A less common approach involves capacitance measurements to obtain water activity results. A sensor made from a thin-film
hygroscopic polymer relates the film capacitance to the headspace moisture content. Because this instrument relates an electrical
signal to relative humidity, the sensor must be calibrated with known salt-solution relative humidity standards. In addition,
for successful measurement, the sample and sensor must be at the same temperature. Although both of these instruments can
be effectively applied to headspace moisture measurements, the nondestructive nature of frequency modulation spectroscopy
(FMS) seemed to make the instrument ideal for exploration for examining the headspace moisture over pharmaceutical solids.
The major shortcomings of the present techniques relate to the introduction of bias to the measurement and the inability to
control measurement temperature over a wide range. Adding another sophisticated tool to the available arsenal of techniques
to conduct critically important water activity measurements seemed to be worthwhile from the perspective of further refining
the interface between measurement science and packaging research and development (7–9).
Figure 1: Principle and schematic of frequency modulation spectroscopy. Top figure (a) shows the frequency and intensity
profile of a diode laser beam. Diagrams from left to right show an unmodulated, modulated with no absorption, and modulated
with absorption by the upper sideband. Bottom figure (b) is a schematic diagram of an instrument for frequency modulation
Fundamentals of frequency modulation spectroscopy
Water molecules in the gas phase absorb near infrared (NIR) light in a band of rotational transitions centered at 1400 nm.
Absorbance measurements at this wavelength on typical NIR spectrometers using incoherent white-light sources lack the sensitivity
to provide a useful measure of headspace moisture levels because of low-frequency lamp-intensity fluctuations. The measurement
signal-to-noise (S/N) ratio can be vastly improved (100–10,000X), however, by laser-light sources and frequency modulation
detection techniques (10–11). When a tunable diode laser is modulated using a radio frequency oscillator, the detection bandwidth
can be shifted to higher frequency where intensity fluctuations, inherent to low frequency measurements, are minimized.
Figure 2: Frequency modulation signals from moisture absorption. The peak-to-peak amplitude of each spectrum is proportional
to moisture concentration. The relative humidity is noted to the right of the 0% and 100% scan.
The frequency modulation spectroscopy measurement is conducted by frequency modulating a diode laser by superimposing a radio
frequency oscillation, Ω, onto the diode injection current. The spectral output of a frequency modulated diode laser (see
Figure 1) consists of a carrier frequency ωc and side band frequencies, ωc ± Ω. When the laser is scanned through the wavelength of moisture absorbance, the amount of light absorption, which is proportional
to the concentration of the water molecules, is "written" into the side band frequencies by recording the difference in absorption
between the two sidebands. The differential absorption information is recovered with phase-sensitive detection techniques.
The demodulated absorption line shape is shown in Figure 2. The amount of light absorbed is directly proportional to the water
concentration in the gas phase. The gaseous water density n is related to the peak-to-peak signal amplitude ΔI by Beer's law, which for a weakly absorbing molecule is given by: