Application of pressure-sensitive paint for explosive blast measurements

This study demonstrates the application of fast response pressure-sensitive paint (PSP) to explosively driven blast wave testing. A sprayable polymer ceramic fast response PSP was applied to an aluminium disc before being coated with platinum porphyrin compound as the active luminophore. The disc was then exposed to a blast wave and the response was measured using a high-speed video camera. The PSP measured the transit of the incident shock wave clearly, albeit with a slight response delay following the instantaneous change in pressure. A time domain-based method for improving temporal response, whilst considering both spatial and temporal effects, is described. This study clearly demonstrates that the spatial distribution of a blast wave on a surface may be captured by PSP technology. Integrated parameters such as impulse can correctly be characterised using this method. This technology offers an enhanced and more efficient way of characterising blast.


Introduction
Pressure-sensitive paint (PSP) is an optical method for quantifying static pressure spatially over an entire surface.The technique has enjoyed great success over recent years and has been applied successfully to full vehicles [1][2][3], rotating components [4][5][6], and even moving targets [7,8].The study by Casper et al [9] demonstrated the use of polymer ceramic (PC) PSP to measure the blast response on a model in an outdoor environment.The authors note the challenges of this approach due to light pollution from the sun and also from the fireball generated by the explosive charge.A processing algorithm to account for the varying light due to the explosion was required to yield credible results.In the current work, an explosively driven blast is measured using a blast tube which features a 90-degree bend to mitigate the impact of any illumination from the explosively generated fireball.
Understanding the propagation of blast waves over a surface is extremely challenging.Peak pressures are often generated by interaction between reflecting shock waves, making such a flow difficult to understand with point transducers alone.When combined with complex geometries, blast wave interactions provide a temporal and spatial challenge to experimentalists.Wave structures can be measured with techniques such as schlieren or (more practically in explosive environments) background-oriented schlieren [10] (or derivatives thereof [11]); however, this method does not directly quantify physical properties such as pressure.Attempts have been made by researchers to correlate between indirect measurement methods (such as wave time of arrival or wave shape) and pressure [12][13][14].Good correlations have been found using optical technique to track wavefronts and applying scaling laws to estimate overpressure; however, this approach is limited to simple waveshapes such as explosions in free air and not propagation around complex objects.By measuring temporally and spatially varying pressures across a whole surface or model, engineers are able to integrate unsteady panel loads, something which is currently difficult to achieve.Additionally, the damage potential from blast loading is generally estimated by the integrating the duration of the positive pressure phase (referred to as the impulse) following the arrival of the shock, using PSP as an input to this calculation enables it to be evaluated spatially across a model to estimate damage, or potential failure, under blast loading.
This study aims to demonstrate the use of PSP for quantitative measurement of surface pressure which can be applied to more complex geometries.To achieve this aim, a commercially available fast response PSP from Innovative Scientific Solutions Incorporated (ISSI) [15] is used to measure the progress of the shock wave emanating from the blast tube.Methods of post-processing to improve the temporal response of the PSP of the measurement are shown along with wavefront measurements and quantitative measurements of pressure behind an explosively generated shock.

PSP methodology
The basic methodology of the PSP technique involves quantifying a reduction in the luminescent output of a coating applied to a surface in response to increasing oxygen concentration (and therefore pressure).When the luminescent coating is excited with the appropriate wavelength of light (often ultraviolet or blue), the coating will emit a longer wavelength (often orange or red).The change in the output of the coating can be measured with a camera with suitable filters which, after an appropriate calibration, yields a spatial measurement of surface static pressure.
In PSP measurements, it is traditional to describe the response of the coating to pressure using the modified Stern-Volmer equation (1) where I is image intensity, P is pressure, subscript ref denotes a reference condition without any flow (often called wind-off), and A x (T) are calibration coefficients which are functions of temperature, T. The Stern-Volmer equation is sometimes extended to include higherorder terms (2) which account for non-linearity in response, particularly over large pressure ranges [16].However, given that the input to these equations is image intensity and the desired output is pressure, an alternative approach is to formulate this calibration curve as P = f (I, I ref , P ref , A (T) , . ..), as will be conducted in this study and is shown in (3),

