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Some examples of the influence of optimal extraction

The algorithm is:

displaymath242

displaymath318

We will analyze the influence of the background on optimal extraction for the segment Lif 1a of the object: SK-66D172, ID: P117-22.
The average flux by pixel on the extraction area is 0.231658 counts/pixels.
Here are the weights for the real background which is 2.137617E-03 counts/pixels (a nearly 2ks exposure). The green correspond to tex2html_wrap_inline320 1, and the red to nearly 1.5:
tex2html_wrap334

Now, let's have a look of the different tex2html_wrap_inline248 with different S/N ratios:

With a background of 0.0001 counts/pixels ( tex2html_wrap_inline324 ):
tex2html_wrap336

With a background of 0.001 counts/pixels ( tex2html_wrap_inline326 ):
tex2html_wrap338

With a background of 0.01 counts/pixels ( tex2html_wrap_inline328 ):
tex2html_wrap340

With a background of 0.1 counts/pixels ( tex2html_wrap_inline330 ):
tex2html_wrap342

You can see clearly that for a given flux, the larger the background, the more the extraction is restricted to a small number of pixels.

You can also see that for a low background, the weights (well, most of them) are equal to 1 (green), which mean an extraction on the entire segment. This happen when you have a bright target, so already a good S/N ratio. But anyway, it is still unlogic to extract the spectrum on pixels that we known have only background. So we modified the tex2html_wrap_inline258 calibration file and put all probability which are below 0.05% equal to 0. Here are the new weights for the real background (2.137617E-03 counts/pixels), after doing the modifications:
tex2html_wrap344


Sylvestre Lacour
Mon Nov 5 22:07:31 EST 2001