A framework is proposed for modelling the uncertainty in the measurement processes constituting the dosimetry chain that are involved in internal absorbed dose calculations. The starting point is the basic model for absorbed dose in a site of interest as the product of the cumulated activity and a dose factor. In turn, the cumulated activity is given by the area under a time–activity curve derived from a time sequence of activity values. Each activity value is obtained in terms of a count rate, a calibration factor and a recovery coefficient . The method to determine the recovery coefficient and the dose factor, both of which are dependent on the size of the volume of interest (VOI), are described. Consideration is given to propagating estimates of the quantities concerned and their associated uncertainties through the dosimetry chain to obtain an estimate of mean absorbed dose in the VOI and its associated uncertainty. This approach is demonstrated in a clinical example. Internal dosimetry following the administration of radiolabelled pharmaceuticals for diagnostic and therapeutic purposes is a prerequisite for radiation protection, imaging optimization, patient-specific administrations and treatment planning. The medical internal radiation dose (MIRD) schema  has becoSpecific aspects of uncertainty within the dosimetry chain have been addressed, including the selection of measured time points, , 10, the177Lu-DOTATATE therapy, using simulated gamma-camera images of anthropomorphic computer phantoms. In principle, this approach allows all aspects of the dosimetry process to be taken into account, but the need for multiple samplings from the assigned probability distributions for the quantities involved makes it computationally intensive, and its use for uncertainty assessment in an individual patient basis is challenging.Gustafsson et al.  adopted The Joint Committee for Guides in Metrology (JCGM) Guide to the Expression of Uncertainty in Measurement (GUM)  providesThe uncertainty propagation schema examines each step of the absorbed dose calculation to estimate the standard uncertainty in the mean absorbed dose measured at the organ or tumour level using SPECT imaging. The examples given have been simplified and concentrate only on the mean absorbed dose to a target. However, the approach can be used in different scenarios and expanded to include more complex dose calculations, including cross-dose and multiexponential time–activity curves (TACs). Similarly, aspects of the methodologies described can be implemented in different applications of dosimetry such as those utilizing a hybrid imaging approach or those used to generate 3D dose maps.n generic input quantities X1, …, Xn andm output quantities Y1, …, Ym. GUM Supplement 2 T and will provide a means for estimating a recovery factor specific to the volume under investigation. The standard uncertainty u(R) associated with the recovery factor can be derived from the fitted parameters b. A covariance matrix Vb of dimensions q × q corresponds to the estimate of b determined by ordinary least squares fitting under the assumption of equal uncertainty in all data points that make up the dataset. For a perfectly specified volume v, the squared standard uncertainty associated with R is, using Eq. gb is the matrix of dimension q × 1 containing the partial derivatives of first order of R with respect to b. The covariance matrix Vb can be determined as a by-product of the least squares fitting process. In reality the standard uncertainty u(R) obtained in this manner for a given volume will underestimate the actual uncertainty. To provide a more realistic value for u(R), the standard uncertainty u(v) associated with the clinical outlined volume v has to be taken into consideration. Since this volume is independent of the recovery curve parameters, there will be no covariance associated with v and any of the bj. Accordingly, Vb in Eq. 0 is a matrix of zeros of dimension q × 1 and gb is extended by one element, namely the partial derivative of first order of R(v) with respect to v.A dataset comprising a series of volumes and the corresponding factors on the right side of Eq. Cref of a source of known activity Acal, commonly referred to as a “standard”, under the same acquisition and reconstruction conditions as the study data:The final conversion of a partial volume-corrected count rate to activity is achieved by the use of a quantification or calibration factor. The sensitivity of the system is determined by measuring the total count rate u(Q) associated with Q can be determined by Eq. The quantification factor will therefore depend on the standard activity measurement within the dose calibrator and the reconstructed count rate, and its associated uncertainty accordingly calculated. Methods to determine dose calibrator uncertainty are described by Gadd et al. . UncertaAi determined from the measured count rate Ci in a target VOI at time ti is:The expression relevant to the assessment of the uncertainty associated with the activity ti, for i = 1, …, n. Using matrix notation:Equation n + 2 input quantities Q, R, C1, …, Cn and n output quantities A = ⊤. With no loss of generality, in order to keep the mathematical expressions simpler than they otherwise would be, only two of these activity values, namely, Ai and Aj, are considered, measured at times ti and tj, respectively:Equation Q, R, Ci and Cj, and two output quantities Ai and Aj. Using Eq. Equation and the input covariance matrix is:Q is independent of volume and hence independent of R, Ci and Cj, the covariance terms u, u and u are zero. Application of Eq. Ai and Aj, the elements of which may be expressed as:Since u and u associated with Q, R and the Ci must be derived.It follows that the covariances u for this situation, Eq. Regarding Using Eqs. Hence:R and the measured count rate Ci depend on the VOI outline they can be expressed as functions of volume v. Again applying the GUM ⊤given in Eq. Application of Eqs. xnom is the nominal value of some parameter x, and r and s are random and systematic effects, respectively. Then, applying LPU:Random and systematic components can be combined by considering the general model:For cumulated activityUncertainties associated with S-factors are somewhat less complicated than in the case of cumulated activity, and are predominantly influenced by the uncertainty associated with the volume. The general approach to determining S-factors is to choose a value calculated for a model that closely approximates the organ or region of interest. If a model of the corresponding size does not exist, a scaling can be applied to adjust the S-factor accordingly. Alternatively, an empirical S-factor versus mass representation can be obtained by fitting suitable S-factor data against mass , 22. TheS is:It is possible to apply the same principles as employed in the previous section to determine a covariance matrix for the estimated parameters in the fitting function. However, in this instance the standard uncertainties associated with these fit parameters tend to be very small (<1%) and the mass uncertainty dominates. Therefore, these estimated parameter uncertainties can be ignored and, using Eq. S is:Given that mass is proportional to volume, and assuming a known tissue density with negligible uncertainty, the fractional standard uncertainty associated with S is thus proportional to the fractional standard uncertainty associated with volume v, the proportionality constant being the magnitude |c2| of the slope of the fitting function on a log-log scale.The fractional standard uncertainty associated with S, it is evident that both parameters have a dependence on volume. To determine a final uncertainty in the absorbed dose, the covariance between these parameters should therefore be determined. Applying the GUM, [Having established standard uncertainty expressions for the GUM,   that originated from the insert volume. A recovery coefficient for each insert was then determined using Eq. v [Recovery data were generated by imaging multiple phantoms with the same acquisition and processing parameters as described for the patient data. The phantoms consisted of a 20 cm × 12 cm cylindrical phantom within which smaller inserts could be placed. Insert volumes ranged from 0.1 ml to 200 ml and were filled with a known concentration of ng Eq. v , namely:r, defined as:Fit parameters of the curve with associated uncertainties were determined using GraphPad Prism fitting software  and are detailed in Table Equations Count rates for each lesion with each scan time are shown in Table u, is defined in Eq. The covariance between the recovery coefficient and count rates, Substitution of the fit parameters, volumes and count rates into this expression is used to generate the values for covariance which are shown in Table 111In at various activities (8 MBq to 30 MBq) in air using the same acquisition parameters as for the patient scans. Images were reconstructed according to the clinical protocol and a spherical VOI was placed over the reconstructed point, ensuring that all counts from the source were contained. A plot of VOI count rate versus activity is given in Fig. The system was calibrated by imaging point sources of 111In as given by Gadd et al. [The fractional standard uncertainty in activity was taken as 1.5%, the typical uncertainty for secondary standard calibrators for d et al. . The sta111In activity within each lesion is obtained from Eq. Ci, volume-specific recovery coefficient R and calibration factor Q. 111In activity was converted to 90Y activity by scaling the ratio of the administered activities and correcting for decay according to the different half-lives of the two isotopes, such that the 90Y activity is expressed as:Calculation of Q, R and C to form the required uncertainty in Ai. These activities and associated uncertainties are shown in Table The variance associated with the measured activity is given in Eq. A0 and λ were determined using Eq. The Gauss-Newton algorithm was used to minimize the objective function described by Eq. Solution parameters with associated random and systematic components of uncertainty for each TAC are shown in Table Vp is given in Table gp was used to determine the random component of the variance of The covariance matrix for the solution parameters Random and systematic components of uncertainty in the cumulated activity were determined according to Eqs. 90Y S-factor data for unit density spheres against mass [The S-factors for the lesions were determined by fitting nst mass , empiricThe fit parameters of the curve with associated uncertainty were determined using GraphPad fitting software  and are shown in Table u(v). For the recovery function defined in Eq. The uncertainty in the absorbed dose is determined from Eq. S is highly significant. In addition, the negative nature of the correlation results in a reduction in the final absorbed dose uncertainty, as shown in Table Solutions for mentclasspt{minimaPropagation of uncertainty can be visualized by examination of the fractional uncertainty of each parameter calculated along the dosimetry chain. Figure Using the methodology described, absorbed doses to lesions and normal organs were calculated. In addition, the treatment was repeated for four cycles and an equivalent methodology was employed. Dosimetry results for lesions and normal organs delivered at each fraction are presented in Table T eff (th) and Teff (tr) are the effective half-lives of the therapeutic and the diagnostic radionuclide, respectively.A further potential source of uncertainty is the use of a pretherapy or concomitant diagnostic tracer study to predict the absorbed dose that would be delivered from a different therapeutic agent. It has previously been shown that uncertainty in the estimation of the biological half-life of the tracer will have an impact on the uncertainty of the absorbed dose calculated for the therapy procedure as a function of the relative values of the biological and physical half-lives . The unc111In  will therefore produce a similar uncertainty in the absorbed dose for a 90Y calculation (Tphys = 64.1 h). However, a small uncertainty in, for example, an absorbed dose calculation for 68Ga (Tphys = 1.13 h) would propagate by a factor of ~60 to give potentially significant uncertainty in a 90Y calculation.In the limiting case of infinite biological retention, the ratio of the uncertainties for the tracer and therapeutic agent will be the ratio of the physical half-lives. An uncertainty in the absorbed dose calculated for 