Fast response PSP
The traditional approach of applying PSP to a surface involves the use of an oxygen permeable polymer binder which severely limits the response time of the coating.Substantial efforts have been made to improve the temporal response of PSP as detailed in the review papers by Gregory et al [17] and more recently by Peng and Liu [18].A crucial component affecting the temporal response of PSP is the substrate used; more specifically, how the active PSP luminophore is attached to the surface.Fast response substrates are often described as porous in nature; allowing the test gas under investigation to directly interact with the luminophore, without the need for a slow diffusion process.Commonly used methods of applying a porous substrate to a surface involve either spraying a ceramic-filled coating with high micro-porosity, or anodisation of the surface as described in the extensive body of work by Sakaue [19][20][21][22][23] and collaborators.Recent development work on sprayable substrate has been completed by Egami et al [24,25] and Kasai et al [26] demonstrating extremely fast response times by varying the ceramic particle fraction in the substrate and including treatments for the ceramic filler (commonly TiO 2 ) to improve its hydrophobicity.Shock tubes provide excellent methods of testing the response time of sensors such as PSP, whilst also providing an analytically predictable yet challenging environment to measure within [27].Asai et al [28] used shock tubes to demonstrate that PSP coatings with different luminophore and substrate combinations could deliver millisecond (and faster) response times.In the 2017 work of Numata et al [29] transient shock wave measurements were conducted with PSP using anodised aluminium as the substrate which was generated using phosphoric acid as the electrolyte.By controlling the temperature during the anodisation process, pore depth was optimised to give a fast response time.Using a ruthenium-based luminophore and optimised anodisation parameters, time constants as short as τ = 0.35µs were achieved.Alternative substrates, such as thin layer chromatography plates, have been used with success and have excellent response rates [27,30] with time constants of the order of τ ∼ 10µs ; however, these are limited to flat and simple geometries.
Despite using a porous substrate, PSP does not respond instantaneously and as such PSP often struggles to measure very high frequency content ( f > 10 kHz).The work of Sugimoto et al [31] showed a very clear and well characterised first-order response of PC PSP and a platinum porphyrin (PtTFPP) luminophore with time constants of τ ∼ 25 µs.Pandey and Gregory [32] measured the step response of PSP in an air-driven shock tube and showed time constants of 20 < τ < 60µs depending on the luminophore and substrate combination.Pandey and Gregory also commented that fast response PSP can exhibit potentially significant hysteresis effects.
In 2001 Winslow et al [33] demonstrated a dynamic correction technique which highlighted the benefits of correcting the frequency response of PSP.Winslow showed that after characterisation of the frequency response using a physicsbased model, a transfer function could be derived which corrected the magnitude and phase response of the PSP output.Later work by Funderburk and Narayanaswamy [34] demonstrated a frequency correction algorithm based on the ratio of power spectral values from both PSP and transducers as a function of frequency; however, the authors noted that this method does not account for changes in phase as a function of frequency.Liu et al [35] and Numata et al [29] showed a correction for PSP frequency response by including both the influence of the camera exposure time and the physical frequency response of the PSP.The dynamic correction of PSP results for non-unity gain and phase lag across a wide range of frequencies is not often performed.In most cases, the frequency response is not actually known a-priori or quantifying it is the aim of the experiment.For different substrates, paint solvents, ceramic fillers, paint thicknesses or even different painters, the frequency response characteristics may be different.Correction of frequency response for non-unity gain is only applicable to stationary unsteady signals with long time history recordings.The study by Liu et al [35] demonstrated application of temporal response correction in the frequency domain and highlighted the challenges of overcorrection in the frequency domain (particularly at higher frequencies) resulting from relatively low signal to noise ratio.In order to correct for the low-pass filtering effect of the PSP response time, it is necessary to amplify high-frequency content; however, if frequency-domain information is the desired outcome of the experiment, care must be taken to not overcorrect highfrequency content [34,35].

PSP temporal deconvolution
The PSP response to a step change has historically been considered a first-order type response which can be modelled with a single exponential, typically in the form of f (t) = 1 − e − t τ .Hayashi and Sakaue [36] expressed doubt that a single exponential would be sufficient to completely represent the response of a PC PSP to a step change, due to what they called fast and slow content.The slow content comes from the inherent diffusion through the polymer.Sugimoto et al [31] showed that a single exponential does model the response of PC PSP adequately over a wide range of frequencies, even if the exact frequency response is slighty more nuanced [21].
Assuming PSP responds as a first-order system to a step input such as a moving shock, the PSP data can be said to have been passed through a transfer function which obscures any instantaneous response.In this study, the PSP is exposed to a blast wave, a near instantaneous rise in pressure, followed by a relatively slow decay.Given the purely transient nature of this flow, characterising and correcting a frequency response is impractical.Rather than trying to evaluate a frequency response, a time-domain based approach utilising convolution and deconvolution is demonstrated.If a step change is expected, an estimate of the convolution kernel shape required to turn a step change into a first-order response can be made.Based on previous PSP studies demonstrating exponential response, a deconvolution kernel of an exponential decay can be utilised.
The deconvolution kernel, k, used in this study is in the form where t is the time and τ is the time constant associated with the exponential decay.The kernel is normalised by its total sum such that when used for deconvolution, the amplitude of the deconvolved signal remains the same.This kernel is evaluated at integer values of time which corresponds to frame interval times of PSP capture (as shown in figure 7).Deconvolving a PSP pixel time history with this kernel can be applied to every pixel in the PSP video to improve the temporal response.This study refers to this approach as temporal deconvolution to distinguish from other uses of deconvolution in PSP literature (primarily associated with spatial motion blur [37,38]).This study refines previous work utilising this approach [39] and demonstrates that a variety of deconvolution kernels should be evaluated, and their output assessed and verified in space, not just time.

