Radiometric Temperature Measurement for Metal Additive Manufacturing via Temperature Emissivity Separation

All experiments reported here use the custom-built LPBF testbed visible in Fig. 2b. The testbed is fully described in [44, 45] and builds upon prior work described by [46, 47, 48]. This machine replicates the features of commercial LPBF equipment, including a piston-fed powder supply, mechanized recoater with a compliant blade, inert atmospheric control, and directed gas flow for spatter removal. Uniquely, the distance from the build plane to the inner surface of the environmental window is only $60$ mm. This provides a short working distance for laser delivery and imaging optics, including the ADM lens. Figure 2b also shows a scan head affixed to a boom above the printer enclosure. This assembly comprises a $500$ W, $1.075$ µm single-mode fiber laser (redPOWER qube, SPI) and a $250$ mm collimator (Coherent PN 106402X01), which generate a $20$ mm diameter beam. This beam is first redirected by a turning mirror (Thorlabs PN NB2-K14) before entering a galvanometer mirror set (Thorlabs PN QS20XY).

The laser has a minimum rated power of $50$ W and this power is too high to perform the point melting experiments described below as the spot is stationary. Accordingly, for those experiments the turning mirror is substituted with a beam splitting optic (Thorlabs PN BSS17) that reduces the power reflected to the galvanometers by $\approx 70$%. The unused portion of the beam, which is transmitted through this optic, is directed into a beam dump (Ophir PN BDFL500).

To provide the spectrally and spatially resolved data necessary for temperature emissivity separation, the imaging spectrometer shown in Fig. S1a is used (a labeled CAD model is provided in Fig. S1b and it is shown as-integrated in Fig. 2b). The instrument is coupled to the rest of the apparatus with a custom $2$ m long fiber bundle (Berkshire Photonics). It comprises $19$ individual low-OH fibers with a $100$ µm core, $125$ µm cladding, and $0.22$ NA. At the spectrometer end of the bundle, the fibers are stacked in a line within a $10$ mm diameter ferrule. This is positioned at the object plane, without a slit. The spectrometer itself is a half-crossed Czerny-Turner design operating at $f/2.3$. One end of the operating band is set at $1.2$ µm via an interference filter (Thorlabs PN FELH1200). Instrument response rolls off at $2.4$ µm as a consequence of transmission through the optical fiber bundle. The spectrometer design and calibration are fully explained in § S1 and suggest a limiting spectral resolution of $40$ nm ($30$ bands). Finally, a high-speed MWIR camera (IRCameras IRC806HS) is used as a detector, equipped with an $f/2.3$ cold stop but not a cold filter.

Figure 2c shows both the laser and spectrometer are interfaced with the LPBF testbed by a single optic called the ADM (aperture division multiplexing) lens; the reader is referred to [49] for a general overview of this technology and to [21, 44] for complete details of this specific implementation. To summarize, this nominally $125$ mm focal length optic provides two optical paths. Collimated laser light enters one optical path, after redirection by the galvanometer set, that is designed to focus the laser to an $\approx 77$ µm diameter (D86) spot with the theoretical focus lying below the build plane. The second optical path uses a different portion of the same optic, albeit in the reverse direction, as one half of an imaging relay for process monitoring. This path is nominally designed to function with the experimental setup described in [21], where the relay is completed with a $50$ mm, $f/2.3$ optic that defines the limiting aperture of the system. For the present spectrometer configuration, also shown in Fig. 2c, the relay is completed by a $136.1$ mm off-axis parabolic mirror (Edmund Optics PN 35-614). This optic focuses light exiting the ADM lens onto the testbed-end of the fiber bundle, where the fibers are disposed in a close-pack hexagonal array in a standard SMA connector. The ratio of focal lengths suggests that the image of the build plate on the process end of the fiber bundle is magnified by a factor of $1.09$. Optical throughput is limited by the finite dimensions of this optical path through the ADM lens, namely by the D-shaped element at the top that forms the limiting aperture of the ADM optic, and so the fibers are slightly underfilled. A final consequence of this arrangement is that reflected laser light comes to a focus near the testbed-end of the fiber bundle. To prevent this from causing damage, a reflective longpass filter (Thorlabs PN FELH1200) is placed between the parabolic mirror and the fiber bundle tip.

TES resolves the present obstacle, which is made clear by considering it as a system of equations. When imaging in a single band, one measurement is available to solve for temperature and emissivity. Two-color pyrometry makes two measurements available, yet it is necessary to solve for temperature and two emissivities (if greybody behavior is not assumed). This line of logic continues for an arbitrary number of measurements,

where radiance measurements at $n$ wavelengths underdetermine $n$ emissivities and $1$ temperature. In other words, spectrally-resolved data do not independently provide a solution for emissivity correction. Thus, the objective of TES is to provide a sufficient number of equations to solve this system, in view of at least one spectrally-resolved radiance measurement and through minimally-limiting assumptions of emissivity that can match the optical character of real materials [50, 51, 52, 53, 54, 55, 56, 57, 58].

The three TES methods used in this study break the dependence between the number of spectral measurements and number of variables to be fit by assuming at least some degree of invariance along one axis of the spatial-spectral-temporal (three-axis) datasets generated. To their advantage, these are some of the least limiting TES methods, while being straightforward to implement. Specifically, two methods make no assumptions about the shape or mean of the emissivity values retrieved and the third only requires that emissivity be the same for a pair of spectral bins among a larger number measured.

The first selected approach to TES is described by Watson in [40], and is now commonly called the Two Temperature Method (see [59] for an updated derivative). Rather than be concerned with recovering temperatures, however, Watson is originally interested in measuring accurate emissivities from spectrally-resolved satellite image data for geographical study. Watson’s approach is to image a region of interest with an $n$ band imaging spectrometer during the day, when the sun has warmed the ground surface, then return at night and measure the same scene again when it has cooled to a second, lower temperature. Assuming that the emissivity did not appreciably change between the two measurements, i.e., it is only a weak function of temperature, only $n$ spectral emissivity values need to be determined. Thus, $2n$ measurements are available to fit $n+2$ unknowns ($n$ emissivities and two temperatures) in an over-determined system of equations, and these variables are determined with no prior knowledge. In the context of LPBF, it is quite easy to measure the same point at a wide range of temperatures and so this approach can be well-suited.

Spatial correlations are also commonly leveraged in TES [60, 57] and at a simple level can be applied analogously to the two temperature method. In this case, one collects a spectrally-resolved radiance measurements in $n$ bands for each of a first and a second location, and assumes that emissivity is constant between them. Then, and same as before, $2n$ measurements are available to fit $n+2$ unknowns ($n$ emissivities and $2$ temperatures). Selection of the locations is fixed in the implementation used here, where a neighboring channel has been chosen. However, it should be noted that it is possible to pick the second location dynamically. For example, the spectral angle (or any other metric of spectral distance) can be computed between the spectral radiance measurement at first location and each of the measurements of the 8 surrounding pixels. The surrounding pixel with the most similar spectrum is then used as the second location for TES.

A third and final approach assumes invariance along the spectral dimension of such a dataset and is known as the greybody method, as described by Barducci and Pippi [61]. The greybody method operates on only a single measurement in $n$ bands. For two bands, which can be chosen arbitrarily or in view of prior knowledge, the emissivity is set to be equal. Then, $n-1$ emissivities and $1$ temperature ($n$ parameters in total) are fit to the $n$ radiance measurements. This can be a good fit for instruments with fine spectral resolution. The emissivity for the two longest-wavelength bands are set equal here.

In all cases, temperature and spectral emissivity values are fit using the minimize function of Sicpy.optimize [62] that is configured to use the Nelder-Mead method. The optimization is initialized using a temperature of $1700$ K and a constant spectral emissivity of $0.2$. No regularization of the optimization or post-fit filtering are applied, although this may bring substantial benefits to future work.

Point melting experiments are performed to quantify temperature measurement accuracy, using a strategy similar to that employed in [36]. For this purpose, the laser in the LPBF testbed is used to heat a point on a metal specimen that is also monitored with the spectrometer. Pure metals demonstrate consistent heating as the experiment proceeds, followed by a pause in temperature change as the latent heat of fusion is overcome at the melting point (i.e., a meltpool forms in the region observed), and then resume increasing in temperature once the region is liquid. Comparing the optically-measured temperature at the pause to the textbook values provides a means for assessing instrument accuracy. Melting events are identified via a filtered derivative. In pure-metal experiments, melting is taken to begin at the first zero crossing and end at the last zero crossing of the filtered derivative. The average temperature between these times is taken to be the measured melting point and the standard deviation is also computed to understand measurement uncertainty. Alloys are considered similarly and, while their melting behavior is more complex, their liquidus points are also observed and compared to textbook values. Liquidus is identified by a significant inflection point, again made clear via filtered derivative of the temperature data.