111In- and 90Y-DOTATATE are equal, whereas the renal uptake of the indium-labelled compound might be higher [It is important to note that nonconformance, for example different administered amounts or affinities between diagnostic and therapeutic radiopharmaceuticals, will also introduce additional uncertainties into the prediction , 27. Fore higher .The methodology presented allows uncertainty analysis to be incorporated into absorbed dose calculations using the MIRD schema , the mosThe main objective of this uncertainty propagation schema is to evaluate the standard uncertainty in absorbed dose to a target. The tasks that directly support that objective are the determination of cumulated activity and the S-factor. The cumulated activity, given by the area under a TAC, is obtained from a sequence of quantitative images. Each activity value is expressed in terms of an observed count rate, a calibration factor and a recovery coefficient. The recovery coefficient is based on a recovery curve derived from multiple phantom scans. The presence of a common calibration and recovery factor in all activity values, and the covariance between volume, recovery and measured count rate, can be considered as a systematic uncertainty applied across all TAC data points, and therefore may be applied directly to cumulated activity. For the effects of uncertainties associated with random components of TAC data, a statistical approach using a “goodness of fit” measure is used.Within the described schema particular functions are used to fit the acquired data, for example for the TAC, recovery and S-factor models. The choice of these functions is not discussed, and an obvious fit function from theory may not always be known. In this case an optimal function can be found, and uncertainties reduced by using model selection criteria and model averaging , 29, 30.It is suggested that the major factors affecting uncertainty in the absorbed dose originate from the uncertainty in the delineation of the VOI. Two approaches to determine this uncertainty using statistical and analytical methods are presented. In this example an assumption is made that only a single VOI is applied to all datasets. An alternative approach involves the individual delineation of VOIs for each time point, for which the described methods may need to be varied, taking care to account for any commonalities applied across time points.Propagation of these uncertainties to derive those further along the dosimetry chain requires the covariance between parameters to be evaluated. An understanding of the variation in VOI counts with VOI uncertainty is challenging as there is no prior knowledge of the count distribution. A method for estimating the count distribution is therefore proposed. However, this approach does not model noise or background counts spilling into the VOI. A more rigorous approach would be to determine a function for change in counts versus volume for the dataset being analysed. However, it is considered that the approach suggested is sufficient since it does not overly complicate the methodology or require additional image processing or analysis, which is not available to the wider nuclear medicine community.An important feature of the schema is that it can be easily implemented using standard nuclear medicine image processing techniques. This feature is demonstrated in the clinical example in which absorbed dose calculations were performed using a standard image processing workstation and a commercial spreadsheet with curve-fitting software. Clinical implementation of this approach clearly demonstrates how different aspects of the dosimetry calculation can influence uncertainty. Uncertainty pertaining to a smaller lesion is clearly affected by the ability to define precisely the lesion volume and can be significant. For larger organs (such as the liver) volume delineation is less significant and the fit to the TAC begins to dominate. The ability to determine the source of larger uncertainties facilitates optimization of dosimetry protocols.The clinical example given in the appendix demonstrates the importance of uncertainty in reviewing the significance of results. Figure Whilst the clinical example demonstrates the use of the schema for SPECT-based dosimetry, the methodology can easily be adapted to suit alternative dosimetry protocols . However, variations to the proposed schema should always follow the uncertainty guidelines set out by the GUM.Uncertainty analysis is important for any measured or calculated parameter, whether physical or biological. Such calculations for MRT are rare  and leav


Muography (or muon radiography) is a technique that exploits the penetration capability of muons, elementary particles similar to electrons but with a mass about 200 times larger. High energy muons are naturally produced in the interactions of cosmic rays with the Earth atmosphere. The measurement of their absorption in matter allows the imaging of the inner structure of large bodies. The technological developments in the detection of elementary particles have opened the way to its application in various fields, such as archaeology, studies of geological structures, civil engineering and security issues. We have developed a new approach to the three-dimensional muography of underground structures, capable of directly localising hidden cavities and of reconstructing their shape in space. Our measurements at Mt. Echia, the site of the earliest settlement of the city of Naples in the 8th century BC, have led us to the discovery of a hidden underground cavity, whose existence was not evident with the usual two-dimensional muography graphs. We demonstrate here that our original approach definitely enhances muography discovery potential, especially in case of complex underground systems. In all fields, imaging techniques capable of seeing inside physical bodies have brought an extraordinary progress to the power of investigation procedures. Muography is an imaging technique that profits from the penetrating power of elementary particles called muons, similar to electrons but with a mass about two hundred times larger. Muons are naturally produced in the interactions of cosmic rays with the Earth atmosphere. A conspicuous flux of muons is constantly hitting the