PSP hardware
Two in-house manufactured UV LED lights consisting of seven SBM-120-UV-R34-L395 LEDs were used to illuminate the PSP which have a peak wavelength of 395 nm and a full width half maximum of 17 nm.The lamps, along with additively manufactured collimators, were mounted close to the PSP coated sample as shown in figure 1(d).The LEDs were powered on for approximately 6 s prior to the firing.A Phantom V2512 high-speed video camera was mounted in an adjacent room to the blast chamber with viewing access afforded through two plexiglass sheets to avoid any damage to the camera.The camera was fitted with a 60 mm Nikkor macro lens and a 610 nm long-pass filter to remove unwanted light.The PSP was measured at a frame rate of 96 kHz with an exposure time of 9.95 µs.The exposure level on the sensor was approximately 45% of the 12 bit sensor ADC range prior to shock arrival.The aluminium target disc was painted with an epoxy-based primer coat to ensure good adhesion of subsequent layers.The epoxy was left to cure under infra-red lamps for several hours before application of additional layers.The surface was then coated with the porous, fast-response layer from ISSI, yielding a uniform white surface.The ISSI fast-response layer was chosen over more recent PC-PSP formulations [24,26] due to its commercial availability.All porous basecoats are extremely absorbent, and care must be taken to avoid contamination (such as oils in human skin).The porous basecoat was then left to cure under IR lamps as before.Finally, approximately 1 h before the test, the final sensitive PSP layer was applied.The luminophore used in this test is PtTFPP (CAS number 109781-47-7) which is dissolved in trifluorotoluene.Once all layers were sprayed, the PSP was kept in a dark environment, as much as was practicable, to reduce the impact of photodegradation (of key importance given the short exposure times required for this test).
Spraying of all layers was conducted on-site in a portable spray booth with a miniature compressor and a high-volume, low-pressure spray gun.To maintain operator safety, concentration of volatile organic compounds was monitored using an Ion Science Tiger volatile organic compound meter and potential oxygen depletion was monitored using a Crowcon T4 oxygen sensor.

