2515-7647/7/2/025012

Non-destructive testing and evaluation of targets with low contrast and sub-wavelength features tends to be challenging. By illuminating the target off-axis, dark-field imaging techniques can resolve diffracted or scattered features that are typically challenging to discern with conventional bright-field imaging, which relies on specular reflection exclusively. Traditional dark-field methods achieve off-axis illumination by blocking the central portion of the incident beam, but this unfortunately incurs significant power losses of up to 99%. This level of power loss is unfavorable at terahertz frequencies where source power is relatively scarce. To address this, we propose a terahertz dark-field imaging system that makes use of a double axicon beam expander to create an annular beam, which is then focused down upon the target through an objective. The system permits simultaneous bright- and dark-field imaging in reflection without modifying the optical train, making greater use of raster scan time while achieving an average transmission efficiency of 33.15% and bright-field spatial resolution of 0.391 lp mm−1. The proposed dark-field imaging system is able to enhance the detection of fine features such as growth rings in wood, superficial imperfections on bulk materials, and defects in fiberglass. This approach to achieve dark-field imaging will be valuable for biomedical imaging at the terahertz range that harbors interesting molecular vibration activities.

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Many methods exist for performing non-destructive testing and evaluation (NDT&E) which make use of x-rays, visible light, magnetic fields, and ultrasonic waves. For in-situ systems, it is desirable for an imaging system to be non-ionizing to ensure the safety of operators and potential targets, in scenarios such as: security screening, biomedical imaging, and process line monitoring. The capability to penetrate optically opaque materials with non-ionizing radiation, while maintaining reasonable spatial resolution is the main advantage of terahertz waves for NDT, useful in the detection of subsurface defects in structural materials [1] and frost damage in biological samples [2]. Improvements to these techniques will therefore increase the applicability and versatility of such terahertz imaging systems. Terahertz imaging serves to complement existing NDT techniques, providing a balance between spatial resolution and object penetration. Conventional bright-field terahertz imaging typically relies upon the spatial dependence of the specular reflection or transmission across a target, measuring the change in received power as image contrast [3]. For such raster-scanning schemes, the apparatus typically involves focusing a Gaussian beam to a small spot and moving it across the sample at normal incidence, maximising the signal to noise ratio [2, 4]. To achieve high bright-field contrast at terahertz frequencies, samples should exhibit high variation in absorption across scanned areas [3]. However, incident power scattered by or transmitted through a sample will also provide contrast in reflected power. When imaging samples with uneven surfaces or intricate granules, a large portion of power is typically lost through diffraction and scattering effects [5], which are an ambiguous source of loss from the perspective of a receiver in a bright-field imaging setup. This work addresses this limitation by capturing the scattered power, and uses it to differentiate between scattered and absorbed terahertz power in a bright-field system.

Dark-field techniques are well established in the optical domain, and address this issue of ambiguity by illuminating samples off-axis and collecting only the scattered or diffracted power [6, 7]. This capability for resolving features, which might otherwise go undetected with a bright-field scheme, is useful for terahertz imaging, where features may not be discernible with bright-field techniques [8]. Such techniques are particularly useful for surface characterization at terahertz frequencies, permitting the discernment between convex and concave surface imperfections [9, 10]. A typical dark-field setup achieves off-axis incidence by blocking the central portion of the incident Gaussian beam before passing through an objective lens [11]. This technique significantly reduces the transmitted power, as this is where the majority of the beam's power resides [3, 12, 13]. While the high source power requirements may be manageable at shorter visible wavelengths, terahertz source power is modest, necessitating optical schemes to conserve power where possible. Generally, the use of dark-field systems in the terahertz domain is limited [13], and systems proposed almost exclusively use some form of aperture obstruction [3, 8, 13], significantly reducing the power incident upon the target. An alternative method for off-axis illumination is to use a pair of conic lenses, known as axicons [14], to expand a collimated beam into a ring shaped, annular beam, and then focus it with an objective lens [15, 16]. This beam expansion technique is used in optical dark-field imaging [7, 12], fluorescence imaging [17], and laser machining [18].

