4.1 Immersion Ultrasound Analysis
The honeycomb test object was inspected using a commercially-available scanning (6-axis) immersion ultrasound system (MISTRAS Group, Inc.). We used a spherically focused immersion sensor with a center frequency of 20 MHz, 9.5 mm aperture, and 35-mm focal length. The part was scanned in pulse-echo mode through its thickness with the sensor directed at the top of the part proximate to the simulated defects (“top plate”). The height of the sensor (z-axis) was adjusted so that the back wall echo of the “top plate” was maximized, which set the focal point of the beam on the back of the “top plate”. The sample was scanned using a unidirectional grid in the x-y plane, where the grid spacing was 0.254 mm2. At each inspection location on the x-y scanning grid, 10 waveforms were averaged, digitally filtered with a bandpass filter 5–35 MHz, digitized at 250 MHz, and recorded as a single amplitude-time trace (a-scan).
When the sensor is located over a portion of the top plate that does not have supporting structure connected to it, the sound bounces between the front and back walls of the top plate and multiple acoustic echoes are observed, as shown in the a-scan in Fig. 9a labeled “No Support. Alternatively, when the probe is located over a portion of the “top plate” that has lattice bonded to its underside, the ultrasound leaks into the strut material and the backwall echo is greatly diminished, as seen in the a-scan in Fig. 9a labeled “Supported”. The UT data is processed by normalizing each a-scan such that the peak absolute magnitude is unity and occurs at time = 0 µs. Then, the root-square-sum (RSS) is calculated between t = 0.6–2.6 µs since this is when the echoes from the “top plate” backwall occur. The RSS is shown on the color scale in the c-scan image, Fig. 9b. Here the location of the honeycomb lattice network is clearly observed by the regions with a reduced RSS.
The mid lattice crack defect A, shown in Fig. 8(a), is not detected in the UT c-scan. This is expected since the defect lies midway through the lattice and no ultrasound echoes were observed from sound that propagated through the lattice and reflected off the mid-lattice hole or the “back plate”. Because of the focused beam and the size and geometry of the struts, any ultrasound that leaks into the struts does not get coherently reflected back to the sensor. The simulated layer bonding defect C, shown in Fig. 8(c), was detected in the UT c-scan as shown in Fig. 9(c). Here, around x = 140 mm and y = 105–110 mm, the low RSS indicative of a bonded strut was not observed. Interestingly, the simulated partial fusion bond flaw B, shown in Fig. 8(b)b, was not detected in the ultrasound c-scan. It is likely that the transducer spot size was too big compared to the percent of unbonded strut area. With further data processing it may be possible to detect this feature with statistical significance, however this was not the focus of the present work.
4.2 X-Ray Computed Tomography Analysis
X-ray CT was performed using an in-house built x-ray system. This system uses a Yxlon MGC41 x-ray generator and a Perkin Elmer 1621 AN14 ES detector. The x-ray source was operated at 300 kV peak energy and 2.3 mA, using a 6 mm Cu filter. Using a magnification of approximately 1.27, a total of 1,800 projections were acquired at equally spaced angles as the object was rotated 360°. For each projection, 12 frames were averaged with exposure times of 1.3 seconds to generate the digital radiograph at that orientation. The 3D volume was reconstructed using Livermore Tomography Tools (LTT) [33] with an effective voxel size of 157 microns. The three flaw locations were then inspected at various angles and cross-sections to gauge their visibility. Figure 10 shows representative results, with the flaws circled. Figure 10a is a cross-section through the centerline of the side-wall holes at the site of flaw A, Fig. 10b is the image of a cross-section plane containing flaw B, and Fig. 10c is the image of a cross-section through the plane containing flaw C. Based on the CT imagery, all three flaws are verified to be present and as designed, though not necessarily easily identifiable; flaw C is revealed only by a subtle grayscale shift that, in practice, may escape post-build inspection (particularly if the component is large).