Blast tube and target
The Atomic Weapons Establishment (AWE) Aldermaston Mini Air-Blast Tube (MABT) is 4 m long and has 0.2 m internal diameter and includes a 90-degree bend to block line of sight between afterburning detonation products of the charge and PSP coated sample.The PSP used in this study can respond up to pressures of 0-200 kPa absolute pressure [15].This can be considered a 'soft limit' and greater pressures may be measured, albeit with potentially reduced fidelity.As the pressure increases on the PSP surface, the PSP emission decreases (as will be shown in the results section), resulting in a gradually poorer and poorer signal to noise ratio.Eventually the luminophore will become so quenched by the oxygen in the high-pressure test gas, and no further pressure measurement will be possible as changes in PSP response will be smaller than the noise of the camera.One of the original objectives for this work was to design an explosive driver charge to firstly achieve 200 kPa overpressure (∼300 kPa absolute), and then to determine if higher pressure responses were possible by increasing the charge.
A simple two-dimensional axisymmetric model was generated in Ansys Autodyn which was used to guide the design of a charge which would achieve approximately 200 kPa overpressure on the face of the instrumentation plate.The main purpose of the modelling was to show that charge driver section pressures would not induce plastic yield in that section of the tube.For expediency, the model was a 10 cm radius, straight, 4 m long tube and did not include the 90-degree bend.
The explosive used was pentaerythritol tetranitrate (PETN) explosive and is available in 10 g m −1 linear charge density form.Note that the real PETN charge included a plastic sleeve which was not included in the model.The charge was modelled to achieve linear charge densities of approximately 10 g m −1 , 20 g m −1 , 30 g m −1 , 40 g m −1 and 50 g m −1 .An Eulerian mesh was used to model the flow of air through the tube.There is a balance to be found regarding refining the Eulerian air mesh.If the mesh is too refined the model will take a long time to run and if the mesh is coarse the simulation will not be accurate.For example, for the 20 g m −1 model, the air mesh was well refined around the PETN driver charge, with a cell radius of 0.4 mm, meaning that the PETN radius was 5 cells.Modelling showed that a linear charge density of 50 g m −1 would achieve peak stress of around 200 MPa on the driver section wall; well below the 355 MPa plastic yield limit for the steel.Modelling showed that 10 g TNT equivalent would likely reach the 200 kPa requirement for a straight tube (for configurations of between 10 g m −1 and 30 g m −1 PETN, all well below the 50 g m −1 maximum).
The final charge design was empirically and iteratively determined.The starting point for this determination was the modelling, but an additional consideration was the removal of any fireball effects from the end of the tube and the driver end of the tube.Soot can clearly be seen on the chamber wall from previous firings of the MABT (figure 1(a)), caused by a result of the interaction of the fireball from the inlet (or driver charge) end of the tube with the wall.Early tests showed the light from this fireball would reflect off the wall and contaminate the high-speed video of the PSP response.The final driver charge comprised of three parallel strands of PETN, each 150 mm in length, aligned along the central axis of the driver end of the tube and inserted 0.5 m from the driver end.The final charge per unit length was 30 g m −1 .The driver charge was initiated from the driver end of the tube, with a single RP80 detonator which contained 80 mg PETN and 123 mg of Research Department eXplosive (RDX).
To remove the reflection of the explosive fireball off the firing chamber wall, the location of the driver charge was empirically optimised by inserting it into the inlet of tube by varying amounts (up to 0.8 m).Unfortunately, deep charge positions led to light contamination issues from the fireball at the outlet end of the tube.The design, and positioning of the charge was therefore a compromise between the charge being large enough to attempt to meet the 200 kPa overpressure requirement whilst minimising the light contamination at the outlet end of the tube.Due to the compromises needed for the optical measurements, the peak pressure on the target face was slightly under the 200 kPa requirement, and it was not possible using this experimental arrangement to explore PSP response at significantly greater pressures.
Figure 1(a) shows the round target disc placed orthogonal to the shock tube exit.The target disc (shown in figure 1(b)) has a 100 mm frontal diameter with two tapped holes for the pressure transducers.The upper, larger, hole contains a PCB113B28 sensor whilst the lower hole contains a Endevco 8510C-50 gauge.Both transducers were recorded at 1 MHz per channel.This high recording rate facilitated down-sampling to the anticipated slower PSP measurement frequency as required.In all subsequent calibrations and data processing, only the PCB data will be used.The location of the PSP painted disc in relation to the exit of the blast tube is shown in figure 1(c).The target disc was securely strapped down and multiple blasts were detonated without PSP to ensure that there was no relative motion of the disc caused by the explosion.
As this flow is driven explosively and not by traditional diaphragm-based shock tube, the pressure response should be characterised as a blast wave.Unlike a regular shock tube where a period of uniform flow and pressure is expected behind the shock, a blast wave is characterised by an immediate decay of pressure [40].
As PSP is an oxygen sensor, it was necessary to validate that the gas composition over the PSP sample would not change due to the products of the explosive charge.To rapidly simulate this, a shock tube simulation was conducted using the Wisconsin Shock Tube Laboratory x-t diagram code [41].Initial conditions (P 4 /P 1 = 6.4) were set based on the shock exit Mach number (estimated from previous tests).The contact surface in a shock tube represents the interface between the gas exposed to the moving shock wave and the gas formed from the driver or explosion products.This simulation found that the contact surface does not impinge on the PSP disc within the test recording time.Further simulations were performed using the Viper::Blast code [42], Viper::Blast is a computational fluid dynamics (CFD) simulation tool for modelling air blasts from the detonation of high explosives.A three-dimensional simulation of the charge in a straight, 4 m long tube of internal diameter 0.2 m was performed.A straight tube was modelled for expediency.The simulation showed that, at the time the pressure exited tube the outlet, the burnt detonation products has propagated no more than 2 m down the length of the tube.The detonation products were shown to not be reaching the target disc, over the full blast positive phase duration time.

Pressure transducer processing
As mentioned, pressure transducer measurements were captured at 1 MHz; however, the camera measurements were captured at 96 kHz.To enable the use of transducer data to provide an in-situ calibration for the PSP, it was necessary to resample the transducer data to the same rate as the PSP whilst maintaining temporal alignment.The data was resampled using the MATLAB function 'resample' [43] with an optimised Kaiser window to avoid any non-physical fluctuations in pressure around the shock arrival as shown in figure 2.
In blast wave testing, the transient response of the pressure transducer to a step change can cause fluctuations in the observed pressure [44].The instantaneous change in pressure will excite the natural frequency of the sensor, its mountings, and any other components utilised in its installation.An electrical step response produced by the transducer can also cause challenges in selecting termination resistors and characterising cable capacitance [45].As a result it is common to be sceptical of the peak overpressure values such as those shown when the shock arrives in figure 2 (∼350 kPa).The transient response of the transducer decays very quickly and the reliable pressure readings are from approximately 30 µs onwards after the shock arrival.The response of pressure transducers is often modelled using a modified Friedlander curve [46] of the form ) × e −α t t * + P a (4)  where P s is the peak overpressure, P a is ambient pressure, t * is the positive phase duration and α is an empirical constant.
For the raw transducer data shown in figure 2, a Friedlander fit using, equation ( 4), has been calculated utilising pressure data from three positive phase durations after the arrival of the shock wave.Three durations was found to fit the data very well.For more robust methods on fitting parameter selection and optimisation, refer to [11].The Friedlander fit in figure 2 has the following values P s = 175.5 kPa plus ambient of P a = 99.3 kPa, t * = 578 µs, and α = 0.958.The peak overpressure from the Friedlander fit is the maximum pressure behind the shock front, not the overshooting of the pressure transducers in the initial 30 µs after the shock arrival.