To achieve off-axis incidence and maintain high transmission efficiency, our work realises a terahertz dark-field imaging system with a 3D-printed axicon pair for beam expansion and annular-beam generation, avoiding the use of an inefficient beam block. Placing a mirror inside the center of the annular-beam allows for the reflected scattered and diffracted waves to be collected for dark-field imaging. Combined with low loss cyclic olefin copolymer (COC) quasi-optical components, our optical train design permits terahertz dark-field imaging at an average transmission efficiency of 33.15%, improving upon the efficiency observed in the literature [9]. The low absorption of the COC components also avoids unnecessary power loss during the measurement of the low power scattered and diffracted waves. By using a vector network analyzer, we simultaneously collect bright-field information, allowing for reflected bright- and dark-field images to be acquired with a single raster-scan. We wish to acknowledge that an optical scheme capable of acquiring both bright- and dark-field images has been demonstrated at visible wavelengths [6], but does not capture both images simultaneously, requiring manual reconfiguration to switch between imaging modes. In contrast, our present simultaneous bright- and dark-field system also maximizes the information collection in comparison to standard raster imaging schemes, making the best use of limited terahertz power and scan time within a single acquisition. The reflection mode of our system is also beneficial for samples with high moisture content, which has been identified as an issue for terahertz dark-field imaging operating in transmission mode [8]. In such scenarios, the low transmitted power from beam-blocking is exacerbated by the high absorption of water at terahertz frequencies. With a focal length of 47.3 mm and bright-field spatial resolution of 0.391 lp mm−1, we demonstrate the capability of our design by detecting features within natural wood-grain, for future non-invasive biological imaging, and defects inflicted to fiberglass, for NDT of composite material integrity.

The key feature of the design shown in figure 1(a) is to launch an annular beam with a double-axicon expander, and then focus this beam onto the target for oblique incidence. In this way, the annular beam is generated by deflecting the central portion of the input Gaussian beam, rather than obscuring it with a conventional beam blocker. Since the central portion of the Gaussian beam contains the majority of the power, the double-axicon conserves the limited terahertz power. To simultaneously measure the bright- and dark-field information, we use terahertz frequency extension modules from Virginia Diodes Inc. attached to a Keysight precision network analyzer to acquire complex reflection and transmission spectra across 220–330 GHz. The transceiver unit contains a directional coupler, allowing the power reflected back from the system to be measured during transmission. In the bright-field path, power that is specularly reflected from the target, which contains the low spatial-frequency information, travels back through the same lenses to the transceiver. In the dark-field path, power that is scattered from the target containing the high spatial-frequency information is collimated by the objective and directed towards a mirror placed inside the center of the annular-beam, reflecting it 90∘ towards the receiver. The design of the optical train can be easily adapted to work with other systems, provided they have some form of free-space coupling.

Figure 1. Lens train model of the imaging system. (a) Lens diagram showing the path from the transceiver to the target through L1: horn collimating lens; L2: Diverging axicon lens; L3: collimating axicon lens; L4: objective lens; M1: 45∘ mirror; L5: collector collimating lens. (b) Cross section of collimated annular-beam, indicated by the purple dashed line, with 24 mm axicon separation, computed with the Physical Optics Propagation mode in ANSYS Zemax OpticStudio. All three frequencies have at least 36 mm center null diameter at −10 dB.

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Ray-tracing is used to design the dark-field optical train within ANSYS Zemax OpticStudio, and scalar diffraction theory simulations performed to take diffraction into consideration and validate the field distribution of the desired annular-beam. All lens components are designed as COC, a 3D-printable polymer that features low dispersion and low loss over terahertz frequencies, advantageous for optical components [19]. While the 3D-printing process slightly increases scattering losses in comparison to traditional injection moulding techniques, 3D-printed lenses maintain reasonable optical performance in the range of 220–330 GHz, where imperfections are sub-wavelength [20]. These properties permit low chromatic aberration over the 220–330 GHz range, with no absorption peaks or molecular resonances. Refractive index and is used from previous lens design work [21].

We first design the plano-convex collimating lens to transform the quasi-spherical wavefront emitted by the horn antenna to a collimated beam, indicated by L1 in figure 1(a). The aperture of 48.5 mm accommodates a beam diameter of 40.76 mm at 220 GHz, 100 mm away from the end of the horn antenna that is attached to the transmitter. The larger aperture is left as a margin in order to avoid truncating the diverging Gaussian beam.