Earth surface from all directions, from the Zenith to almost horizontal, providing an abundant “light” source for muography.In absorption muography, a muon tracker is located downstream of the body under investigation. By tracking back the muon trajectories, one obtains an angular map of their flux as seen from the location of the muon tracker itself. A comparison with the muon flux impinging on the Earth surface provides a map of the muon transmission  in the traversal of the body being investigated. As the penetration of muons in matter depends on its density, such a map can provide a muographic image of its internal structures. These could be cavities or high-density zones. Muography (or muon radiography) is thus in principle similar to X-ray radiography, but capable of probing the interior of large bodies, thanks to the penetrating power of muons which is much higher than that of X-rays.1. Almost forty years later, muography was applied to the investigation of the inner structures of volcanic edifices13, facing the challenge posed by the observation of the low muon fluxes surviving the traversal of a large rock thickness typical of this application. However, the problem of low fluxes does not affect a very wide range of applications (from archaeology to risk assessment and prevention in civil engineering or geology), where the thickness of matter being traversed is at most several tens of meters22. The results obtained by the ScanPyramids project at the Khufu’s Pyramid23 and by our group in exploring underground cavities at Mt. Echia in ancient Naples24 belong to this domain.The first muography was performed by the Nobelist Louis Alvarez in 1970, who disproved the possible existence of a hidden burial chamber in Chefren’s PyramidMt. Echia  is the site of the earliest settlement of the city of Naples in 8th century BC. It is a headland with a maximum altitude of about 60 m a.s.l. and mainly consists of yellow tuff, a soft volcanic rock. In the course of history a very complex system of underground tunnels and cavities has been excavated and used for an astonishing variety of purposes, thus carrying a wealth of peculiar information on the past life of the city. This system of cavities has recently become the subject of systematic investigations and is partially available to visitors who are curious about the underground history of Naples, with access through the so-called Bourbon Tunnel that was excavated around the middle of the 19th century.24, we have shown that muography is mature to go beyond the stage of a technique reserved to highly specialized groups and can legitimately aspire to become a standard investigation tool using low-cost instrumentation. At the time, we provided first indications of hidden underground cavities. However, the complexity of the system of cavities underground Mt. Echia makes it difficult to identify hidden cavities without the ambiguities originating from the fact that standard 2D muographies are projective transmission maps, in which the shadows of other cavities are difficult to disentangle from one another. To continue the investigation, we pursued a new development: a novel approach to three-dimensional (3D) muography, where the usual 2D muographies taken from at least three different locations are directly combined in a single analysis in order to localise cavities in space and reconstruct their shape.In our study of underground cavities at Mt. EchiaThe new approach is based directly on muographic data, providing a 3D image with high resolution. The method is suitable for the detection of sharp discontinuities in density related to the presence of cavities and can be applied even to complex systems such as at Mt. Echia and other anthropic environments. Moreover, no a-priori information about the location of the cavities and on the density distributions are required. The success in identifying a hidden cavity at Mt. Echia demonstrates the discovery potential enhancement achievable with our approach to 3D muography, especially in case of complex systems of underground structures.28 are qualitatively and quantitatively different from the 3D muography developed by us. They are based on the subdivision of the object under investigation in voxels (volume pixels), with a subsequent fit of their density to data. The constraints usually applied to the density of nearby voxels make them suitable in cases where the variations in density are rather smooth and a high resolution is not required. They have typically been applied to volcanoes and other geological structures.The 3D reconstructions based on inversion methods reported in previous works24 for technical details about 2D muography that are of interest to specialists.With the intent to make this paper readable by a large audience, we refer to our previous publication on Mt. Echia24.The two muon trackers  used for the measurements reported in this paper are real-time electronic devices that operate autonomously, with remote control and readout. The basic elements are bars of plastic material doped with a scintillating compound, following a simple and widespread technique for particle detection. The light generated by muons in the plastic scintillator bars is detected by Silicon Photomultipliers (SiPMs). These photosensors, recently developed, are solid-state devices that, as such, do not require any high voltage supply and have a very low power consumption. These features allow us to operate the detectors with relative ease also in remote environments. For a detailed description of the technology we address the reader to ref.24 is a planar array of 64 plastic scintillator bars. The section of the scintillator bars has the shape of an isosceles triangle with 3.3 cm basis and 1.7 cm height. A central hole hosts a wavelength shifting optical fibre that carries the light to the SiPM. The scintillator bars were extruded at the NICADD facility of the Fermilab Laboratory. The triangular bars are packed together so that each one is half superimposed to its neighbours. The coordinate perpendicular to the bars is measured with a resolution of about 2 mm. The module is subdivided in two arrays of 32 scintillator bars. Figure The basic module of the MU-RAY muon trackerTwo modules with orthogonal bars form a XY plane. The muon