PSP image processing
Raw PSP images showing the illumination pattern on the PSP surface, and the change upon the arrival of the shock, are shown in figure 3. The shock front is clearly visible as a reduction in brightness compared to the wind-off image.
In order to generate a reference (wind-off) image, 20 frames just prior to the arrival of the shock wave were averaged.Due to the clear contrast between the dark background and the PSP sample, a mask was automatically generated using a k-means clustering algorithm [47].The mask was applied to all subsequent images to remove the background.Wind-on images were then divided pixelwise by the wind-off image to produce an intensity ratio as a function of time.
The standard approach to generating an in-situ calibration using pressure tap data is to extract the PSP signal around the transducer.However, given the transient nature of this flow, using such an approach will produce an unwanted spatial averaging effect as the shock moves through the extracted PSP region (as was present in [39]).A 100 pixel rectangular area (5 pixels wide and 20 pixels tall) was extracted slightly vertically offset from the transducer with the major axis of the rectangle approximately orthogonal to the shock front as shown in figure 4 (red rectangle).
The intensity ratio in this area is then compared to the pressure ratio values from the PCB transducer, giving a calibration curve as will be shown in the results section.Equation (3) (a second-order polynomial) was utilised as the calibration curve and was evaluated using the polyfix function [48] which forces the PSP calibration curve to pass through the point 1, 1.This should be a requirement for PSP calibration as the reference conditions should dictate that at the reference intensity, the pressure value should be the reference value; however, when using transient PSP calibration like this it is not uncommon for the curve to be heavily skewed by outliers.When calibrating over a large pressure range (such as blast wave testing) the inherent non-linearity of PSP can result in calibrations not passing through the point 1, 1.In addition to fixing the calibration curve through a point, an outlier analysis was used to remove values which do not follow the initial calibration curve.The removed values are a result of the transient response of the PSP being slower than the transducers or potentially the transducer overshooting the physical values [44].A total of 50 data points are used to generate the PSP calibration curves with 20 being before the shock arrives and 30 after.
No additional spatial filtering was applied to any of the PSP images presented in this study; however, an edge preserving filter such as a median or a bilateral filter could be used to reduce the level of spatial noise without smearing discontinuities.

Results
Results including time history plots extracted from the PSP are compared to transducers.Calibration plots, and montages of the shock wave progression are shown for the regular PSP process and temporal deconvolution in the following sections.
There was no motion of the PSP sample due to the impact of the shock wave, meaning no image alignment steps were necessary for PSP processing.However, beyond approximately 500 µs, the blast wave in the chamber impacts the LED lamps causing them to vibrate, having a serious impact on the PSP results and making the data unreliable.This discrepancy is also visible in figures 5(a) and 9(a) as the PSP and transducer response diverge beyond this time; however, there may be alternative sources for this result as will be discussed in section 4.6.Fortunately, the instrumentation plate has already experienced most of the blast impulse by 500 µs [15].In all results shown, time t = 0 is when the incident shock wave is first detected by the pressure transducers, x = 0 and y = 0 indicate the centre of the target disc with the image scale being set by the 100 mm disc diameter.The spatial resolution of the images is 3.16 pixels mm −1 .

Regular PSP processing
The response of both PSP and the PCB pressure transducer are shown in figure 5(a) for the region of interest shown in figure 4. Behind the initial rise in pressure there is a small plateau shown in the PCB trace at 240 kPa before a continuation of the exponential decay.The PSP response follows the transducers well during the positive phase duration until around 500 µs for the reasons described above.The initial rise in pressure is temporally under resolved; however, the two traces fit well from approximately 90µs onwards.The calibration curve used for the PSP is shown in figure 5(b).As mentioned previously, there are several outliers which have been excluded from the fit.These outliers are immediately after the shock arrival, due to the relatively slow response of the PSP.The calibration curve constants from this fit are B 3 = 3.827, B 2 = −6.125,B 1 = 3.298.
Figure 6 shows a montage of shock wave progression across the PSP coated disc.The incident wavefront is mildly curved, as would be expected following a shock wave emanating from a tube into free space, and shows a clear propagation across the disc.After t = 31.2µsthere is a faint reflected wave coming from the PCB transducer location as a result of the transducer not being perfectly flush to the surface.