A double axicon expands the collimated beam into a large annular shape by first deflecting the power away from the optical axis, and then correcting the diverging beam such that it propagates parallel to the optical axis. This is done in order to fit a small, off-axis reflector inside the center-null. To diverge the collimated beam, we use a negative axicon lens with a diameter of 46 mm and 36∘ incline angle as indicated by L2 in figure 1(a). This lens is placed against the first collimating lens L1. To then correct the divergence of the first axicon into a collimated annular-beam, we use a positive axicon with a diameter of 96.8 mm and identical incline angle as indicated by L3 in figure 1(a). The distance between negative axicon L2 and positive axicon L3 is chosen such that the outer diameter of the annular-beam is smaller than the lens holder's clear aperture of 96.8 mm, and so that a mirror of 30 mm diameter can be placed inside the center of the beam. This design optimization is performed by computing the cross section of the collimated annular beam at increasing separation distances. For a 24 mm separation between the axicons, at −10 dB from the peak of the ring, the center null is approximately 35 mm wide at 220, 275 and 330 GHz, as shown in figure 1(b). Therefore, a 30 mm diameter cylinder is removed from the center of the positive axicon, allowing mounting holes for the reflector to be incorporated onto the base. Since the axicon lenses are modelled as standard spherical surfaces with a near-zero radius of curvature, a small region in the center of both axicon lenses is not perfectly conical. As such, the simulations show that a portion of the collimated beam passes directly down the optical axis, visible as a small null-central spot in figure 1(b).

For the objective lens, L4, a large aperture of 92.7 mm, and short focal length of 47.3 mm are chosen for a small spot size and steep angle of incidence on the target. The theoretical FWHM of the focused annular-beam is [16],

At 220, 275 and 330 GHz, the wavelength λ0 equals and numerical aperture . Assuming approximately equal beam diameter of 70 mm from figure 1(b), the expected FWHM is therefore respectively.

The cylindrical body of the 90∘ reflector is 3D-printed from polylactic acid (PLA). Although PLA is lossy at terahertz frequencies [22], the body of the reflectors does not interact with the annular-beam, imposing no loss. A diameter of 30 mm is chosen to stay well within the center null of the collimated annular-beam, to avoid unwanted shadowing and diffraction effects. This results in the dark-field imaging path having a numerical aperture of 0.32, limited by the diameter of the reflector. To construct the reflector, the elliptical profile is traced onto and cut from copper film with an adhesive backing. The PLA surface is sanded smooth and the copper tape is adhered to form a reflective surface. This assembly is mounted to the flat side of the positive axicon with M4 bolts. To capture the reflected waves, a plano-convex lens with an aperture of 40 mm and focal length of 75 mm is positioned off axis, focusing the scattered power to the horn antenna on the receiver unit.

3.1. Annular-beam collimation

To ensure the annular-beam is collimated and the center-null is compatible with the mirror, we use the near-field probe setup shown in figure 2(a) to take transmission raster scans of the xy plane at increasing distance away from the tip of the reflector M1. Our raster scanning system typically requires 3.3 s mm−2 for a mechanical step resolution of 0.15 mm. Improvements to the scan time could be made by fine tuning the control system for the scanning stage, as some sacrificial margin is typically added around the area of interest to avoid distortion from mechanical vibrations and instability during acceleration and deceleration movements. Over , the beam stays approximately the same size, with very minor beam non-uniformity visible inside the null, which is not expected to impact performance. The beam features an approximate inner diameter of 68.09 mm and outer diameter of 94.59 mm measured at , indicating reasonable collimation as shown in figure 2(b).

Figure 2. Near field scanning setup of the imaging system. (a) Photograph of scanning setup to observe the collimated annular-beam. L1: horn collimating lens; L2: diverging axicon lens; L3: collimating axicon lens; M1: 45∘ mirror. The dark-field collector components are not included here. (b) Transmission raster scans along of the xy plane at , showing the collimated ring at 275 GHz. (c) Photograph of the objective lens, L4, positioned after the second axicon, L3, with scanning setup to measure the spot size. (d) Transmission raster scan along the xy plane showing the location of the system focus at 275 GHz, cropped to mm. (e) Cross section at y = 0, showing a FWHM of 0.763 mm, calculated from the fitted Gaussian curve.

