APLICAR LOS PIGMENTOS CREADO EN LA CREACIÓN DE OBRAS

In Chapter 6 it was shown that there is a characteristic curve that relates the true centroid

position to the computed centroid position. The systematic errors associated, which are dependent on the centroiding algorithm that is employed, can be compensated for by defining boundary positions that give equal weight to the sub-pixel results programmed into the centroid LUTs. This technique, though, only provides the greatest accuracy if there are no changes in the characteristic curve over the imaged field. As will be shown here, if there are changes in the event profile as captured by the CCD over the field this then leads to locahsed residual characteristic curves. Although, from the error analysis carried out in Section 6.7, the residual minimally affects detector resolution it does lead to a degradation in image quality.

If a residual curve is present then the results as programmed into the centroid LUTs will not give equal weight to each sub-pixel. This then results in a Fixed Pattern Noise (FPN) in accumulated images that repeats every CCD pixel. The problem is then exacerbated if the residual is a variable over the imaged field as this will lead to different levels of FPN over that field. Simplistically, the error on any event centroid will depend upon:

• The size of the residual

• The position of the centre of that event with respect to the CCD pixels it subtends. Typical examples of FPN for the three algorithms defined in Section 6.2 are shown in Fig 7.1. When centroiding to 1/8 of a CCD pixel in both X and Y and being limited to a relatively low data rate by the dynamic range limitation of the detector (Section 8.3) it can take a very long

exposure (typically 1 2 hours) to accumulate sufficient data per sub-pixel to adequately measure

the level of FPN. To overcome this, it is assumed that over locahsed areas the FPN is a constant

which permits, via modulo 8 addition in both X and Y of the data in each CCD pixel, generation

of a high signal to noise ‘standard pixel’ that is also shown in Fig 7.1. This can then be used for accurate measurements.

In order to quantify this modulation a parameter called fpn has been defined as:

fpn = {max -min) / mean (7.1)

where max is the maximum value, min the minimum and mean is the mean value in the 8x8

'3^. * GAUSSIAN $ PARABOLA 4 CENTRE OF GRAVITY

F ig u r e 7.1. Flat field im ages (128x128 sub-pixels) acq u ired by the M IC system . An identical contrast level on the three im ages is used. A fixed pattern noise w ith a period o f 8 su b-pixels (1 C C D pixel) is clearly visible in the im ages generated by the C en tre o f G ravity and Parabola algorithm s. The im ages on the right rep resen t the m odulo 8 addition o f the d ata in each flat field im age and are used to calculate the FPN p aram eter being, in this case, 27% for the gau ssian , 66% for the parabola, and 75% fo r the centre o f gravity.

y\x 0 1 2 3 4 5 6 7 0 0.397 0.693 0.704 0.711 0.724 0.744 0.722 0.412 1 0.680 0.929 0.890 0.893 (1888 0.952 1.000 0.716 2 0.742 0.924 0.873 0.864 0.873 0.906 0.972 0.747 3 0.761 0.909 0.858 0.842 0.842 0.870 0.917 0.731 4 0.762 0.909 0.856 0.871 0.846 (1886 0.940 0.735 5 0.751 0.922 0.862 0.866 (1862 (1908 0.960 0.728 6 0.680 0.919 (F886 (1882 0.891 0.947 (1988 (1688 7 0.446 0.721 0.746 0.752 0.751 0.778 0.736 0.402

T a b le 7.1. Array form ed by the addition o f the values o f the corresponding sub -p ix els on an im age (the one labelled as C en tre o f G ravity in Fig. 7.1). T he resu lts are presen ted in the n orm alised form (each cell is divided by the value o f the biggest elem ent on the array). In this case m a x = 1.000, m in

If it is assumed that there are no variations in event profile across the detector field then the residual characteristic curve will just be governed by the CCD pixel sampling of the event profile. As an event typically covers 1 CCD pixel at FWHM it is undersampled by the CCD leading to a position dependent variation in captured profile and hence residual curve. It is important to note here that this affect alone inherently defines the curve and resultant FPN as being two dimensional in nature whereas centroiding in X and Y are carried out independently. This is discussed further in Section 7.2.4.

Any variations in event profile then add an additional FPN in accumulated images. These could result from a number of potential sources including :

• Tilt between, or non-uniformities in the surfaces of, the fibre optic components that optically couple the intensifier to the CCD.

• Non-parallelism between the MCPs and the output phosphor of the intensifier. • Shear and pin-cushion distortions in the fibre optic components, in particular the

fibre optic taper.

• Defects in the pore structure of the MCPs.

• Signal induced background (SIB) in the image intensifier contaminating the real event scintillations on the output phosphor.

• Charge transfer inefficiency in the CCD.

• Spatial coincidence between events in a CCD frame period.

Of importance to note is that all of these except SIB and event coincidence are fixed providing that the detector is mechanically stable and can thus be compensated for during data reduction. With high quality photon counting image intensifiers SIB should be minimal and can

be discounted. The errors associated with event coincidence are data rate dependent and cannot

he removed by, fo r example, dividing by a flat field.

Thus it can be expected that a level of FPN will be present in all images. How will this affect the quality of scientific data?. This can best be envisaged by using an example in spectroscopy. A single row slice (or cross section) through the Parabola flat field in Fig. 7.1 can be seen in Fig. 7.2. Now imagine that the detector is being used for analysis of faint absorption lines in a continuum spectra where the continuum will inherently contain this FPN. The absorption lines cannot be seen directly. As will be shown, flat field division during data reduction does not work accurately - it will bring out the features but their level will be wrong - for this type of detector artefact. To minimise the affect it is then necessary to fully understand the mechanisms associated and define observing constraints to meet scientific objectives. This analysis has been carried out by computer simulations and then a comparison against acquired data.

in n ni

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P o s i t i o n ( s u b - p i x e l s )

F ig u r e 7 .2 . A cross section o f the im age corresponding to the Parabola algorithm in F ig. 7.1.