Pulse dispersion

Figure 3.2 Variations in the relative degree of transit pulse dispersion in the case of conventional carrier transport. The specimen thickness is least for the broken curve and greatest for the dotted curve.

Fig. 21. Cumulative distribution of the pulse dispersion values of the same fibers as used in Fig. 20. Both the 50% and the 10% values are given which indicate the broadening at 50% and 10% of the pulse bright, respectively24). (Reproduced by permission of the Institute Internazionale delle Comunicazioni)...

Simple systems such as that shown in Fig. 5.11 yield an excellent optical efficiency, and are almost free of pulse dispersion and wavelength-dependent pulse shift. Another benefit is that the detection path is almost free of polarisation effects compared to monochromator-based systems. The high numerical aperture of the light eollection system further reduces the influence of the rotational relaxation see Fig. 5.9. With aspheric lenses an NA of around 1 can be achieved, and at an NA this high the polariser in the detection path can often be omitted. In the setup in the left graphic of Fig. 5.11, residual depolarisation effects can be removed by slightly tilting the polarisation direetion of the laser. 

The typical width of the time-of-flight distributions recorded in DOT is of the order of a few ns see Fig. 5.51 and Fig. 5.52, page 109. Therefore a detector IRF width of 150 to 300 ps is normally sufficient. Even longer detector IRFs are sometimes tolerated, especially if the pulse dispersion in long fibre bundles dominates... 

A cracial part of optical tomography instruments are the fibres or fibre bundles used to transmit the light to the sample and back to the detectors. The problem of the fibres is mainly pulse dispersion. The pulse dispersion in multimode fibres increases with the numerical aperture (NA) at which they are used. In particular, the detection fibre bundles, which have to be used at high NA, can introduce an amount of pulse dispersion larger than the transit time spread of the detectors [326, 443]. If the length of the bundles exceeds 1 or 2 meters, a tradeoff between time resolution and NA must often be made. 

In practice, the only feasible solution is often to transfer the light to the poly-chromator slit plane by an optical fibre. The slit is removed, and the numerical aperture at the input of the fibre is reduced to match the numerical aperture of the polyehromator. Because only moderate wavelength resolution is required, a relatively thick fibre (up to 1 mm) can be used. Therefore a reasonably high coupling efficiency with a single fibre can be obtained, even for nondescanned detection systems. The fibre should be not longer than 50 cm to avoid broadening of the IRF by pulse dispersion. 

A TCSPC oscilloscope mode is implemented in most advanced TCSPC modules. The mode has become an indispensable tool for a large number of technical jobs. Alignment and optimisation of optical systems often requires not only maximising the efficiency but also localising and removing optical reflections, leakage of excitation light, or pulse dispersion. 

Pulse dispersion and pulse shift can be avoided by using a double monochromator of the subtractive dispersion type. In this design the second monochromator is turned 180 °, and the gratings are moving in opposite directions. Thus the path length differences for both sides of the gratings and for different wavelength cancel. 

Due to their high throughput eapability, multimode fibres are frequently used to transmit light in optical systems for TCSPC. Figure 7.22 shows how NA and pulse dispersion can be traded against fibre diameter. 

The light from the source, in this case a laser diode, is transferred to the fibre input cross section by a transfer lens system. The first lens is the laser collimator, with a focal length, fl, which is normally a few mm. If the collimated beam is focused into a fibre by a lens of a longer focal length, 12, all aberrations in the laser beam profile are magnified by a factor M = 12 / fl. This requires a fibre of a eorrespondingly large diameter. However, the NA of the beam coupled into the fibre, and eonsequently the pulse dispersion in the fibre, is reduced by the same ratio. 

If a lens of short foeal length is used, e.g. a seeond laser diode collimator, magnification of the aberrations is avoided. Now the laser ean be coupled into a thin fibre. However, the NA is large, and so is the pulse dispersion. An example is shown in Fig. 7.23. Pulses from a 650 nm, 45 ps diode laser were sent through a 1 mm fibre of 2 m length. The pulse shape shown left is for an NA of 0.3, the right pulse shape is for an NA of < 0.1. 

Fig. 7.23 Pulse dispersion in a multimode fibre of 1 mm diameter and 2 m length. The pulses of a 650 nm, 45 ps diode laser were sent through the fibre and detected by an R3809U MCP PMT. Left NA = 0.3, fwhm = 117 ps. Right NA < 0.1, fwhm = 54 ps...

Another point to be considered is the pulse width of the light source and the pulse dispersion in the optical system. Multimode fibres or fibre bundles used at high NA can easily add a few hundred ps to the IRF widths. It is, of course, not necessary to use a detector that has an IRF width shorter than 30-50% of the pulse dispersion of the optical system. 

FIGURE9.il Pulse dispersion. (Courtesy of Corning Cable Systems LLC and Corning Inc.)... 

The slight change in value of the optimum profile exponent from to q due to profile dispersion is given approximately by 5q = — 2p, assuming the weak-guidance expressions in Eqs. (3-8) and (3-20). Althou dq, is small, it nevertheless has a dramatic effect on pulse dispersion. We calculate the ray dispersion t = —... 

Olshansky, R. (1978) Optical waveguides with low pulse dispersion over an extended spectral range. Electron. Lett., 14, 330-1. 

Barrel , K. F and Pask, C. (1980) Pulse dispersion in optical fibres of arbitrary refractive-index profile. Appl. Opt., 19, 1298-1305. 

We begin by determining the power exciting leaky rays on fibers illuminated by a diffuse source, and then show that the spatial transient is accurately and simply described in terms of a single dimensionless parameter which embraces all the physical quantities of the problem. The effect of leaky rays on pulse dispersion is also expressible in terms of this parameter. We then show how... 

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