Comparison of time domain and frequency domain systems

The relative advantages and disadvantages of frequency-domain optical imaging systems compared to time-domain systems have been subject to debate for more than ten years. Frequency-domain systems are relatively inexpensive, easy to develop and use, and can provide very fast temporal sampling (up to 50 Hz). Time-domain systems, on the other hand, tend to use photon-counting detectors which are slow but highly sensitive. Hence, frequency-domain systems are well suited to acquiring measurements quickly and at relatively high detected intensities (such as for topography applications). However, when imaging across large (> 6 cm) thicknesses the light intensity is very low, possibly only a few photons per second, and can only be detected using the powerful pulsed laser sources and photon counting techniques incorporated into time-resolved systems.

The information content in a temporal point spread function (TPSF) is inevitably greater than that in a single phase and amplitude measurement at one source frequency, but the magnitude of this benefit has yet to be thoroughly explored. The frequency content of the TPSF extends to several GHz, and while in principle a frequency-domain system could be designed to acquire this information, it is not yet possible to modulate high-intensity sources at such high frequencies. The intensity and mean photon flight time calculated from the TPSF are almost equivalent to the amplitude and phase of a frequency-domain system (Arridge et al. 1992). Other datatypes calculated from the TPSF such as variance, skew and the Laplace transform can provide enhanced separation between µa and µ's (Schweiger and Arridge 1999), but may be more sensitive to noise. These additional datatypes have no simple equivalent in the frequency domain. Other approaches, such as time-gating to distinguish between µa and µ's (Grosenick et al. 2003) or to provide depth discrimination (Selb et al. 2004) also demonstrate the additional information available in the TPSF.

Practical optical measurements, particularly in the hospital, are commonly contaminated by constant (or temporally uncorrelated) background illumination. Frequency-domain systems are able to reject uncorrelated signals (but not the uncorrelated noise associated with these signals) by the use of lock-in amplifiers, while time-domain systems reject photons which reach the detector outside a finite temporal window. However, frequency-domain systems are unable to identify unwanted light which is temporally correlated with the measurement, such as light which has leaked around the object being imaged. In the time-domain, inspection of the TPSF can enable these contaminated measurements to be rejected (Hebden et al. 2004).