Temporal deconvolution PSP processing
The temporal deconvolution method described in section 2.3 and [39], was applied to the time history of each pixel to attempt to recover extra information.In order to quantify the performance of different exponential deconvolution kernels, the PSP data was temporally deconvolved with six different kernels with different values for τ .The values for the time constant were derived from multiples of frame intervals (96 000 fps gives a frame interval of 10.4 µs).For an exponential response to a step change, 95% of the change is reached by three time constants.In this study the deconvolution kernels were chosen as 2/3, 2.5/3, 3/3, 3.5/3, 4/3 and 5/3 frames which equates to τ = 6.93, 8.67, 10.40, 12.13, 13.87 and 17.33 µs.The deconvolved PSP videos then had a centreline profile extracted across the disc which was averaged between values of y = 0 ± 3 pixels.The shock front is approximately planar over such a small vertical region and averaging significantly improves the signal to noise level for visualisation of spatiotemporal performance.
Figure 7 shows the spatial response of the PSP when deconvolved with exponentials with different time constants.The raw PSP signal shows a relatively slow increase to a steady value and follows a pattern of a first order response with motion blur as described by Numata et al [29].The value of τ = 17.33 µs, used in the previous study [39], clearly demonstrates an overshoot which is non-physical and can be deemed too aggressive when considering the spatial performance of this approach.Values of 8.67 < τ < 10.40 µs demonstrate appropriate responses as the pressure value behind the shock is reached quickly with minimal or no overshoot above the 'steady' value of approximately 242 kPa.
Comparison of the response of each deconvolution kernel in time, and the pressure transducer, is shown in figure 8.For each deconvolution kernel, the calibration region of interest (figure 4) is extracted and plotted against time.For values of τ = 13.87 µs, the PSP response approaches the transducer response very quickly; however, as shown above, the spatial response demonstrates this is not an appropriate length of kernel.Values of τ = 12.13 µs demonstrate a marked improvement in response time over the raw PSP signal; however, figure 7 highlights a non-physical pressure response.A value of τ = 10.40 µs yields a significant temporal improvement over the raw PSP signal and, given the appropriate spatial response shown above, will be the kernel used for the remainder of this study.

Temporal deconvolution results
The response of the extracted region of interest after performing pixel-wise temporal deconvolution on the PSP video is shown in figure 9(a) demonstrating a sharp pressure rise followed by the expected pressure decay.The associated calibration curve in figure 9 A montage of the temporally deconvolved (τ = 10.40 µs) PSP data is shown in figure 10 and demonstrates a sharper pressure rise behind the incident shock.The wave reflected from the transducer port is more visible too; highlighting that weak features are not obscured by the increase in spatial noise.

Spatio-temporal results
Shock propagation is commonly described using an x − t diagram.By extracting a centreline section of the PSP data, an x − t diagram can be generated to help calculate shock wave properties.Figure 11 was generated by averaging a seven pixel high vertical strip (as before) at all horizontal locations across the width of the disc.Both PSP processing approaches show broadly the same features; however, the temporally deconvolved data shows a sharper rise and slightly higher levels of spatial noise.
Applying an edge detection algorithm to the x − t diagrams in figure 11 enables the shock front to be curve fitted with the gradient of this curve the propagation speed.Using a Canny edge detection on figure 11(b), and fitting a firstorder polynomial through the resulting edge, yields a shock speed of 532 ms −1 .During the test, the ambient temperature in the room was approximately 283 K, giving a sonic speed of 337 ms −1 .The velocity measured from the x − t diagram can be converted into a Mach number of 1.58.A Mach 1.58 normal shock wave will generate a static pressure ratio of 2.75 according to one-dimensional compressible flow theory which, given the climatic conditions of the test day, yields 273 kPa after the shock.The value of 273 kPa agrees very well with the peak overpressure value from the Friedlander fit of the pressure transducer data shown in figure 2, (P s = 269.3kPa).The value of pressure behind the shock extracted from figure 7 is 242 kPa.This lower pressure may be partially explained by the nature of a blast wave as the pressure behind the incident shock is expected to decay rather than be constant.Additionally, when considered locally, the shock is one dimensional and planar, in reality it is not, and is expanding spherically, which will result in a lower pressure behind the wavefront than predicted by one-dimensional theory alone.
Given the shock propagation speed, a motion blur during the exposure time of one frame (10.4 µs), is around 5.5 mm. Figure 7 shows that for a deconvolution kernel of τ = 10.40 µs, the PSP signal has reached a maximum value approximately 7 mm behind the wavefront whereas without any temporal processing, the maximum is reached after approximately 20 mm behind the wavefront.The equivalent half power bandwidth for such a time constant is 15.3 kHz which correlates well with most PC PSP studies [25,26,32,49,50]; however the actual value can vary depending on spraying technique, thickness, and the luminophore used.Numata et al [29] reported that the time constant of ultra-fast AA-PSP, which combine pyrene-derivatives and anodized aluminium with a large pore size, ranged from 0.