trajectories are tracked by a sequence of three XY planes. At Mt. Echia, the distance between the outer planes was 0.50 m. The angular resolution in the measurement of the muon trajectory with this configuration was around 6 mrad. The XY planes have an active area of about 1.0 × 1.0 m. Muons are tracked up to a maximum angle of 60° with respect to the view axis of the tracker, i.e. to the direction perpendicular to the tracker planes. The left side of Fig. 29 is a smaller muon tracker basically using the same technique, except that the SiPMs are in direct contact with the scintillator bars (i.e. no wavelength shifter is used). Like the MU-RAY tracker, it consists of three XY planes. The outer XY planes are formed by two orthogonal arrays of 21 scintillator bars. The section of the scintillator bars has the shape of an isosceles triangle with 4 cm basis and 2 cm height. The coordinates of the muons are measured with a resolution of about 3 mm. The outer XY planes are 0.34 m apart. Muon tracking is carried out with an angular resolution of about 14 mrad. The central XY plane, with a coarser structure and formed by scintillator bars of rectangular section, is used as a constraint in muon tracking. However, its use was not required for this measurement. Muons are tracked up to a maximum angle of 45° with respect to the view axis of the tracker. The active area amounts to about 0.4 × 0.4 m (1.0 × 1.0 m for MU-RAY). The right side of Fig. MIMA24 for the MU-RAY tracker and in ref.29 for the MIMA tracker.Each muon tracker determines the muon trajectories after the traversal of the volume under investigation. The procedure for the analysis of the events with a muon trigger acquired in the data taking runs, in order to select those with a recognizable muon and to reconstruct its track, is described in ref.α and of the azimuth angle ϕ of the track, as defined in the reference system of the tracker itself. The elevation angle (complementary to the zenith angle) is zero in the horizontal direction and 90° at the Zenith.The muon flux is measured as a function of the elevation angle T is defined as the ratio between the muon flux measured underground as described above and the flux measured at the surface in dedicated runs carried out in the laboratory (free sky)24. Since no damage to the detectors or change of operating conditions happened during the runs, we assume that the geometrical acceptance, the trigger efficiency, and the selection efficiency are the same in the data samples taken underground and at the surface, effectively cancelling out in the ratio giving the muon transmission. For a detailed mathematical formulation, see the Section Methods or ref.24.The muon transmission R is defined as the ratio between the measured and the expected muon transmission, the latter evaluated by taking into account the absorption of the muon flux in the absence of internal structure such as cavities. The relative transmission equals unity in case no internal structures are present and the correct rock density ρ is inserted in the evaluation of the expected transmission.The relative transmission 30. The muon flux reaching the tracker was evaluated by integrating the flux impinging on the surface above a muon energy threshold that takes into account the energy loss in the rock traversed31. The path length of muons in the rock was obtained using a Digital Terrain Model (DTM) describing Mt. Echia. The DTM was obtained from LIDAR observations elaborated with the software packages Terrasolid - Terrascan, LP360, RIEGL Riscan Pro, Golden Software - Surfer 12 and Root24. We assumed an uniform density of the rock (tuff at Mt. Echia) and used its best estimate ρ = 1.71 g/cm3, as previously determined from our data24.The expected transmission was evaluated using the muon flux as a function of energy measured at the surface by the ADAMO experimentR, as measured at the three locations A, B and C of the muon trackers, each one giving a projective muographic image. Regions with high relative transmission (green in the figure) signal the possible presence of cavities.Figure 24 were obtained with the MU-RAY muon tracker installed at location A. A second set of data was taken immediately afterwards with the same MU-RAY tracker at the location denoted by B. At both locations, the XY planes of the tracker were placed horizontally parallel to the cavern floor, so that the view axis of the tracker was vertically oriented.The results presented in ref.24. We focused attention on the (green) signal of high transmission visible near the bottom-left corner, which suggests the presence of a hidden cavity. The high transmissivity region of interest is within an angular boundary indicated by a red rectangle that corresponds to an elevation angle αA in the range of 30° to 50°, and an azimuth angle ϕA in the range of −100° to −75°.Figure αB in the range of 45° to 60° and ϕB in the range of −10° to 20°. The muography carried out from location B thus confirmed the presence of a hidden cavity and roughly localized it in space at the intercept of the two projections.The projection in space of this angular region from location A intercepts the projection from location B of a similar region of high transmissivity that lies within the angular boundary indicated by the rectangle in Fig. We then took data, using the MIMA tracker, at the location denoted by C in Fig. The hidden cavity under investigation is viewed from location C at an angle that is different than that at locations A and B. This choice of the viewing site C effectively allows us to perform a high resolution 3D study in combination with the muographies taken at locations A and B. However, the choice of tracker locations was done compatibly with the logistics of the underground site, where we used pre-existing caves and tunnels. Hence the chosen locations are adequate but not optimal for a 3D muography.