for the performance of the tested procedures. It is clear that the general flux reconstruction error (taken to be the spread of the points around the unity line in Fig. 3) is about 15% for brighter sources and goes down to 20-25% for the faintest ones. [In our 10 ks exposure tests and with the adopted background in band [0.5-2] keV, we assume the objects with input counts of 20 photons ($\sim$10^-15 erg/s/cm²) to be at the detection limit when there is no confusion by nearby sources.]

4.4 Discussion

After this simple test we can eliminate the VTPDETECT: in addition to the very large execution time, some of the VTP-detected object centres were shifted by more than $20\hbox{$^{\prime\prime}$ }$ from their input positions - a consequence of its ability to detect sources with different shapes where the object center can be far from the input position. Moreover, VTPDETECT percolates all the double sources into single objects at $\delta r=30\hbox{$^{\prime\prime}$ }$, which all other procedures were able to separate.

No procedure unambiguously shows best results - both in terms of the detection rate, spurious sources and photometric reconstruction. EMLDETECT outperforms the others in terms of detection rate but with the price of many spurious detections. Using exactly the same PSF model as the one hard-coded in EMLDETECT leads to much better photometric reconstruction.

All other procedures are comparable: EWAVELET showing better detection but its photometric reconstruction is far from satisfactory - about half of the photons were lost at $\delta r=30\hbox{$^{\prime\prime}$ }$ and $60\hbox {$^{\prime \prime }$ }$, because of the assumed Gaussian shape used to derive analytically extension and counts. We have applied a simple correction for the object size to arrive at the good photometric results for EWAVELET presented in Fig. 3.