Fig 1.
Sample and experimental setup.
(a) The pellet with two different materials with unique spectral peaks in the THz regime is shown. (b) The sample location is shown in a cross-section of the sample holder which is made from two HDPE slabs. (c) The optical setup used for measuring diffused granular scattering signal is depicted. The THz detector arm was on a rotation stage and measurement angles, θ±n, were in steps of 18°.
Fig 2.
The flowchart describes the signal processing steps taken during the cepstrum analysis.
Fig 3.
The power spectra of the 180 μm HDPE particles (blue), lactose (red), and riboflavin (magenta) are shown, vertically offset for clarity.
Fig 4.
The cepstrum, , of the 180 μm HDPE scattering particles (blue), κ of riboflavin (magenta) and κ of lactose (red), and the shape of the Gaussian filters, G(q), for each respective material are shown.
Fig 5.
Before and after cepstrum filtering.
Davg (f, θ0-±5) of a single pixel propagating through only HDPE particles (blue), the lactose pellet and scattering particles (red), and the riboflavin pellet and scattering particles (magenta). The Davg (f, θ0-±5) is shown before (dashed) and after (solid) cepstrum filtering.
Fig 6.
Visual and time-of-arrival image.
(a) The visual image of the pellet that was buried beneath 2 mm of 180 μm HDPE particles is shown with dashed outlines for lactose (red) and riboflavin (magenta). (b) The time-of-arrival image of the pellet at θ0 is also shown with outlines for each pellet material.
Fig 7.
(a) The θ0 optical configuration used in Fig 7 is shown. The derivative spectra of all pixels is shown (b) before filtering and after using the (c) lactose Gaussian bandpass filter and the (d) riboflavin Gaussian bandpass filter in the quefrency domain.
Fig 8.
The NSSlactose parameter is shown (a) before and (b) after cepstrum filtering. The NSSriboflavin parameter is shown (c) before and (d) after cepstrum filtering.
Fig 9.
Diffuse angle measurements from θ(±1 to ±5).
(a) The optical configuration used in Fig 9 (θ(±1 to ±5)) is shown. The derivative spectra of the pixels are shown (b) before filtering and after the signal has been filtered using the (c) lactose Gaussian bandpass filter and the (d) riboflavin Gaussian bandpass filter.
Fig 10.
Diffuse angle measurements from θ(±2 to ±5).
(a) The optical configuration used in Fig 10 (θ(±2 to ±5)) is shown. The derivative spectra of the pixels are shown (b) before filtering and after the signal has been filtered using the (c) lactose Gaussian bandpass filter and the (d) riboflavin Gaussian bandpass filter.
Fig 11.
Diffuse angle measurements from θ(±3 to ±5).
(a) The optical configuration used in Fig 11 (θ(±3 to ±5)) is shown. The derivative spectra of the pixels are shown (b) before filtering and after the signal has been filtered using the (c) lactose Gaussian bandpass filter and (d) riboflavin Gaussian bandpass filter.