αC and ϕC, respectively. Actually, the three angular regions indicated by rectangles in Fig. In Fig. 6 at location A and 5 × 106 at location B. The MIMA tracker data taking at location C lasted 50 days, corresponding to 5 × 106 muon trigger events. The runs to measure the muon flux on the surface were taken keeping the same orientation of the muon trackers as underground. The run lasted 2 days, corresponding to 12 × 106 acquired muon trigger events for MU-RAY, and 18 days, corresponding to 19 × 106 muon trigger events, for MIMA.The MU-RAY tracker data taking at locations A and B lasted 26 and 8 days, respectively. The numbers of acquired events with a muon trigger were 14 × 10R in Fig. R above 1.51 in the muographies acquired with the MU-RAY tracker  have a high-enough value of R (1.37 for MU-RAY and 1.39 for MIMA) to be associated to the cluster. In this second selection the probability for a rock filled bin to exceed the thresholds was higher (16%) but the request of proximity to a signal region ensures a low background. The regions selected by the clustering algorithm are indicated by solid lines in Fig. The threshold obtained in this manner is used to search for the “seeds” (i.e. the starting regions) of the clustering algorithm. Subsequent recursive aggregation of points appearing in the 2D muography to each cluster is made by lowering progressively the threshold in In order to reconstruct in space the hidden cavity, we started by defining a grid of points in a cubic volume that encloses the region of space where the cavity is supposed to be, according to the angular ranges defined above. As a general criterion, a point was considered to be located inside a cavity if in each of the three projective muographies it corresponded to a direction lying inside a signal cluster as defined above.24 as quoted above in this paper. The minimum cavity size for our experiment sensitivity, was estimated to be 1.5 m over 50 m total rock thickness24. The spherical shape was chosen in order to study the effects of the non optimal choice of the trackers’ locations, and in particular to highlight possible ensuing asymmetries.This procedure was tested by simulating the presence of a spherical cavity with 6 m diameter, approximately located at the presumed position of the hidden cavity and having a similar size. The simulated cavity was surrounded by rock using our best estimate of density for Mt. EchiaThe result of the simulation is shown in Fig. The criterion is satisfied also by points that in a projection appear in the shadow of the cavity, rather than inside. The halo that is observed in Fig. Figure Especially when compared with the single muographies given in Fig. 32.The existence of a hidden cavity in the region of space localised by our 3D muography, is consistent with previous hints from surveys carried out on site by one of the present authors (G. Minin), together with personnel of the Bourbon Tunnel. The cavity outlined with the ellipse in Fig. Presumably, the hidden cavity was originally a quarry from where tuff was extracted to construct a building above it. Subsequently it was probably turned into a cistern, and tied up to branches of the aqueduct dating from the Renaissance. Clues have been found, indicating that during the Second World War work had started to access the underground shelters from the surface through a staircase, presumably within this hidden cavity. After the war, the cavity was partially filled with debris, on several occasions.The hidden cavity was reconstructed in space on the basis of its correspondence with the presence of a high muon transmittivity cluster in each of the three projective images. These clusters were defined through the use of algorithms based on setting a threshold in the transmittivity. The technique could be further refined through the development of algorithms that fully exploit the quantitative information carried by the transmittivity.33. This technique is based on a stereoscopic principle similar to that of the human sight and is applicable wherever the size of the muon tracker is not negligible with respect to its distance to the structure being investigated. In this case, a rough estimate of this distance can be obtained by projecting backwards the muographic image of the object and minimizing its angular width as a function of the distance of the plane onto which it is projected.We also developed and started to apply an innovative technique that allows a first localisation in space already from a single muographyCumae was settled as a Greek colony in the 8th century BC and in the surrounding area of the Phlegraean Fields, very rich of archaelogical remains. The Phlegraean Fields were of primary strategic importance in the Roman times, with the commercial harbour at Puteoli and the military harbour at Misenum. Moreover, Baia was hosting a rich residential and thermal area. In addition, a measurement campaign with MIMA tracker is ongoing inside the Temperino archaeological park, a mine from the Etruscan age located in Campiglia Marittima (Tuscany).Our group is now planning the study of underground structures in the mountain where the ancient city of We have developed a new method for a 3D muographic reconstruction directly from the data, exploiting the resolution obtainable with the muographic technique. We have proven the existence of a hitherto unknown cavity inside Mt. Echia, of which only hints were present, and reconstructed its position and shape in space. The search at Mt. Echia was motivated both by the need to investigate an area of potential geological risk and by the curiosity about the history hidden underneath the ancient city of Naples.Because of its complex system of cavities, Mt. Echia also represents a testing ground fraught with difficulties in which to develop muography techniques for application in the field of archaeology and, in general, in the investigation of hidden structures. Especially in complex situations, our 3D muographic reconstruction method definitely enhances the discovery potential of the technique.