source size (for example, calibration lamp or melt pool) as well as sensor gain settings. It can be reasoned that the standard deviation of a coaxial melt pool monitoring sensor’s response will depend on multiple factors pertaining to the melt pool and region within the sensor’s field of view. For example, changes in sensor signal standard deviation may stem from the surface area of the melt pool, sensor gain/material processing window, melt pool emissivity, and other incandescing sources, such as spatter or plume. For example, if a hypothetical melt pool was a uniform 1300 °C and larger than the 2 × 8 mm tungsten filament of the calibration lamp, more photons would reach the sensor, which would then have a higher signal-to-noise ratio. The readings would have a smaller standard deviation of the data over time. The opposite would be true if the melt pool was smaller than the tungsten filament. As well, if a different material was chosen for processing with a lower relative melt pool size or temperatures, higher gain values would need to be selected. The standard deviation of sensor data over time would be reduced due to the increase in gain increasing the signal-to-noise ratio, and measurements could be recorded at reduced temperatures. However, the maximum temperature detectable would also be reduced, as the sensor would be more prone to saturation. The opposite trend would be observed for reducing the sensor gain. Changes in melt pool emissivity would have a similar effect as changes in melt pool size. Everything else held constant, a reduction in melt pool emissivity will reduce the number of emitted photons. The sensors’ signals will be reduced, and the standard deviation of the temperature calculated will be increased. The argument that the measured temperature’s uncer- tainty is a function of signal strength or melt pool/filament length is put to the test in a second round of experiments. The lamp’s aperture is enlarged to increase the amount of signal reaching the photodiodes. To prevent the photodetectors from saturating at higher temperatures, a neutral density (ND) filter is introduced at higher temperatures. In a separate round of experiments, the ND filter is optically characterized: it reduces the signal of the high photodiode to 13.71 of its unfiltered signal and the low photodiode to 10.57 of its unfiltered signal. These values are used to normalize the signals measured when the ND filter is placed over the aperture, to account for imper- fections in the filter. The tungsten lamp source’s aperture is enlarged such that the higher of the two signals is 85 of the photodiode’s satu- ration voltage while the ND filter is placed above the aperture. The calibration is repeated with the enlarged aperture after removing the ND filter, increasing the signal intensities at lower temperatures. However, to avoid the signal from saturating the photodetectors at the first temperature that either signal is above 75 of the photodiode’s saturation voltage, the ND filter is placed on the aperture for the remainder of the experiment. Although the ND filter directly affects the measured signal for both individual detectors, it does not affect the ratio of the signals, after accounting for the transmission percentages as described previously. It is expected that because relative sensor noise is higher whenever the signal is lower, that the standard deviation of the measured temperature will decrease with increasing temperature, except for the temperature at which the ND filter is added. The results, regressing the median value of Ri(t) (over the central 400 points) for each temperature set point, are shown in Figure 5. 2250 2000 1750 1500 1250 1000 750 500 Ratio (low/high) 0.42 0.44 0.46 0.48 0.50 0.52 Figure 5. Set point temperature versus mean signal ratio (blue dots) with curve fit (blue line). Note that the error bars do not indicate prediction uncertainty, but the ± 1σ standard deviation of measured temperature using the regression model at a given set point. T A B L E 3 Amount of time (μs) needed to produce sampling with given standard error (°C) Standard error (°C) Set point (°C) 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 100 270 75 30 20 15 10 10 10 5 5 5 75 480 130 45 35 20 20 15 10 10 10 5 50 1080 295 105 75 45 35 25 25 20 15 15 25 4315 1170 405 290 180 140 100 90 65 50 45 10 26 940 7300 2535 1805 1100 845 595 545 390 305 270 A P R I L 2 0 2 2 • M A T E R I A L S E V A L U A T I O N 69 Temperature (ºC)

The ND filter was added at the 1800 °C set point. The model fits to this data with an R2 value of 0.996, A = 447.52, and B = 1.0523. The model estimates the set points with an RMSE of 19.70 °C. As expected, the standard deviations of this model are overall lower compared to the previous model, particu- larly at lower temperatures. There is an increase in deviation at the data point where the ND filter was added, as the signal decreased. The model predicts temperature with a standard deviation which is 1.3 to 6.1 of the set point temperature. The predictions of the regression model and standard devia- tions of the temperature predictions can be found in Table 4. In a similar construction as the previous data set, the sampling time needed to produce a sample with a given standard error was calculated for this data set, shown in Table 5. It should be noted that neither the standard deviations or durations for a standard error for this data set or the prior data set are necessarily characteristic of the standard devia- tions and sampling periods during AM processing. As stated, there are other inputs that will affect these values. Spatial Normalization Results For the full build plate measurements, the data is sampled at 200 kHz and the standardization formula is applied to each individual data point to predict a temperature for that location. A scatterplot of the temperature values from the full build plate build is shown in Figure 6. As described in the “Spatial Normalization Calculations” section, for every data point, the ratio of the signals was divided by the spatially nearest correction value, which was used to calculate an adjusted temperature. A plot of the cor- rected values from the ratio image is shown in Figure 7. Note that the ratio values are similar to the temperature values because the function that relates them is nearly linear. A scat- terplot of the corrected temperatures is found in Figure 8. Qualitatively, it is clear that this standardization reduced the spatial variations in the original data. Quantitively, the 200 150 100 50 3000 2500 2000 1500 1000 X position (mm) 25 50 75 100 125 150 175 200 225 Figure 7. Scatterplot of the temperature data over the full build plate. 2200 2000 1800 1600 1400 1200 Ratio (low/high) 0.74 0.76 0.78 0.80 0.82 0.84 0.86 Figure 6. Set point temperature versus mean signal ratio (blue dots) with curve fit (blue line) for the neutral density experiment. Note that the error bars do not indicate prediction uncertainty, but the ± 1σ standard deviation of measured temperature using the regression model at a given set point. T A B L E 4 Regression prediction and data standard deviation by set point, variable aperture run Set point (°C) 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 Standard deviation (°C) 79.7 49.2 34.4 29.0 22.7 69.0 58.3 52.7 44.4 40.0 34.6 Model prediction (°C) 1352 1389 1477 1591 1703 1800 1891 1984 2095 2195 2321 T A B L E 5 Duration (μs) needed to produce sampling with given standard error (μs) Standard error (°C) Set point (°C) 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 100 5 5 5 5 5 5 5 5 5 5 5 75 10 5 5 5 5 5 5 5 5 5 5 50 15 5 5 5 5 10 10 10 5 5 5 25 55 20 10 10 5 40 30 25 20 15 10 10 320 125 60 45 30 240 175 140 100 80 60 ME | MELTPOOLMONITORING 70 M A T E R I A L S E V A L U A T I O N • A P R I L 2 0 2 2 Y position (mm) Temperature (ºC) Temperature (ºC)