These experiments begin by placing a metal specimen on the build platform of the LPBF machine and adjusting the position of the build platform such that the top surface of the metal specimen lies in the build plane. Next, the enclosure is purged to $\leq 400$ PPM of oxygen using argon (Linde, 99.999%), as measured via MTI W1000 trace oxygen sensor. Operating the laser at a low power, the turning mirror is adjusted to maximize the net optical power recorded in the central fiber of the hexagonal pattern (i.e., the laser spot is made co-incident with the center of the field of view of the spectrometer). Then, a series of trials determine laser parameters that induce a clearly-visible melting event in the spectrometer data, where laser power is applied as a ramp over $4$ s in all experiments. Only the starting and ending laser powers are adjusted, which must be tuned for the optical and thermal properties of each specimen individually. The LPBF testbed enclosure is then opened to reposition the metal specimen, such that a fresh location on its surface is placed at the at the center of the field of view. Then, the enclosure purged to $\leq 100$ PPM of oxygen over approximately $45$ minutes, and laser melting and temperature retrieval are performed for the final time. This two-step protocol is specifically used to limit meltpool oxidation, which is significant in view of the low volume of hot material and extended experiment duration.

Using this method, the selection of pure metals and alloys in Table 1 are used as benchmark materials; melting point and liquidus data are taken from the compilation in [63]. In all, they are chosen to provide a range of melting points over roughly a $1000$ K range representative of temperatures in LPBF. The five pure metals are sourced from Goodfellow as roughly $25\times 25\times 3$ mm³ squares except for the copper specimen which is smaller ($10\times 10\times 3$ mm³). Certified alloy specimens are obtained from McMaster-Carr and are cut to similar size with a band saw. As it has the highest melting point, titanium is used to set the the camera exposure time ($0.125$ ms) to avoid detector saturation; this is held constant when testing the remainder of the specimens. A $100$ FPS sample rate is used to limit the size of the resulting dataset.

Efficacy of the MWIR imaging spectrometer instrumentation and the data processing approach are shown in an industrially-relevant setting by monitoring the printing of an LPBF test artifact. Figure 2d shows the design: a simple $5\times 5\times 6$ mm³ cube with a $1\times 1$ mm chamfer added along one vertical edge to track component orientation. After defining this basic geometry in Solidworks (Dassault Systems), print planning is completed using Autodesk Netfabb software. This software is used to slice the component to achieve a $30$ µm layer height, then the perimeter of each slice is offset inward by $35$ µm (roughly half of the laser spot diameter). An infill pattern is generated within this infill region, rotated $67^{\circ}$ between each layer, where all hatches in a layer are scanned in the same direction using a $30$ µm hatch spacing. A copy of the slice perimeter is then made after the hatches, and these two items are exported as a .cli file in that order (i.e., the printer is commanded to fuse the infill, then scan the part perimeter). In turn, the .cli is converted to machine code using a custom Python script that also sets laser power and scan speed. For the present experiments, the power is set to $100$ W except for layers 100 to 150 that are printed with $90$ W. A $250$ mm/s scan speed is used at all times.

To prepare for printing the D86 laser spot size ($77$ µm) is verified by direct imaging per [21], then the galvanometer null position (defined to be coincident with the center of the component in the machine code) is aligned with with the center of the spectrometer field of view using a process similar to § 2.5. Next, the printer is loaded with 316 stainless steel powder (Carpenter Technology, $15-45$ µm) and ultra-high purity argon (Linde, 99.999%). Finally, the camera in the spectrometer is configured to sample at $475$ FPS with the same exposure time of $125$ µs used in the point melting experiments.

Typical results for point melting experiments are exhibited in Fig. 3. A pure titanium specimen is considered in Fig. 3a, wherein the top panel shows that an average temperature of $1919$ K is observed with the two time TES method at the transition from solid to liquid; this compares closely to the expected value of $1940$ K. During this transition, the measured temperature fluctuates with a standard deviation of $15.2$ K. In the bottom panel, the two time method is compared to the other TES methods described above, and no significant variation is observed. Figure 3b shows the features that underlying a temperature estimate made in the estimated melting period, including the spectrally-resolved radiance measurement made by the spectrometer as well as the estimated emissivity.

Figure 3c shows a similar result for a 316 SS specimen; again, a clear pause in temperature is not evident because this is an alloy. Nonetheless, the top panel shows a significant inflection point at around $1723$ K which we associate with the liquidus point that is nominally at $1739$ K. Also like the Ti case, temperature measurements provided by the different TES methods are compared in the bottom panel.

