Development of a New Temperature Measurement System for the Observation of Adiabatic Shear Band

This paper presents the development of a new system designed to measure the local temperature field in adiabatic shear band. Transient temperature field are simultaneously recorded by an array of 32 InSb infrared (IR) detectors and a streak camera working in visible-near infrared (VIS-NIR). Observations in IR offer a low temperature detection limit (350°C) but they are highly sensitive to uncertainty in the emissivity. Observations in VIS-NIR allow for measurement only at high temperatures (750°C) but they are less affected by uncertainty on emissivity and present a higher temperature sensitivity. By performing simultaneous measurements, it is possible to obtain data on a large temperature range with an improved accuracy at high temperature. The different sources of errors caused by uncertainty in the emissivity, spatial and temporal resolution of the detectors has been analyzed and an estimation of the total measurement uncertainty of the system is given.


I. INTRODUCTION
with c 1 = 5.9635 × 10 7 W m 2 µm −4 and c 2 = 14388µm K. Expression 1 is define for a 67 blackbody witch is a ideal emitter, for a real opaque surface the luminance is define as : Where ε(λ, T ) is the spectral emissivity of the surface. The accuracy of the emissivity 69 data is essential to perform precise temperature measurements; however, emissivity depends Where ∆ε = ε L − ε V is the difference between the supposed emissivity (ε L ) and true 78 emissivity (ε V ). ∆T = T L − T V is the difference between luminance temperature (T L ) 79 and true temperature of the surface (T V ). The luminance temperature correspond to the 80 measured temperature if we consider ε L instead of ε V . Figure 2 show the error on measured 81 temperature if we consider a theoretical emissivity ε L = 0.5 while the true emissivity value lie 82 between 0.01 and 0.99 ( ∆ε ε V = ±0.98). This example show the advantage of short wavelength 83 measurement: even if we have almost no information on the true emissivity, we can see that 84 for wavelengths below 1 µm, the maximum error is less than 10 % while it is above 50 % if 85 we work at 5 µm. temperature, we see that there is a peak of emissive power shifting to the short wavelength as the temperature increase. The wavelength of maximum emissive power can be calculated 90 using the Wien's displacement law : This relation show that at ambient temperature, the peak of emissive power will be close 92 to 10 µm, so almost no photons will be emitted at short wavelengths, the temperature of the 93 observed surface will need to increase to emit enough short wavelength photons, so that the 94 detectors generates a signal above the noise level. sweep onto a phosphor screen who convert the temporal evolution into a spatial variation.

111
The streak tube is follow by an image intensifier that amplify the number of photons, the 112 output image produce on the screen of the intensifier is then record by a readout camera.

113
This system allow the detection of low light level with a high temporal resolution. Our In the present setup, detectors and their optics act as low pass filters of spatial frequencies.

178
In the spatial domain,an image can be calculated as the convolution of the object and the 179 impulse response of the optical system : The function g i (x, y) correspond to the irradiance distribution of an ideal image which is Instead of using equation (6) it is usually more convenient to work in the spacial frequency 187 domain 14 . By doing so, convolution product turn into a simple product, and equation (6) 188 becomes : where : In equation (6) to the spatial response of the detector itself.

196
For the InSb array, DTMF is the product of two functions taking into account the finite 197 dimension of the detectors (∆x Det ) and the pitch between two detectors (∆x pitch ) 15 : For the streak camera, the DMTF has a Gaussian profil define as : The parameter σ Streak depends on the performances of the elements constituting the camera 200 (streak tube, micro-channel plate, readout camera) and can be measured experimentally.

(11)
Where f c is the cut-off frequency. As explained in section II D, the bandwidth of the InSb 219 amplifier as been reduce to f c = 13 kHz in order to limit the influence of crosstalk effects.

220
For the streak camera, temporal resolution will depend on the camera architecture but 221 also on the sweep speed and input slit width. The temporal response can be measured by 222 making a static image of the input slit, an example is given in Figure 6. This image shows 223 the dispersion of the photons along the temporal axis which corresponds to a temporal LSF.

224
Because the streak camera performs a temporal to spatial conversion, the sweep speed should 225 be taken into account in order to express the LSF in the temporal domain. The relation 226 between a distance y on the readout camera's focal plane array and the time is : Where v s is the sweep speed of the streak unit. In Figure 6, From this expression, we can express the modulation transfer function (H Streak (f )) as: The Fig. 7 shows the transfer function of both detectors. We can see that the streak camera which extend to lower temperatures 11 , therefore we will consider both set of data to define 243 ε(λ, T ).

244
If it is essential to characterize the emissivity of our material in IR this is not sufficient, 245 because we can suppose that the high strain within ASB will have an influence on ε(λ, T ) 246 leading to an error ∆ε ε . This error is difficult to quantify precisely but we can make as-247 sumptions on its sign: we can suppose that the high strain within the ASB will always Overestimation of the temperature Underestimation of the temperature Emissivity assumptions in IR (ε meas < ε V ) Spatial resolution ( f (T V (x)) ) Emissivity assumptions in VISNIR (ε meas < ε V ) Temporal response of detectors ( f (T V (t)) ) Emissivity assumptions in VISNIR (ε meas > ε V ) Results for each detector is presented on Fig. 10 and 11. These figures show that both 282 detectors uncertainty is more sensitive to δ x than t pulse and T max V , we can then conclude 283 that the major source of uncertainties come from the spacial resolution. In order to find 284 the precise value corresponding to our experiments we should take an assumption on δ x , to   The figure 12 give an example of temperature profiles measured by InSb detectors and 291 streak camera. In order to reduce the noise caused by crosstalk effects, InSb data has been 292 filtered using a low-pass FIR Butterworth filter (cut-off frequency: 57.5 kHz, order: 5) and 293 temperature contour have been interpolated along the spatial axis. The image of the streak 294 camera correspond to a 50 µs/mm sweep speed and was not filtered or interpolated. We arbi-295 trary fixed the origin of spatial and temporal axis at the maximum temperature point. Both 296 profiles present a good similarity and we can identify a hot spot around (−100 µm,−20 µs).

297
As expected, Insb detectors allow measurements on a broader temperature range than streak 298 camera but at the price of higher uncertainty (see Fig. 13). On figure 12, the maximum tem-299 perature measured by InSb and streak camera are respectively 1276 K and 1313 K. Those 300 value are coherent with the data of Ranc and al. 6 and Pina 5 , however in their work these 301 authors used VIS-NIR intensified camera which was able to take only one 2D image for each 302 test furthermore, the integration time of such camera is problematic for the observation of 303 ASB. The main advantage of the present system is to allow transient observation in both 304 IR and VIS-NIR giving more information on the phenomenon.

305
In Fig. 13, we present the result of a series of experiment with impactor speed from 306 28 m s −1 to 61 m s −1 . Error bars have been estimated following the method described in 307 section III. We can clearly see the benefit of short wavelength measurement which present a 308 much smaller range of uncertainties. For all tests, the maximal temperatures measured by 309 InSb detectors tend to be lower than those of the streak camera, this can be imputed to a 310 lower temporal resolution and a lower sensibility of the detectors.

311
By performing simultaneous measurements in both IR and VIS-NIR spectral range, our 312 system allowed for a precise evaluation of the maximum temperature with a very low influ-313 ence of emissivity uncertainty. Through a practical case we analyzed the influence of optical 314 assembly and different sources of measurement errors. We detailed the process and steps 315 to present realistic error bars. This approach is relevant to any ASB temperature measure-316 ment. Many other applications of this system can be anticipated for the study of ASB or 317 high speed phenomenon (ballistic impact, cold spray, intermetallics reactions).