4.3 Real-Time Holographic Interferometry Analysis
Prior to implementing the experimental methodology outlined in section 3.1, real-time holographic interferometry was used to generate a ground truth deformation image of the test object under differential pressure conditions. The test object was rigidly mounted in a vertical position in a standard side-band Fresnel optical arrangement for hologram (re)construction. Holographic plates from LitiHolo™ Corp. were used for hologram recording. These were 2 mm glass plates with a pre-applied 16 µm photopolymer film (C-RT20 instant holographic film) on a 60 µm plastic substrate, and plate dimensions of 6 in. x 8 in. (width x height). The holographic film is photopolymerizing, such that no wet chemical processing was needed. This allows the plate to remain in place during photo-exposure and subsequent reconstruction, thus creating ideal conditions for real-time holographic interferometry. The camera used in this study was a FLIR Oryx ORX-10G-310S9M CMOS camera with resolution of 6464 x 4852 pixels (W x H). The camera’s optical axis was positioned normal and centered relative to the surface of the honeycomb test object, with the holographic plate positioned approximately 5 inches in front of the camera lens such that it filled the camera field of view. A Coherent Sabre™ argon laser emitting at the 514nm line was used as the illumination source. Figure 11 illustrates the optical arrangement.
A hologram of the test object in its reference state (i.e., zero differential pressure) was recorded by exposing the hologram plate for approximately 2 minutes. Pressure was then slowly introduced into the interior of the test object using a manual air pump while the fringe formation, as imaged by the CMOS camera, was observed on the computer monitor in real time. This process continued until clear fringes were visible, at which point the pressure increase was arrested. The final differential pressure was 40 psi. The fringe pattern that formed in response to this pressure encodes the surface deflection, and is shown in Fig. 12a. The deflection fringe pattern consists of a sequence of low-frequency fringes corresponding to overall shape distortion, superimposed with a high-frequency fringe pattern corresponding to the honeycomb internal truss deflection pattern. The high-frequency pattern has the primary diagnostic value. To estimate the out-of-plane deflection resulting from the hydrostatic pressure, a line profile of grayscale values was extracted and plotted. To minimize any contribution from the global (low-frequency) fringe pattern, the region chosen for profile extraction was selected such that it was fully contained within a low-frequency fringe, with the fringe’s direction parallel to the line profile path. The underlying region is shown highlighted in Fig. 12a, along with the interpretation of the high-frequency honeycomb fringe pattern in Fig. 12b. From the geometry of the honeycomb component, it is known a priori that the region corresponding to a vertical interior support will correspond to a local deflection minimum while the central unsupported portion overlying each honeycomb cell will correspond to a local deflection maximum. Referring to the grayscale overlay plot in Fig. 12b, it can be seen that the central portion of a bright fringe corresponds to the local deflection maximum, and then gradually transitions to a dark fringe as one traverses from left to right, ultimately reaching a minimum grayscale value before reversing direction and briefly climbing again. This reversal of direction is the result of the optical path length between the reference and deformed wavefronts exceeding 180-degree phase shift and is mirrored about the long axis of a hexagonal cell wall, a feature which is known a priori to be a local deflection minimum. The total cumulative phase shift from the center of the hexagonal cell to its supporting wall consists of the initial 180-degree phase shift from maximum to minimum, plus the reversal portion which is approximately 25% the height of the main lobe (25% of a 180-degree phase shift, or 45 degrees). Therefore, the total pressure-induced angular phase shift from the center of the honeycomb cell to the vertical support is approximately 225 degrees, or ~ 63% of the source wavelength. Considering the 514 nm illumination wavelength, this corresponds to an out-of-plane deflection of approximately 320 nm.
The diagnostic utility of holographic interferometry for this application can be evaluated by examining Fig. 13, where the three areas overlying the internal flaws are shown in detail. Flaw C (see Fig. 8) is clearly visible as an irregularity in the fringe pattern. Flaws A and B, however, are not readily apparent despite the sensitivity of the method, leading to the conclusion that these two flaws do not sufficiently alter the mechanical behavior of the component as to become visible as fringe pattern irregularities at these stress levels.
