Identification of overlapping spectra

On the direct image, let the location of an object i be x_i and y_i. On the grism image, the location of corresponding spectrum is from x_{min, i} to x_max,i and y_min,i to y_max,i, where x is the direction of the wavelength dispersion.

x_{min, i} and x_max,i are computed from the position of the object x_i, and the dispersion length as specified in grismspec.dat.

y_min,i and y_max,i are computed from the position of the object y_i, and, for point sources from the "width" of the weight and, for extended objects, from the size of the object as determined by SExtractor.

Two objects i and j overlap if they overlap in wavelength in the sense that

$$x_{min,j} < x_{max,i} \ \ OR\ \ x_{max,j} \gt x_{min, i}$$ (10)

and they are close in y

$$\vert y_i - y_j \vert < t_i \cdot (y_{max,i}-y_{min,i} + y_{max,j}-y_{min,j})$$ (11)

where t_i is one of several user-defined thresholds.

The user can define three thresholds called o_thresh1 (default: 0.05), o_thresh2 (default 2) and o_thresh3 (default: 3).

Three levels of overlap are used:

1.

overlap with o_thresh1, i.e. spectra almost aligned AND objects have same size (e.g. both point sources). In this case, we cannot correct for it and we only identify the wavelength range of the contamination. This wavelength range will be marked in the output plots in future releases of Calnic C.

2.

overlap with o_thresh2, but not case 1. This is the most interesting case: here we can correct for it.

3.

overlap with o_thresh3 but not with o_thresh2. In this case, there is no (or only very small) contamination, and therefore only a warning "potential contamination through nearby spectrum" is issued.

Below, only case 2 is discussed.

The first step is to identify overlap between any 2 spectra. Note that a spectrum can overlap with several other spectra.

Not every wavelength in the contaminated spectrum is affected. Say, the k-th wavelength point in spectrum for object j is called F_j,k, and the l-th wavelength point in spectrum for object i is called F_i,l. Let x_max,j and x_{min, i} be the minimum and maximum of the x-coordinates of a spectrum i, and similarly y_max,j and y_{min, i} be the minimum and maximum of the y-coordinates of a spectrum i (see figure 3.4).

For the case x_min,j < x_max,i, the following points in spectrum j are contaminated: F_j,k, where k=1 ... (x_max,i-x_min,j -x_i) AND the following points in spectrum i are contaminated: F_i,l, where l=(x_max,i-x_min,j -x_j) ... x_max,j-x_j

The case x_max,j > x_{min, i} can be written in an equivalent way.

 

Figure 3.4: Coordinates used to decide overlap of spectra.