CARRETE DE ALMACENAMIENTO

The effectiveness of the convolution relations for datatypes described in section 2.1.3.1 depends on the influence of the additive noise term /(t) in [ 2.1.1 ]. Stochastic noise, shot noise and cross-talk are not convolved functions. Higher order moments such as skew are heavily dependent on such noise and its effects may overwhelm the corrections calculated for individual source - detector combinations. Background noise on calibration TPSFs may have far more effect on the datatype derived than the shape or temporal position of the actual TPSF, hence limiting the usefulness of the subsequent calibration. Although shot noise, stochastic noise and cross-talk can be reduced via hardware alterations (see section 2.1.1 ), processing for remaining non-convolved features is necessary.

2 .1 .3 .2 .1 Low p a s s filtering

High frequency noise removal using a low pass filter is inappropriate as a method of removing stochastic noise from TPSFs. This is because a low pass filter is simply a multiplication of the Fourier transform by a chosen window, which in turn represents the convolution of a constant function (the inverse Fourier transform of the window) in the time domain. As demonstrated in section 2.1.3.1, in most cases, convolving TPSFs with any constant function will simply change the subsequently derived datatype by a constant amount. Hence the absolute values of some datatypes (variance, intensity and Laplace) will be adversely affected by low pass filtering whereas mean and skew will be unchanged, the effects of the stochastic noise will remain. However, potentially, high frequency spikes due to shot noise could be removed using a median filter, which may help to reduce spurious errors in higher order datatypes.

2 .1 .3 .2 .2 Background subtraction

A background offset intensity will influence the calculation of datatypes. For example, the existence of apparent photon counts at flight times shorter than the ballistic photon time (where t = source detector separation / (c / n)), where c = speed of light and n is the refractive index) will produce an effect on datatypes not accounted for by the forward model. A background subtraction scheme will reduce the effects of a constant offset, such as that due to the level o f temporally un-correlated noise on a particular TPSF (dependant on thermal noise from the MCP-PMT and ambient light). To avoid features such as the pre-peak (section 2.1.1.3) representative background noise can be sampled at long photon flight times (i.e. following the region containing the main TPSF, where the tail of the TPSf is < noise). For datatype extraction from MONSTIR TPSFs, the last 160 data points are averaged into 16 bins

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(10 data points = 50 ps). The lowest value bin is then assumed to represent the background level. This method avoids the possibility of including the reflection peak (section 2.1.1.1). This background level value is subtracted from every data point in the TPSF automatically and before extraction of datatypes.

The low frequency background variation due to cross-talk in the 8-anode MCPs (section 2.1.1.4), may continue to affect datatypes following ’constant background’ subtraction. However it may be possible to adequately predict the magnitude and temporal position of such cross-talk, if the fraction of cross-talk occurring can be measured, and assumed to remain constant. However, note that if a cross-talk correction based on measured values is to be applied it must be subtracted before constant-background subtraction is performed.

2 .1 .3 .2 .3 D ynam ic windowing

The position of a TPSF in the data acquisition temporal window depends solely on the length of the fibres and cables for a particular channel compared to the length of the cables delivering the reference pulse to the PTAs. So a length of recorded data representing a 12500ps temporal window may have the TPSF in the centre, or perhaps shifted to the left or right. The position of the TPSF in the window, and its corresponding unique time-scale is accounted for in calibration, although central datatypes such as variance are unaffected by relative time-scale shifts. However, when we calibrate, we combine calibration TPSFs acquired on a number of different channels (e.g. all source calibrations are acquired using detector 1). We need to devise a way to ensure that the position of the TPSF in its temporal window does not adversely affect calibration of extracted datatypes. Figure 2.1.13 shows a typical TPSF along with a system IRF measured using the tool shown in Figure 2.1.2. Appropriate selection of the range over which to calculate a datatype from a TPSF can reduce the effects of the stochastic noise, shot noise and cross-talk either side of the TPSF which isn’t accounted for in modelled datatypes.

Figure 2.1.13 demonstrates that measurements from MONSTIR imply the arrival of photons before the ballistic photon time. Also, while the TPSF tail decays exponentially with increasing time, there is a clear point in this log-plot where background noise overwhelms any signal from the TPSF tail. Furthermore, not all channels have the same amount of data before or after the TPSF as each other. If we calculate TPSFs including these regions, we will extract datatypes that will never match those modelled by TOAST. This is particularly important for the central moments (variance and skew), which are more dependent on photons far from the mean of the TPSF (as shown in Figure 2.2.16 in section 2.2.6.2.1).

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