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In order to ensure the optical train is focusing the beam as expected, we place the objective L4 after the second axicon lens L3 and take a near-field xy raster scan of the focal plane with the apparatus shown in figure 2(c). From the plane shown in figure 2(d) we use the cross section shown in figure 2(e) to extract the FWHM spot sizes of 0.929, 0.763, 0.667 mm at 220, 275 and 330 GHz respectively. The shortening wavelength leads to this decrease in spot size, and a corresponding improvement in imaging resolution. These values approximately align with those calculated earlier, 0.655, 0.524, 0.436 mm. Some discrepancy is attributed to system misalignment and surface imperfections of the 3D-printed lenses.

3.3. Spatial resolution

To assess the bright-field spatial resolution of the system, we configure the complete system as shown in figure 3(a) to image a resolution test target. We use the Siemens star target shown in figure 3(b) to extract the modulation transfer function (MTF) from the bright-field time-domain image in figure 3(c) with the method detailed in [23]. The Siemens star features fifteen planar, triangular patches of copper, arranged in a circular pattern to form highly reflective 'spokes.' We use the time-domain image here to avoid interference artifacts that are present at single frequencies, which can degrade the image. The time-domain image is obtained by performing an inverse fast Fourier transform on the complex frequency spectrum measured from 220–330 GHz, as described in [21]. As the spot moves closer towards the center of the Siemens star, the dark-field image in figure 3(d) shows that power diffracts from the target as the spokes form a grating, corresponding to the expected decrease bright field contrast. We also note that the dark-field image resolves the subtle change in depth along the perimeter of the spokes where the edge scatters the incident wave. No information from the center of the spokes is resolved in the dark-field image, since there are no changes in depth or absorption across the surface. The expected and opposite effect is seen in the bright-field image, where the uniform copper regions appears bright and fine features appear darkened. The Siemens star target provides an intuitive demonstration of the expected dark- and bright-field results, showing where power is lost from the bright-field image due to scattering and diffraction. Measuring the MTF of the bright-field image at a radius of 0.1–24 mm, we obtain a MTF10 of 0.391 lp mm−1 and MTF50 of 0.192 lp mm−1, indicated in figure 3(e). To improve the spatial resolution of the system, the dimensions of the lens components could be increased.

Figure 3. Spatial resolution test of the imaging system. (a) Photograph of the experimental imaging system with the resolution test target positioned at the focal plane of the objective. L1: horn collimating lens; L2: diverging axicon lens; L3: collimating axicon lens; L4: objective lens; M1: 45∘ mirror; L5: collector collimating lens. (b) Photograph of the resolution test target. (c) Bright-field time-domain image. (d) Dark-field time-domain image. (e) Modulation transfer function of the bright-field scan, indicating a MTF10 of 0.391 lp mm−1 and MTF50 of 0.192 lp mm−1.

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A key motivation behind the development of the non-blocking design is to increase the power incident upon the target with the use of the axicon pair. To measure the system efficiency, we raster scan the output of the horn antenna at the location of the first lens L1, shown in figure 4(a), and compare it to the raster scan of the focal plane, shown in figure 4(b). For this measurement we use the same raster-scanning setup as figure 2(a). The raster scanning apparatus measures semi-continuously, recording the stage position when a new complex transmission measurement is available. Both scans do not share a common set of points along the x-axis, so both scans are interpolated to a common and regularly spaced Cartesian grid in order to integrate over the same number of pixels. For each of the 1000 frequencies in the span of 220–330 GHz, we integrate the intensity of the horn scan and the focus scan, and take the ratio of the two as the power efficiency for that frequency. This result is displayed in figure 4(c), showing an increased efficiency at higher frequencies. This may be due to the beam divergence angle of the horn antenna decreasing proportional to wavelength; if the probe has minor misalignment along the optical axis, the longer Rayleigh range at higher frequency will better compensate for any error. An average efficiency of 33.15% is measured across the frequency range, lower than the 54.51% estimated in ANSYS Zemax OpticStudio. The lower efficiency is likely due to the fact that the diverging axicon is not modeled as a perfectly inverted cone but features a near-zero radius of curvature in the center. Since the 3D-printer cannot reproduce such infinitesimal features, the apex of the inverted cone is larger than designed, which transmits more power than expected through to the center of the collimating axicon. In the experimental setup, this additional unwanted power is blocked by the base of the reflector. Other losses are attributable to several factors including lens misalignment, lens surface roughness, and dissimilar coupling characteristics of the probe tip between the diverging horn beam and the focused spot. Despite the discrepancy between simulated and measured performance, our system still outperforms the efficiency of conventional dark-field systems in the literature [9].