α, ϕ), the muon transmission T is defined as the ratio between the muon rate observed underground and the rate observed on the Earth surface. The latter is measured in a dedicated run at a surface laboratory without overburdens or overhead structures (free sky run)24.For any given angular bin  cancel out in the ratio. This is not the case for the data taking time ΔT and for the data acquisition efficiency ϵDAQ(ν), which depends of the trigger rate ν that is much lower underground.As the muon tracker and its operating conditions are the same at the two locations, most factors  linking the muon rates to the number of recorded events Tm is thus given byu and fs indicate quantities referring to the underground and to the free sky data taking, respectively.With good approximation the measured muon transmission T that is expected in the absence of internal structures (such as cavities) is given byα, E) is the differential muon flux impinging on the Earth surface as a function of the muon energy E, which also depends on the elevation angle α and has been measured by the ADAMO experiment30. The lower limit Emin of the integral at the numerator is the minimum energy that muons must have in order to cross the rock overburden and be recorded underground by the muon tracker. It depends on average rock density ρ and on the rock thickness, the latter being given by the DTM for any given . Emin is evaluated using a model that parametrises the muon energy loss in matter31. The lower limit E0 of the integral at the denominator is the minimum energy required for muons to be recorded by the muon tracker. For the MU-RAY muon tracker it is estimated at about 100 MeV, supposedly independent on  in the angular range under study. The sensitivity of the expected muon transmission on E0 is such that a value of 200 MeV would result in a transmission higher by at most 4%. The estimate for the MIMA muon tracker is E0 = 170 MeV.The muon transmission R is defined asThe relative muon transmission R given in each muography of Fig. The distribution of the relative transmission


Further we elucidate the selection of monomer chemistry and discuss details of the recording conditions based on the concept of exposure dosage and exposure time. Influences ranging from high dosage recording to low power recording are explained and how to affect the desired diffraction efficiency. Finally, we outline and demonstrate the process to mass manufacturing of volume phase gratings.Holographic photopolymers are a new technology to create passive diffractive optical elements by a pure laser interference recording. In this review, we explain the chemistry concepts of light harvesting in an interference pattern and the subsequent grating formation as chemical response. Using the example of the newly developed Bayfol In human history, the ability to control light had a fundamental impact on how we interact and work with each other and with our environment. From the control of the fire to Edison’s light bulb to modern light emitting (laser) diodes the creation of light and managing it is fundamental to our life. For a long time, passive optical elements were based only on refraction and reflection. Diffractive optical elements remained in niche applications like scientific instruments. This is due to the fact that manufacturing is labor intense and their fragility prevented a wider use in mainstream applications.We describe here the technology of holographic photopolymers that enable a much wider and more flexible use to manage light by engineering specific volume holographic optical elements (vHOEs). Those materials, specifically when they are made available in film format, push forward the boundaries that diffractive optics exhibited in the past. Photopolymer in general are materials that are sensitized to react upon light with a chemical response. Holographic photopolymers record an interference pattern thus exhibits chemical formation of diffractive gratings. A specific benefit to the ones described herein are those that do not require any chemical and thermal post processing, which is of specific benefit for the creation of optical components. Mass manufacturing becomes easier and precise and drives forward the adoption in the consumer space. Their chemical basis as plastic products links them to classic plastic processing to reach out into popular post hologram recording conversion techniques.® HX films  is discussed. Key aspects of influences on the grating formation as function of the spatial frequency (SF), the exposure dosage and the exposure power are explained. We discuss the photochemistry that is used and how this influences the photon yield. After the initial chemical response we describe the influence of the photo-polymerization on the formation of index modulation of the phase grating including proper selection of polymerizing monomers .The basic chemical concept, the mechanics of the diffractive grating formation as chemical response in those new products made available as BayfolHolographic recording is done with an interference setup, where a coherent laser light source is split and illuminates from two angles the photopolymer film which is the recording medium. This concept is universal and can be used for individual holographic optical element recordings, while also specific master-to-copy setups are discussed. As the last step in this pure photonic recording process we explain the bleaching process of these photopolymers and give an insight into digital holographic recording.vHOEs are thin and lightweight film optics, where the film type influences the optical function. In contrast to surface gratings vHOEs exhibit an angular and spectral selectivity  that canHolographic photopolymers are essential for many future optic designs and complement other technology developments like light emitting (laser) diodes, spatial light modulators and mobile computing in compact designs. vHOEs are always linked to full optical system designs, so their spectral and angular selectivity has to be considered. Advanced vHOEs comprise spatial and/or spectral multiplexing, which means that several vHOEs can be integrated in one single recording media film. This ability will drive their adoption into the consumer electronics space. Unique is the ability to design the diffraction efficiency in wide ranges from sub percent level to close to 100%. In this review, we discuss the details of this holographic photopolymer technology which is another example of a beautiful marriage between physics and chemistry.The need for an easy to use, size scalable recording medium prescribes material properties that in turn determine the necessary chemistry. A suitable recording medium must not require pre- or post-processing, has to provide high transparency and low haze after recording and will allow a high diffractive performance. Additionally, the unrecorded medium has to be manufactured at high quality