Full results are provided in Table 1 and show that the instrument is fully capable of resolving temperatures typical of LPBF with a maximum error of $28$ K across the materials studied. Alternatively, these data are graphically presented in Fig 4. In Fig 4a, the observed melting and liquidus points are plotted against their theoretical values. Error bars are provided for the pure metals and, as described in the methods section, represent the $1$\textsigma standard deviation of temperatures spanning the beginning and ending of the observation of melting. They are largest where low signal levels are recorded, for the copper and aluminum, and shrink as the signal-to-noise ratio improves for meting points at higher temperatures. No error bars are provided for the alloy measurements as liquidus occurs at a single point in time in these experiments. Finally, a linear regression is provided to assess the presence of systematic errors in these measurements, which is evident as an overestimate of $2.33$%. This is attributed to calibration error and improvements to the calibration process are expected to further improve instrument accuracy. Examination of the residuals to this regression, provided in Fig. 4b, indicates no obvious additional systematic trends.

Figure 5a shows temperature data, retrieved using the two time TES method operating on data from the center spectrometer channel, for two representative layers during fabrication of the LPBF test artifact. Layer 20 is characteristic of regions that achieve full density, evidenced via the micro-CT slice in Fig. 5b. An initial increase in temperature is observed at the beginning of layer fusion (around $100$ ms), where thermal energy is conducted from the distant meltpool (i.e. hatching begins a point on the perimeter of the part about 2 mm from the location of observation). This is the primary cause of the temperature fluctuations leading up to around $950$ ms into the layer, and it increases in magnitude as the scan trajectory approaches the center of the test artifact. Cyclic heating becomes great enough approximately $1000$ ms into fusion of the layer, where direct laser heating brings the observed material through the liquidus point at $1708$ K no fewer than four times. Rapid cooling is also observed, where the molten material reaches at temperature of less than $1000$ K between subsequent hatches. A comparison to the other TES methods can be made with the figures in § S2, which minimal variation much like the point-melting experiments. The only notable difference is that the two-time method more often recovers temperatures near the noise floor of the instrument, where the optimization fails to converge for the others.

The temperature traces in Layer 20 are contrasted with the traces corresponding to layer 117, where the obvious differences are impaired cooling (particularly from $700$ to $1100$ ms) and a melting event around $1000$ ms where the material takes an extremely long time to cool.

Inspection of the micro-CT data from these selected layers, plotted in Figs. 5b and 5c, shows that layer 20 is nearly homogeneous, while layer 117 contains a large number of flaws in the cross section. The geometric attributes of the flaws are fairly consistent, often comprising large blob-like features of solid material surrounded by a horseshoe-shaped pore. While these pores sometimes have unfused powder within them, the blobs are far too large to be powder particles themselves and so the underlying mechanism is not lack-of-fusion from insufficient laser power. Rather, combination of extended cooling and pore shape resolved in micro-CT images suggest that these defects are largely caused by balling; the extended cooling seen in the spectrometer data is molten material that has been pulled into a ball via surface tension and cools slowly on account of its size and limited contact area with the underlying material. Once formed, this ball continues to disturb the fusion process around it by failing to fully remelt and become consolidated with the surrounding feedstock. The enlarged area in Fig. 5d shows the ball and a pair of severe pores that caused the cooling anomaly in Fig. 5a.

Moreover, as highlighted in the introduction, the LPBF process is extremely sensitive to the boundary conditions of the fusion step and these changes are visible in the process signatures compiled in Fig. 6. The top panel, derived from the micro-CT data, shows that density typical of quality LPBF is achieved for about the first $100$ layers. After layer 100, where the laser powder is reduced to $90$ W, significant porosity results; moreover, the stability of the process does not return to its prior equilibrium when the laser power is returned to $100$ W at layer $150$. As the density is also observed to decline in this range, as far as $\approx 92$% in layer 175, this may imply incipient print failure. Considering all cooling events observed by any spectrometer channel, Fig. 6b shows the average cooling rate of the part decreases from around $0.3$ ms^-1 to $0.2$ ms^-1 over approximately the first 40 layers, where thermal energy is rapidly dissipated into the cool build plate.

As the print progresses, thermal conduction to the build plate is decreased and thermal energy begins to accumulate in the part and build plate. Considerable, yet stable, variation is observed in the cooling rate signature through layer 100, including a cyclical pattern that is hypothesized to result from interaction of the meltpool plume with the process laser (i.e., a process disturbance when the laser scan direction is approximately in opposition to the direction of gas flow). From layer 100, a rough pattern of lower highs is observed and coincides with layers having low density.