Figure 4. Power transmission efficiency of the optical train. (a) Transmission intensity at 275 GHz, measured 100 mm away from the horn antenna, without the dark-field system. (b) Transmission intensity at 275 GHz, measured at the focal plane of the dark-field system. (c) Percentage transmission efficiency at the focal plane relative to the horn antenna.

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To demonstrate the capture of scattered information by the dark-field imaging component of our system, we place the cut section of Eucalyptus cladocalyx branch shown in figure 5(a) at the focal plane of the system. We see in figure 5(b) that the bright-field image is able to capture the various growth rings from the section of branch. This bright-field image exhibits low contrast, indicating moderately uniform specular reflection across the sample. Observing the dark-field image in figure 5(c), we see a higher degree of contrast from the ring features. To exploit the merits of both modes of imaging, we clip the data to the central 95% intensity distribution of each monochrome image, map the intensity to the transparency channel of red and blue layers, and overlay the dark-field onto the bright-field to form the composite image shown in figure 5(d). While the biological origin of this scattering mechanism is outside the scope of this work, here we speculate that the interface between the lighter (less dense) and darker (more dense) regions of the wood essentially act as an abrupt change in refractive index, scattering the focused terahertz power. The red shows bright-field information, with darker regions indicating where power is lost to absorption or scattering. As expected, some of these nulls in the bright-field image are resolved as scattering in the dark-field layer, shown in blue. From these results, the bright-field image contains the bulk of the information from the sample and the dark-field image detects subtle outlines and edges, forming a useful complimentary image capability.

Figure 5. Detection of growth rings in cut Eucalyptus cladocalyx branch. (a) Photograph of the tree branch cross section. (b) Bright-field time-domain image. (c) dark-field time-domain image. (d) Composite image of bright- and dark-field images mapped to red and blue colour channels respectively. We clip both images to the central 95% intensity distribution of data and map the intensity to the alpha channel of red and blue colour mattes, overlaying the dark-field onto the bright-field to form the composite.

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To demonstrate the difficulty of imaging superficial sub-wavelength features and the enhanced contrast of the dark-field images, we present the acrylic block with several surface scratches shown in figure 6(a). An optical microscope is used to measure the approximate scratch width of 180 µm, as annotated in the inset figure 6(b). Since the acrylic substrate is smooth and flat, we expect the bright-field image to contain a high amount of reflected terahertz power. This is evident in figure 6(c), where the majority of the scanned area is brighter. The small feature size relative to the spot size makes the scratches difficult to distinguish, as the change in reflected power across the scratches is low. The dark-field image in figure 6(d) shows improved contrast, as the background level of scattered power from the smooth and flat substrate is low. This comparison demonstrates where the dark-field imaging is the most effective, for highly reflective targets which suppress the features of interest in a traditional bright-field scheme.

Figure 6. Detection of surface defects on acrylic substrate. (a) Photograph of the acrylic slab with several surface scratches. (b) Optical micrograph of surface defect, indicating the scratch defects are approximately 180 µm in width. (c) Bright-field time-domain image. (d) Dark-field time-domain image. We clip both images to the central 98% intensity distribution of data to remove any outliers.