Blast impulse quantification
Although the response of certain brittle materials such as windows may be sensitive primarily to the peak pressure, blast response for many other materials and structures is driven by the blast impulse, that is, the integral of overpressure with respect to time.Blast waves may be parameterised by the peak pressure and the impulse, and therefore it useful to assess PSP's capability to characterise blast impulse.The time histories for the PCB pressure transducer, the PSP 'pressure transducer' (averaged over the area used for calibration), and the full surface PSP response are shown for both regular and temporally deconvolved data below in figure 12.The shaded area is numerically integrated for all sources of overpressure to give the impulse in kPa.The full surface PSP response has an earlier pressure rise because time t = 0 is defined as the time the shock reaches the transducer location.
The impulse recorded by the various pressure recordings is given in table 1.The values between all approaches are broadly consistent; however, the pressure transducer does produce higher values, due to the aforementioned overshoot in pressure which is commonly experienced in blast testing.Despite all reaching different peak values as shown in figure 12, the integrated area is not significantly different between approaches.For reference, the impulse of the Friedlander fit to the data is 37.9 kPa (calculated using the parameters listed in section 3.1).It is interesting to note that the PSP transducer, when temporally deconvolved, yields almost exactly the same answer as the Friedlander fit.In scenarios where large, highly localised, pressure values are present (such as in shock reflection and interaction), the full surface PSP impulse response would be expected to give a more accurate value of the overall impulse than calculations resulting from point measurements.
The impulse time history (defined as the cumulative integral of overpressure over time) is shown below in figure 13.The temporal deconvolution appears to have a small effect on the impulse history aside from increasing the value finally reached and slightly decreasing the time it takes to reach it.

Negative phase measurement
As demonstrated by Rigby et al [51] the negative phase duration of a blast wave can have significant implications on the structures undergoing blast waves.Quantification of the negative phase in this experiment is unlikely to be 100% reliable due to the aforementioned vibration of the lamps.However, heat transfer to the surface from the moving shockwave is also likely to have a significant influence on the long-duration results.
A turbulent convective heat transfer analysis of the flow over the disc assuming a M = 1.58 shock wave (see section 4.4) yielded a temperature rise of approximately 3 K in 1 ms.This analysis assumed no conduction of the heat out of the paint layer into the aluminium model in this time and treated the transient heat transfer analysis as a lumped system.This analysis is linearly dependent on estimated paint thickness and uses an estimated paint thickness of 10 µm.Given the temperature response of this PSP is 3.6%/K [15], longer time histories than the positive phase duration shown here of approximately 550 µs are likely to become unreliable; however, the nature of a blast wave means that the temperature behind the shock front will reduce quickly, making this analysis pessimistic.Significant heat transfer to the painted surface would manifest as an increase in measured pressure, due to the thermal quenching of the PSP by the flow, reducing I and therefore increasing P in the Stern-Volmer equation.
Figure 14 shows the PSP response for 2.5 ms after the arrival of the incident shockwave.Of note in this Figure is that the Friedlander fit follows the transducer response very well, indicating that the negative phase is well captured.Also, the reflection of the incident shock on the far wall of the blast chamber is measured well by both PSP and transducers at approximately 1.8 ms.However, the PSP fails to capture the negative phase well, most likely due to heating of the surface by the flow behind the shock.Assuming the Friedlander fit is correct, at 1 ms the surface pressure should be approximately 75 kPa, at this time the PSP is reporting a value of 100 kPa.A 25% change in pressure (around this range) would equate to approximately 10% change in intensity, something entirely possible given the temperature sensitivity of this PSP.The authors are currently investigating methods to remove this from the data utilising post processing; however, low-temperature sensitivity fast PSP formulations such as those shown by Li [52] and Gu [53] would also help mitigate this effect and enable better measurement of the negative phase.

