In Chapter 11, we considered time-domain methods as one form of time-resolved tissue spectroscopy that is based on pulsed illumination. In this chapter, we consider an alternative type of time-resolved spectroscopy that operates in the frequency space by employing temporally modulated illumination. While these two variations of time-resolved spectroscopy are mathematically equivalent, being related by Fourier transformation, they invoke different concepts, instrumentation, and methods of data collection. The conceptual and theoretical frameworks of frequency-domain spectroscopy are described and developed in this chapter. Experimental and instrumentation aspects of frequency-domain spectroscopy are presented in Chapter 13 (Section 13.4.2).

Basic concepts of frequency-domain tissue spectroscopy

In frequency-domain diffuse spectroscopy of tissue, the optical power incident from the light source is temporally modulated at a sinusoidal angular frequency, and phase-resolved detection yields the amplitude and phase of the resulting fluence rate or flux measured in the scattering medium. The source power, and the fluence rate at any point, are both modulated about an average value. By applying the nomenclature of electrical direct current (DC) and alternating current (AC) to indicate the average value and the amplitude of the modulated component of the optical power, respectively, the modulation depth (or, simply, modulation) (m) is defined as the AC/DC ratio. The modulation is a measure of the amplitude of the oscillations normalized to their average value, and as such is a dimensionless quantity that represents the relative depth of optical oscillations.

This approach can be thought of as analogous to the modulation and carrier frequencies of an amplitude modulation (AM) radio signal, with a difference that the carrier signal is at zero frequency in the case of frequency-domain optical spectroscopy. Given that the optical power and the fluence rate are always positive, the modulation is bounded between 0 and 1 (0 ≤ m ≤ 1). There is, therefore, a fundamental difference between alternating electrical current, which is bipolar, thereby oscillating between positive and negative values, and modulated optical power and fluence rate, which oscillates about an average value, remaining always positive. The average value, or DC component, corresponds to the time-independent optical power and fluence rate considered in Chapter 10 for continuous-wave (CW) spectroscopy. The oscillating optical signal, or AC component, at angular frequency ω is related to the time-domain optical signal of Chapter 11 through a temporal Fourier transform.