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Since NDT of composite materials is a promising area for terahertz imaging technologies [1], we demonstrate the detection of intentionally introduced defects in two samples: a fiberglass and resin laminate block, shown in figure 7(a), and an aluminum honeycomb and carbon fiber sandwich panel, shown in figure 8(a). The fiberglass sample highlights the potential of the dark-field methodology for sub-surface feature extraction, offering additional insight into material composition beyond standard bright-field imaging. To simulate air-filled delaminations, holes of 1.0, 1.5, and 3.0 mm are drilled through the fiberglass block [1]. The block is placed in the imaging system, with the holes approximately at the focal plane. Scans are conducted using both vertical and horizontal polarizations to account for potential anisotropic material properties, with horizontal polarization achieved by introducing waveguide twists before both horn antennas and realigning the system. The three holes are detectable in the bright-field images in figures 7(b) and (c) as the terahertz waves are reflected at the fiberglass and air interface. Some vertical background artifacts are present, which we attribute to the glass fiber matrix. Notably, complementary regions are discernible in the bright-field images, with certain areas reflecting more strongly in vertical polarization and others in horizontal, suggesting polarization dependence due to the sample's construction. The dark-field images in figures 7(d) and (e) show strong scattering from the defects, with the vertical polarization showing the defects more clearly. This indicates a stronger scattering effect is present when using horizontal polarization, in agreement with the stronger contrast of the bright-field image seen in figure 7(b). Drawing conclusions on the nature of the internal fiber composition is outside the scope of this work, but we believe the acquisition of the dark field information is not negligible, and may aid in discerning the orientation of internal composite materials. To further demonstrate the improved detection of composite surface defects with dark-field imaging, the carbon fiber panel in figure 8(a) undergoes a three-point bend test, where mechanical force is applied to the central region of the panel. The test fractures the carbon and resin composite, with the fracture faintly visible in figure 8(a). We place the panel in the imaging system, with the surface at the focal plane. The bright-field image in figure 8(b) shows a reduction in reflected terahertz power around the area of the defect, likely due to surface deformation and subsequent deflection of the reflected beam at the conductive carbon surface. The dark-field image in figure 8(c) shows a reduction in scattered power at the location of the fracture, indicated by the darker vertical region. The dark-field image better localizes the fine fracture feature, while the bright-field image remains useful in finding the defect's approximate location. These two composite samples show that although the bright-field method alone can detect and localize sub-surface and superficial defects, the dark-field images provide additional insight into the nature of these defects and improves localization for surface features.

Figure 7. Defect detection in fiberglass block. (a) Photograph of the fiberglass sample on the scanning stage, with drilled holes aligned horizontally. (b) Bright-field time-domain image with vertical polarization. (c) Bright-field time-domain image with horizontal polarization. (d) Dark-field time-domain image with vertical polarization. (e) Dark-field time-domain image with horizontal polarization. We clip all images to the central 98% intensity distribution of data to remove any outliers.

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Figure 8. Defect detection on carbon fiber panel which has undergone a three-point bend test. (a) Photograph of the panel, with the vertical fracture approximately in the centre. (b) Bright-field time-domain image. (c) Dark-field time-domain image. We clip both images to the central 98% intensity distribution of data to remove any outliers.

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The detection of illicit substances within postal facilities has been identified as an application suited for terahertz technology [24]. Many such substances have spectral fingerprints in the terahertz range, allowing terahertz time-domain spectroscopy systems to classify chemical composition. The scattered power received from the crystalline target is proportional to the grain size, which permits dark-field techniques to assess the granularity [24]. The low received power and hence low signal to noise ratio of dark-field imaging inhibits accurate terahertz measurement at higher frequencies. In future work, by including the bright-field imaging path in our system, we hope to simultaneously perform parameter extraction in reflection mode, whilst maintaining the dark-field imaging system for the localization of crystalline substances. Figure 9(a) shows a photograph of an envelope concealing two sachets of sugar, with the leftmost having its contents replaced with finer 'caster' sugar. By placing the envelope at the focal plane and acquiring an image, we reveal the sachets in both the bright- and dark-field images, shown in figure 9(b) and figure 9(c) respectively. The bright-field image shows a great degree of variation over the two sachets, providing limited information about their contents. On the other hand, the dark-field image shows a more uniform scattering profile, with the rightmost sachet containing larger granules showing an increase in scattered power as expected. This sample serves to reinforce the idea that the dual imaging modes of our system complement each other, providing additional information where one mode may not be as suitable.

Figure 9. Detection of concealed granular substance in paper envelope. (a) Photograph of the envelope, with the sachets containing caster and regular sugar slightly visible through the paper.