Conclusions
This study has presented the application of the PSP technique to measurements of an explosively driven blast wave.The peak pressure measured is over the stated maximum for the PSP used, demonstrating potential for use in higher-pressure environments.The charge in AWE's MABT was designed and positioned in such a way so as to mitigate illumination from the explosive fireball and produced a wave with which to test PSP.The wave front was well captured using PSP with weak flow features being visible.The fact that the shock front may also be extracted from the processed PSP results, and that the pressure derived from the shock front velocity agrees well with the peak pressure, adds confidence to the analysis and could potentially be used as a calibration source in future work.The temporal response of the PSP was improved through the addition of a pixel-wise temporal deconvolution based on the assumption of a step change input to the PSP signal and a first-order response.Implementing a correction to the response of the PSP must be considered spatially as well as temporally to avoid non-physical signal levels.The choice of length of deconvolution kernel may produce improved results in space or time and the correct value for any given experiment will likely be a subjective choice by the researcher.
The deconvolution method shown in this study is unlikely to be appropriate for studies where frequency and phase information is important.In quasi-steady flows (such as those in cavities) as the frequency and phase response of the signal will be significant, the deconvolution technique demonstrated here does not consider the frequency response modification.Any dynamic response correction scheme aiming to improve time history measurements of a stationary flow will be required to map the signal attenuation and phase lag correctly for all frequencies.Although application of deconvolution as shown in this article is analogous to division in the frequency domain, the actual modifications to the frequency content are of little consequence to a transient flow and as such were not investigated in detail.As this study is primarily focused on the shape of the pressure profile for a transient event, ultimately for unsteady loads estimation, the frequency components required to create that event are ultimately unimportant, enabling a time domain-based correction to be effective.
The temporal sharpening applied through deconvolution is mathematically identical to dividing the amplitude spectra of the PSP signal by the amplitude spectra of deconvolution kernel and taking an inverse Fourier transform of the result.This has the effect of increasing the amplitude of high-frequency content (which is required to represent sharp edges) but also amplifies high-frequency noise.Despite the increase in noise, weak flow features were still able to be imaged at such extreme speeds.This extra temporal noise could be filtered spatially in each image given a suitable filtering approach.Different PSP substrates will exhibit different time constants; however, the first-order approach of deconvolution used in this study will be applicable to many different PSP measurements if a suitable time constant is known.
The impulse imparted by the moving shock wave has been correctly captured using the PSP measurements, demonstrating the applicability of this method for measurements on more complex geometries and geometries with complex shock interactions.Applying spatio-temporal sharpening to the data yields higher impulses, albeit not as high as the values recorded by pressure transducers alone.
Issues with measuring the negative phase of the blastinduced flow have been discussed and ascribed primarily to the temperature-induced error in the PSP results.As the heated flow behind the shock wave passes over the PSP surface, the PSP is thermally quenched.Given the reciprocal nature of the Stern-Volmer equation, this manifests as an increase in pressure, resulting in the negative phase being incorrectly represented.Novel luminophore and substrate combinations may improve this error in future measurements; however, the authors are currently investigating methods or reduction of this.
In summary, this study clearly demonstrates that the spatial distribution of a blast wave on a surface may be captured by PSP technology.This technology offers an enhanced and more efficient way of characterising blast, especially in small scale experiments where installation of traditional fast response transducers is impractical or where spatial resolution is paramount for the investigation.The additional spatial resolution provides researchers with the ability to not only validate CFD but also calculate impulse and blast loading on complex geometries.

Figure 1 .
Figure 1.Photographs of the test arrangement.(a) MABT and mounted instrumentation plate, (b) close-up of the unpainted instrumented plate, (c) a schematic showing the placement of the PSP sample and, (d) LEDs and camera mounted near the test article.

Figure 2 .
Figure 2. PCB113B28 transducer captured at 1 MHz and resampled at 96 kHz to overlap with PSP capture rate.

Figure 3 .
Figure 3. (a) raw wind-off image before shock arrival and (b) raw wind-on image 104µs after shock reaches the edge of the model (defined as t = 0) in all subsequent data.

Figure 4 .
Figure 4. Region of interest used for extraction of calibration intensity ratio data.

Figure 5 .
Figure 5. (a) Pressure transducer shock response and calibrated PSP response and (b) PSP calibration curve generated from resampled pressure transducer data and intensity ratio.
(b) is largely similar to figure 5(b); however, there are fewer outliers due to the improved temporal response.The calibration curve constants from this fit are B 3 = 3.749, B 2 = −5.881,B 1 = 3.132.

Figure 6 .
Figure 6.PSP montage calibrated directly with transducer data.
35 − 1.26 µs.The PtTFPP-based fast-responding PSP used in this study responds much slower than Numata's ultra-fast AA-PSP.Numata et al estimated the time constant for PtTFPP-based fast responding PSPs to be 15 − 30 µs.Although the polymer material differs from the PSP in this study, it is considered a reasonable value for time constants.Using different substrates for PSP acquisition of transient blast testing will have a strong impact on the time constant of the response and could be tailored for different applications.

Figure 8 .
Figure 8. PSP temporal response with different length exponential deconvolution kernels.

Figure 9 .
Figure 9. (a) PSP shock response after temporal deconvolution and (b) calibration curve generated from resampled pressure transducer data and temporally deconvolved intensity ratio.

Figure 10 .
Figure 10.Montage of PSP data with temporal deconvolution applied.

Figure 11 .aFigure 12 .
Figure 11.x − t diagram showing pressure across the centreline of the disc for (a) regular PSP processing and (b) temporally deconvolved PSP.

Figure 13 .
Figure 13.Impulse time history through the positive phase for (a) regular PSP processing, and (b) temporally deconvolved PSP.Time base is shown in ms as is commonly seen in blast literature.

Figure 14 .
Figure 14.'Long' response of the PSP (area used for calibration), PCB transducer, and Friedlander fit.