Experimental Data Types

Diffuse optical data is collected from pulsed (time domain,TD), modulated (frequency domain, FD), or steady state (continuous wave,CW), light sources. The relative information content per source-detector pair of these DOS systems is TD>FD>CW. Detectors include photo-multiplier tubes (PMT’s), avalanche photo-diodes (APD’s), photo-diodes (PD’s), streak cameras, andCCDs. Some of the attributes of these data types are summarized in Table2.4.

Time Domain (TD) or Time Resolved Spectroscopic (TRS) techniques introduce a brief pulse of light into a medium and measure the broadening of this pulse due to the different trajectories taken by photons transversing the medium. Together with the tissue index of refraction, the mean of this transit time gives

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Time Domain

TD or TRS

Absolute optical properties with a single source and detector.

Expensive components.

Frequency Domain

FD Absolute optical properties require many frequencies or source-detector combina- tions

Relatively inexpensive components

Continuous Wave

CW Only relative optical properties Very inexpensive (_∼$20) components.

Table 2.4: Diffuse optical data types; note that spatially modulated data can be collected using any of the temporally modulated techniques.

the average photon path length, which is related to the absorption and scattering of the tissue44, 46, 94 (see also Section3.1.1). Most modern techniques use a streak camera95, 96 _{or Time-Correlated Single Photon}

Counting (TCSPC)5, 97_{devices to measure transmitted pulse profiles. The TCSPC technique relies on detec-}

tors (APDs or PMTs) operating in Geiger mode and a low photon flux: on average, each channel receives less than one photon per laser pulse (_∼2-70 MHz). The time of each photon arrival is recorded and a his- togram of arrival times is built up over an integration period; the results are fit to solutions of Eqn. 2.13

appropriate for the geometry and boundary conditions to obtain absolute values forµa [λ] andµ0s[λ].

In practice, TD measurements are limited by the TCSPC electronics maximum count rate (_∼1-10 MHz) to fairly low detected signal intensities, and thus longer integration times are required per source-detector position compared to similar FD measurements.

TD systems permit rejection of unwanted photons (e.g., those due to reflections in the system) through time-gating. For example, the length of optical fibers can be adjusted such that a reflection off the face of the fibers is separated in time from the data pulse; in an FD system, such a reflection could be a source of phase noise. Torricelli and colleagues98extended this concept by placing their source and detector directly

adjacent to one another and enabling their short rise-time detector onlyafterphotons experiencing specular reflection from the surface or only a few scattering events had arrived.

TD systems permit use of time-resolved data directly by fitting to time-dependent solutions to the diffu- sion equation. Information can also be codified by decomposition into temporal moments or by application of the methods of FD analysis (discussed below) to Fourier transformed TD data. These data types are addressed in detail by E. M. C. Hillman in her thesis99_{and by Liebertet al.}45_.

The phase of an amplitude modulated measurement (first suggested by Gratton100) encodes information

similar to the mean tissue transit time; current instrumentation typically utilizes frequencies from 30-200

MHz76, 88, 101–107with a few groups using up to_∼800 MHz108. These frequency domain (FD) measurements

are the Fourier analogues of the time domain measurements, but for practical reasons, most researchers measure one or a few frequencies instead of sweeping the frequency through a range (e.g. 300 kHz to

800 MHz as in Madsenet al.108_{). This frequency restriction reduces the information content of the FD}

measurements: those researchers (e.g. Bevilacquaet al.109_{) who use swept frequency devices have much}

more information per measurement than single frequency FD instrumentation. Swept frequency domain systems are currently limited to less than_∼1 GHz by the practical speed of modulation of source laser diodes and detector response time, while the frequency component of the TD signal extends to several GHz. However, single frequency lock-in electronics are relatively inexpensive and these single frequency instruments can be more economical than the TD or swept FD instruments, especially for systems with many detectors (e.g. Sevick-Muracaet al.110). FD systems also have the advantage of a significantly higher duty cycle than TD: the ‘signal’ is detected continuously, instead of a single photon per laser pulse, permitting very short (e.g. 10-100 ms) integration times for each source-detector pair.

Calculation of absolute optical properties is possible for homogeneous media with single frequency FD devices, but the measurement is markedly improved through use of multiple source-detector separations. Simple measurements of attenuation with continuous wave (CW) light cannot discriminate absolute absorp- tion and scattering except under special circumstances99, 111–113.

Intes and Chance114addressed analysis of multi-frequency data, noting that 7-12 frequencies spanning 0-500 MHz provided optimal results. FD systems with more then one non-zero frequency have been imple- mented for DOS109_{and Tromberg’s group at the Beckmann Laser Institute has applied this system in many}

clinical studies74, 115, 116_{. However, the Beckmann system relies upon a sophisticated network analyzer. Mul-}

tiple frequency data for DOT are generally derived from TD measurements (e.g., by Fourier transformation) as discussed in Section2.2.5and Section2.3.3.

In theω = 0(steady state or continuous wave) case, it is difficult to separate changes in absorption and scattering, except in a few special cases117. However, especially in situations where scattering remains

roughly constant, CW techniques have proven particularly useful to measure changes in the absorption both in space (e.g. hematomas118_{) and time (e.g. exercising muscle}119_{); these techniques can be very inexpensive}

(e.g._∼$20 in opto-electronic parts for a 1 wavelength, 1 source-detector system).

To summarize, CW data simply records intensity, typically referenced to a baseline value I0 as _II

0.

FD data at a single frequencyω =ω1 provides amplitude and phase; many FD systems can collect data at both a finite frequency (ω1) andω =0. The pulse broadening in the time domain of a brief pulse of light passing through a scattering medium is perhaps more intuitively obvious than the phase shift one observes in the more commonly used frequency domain measurements; the time domain is the natural formulation convenient for Monte Carlo simulations of photon transport. Most importantly, TD measurements permit absolute quantification of scattering and absorption coefficients in a homogeneous medium with a single measurement. Technically, FD measurements of phase, amplitude (AC), and average intensity (DC) are sufficient to calculate absolute optical properties, but this approach is more susceptible to systematic errors.

Thus most researchers using FD techniques rely upon either multiple source-detector separations or multiple frequencies. CW measurements lack sufficient information to separate attenuation due to scattering and absorption, unless spectral models are employed.