## Principles of timeresolved reflectance

Consider the injection of a short pulse of monochromatic light within a diffusive medium. By using a simplified description the medium can be regarded as consisting of scattering centres and absorbing centres, and the light pulse can be considered to be a stream of particles, called photons, moving ballistically within the medium. Whenever a photon strikes a scattering centre it changes its trajectory and keeps on propagating in the medium, until it is eventually re-emitted across the boundary, or it is definitely captured by an absorbing centre (see Fig. 8.2).

Fig. 8.2 Photon migration in turbid media: photon paths, scattering (O) and absorbing

Fig. 8.2 Photon migration in turbid media: photon paths, scattering (O) and absorbing

The characteristic parameters of light propagation within the diffusive medium are the scattering length ls and the absorption length la (typically expressed in units of mm or cm), representing the photon mean free path between successive scattering events and absorption events, respectively. Equivalently, and more frequently, the scattering coefficient ||s = l/ls (i.e. |ms = (ls)-1) and the absorption coefficient |ma = l/la (i.e. |ma = (la)-1) (typically expressed in units of mm-1 or cm-1) can be introduced to indicate the scattering probability per unit length and the absorption probability per unit length, respectively. To account for non-isotropic propagation of photons, the effective scattering coefficient |ms' = (1 - g)| is commonly used, where g is the anisotropy factor, that is, the mean cosine of the scattering angle.

In a diffusive medium light scattering in the visible and near infrared spectral region is naturally stronger than light absorption, even if the latter can be non-negligible. This implies that light can be scattered many times before being either absorbed or re-emitted from the medium. The phenomenon is therefore called multiple scattering of light. Multiple scattering of light in a diffusive medium introduces an uncertainty in the pathlength travelled by photons in the medium. Light propagation in turbid medium is therefore addressed by the term photon migration.8

Following the injection of the light pulse into a turbid medium, the temporal distribution of the re-emitted photons at a distance p (see Fig. 8.2) from the injection point will be delayed, broadened and attenuated. A typical time-resolved reflectance curve is shown in Fig. 8.3. To a first approximation, the delay is a consequence of the finite time light takes to travel the distance between source and detector. Broadening is mainly due to the many different paths that photons undergo because of multiple scattering. Finally, attenuation because absorption reduces the probability of detecting a photon, and diffusion into other directions within the medium decreases the number of detected photons in the direction under consideration.

10 I. | | ... . I.' | | | | | 0 0.5 1 1.5 2 2.5 3 3.5 4 Time (ns)

Fig. 8.3 Experimental TRS curve (diamond), IRF (dashed line) and best fit to diffusion theory (solid line).

### 8.4 Instrumentation 8.4.1 Photon migration

Photon migration measurements in the time domain rely on the ability to extract the information encoded in the temporal distribution of the re-emitted light, following the injection of a short monochromatic pulse in a diffusive medium. Typical values of the optical parameters in the red and in the near infrared part of the electromagnetic spectrum set the timescale of photon migration events in the range 1-10ns and fix the ratio of detected to injected power at about -80dB.

The two key points in designing a system for time-resolved measurements are thus temporal resolution and high sensitivity. Temporal resolution is mainly affected by the width of the light pulse and by the response of the detection apparatus. Pulsed lasers, which produce short (10-100ps) and ultra-short (10-100 fs) light pulses with a repetition frequency up to 100 MHz, and photon detection systems with temporal resolution in the range 100-300ps, are nowadays available. When concerned with sensitivity, the power of the injected light pulse should obviously be fixed at appropriate values, so as to avoid possible damage or injury to the sample. In the case of biological tissues the safety regulations9

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Fig. 8.4 Diagrams of the laboratory system (a) and of the compact prototype (b) for TRS

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Fig. 8.4 Diagrams of the laboratory system (a) and of the compact prototype (b) for TRS

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set the maximum permissible value to 2mWmm-2 for laser pulses in the wavelength range 600-1000nm. In the following, two different systems for time-resolved reflectance measurements based on the time-correlated single-photon counting (TCSPC) technique10 are described (see Fig. 8.4). The first system is a laboratory set-up for broad band absorption and scattering spectroscopy by time-resolved reflectance, whose primary use is for basic studies of tissue components and structures. The second is a compact device working at selected wavelengths, which can be easily moved and therefore used in the field. Results from the two instruments will be presented below.

