Detector aperture

There are a variety of potential systematic errors in time-resolved measurements that relate to the effective detector aperture size, uniformity and position. These factors are directly influenced by the actual detector optodes (the fibre bundles), but also indirectly by the VOAs, because they vary the effective aperture of the detection system. While it is not yet fully understood exactly how, and to what degree, these effects compromise the measure­ ments, they are briefly discussed here.

7.6.1 Fibre bundle optode

The fibre bundle aperture size, position and uniformity affect time-resolved, as well as absolute intensity measurements. The latter are not considered here for reasons that were already outlined in a previous chapter. In order to understand the effect of these uncertain­ ties on time-resolved measurements, consider the variation in mean time as the source- detector separation is varied. Figure 7-12 illustrates a simple slab model in which a point source and detector are arranged in a reflection geometry.

Optode positioning uncertainty. The image reconstruction algorithms require the exact

coordinates of the source and detector optodes. Inaccurate values may result in artefacts and a generally degraded quality of the reconstructed image. It is evident from the slab model in Figure 7-12 that even a relatively small separation of 1 mm changes the mean time by about 50 ps. This is comparable in magnitude to the anticipated mean time perturbation (the ‘signal’) due to tissue inhomogeneities in an imaging experiment. It can therefore be

assumed that an error in the knowledge of the true optode coordinates of mm has a noticeable effect on time-resolved measurements. However, since the bundle is about 2.5 mm in diameter one may argue that there is little point in aiming for an accuracy in the optode position measurement of much less than, say, 1 mm.

Finite optode aperture size. The detector fibre bundle has a diameter of approximately 2.5

mm. The source fibre, although only 62.5 p.m in (core) diameter, is slightly withdrawn from the tissue surface in order to reduce the incident optical power density, resulting in an illuminated spot size of approximately 1 mm across. Since the sources and detectors are (currently) modelled by the image reconstruction software as point emitters and receivers, this corresponds to an appreciable systematic error, whose magnitude may again be approximated from the simple model mentioned above. Note that this error is proportionally larger for small source/detector separations.

Optode aperture non-uniformity. Visual inspection of the fibre bundles reveals that they are

not transmitting uniformly. Causes are likely to include imperfect assembly and polishing of the bundles, as well as dirty and damaged ends. The effect on temporal measurements is expected to be similar to those already discussed.

^3= 0.01 m m ' n ; = 1.0 m m ' S ource 50+ m m D ete ctor X 150 c 100 50.0 51.0 52.0 53.0

(a) w-_{70 mm}-M (b) Optode Separation [mm]

Figure 7-12 Chart illustrating the dependence of the mean time on the source-detector optode separation (b). The mean times were calculated using an analytical (Green’s function) model of a homogeneous slab in reflectance geometry (a).

7.6.2 VOA

The VOAs, whose design was described in detail in section 6.2.1.6, deliberately alter the

to mechanically obstruct light emitted from the fibre bundle end facing the VOA. Experi­ ments have revealed that this variation in the effective detector aperture has a non- negligihle influence on the temporal measurements, although the extent of this variation has yet to be fully examined. So far, at least, this problem has not been significant enough to inhibit the performance of imaging experiments, described in the following chapter. There appear to be at least two origins to the problem.

First, since the arrangement of the fibres in the bundles is ‘arbitrary’ (i.e. neither perfectly coherent, nor perfectly incoherent), placing an aperture of varying size (the VOA mask) at its output surface will, to some degree, affect the uniformity of its effective input aperture. The input aperture being the part of the fibre bundle surface facing the object that actually transmits light to the detector. The effect on temporal measurements is likely to be similar to those discussed in the previous section, except that it is also dependent on the VOA setting.

Second, changing the VOA hole diameter may alter the angular distribution of photons transmitted into the polymer fibre. If, for instance, higher order modes are preferentially transmitted, the delay and intermodal dispersion experienced by the detected photons in both the fibre bundle and polymer fibre are also increased. A possible mecha­ nism is that the loss of a proportion of large-angle photons emitted from individual fibres which are located near the edge of the fibre bundle may be greater for larger VOA hole sizes. Conversely, this ‘edge-effect’ is weaker for small VOA hole sizes, because the transmitting fibres are located near the centre of the bundle. There also appears to be a dependence on whether the input to the fibre bundle is collimated or diffuse.

The worst case scenario can be tested experimentally by placing the tip of a MON­ STIR source fibre (62.5 |im core diameter) directly in contact with the fibre bundle, resulting in i) selective illumination of only a fraction of the fibre bundle input aperture, and ii) near-collimated illumination. The instrument responses for this geometry corre­ sponding to the two extreme VOA settings (largest hole = maximum transmission and smallest hole = maximum attenuation) are shown in Figure 7-13. The difference in the two IRFs is very significant: the mean time is shifted by -73 ps and the shape of the curve is changed (broadened).

However, when performing an equivalent measurement on a phantom or actual tis­ sue (by putting the fibre bundle into direct contact), the resulting TPSF is much less dependent on the VOA position, probably because the fibre bundle is uniformly illuminated

with diffuse light. This is illustrated in Figure 7-14, which shows two nearly indistinguish­ able TPSFs recorded on a tissue equivalent phantom at the two extreme VOA settings. Nevertheless, there is a measurable change in the mean time of 13±2 ps^^, but in the opposite direction as compared to the IRFs in Figure 7-13. Note that any change in the TPSF shape is likely to affect other data types, such as the variance, more strongly (data types are discussed in section 8.1.3.1).

VOA P o s 1 (sm allest hole)

Î

B VGA P o s 8 (largest hole) œ 0.5

1

CC 0.0 -500 0 500 1000 Time [ps]

F igure 7-13 Instrument responses recorded for two VOA settings, where a source fibre was placed into direct contact with the detector fibre bundle. VOA Position 8 corresponds to the largest hole (maximum transmission) and VOA Position 1 to the smallest hole (minimum transmission).

I

i

1.0 VOA P o s 1 (sm allest hole)' VOA P o s 8 r (largest hole) 0.5 0.0 -2000 -1000 0 1000 2000 3000 4000 Tim e [ps]

F igure 7-14 Two nearly identical TPSFs recorded on a tissue equivalent phantom at the two extreme VOA settings. The little spike near the top of the curves is artefactual (an unrelated electronic problem in the PTA unit).

A similar measurement was performed for all eight VOA settings (holes 1 to 8), and the corresponding mean times are plotted in Figure 7-15. It confirms that the error in the mean time introduced by the VOAs appears to be of the order of 10-20 ps.

27

As pointed out earlier, this complex problem is not yet fully understood, and further investigations are in progress. Complications that remain to be addressed, but will not be discussed here any further, include:

• In an imaging experiment the expected errors are proportionally larger at small optode spacings because the TPSFs are inherently narrower and the mean time shorter.

• The error may be different for each detector channel, if not each source-detector pair. • There is a possibility that the strength of the reflection peak has a small dependence on

the VOA setting because of the variation in the aperture size.

30

IF

5 25 -

10 -

0 1 2 3 4 5 6 7 8

VO A Pos (smallest to largest hole)

F igu re 7-15 The mean time recorded on a tissue-equivalent phantom for all eight VOA settings (holes). The data points are average values with their corresponding standard deviations and were obtained from ten successive measurements.

In document Development of a Time-Resolved Optical Tomography System for Neonatal Brain Imaging (Page 160-164)