Likewise, the next panel down shows that the time-temperature integral climbs over the initial $40$ layers, indicating that, on average, the meltpool is surrounded by increasingly hot material for a longer duration. This metric trends downward from about layer $80$ and stabilizes at a relatively low value around layer $125$. Finally, average maximum temperature is also plotted in the bottom panel. Maximum temperatures at the beginning of the print are in excess of $2000$ K; this trend decreases to a value just over the liquidus point ($1739$ K) near layer $100$ and remain at that level for the duration of the print. In some layers, the maximum temperature appears insufficient to achieve melting. In combination, it appears that the scan parameters initially generate near full density where maximum temperatures and cooling rate are high. This suggests a small meltpool that is hot enough to completely melt the feedstock and a portion of the previously fused material. As the build progresses, the combination of low cooling rate and low maximum temperatures near liquidus are hypothesized to indicate large areas of the part becoming simultaneously molten (i.e., insufficient scan speed to maintain desirable meltpool dimensions) and this is consistent with the balling defects observed in the micro-CT data. It is interesting to note that none of the process signatures, nor the density, return to their prior level at layer $150$ where the laser power is returned to $100$ W. Again, it appears that the process has become so irregular as to prevent a return to the process window consistent with achieving full density.

While examination of spatial and temporal temperature transients gives qualitative insight into component quality, we now correlate specific process signatures to the presence of voids in the test artifact identified by micro-CT. For this, the volume directly sensed by each spectrometer channel during fusion of a layer in the test artifact is taken to be a cylinder with a volume equal to the product of the area observed by each channel (fiber) and layer thickness. In other words, each of the $3800$ time series is associated with a $92$ µm diameter, $30$ µm tall cylindrical volume in the test artifact. These corresponding cylindrical volumes within the micro-CT dataset are found by a direct accounting of known and measured shifts, scales, and rotations. As described above, process signatures are extracted for each of these cylinders and are thresholded. Process signature values outside of the threshold are taken to indicate porosity in the cylinder and are called alarms.

The severity of porosity within each cylinder is quantified by summing the number of porous voxels and reporting the diameter of a sphere with an equivalent volume. Ambiguity is reduced by this convention where, if a plurality of pores exist within an alarm cylinder, it is impossible to say which pores (individually or in aggregate) contributed to an alarm with the present level of experimental sophistication. A void in the CT data is taken to be detected if it lies in an alarm cylinder in the thresholded process signature data, otherwise it is missed. Conversely, an alarm is positive if porosity is measured in the cylinder and is otherwise false. Finally, it is common that the location of an alarm is vertically displaced with respect to the pore that manifests it (e.g., abnormally high temperatures can result from fusing material above a pore that impedes thermal conduction into previously solidified material). To consider this phenomenon, alarms are given a deviation allowance of $\pm 1,\,2,\,\mathrm{or}\,3$ layers, artificially making the alarm cover a taller region in the test artifact, prior to considering detection probabilities in the following analysis.

It should be noted that this is effectively a worst-case assumption. For example, two small pores in a cylinder that are individually of insignificant size are considered to be indistinguishable from one large, volume-equivalent pore. If a detection is claimed, even if the small pores would have been detected individually, credit is taken only for detecting the volume-equivalent larger pore. If a detection is missed in this example, it is counted as having missed the volume-equivalent pore which is also worse than the physical situation. An additional complication is that each channel is hypothesized to be sensitive to pores that lie in a larger volume that surrounds the volume nominally sensed. As the dimensions of this volume-of-sensitivity are presently unknown, no lateral allowance is made. Thus, it is also possible that a fraction of alarms considered to be false in the present analysis are actually valid, and indicate porosity just outside of the directly-observed volume.

Upon this basis, Fig. 7 presents cumulative detection probabilities for all pores of a certain diameter or larger, using process signatures of low integral, low cooling rate, and low maximum temperature. Low integral is taken to indicate porosity by one of two mechanisms. In one case, material that absorbed insufficient energy to fully melt may have low maximum temperatures, reducing this process signature. Alternatively, and perhaps more relevant to the nature of porosity in the test artifact, low integral may result from rapid dewetting of an area when a balling effect occurs (i.e., high temperatures are maintained only for a short period of time). For this signature $\approx 50$% of porosity greater than $4.3$ µm is detected with no vertical allowance. However, performance is greatly improved with a $\pm 1$ layer deviation allowance, after which 64% of all pores and 71% of pores greater than $20$ µm are resolved with a 5% probability that an alarm is false.

The center panel of Fig 7 presents an identical analysis of low cooling rate, indicating underlying porosity or large balls of slowly-cooling material. Setting the threshold for roughly equal rates of pore detection, this signature shows a comparatively higher rate of false alarms. However, that the shape of the detection probability versus pore size curves differs with respect to the low integral signature. For example, this process signature appears more sensitive to smaller pores than low integral. Finally, the bottom panel of the figure shows that low maximum temperature exhibits a low probability of detection, particularly of intermediate and large sized pores $\geq 100$ µm in diameter.