4.4 Offset-Focused CASI Analysis
With the presence of the build flaws confirmed via UT (section 4.1) and CT (section 4.2), and having established the ground truth deflection behavior via holographic interferometry (section 4.3), we now introduce the CASI analysis of the offset-focused speckle pattern. As in the holographic interferometry analysis, the honeycomb test object was mounted vertically and illuminated off-axis with a Coherent Sabre™ argon laser at the 514 nm line. The illumination angle is almost arbitrary given a sufficiently defuse surface: one need only avoid specular highlighting to achieve a high-quality speckle pattern. The camera was positioned approximately 48 inches from the test object such that it filled the vertical field of view. The offset focus distance was chosen empirically, similar to the differential pressure level for the holographic interferometry. I.e., the interior of the object was pressurized to 40 psi and the computer screen was monitored for visible speckle motion (analogous to monitoring for fringe formation in the case of holographic analysis). If no appreciable motion was observed, the differential pressure was returned to zero, the offset focusing distance increased by one inch, and the test object was repressurized. This procedure was repeated until reasonable speckle motion (on the order of 5–10 pixels) was observed in response to the differential pressure. In practice, where the mechanical response of the object is not known a priori, this method is effective for calibrating the optical offset parameter. In this case, the final offset distance chosen for the honeycomb test object under 40 psi differential pressure was approximately 15 inches from the surface of the object (see Fig. 14).
Two images were collected: a reference image of the test object at zero differential pressure, and a ‘dynamic’ image at 40 psi internal hydrostatic pressure. This image pair was processed via the CASI algorithm as described in section 3.1. Subimage pairs of 32 x 32 pixels/subimage were extracted and processed on a 4-pixel grid (every 4 pixels in the vertical and horizontal directions) to generate the u and v displacement fields on the offset focal plane resulting from the hydrostatic pressure. The Euclidean distance resulting from the u and v displacements at each analysis point was then computed according to Eq. 14. Finally, a 16-bit linear grayscale (0 for minimum Euclidean distance, 65535 for maximum distance) was assigned to the data and used to generate the proportional slope image. The result is shown in Fig. 15a. When compared to the results achieved with holographic interferometry (Fig. 12a), the interior honeycomb cell layout is much more apparent. The presence of the low-frequency fringe pattern in Fig. 12 tends to obscure honeycomb cell boundaries (which also appear more circular in the holographic interferogram). The low-frequency fringes in the holographic interferogram have the added effect of periodically inverting the local high-frequency fringe pattern of the honeycomb cell structure, making automated (or even manual) comparisons between honeycomb cells difficult. In contrast, the lack of low-frequency global fringes in the CASI result of Fig. 15a facilitates honeycomb cell boundary identification. In addition to superior internal layout visualization, the offset-focused speckle method is very tolerant of off-axis imaging geometries. Figure 15b illustrates the results achieved when the imaging axis is rotated 45 degrees relative to the surface normal. The internal honeycomb pattern maintains high visibility, while sidewall deformation can be simultaneously visualized.
To illustrate the results that can be achieved under even lower differential pressures, the previous analysis was repeated for both holographic interferometry and offset-focused CASI but at 10 psi hydrostatic pressure. Results for both conditions (10 psi and 40 psi loadings) are shown in Fig. 16a (10 psi) and 16b (40 psi) for holographic interferometry and Fig. 16c (10 psi) and 16d (40 psi) for offset-focused CASI. The holographic interferogram of Fig. 16a shows the honeycomb pattern and flaw C are barely visible at 10 psi differential pressure. By inspection, the same subregion as that depicted in Fig. 12 appears to undergo approximately ¼-wavelength cycle from the honeycomb support to the center of the adjacent cells. We estimate the out-of-plane deflection in this case to be on the order of 130 nm. By contrasting the 10 psi holographic interferogram of Fig. 16a with the 10 psi result generated via the offset-focused CASI method in Fig. 16c, it can be seen that the interior honeycomb layout is easily visible with good cell boundary definition, and flaw C is as apparent in the 10 psi image as it is in the 40 psi image.
As in Fig. 13, the magnified view of the regions directly overlying the three build flaws are shown in Fig. 17. Flaw C is easily visible in the proportional slope image, whereas flaws A and B are again undetectable. Just as in the holographic interferometry analysis, any influence flaws A and B have on the mechanical behavior of the test object appears to be minimal under the current loading conditions when analyzed via the offset-focused CASI method.
