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(Dt) between the arrival of the air reference and sample pulses can be obtained from the time-domain terahertz spectrum (Figure 2). The RI, h, is obtained using h(group frequency) 5 1 1 Dt [ c ] Equation 1 d where c is the speed of light and d is ribbon thickness. Of course a roller-compacted ribbon is a porous material whose effective RI depends on void volume, provided scattering effects are minor. The terahertz pulse will pass more quickly through a highly porous sample than a tightly compacted one (Figure 3). Therefore, the effective RI, while not an intrinsic property of the ribbon material, is directly proportional to the ribbon's apparent density and solid fraction; it is inversely proportional to porosity (Table 1). Note that in transmission mode, the ribbon thickness must be known in order to calculate the RI. Alternatively, the RI can be obtained from the fre - quency domain spectrum (Equation 2) following Fourier transformation of the time-domain spectrum. h(v) 5 1 1 [ w (v) ] [ c ] Equation 2 v d where h(v) is the RI and w(v) is the phase shift at the angular frequency v. Measuring the RI in the frequency domain gives you the flexibility to select the frequency-dependent beam diameter to obtain optimal spatial resolution in 2D mapping of the density, which will be discussed and shown in more detail later. 28 January 2015 Tablets & Capsules Table 3 Techniques for measuring apparent density of roller-compacted ribbons Technique Advantages Disadvantages Section and weigh Low cost Destructive, poor precision, manual operation, low spatial resolution Terahertz Fast, non-destructive, non-contact, deep penetration Spatial resolution limited by material absorption (transmission), low-energy beam, no effect on sample integrity, suitable for in-line process applications Micro-indentation [2] Sensitive to material's elastic properties and hardness Destructive, indirect, surface only, requires observation by skilled operator Near infrared [3, 4] Fast, non-contact, suitable for in-line process applications Indirect, surface only, sensitive to beam orientation on patterned ribbons X-ray micro-computed tomography [2] High spatial resolution, deep penetration Complex, radiation safety issues, may affect sample integrity Acoustic wave [5] Fast, sensitive to elastic properties and mass density Direct contact with acoustic couplant required between sample surface and transducers, susceptible to interference from roller compactor's vibration Figure 2 Terahertz time-domain signals for measuring time-of-flight for a solid compact vs. an air reference 12.882 13.7 14.39 15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 20 20.5 21 21.5 22 22.5 23 23.5 24 0.5 0.4 0.3 0.2 0.1 0 -0.1 -0.2 Intensity (arbitrary units) Time (picosecond) Air reference peak Sample peak Dt Figure 3 Time-of-flight concept: Air vs. high-porosity and low-porosity solids Air High-porosity solid Low-porosity solid d