8.4.2 Time-resolved spectrometer for absorption and scattering spectroscopy in diffusive media

The optimal trade-off between sensitivity and temporal resolution in a TRS system can be achieved using mode-locked lasers as light sources and time-correlated single-photon counting for detection. The sources available are a dye laser (Mod. CR-599, Coherent, Ca) and a titanium:sapphire laser (Mod. 3900, Spectra-Physics, Ca). Both sources are optically pumped by an argon laser (Mod. Innova, Coherent, Ca) running in mode-locking or continuous wave (CW) regimes, respectively. The dye laser is operated with a DCM (4-(dicyanomethy-lene)-2-methyl-6-(4-dimethylaminostyryl)-4H-pyran) dye that permits tunability between 610 and 700nm. Synchronous pumping mode-locking together with a cavity dumper yield pulses shorter then 20 ps (full width at half maximum, FWHM) at a repetition rate of about 8 MHz with an average power of 10mW. The titanium: sapphire laser is tunable between 700 and 1010 nm using two different mirror sets. The laser structure is properly modified to produce a mode-locking regime by means of an acousto-optic modulator, with pulses of about 100ps (FWHM), a repetition rate of 100MHz, and an average power of 100-1000mW over the entire spectral range.

The laser light is injected to, and collected from, the sample by means of 1 mm core 1 m long plastic-glass fibres set on the fruit surface at a relative distance of 1.5 cm. An appropriate fibre holder keeps the fibres in contact with the sample, one parallel to the other, which avoids collection of directly reflected light. The distal end of the collecting fibre is placed at the entrance slit of a scanning monochromator (Mod. HR-250, Jobin Yvon, France), coupled to a double micro-channel plate photomultiplier (Mod. R1564U, Hamamatsu, Japan). A small fraction of the main laser beam is split off by means of a glass plate, and detected by a fast PIN (P-type doped, intrinsic, N-type doped silicon) photodiode, which provides a triggering (reference) signal. Also, some laser light is coupled to another optical fibre and fed directly to the photomultiplier to provide an on-line monitoring of the system behaviour.

An electronic chain for time-correlated single-photon counting then processes both the photomultiplier signal and the triggering signal. The signals are first delayed by stages, and then preformed by constant fraction discriminators (Mod. 2126, Canberra, Co). The relative delay between the signals is then converted into a voltage signal by a time to amplitude converter (Mod. TC862, Oxford, TN), which is processed by a multichannel analyser (Mod. Varro, Silena, Italy). The temporal width of the instrumental transfer function is <120ps (FWHM) as measured by connecting the injection and collection fibres.

The whole system of measurements is driven by a personal computer that automatically controls laser tuning, light attenuation, scanning of the monochroma-tor, data transfer from the multichannel analyser, data visualisation and eventually data storage for further processing.

8.4.3 Compact prototype for time-resolved reflectance measurements

The system employs two pulsed diode lasers (Mod. PDL 800, PicoQuant GmbH, Germany) at 672nm and 800nm with a pulse duration of about 100ps, a repetition rate up to 80 MHz and an average power of 1 mW. The pulsed diode laser is coupled into a multimode graded-index fibre (Mod. MMF-IRVIS-50/125, OZ Optics, Canada).

The signal is then split into two fibres by a fibre optic splitter (Mod. FUSEDIRVIS 5/95, OZ Optics, Canada). The first fibre receives a small fraction (5%) of the power and is fed directly into the photomultiplier to account for eventual time drifts of the instrumentation andtoprovideatimereference.The other fibre receives most of the power and deliverslighttothesample.The re-emitted light is collected from the sample by 1mmplasticfibres(Mod.EH4001,ESKA) in reflectancegeometry.

The TRS curves are detected by a metal-channel dynode photomultiplier tube (Mod. RS5600U-L16, Hamamatsu, Japan)andaremeasuredbyatime-correlated single-photon counting PC board (Mod. SPC300, Becker&Hickl GmbH, Germany) with 1MHz acquisition frequency and 25 ps temporal resolution. Custom made software, written in LabWindowsand ANSIClanguages,control date acquisition andanalysis.

The typical instrument response function, obtained facing the injection fibre and the collection fibre, has a FWHM of about 200ps for both wavelengths.