4.5 Morphological Post-Processing
Having seen how a simple optical inspection method can be used for flaw detection, we now address the post-processing of the data imagery. The quality of the proportional slope image (Fig. 15) is high enough that post-build validation can likely be satisfied through simple manual image inspection. We acknowledge, however, that in some cases a more rigidly-defined and repeatable methodology may be desired. For such cases, a straightforward approach based on particle/cell analysis is proposed. Such workflows are routine in biological and materials science research where the need to identify particles, cells, and grain structure in optical and scanning electron micrographs is common [34–36]. As a result, many commercially-available software packages exist not only for processing images directly, but also software development kits to facilitate custom line-of-business applications. One commonly used application is ImageJ™, an image processing package originally created for processing biomedical images [37, 38]. We here use the built-in functionality of ImageJ to illustrate the general approach with the caveat that, in the context of this application, any heuristic workflow will be highly specific to the component under inspection and most likely require iterative refinement.
The process begins with an image binarization thresholding operation that splits the image into two categories: cells/particles and empty space. In this case, the particles are the regions overlying the honeycomb cells that respond to the imposed hydrostatic stress and are visualized in the proportional slope image. The morphology and geometric regularity of these features will reflect the underlying structure of the honeycomb core, while deviations from expected behavior will be a result of the influence of an internal build flaw. Therefore, the binarization thresholding process is the most crucial step in the workflow (other than the generation of the proportional slope image itself) and is usually determined empirically for a given component and optical setup to maximize diagnostic quality of morphological processing to follow. In this work, a locally adaptive thresholding operation [39] using a radius of 15 pixels was found to generate the best result in isolating honeycomb cells. Following binarization, a morphological erosion + dilation operation – where the object’s outer contour is sequentially eroded and dilated again - was applied to remove any residual interconnections between honeycomb cells that may have resulted from the local thresholding operation. The final binarized image is shown in Fig. 18a. This result was then analyzed using ImageJ, and a table of statistics was generated (global cell count and location, area, circularity, min/max Feret diameter, perimeter, etc.). The result of this analysis is depicted in Fig. 18b, where random colors have been assigned by ImageJ to differentiate between individual honeycomb cells identified by the morphological procedure.
At this stage, the morphological processing workflow becomes highly application-specific. The general approach is one of utilizing statistical descriptors to probe the proportional slope image for build flaws by inspecting morphological properties of individual cells. It is unlikely that a single descriptor would be sufficient for a robust flaw detection algorithm (for example, a feature may satisfy the required circularity but its size may be much larger than expected). Therefore, multiple properties should be inspected for anomalies. In some cases, however, single properties can be very useful. One such property is the location of each individual cell, as this is an indication of the regularity of the underlying truss structure. This is typically determined by computing a cell’s centroid, which is simply the arithmetic mean of a cell’s X and Y coordinates within the global coordinate system. An example of this is shown in Fig. 19a where, based on the result of Fig. 18b, the location of each honeycomb cell’s centroid is indicated on a cartesian coordinate plane. A missing cell, or a cell in an unexpected location, can be automatically flagged as a candidate flaw.
An additional property that can be diagnostically useful for regular patterns is Feret diameter (maximum caliper dimension), which gives the maximum span distance of a cell without regard to its orientation. A histogram of all Feret dimensions for the detected honeycomb cells is shown in Fig. 19b. The vast majority of cells have Feret dimensions falling within the range of 9–10 mm, which is a reasonable result based on the dimensions shown in Fig. 7. In addition, there are numerous cells with smaller Feret dimensions. These correspond to the partial honeycomb cells that are located around the perimeter of the component. Lastly, there exists one outlier at the upper end of the scale (Feret dimension 19.04). This corresponds to the double honeycomb cell flaw (flaw C) that can be identified in the proportional slope image.
There are many descriptors that can be derived from morphological filtering. Here we have only discussed two. The properties that are most pertinent to a particular inspection application are governed by the internal support structure configuration of the manufactured component. The single most important requirement of this methodology is to obtain a high-quality proportional slope image that reflects the local underlying mechanical response, followed by proper thresholding to generate a representative binarized image. Processing overhead for these operations is usually less than a second.