standards and the recorded vHOE can be applied in mass production assembly lines. This property profile can be realized e.g., with a web coated film product.Several approaches to provide such a material have been reported in the last decades from industrial as well as from academic laboratories. A major motivation for holographic recording material developments has been the field of optical data storage and several material concepts have been described and reviewed elsewhere . While tFor recording a stable optical hologram function, the recording medium has to have a certain minimum mechanical modulus to enable a proper grating formation. Liquid recording media tend to experience shrinkage issues that lead to unacceptable optical aberrations. In simple photopolymer systems, a part of the writing chemistry has to be consumed by flood exposure before the interference pattern recording to generate this minimum modulus. By this, a significant part of the dynamic range is already consumed and moreover due to the pre-exposure the whole recording process becomes less reliable.Matrix formation can be realized by two reactive chemistries that do not interfere with each other , so that the writing chemistry has to be unaffected by this matrix formation ,15.A very important advantage of the 2-chemistry approach is the high miscibility of all liquid precursors ahead of matrix formation. After matrix formation, no de-mixing of the writing chemistry occurs when carefully designing the components. After hologram recording and curing of the writing chemistry a stable interpenetrating network between matrix and writing chemistry is formed .® HX film type photopolymer is composed of two different chemistries, as is shown in The raw material of Bayfold of the photo reactive layer. In the simplest case of recording the interference pattern of two plane waves a sinusoidal modulation of the refractive index represents this phase grating. The amplitude of this sinusoidal refractive index modulation is in the following referred to ∆n1 and represents the performance of the photopolymer under certain recording geometries and recording conditions . φR can be thus expressed as the sum of the contributions from both the singlet state φΡS and the triplet state φRT, respectively. φRS only depends on the singlet state quenching efficiency of the dye by the organo-borate as:0S expresses the lifetime of the singlet excited state of the dye in the absence of a quencher. Similarly, φRT depends on the triplet state quenching efficiency and the quantum yield of the actual triplet state φT.Apart from the correction for the diffusion in the described medium, it has to be taken into account that the quantum yield for the formation of the alkyl radical φ0T as the lifetime of the actual triplet excited state. φT moreover is given by: T0 being the triplet state quantum yield in the absence of a quencher. Therefore, the overall quantum yield φR of alkyl radical formation is expressed by:With τR are shown in R for the photo-initiating systems based on Rose Bengal/organo-borate salt increases with oxE as a consequence of the rather low values of the quenching rate constants. In case of Safranine O, the φR values are similar to each independent of the organo-borate salt used, since the quenching rate constants rk in the resin are diffusion limited.The values of φR. These data are consistent with the results obtained from the RT-FTIR experiments where the photo-initiating system consisting of Rose Bengal/organo-borate 4 is the most efficient system. From these data, the efficiency of the systems based on Safranine O/organo-borate salts is in the diffusion limit and their reactivity is not proportional to the photo-induced electron transfer process.n1 of the holograms obtained for stable photopolymers as a function of the irradiation dose per arm of the 2-beam plane wave recording setup. Note high ∆n1 values indicate high brightness upon vHOE reconstruction, provided over-modulation has not occurred or cannot occur as for reflection holograms. Recording was done in reflection mode with green laser light of 532 nm. Experimental details of the recording setup and data extraction are described elsewhere [n1 values and high sensitivity were found for the systems based on Safranine O/organo-borate 5 and Safranine O/organo-borate 4. For the Rose Bengal based systems, also good ∆n1 values and medium sensitivity was found when using organo-borates 4 and 5, good ∆n1 values and poor sensitivity was found for organo-borate 6.The photopolymer formulations of Rose Bengal and Safranine O with respective borates were investigated in a holographic experiment. Unfortunately not all the dye/organo-borate combinations form stable photo-initiators due to their tendency to undergo a spontaneous self- or dark reaction. For the suitable photo-initiators holographic plane wave grating recordings were performed using the dye/organo-borate photo-initiating system in a photopolymer composed of 25% SR 349, 0.1% dye, and 1.0% organo-borate in a matrix ,18. Figulsewhere . Good ∆nn1 in the Safranine O/organo-borate 4 and Safranine O/organo-borate 5 systems as a result of the high radical quantum yield φR created and the high pR values. A high ∆n1 is also obtained for Rose Bengal/organo-borate 4 and Rose Bengal/organo-borate 5, although in this case, a longer exposure time is necessary due to the lower pR value. Finally, for the Rose Bengal/organo-borate 6 system, a moderate ∆n1 is obtained at high exposure dosage, due to the very low pR and low radical quantum yield φR. Surprisingly, the sequence of increasing inhibition dosages (the dosage needed to start any holographic recording) for each dye exactly follows the sequence of decreasing pR values for each dye/organo-borate couple. By taking e.g., a value of ∆n1 = 0.004, which corresponds to half of the maximum value obtained in holographic recording, R in a viscous medium. Thus, the results of the holographic recording as described quite well correlate with the photo-polymerization experiments.As displayed, a low irradiation dose is required only to create a high ∆The ability to predict and interpret the performance of a photo reactive polymer resin containing a type II photo-initiating system from the reactivity of the excited states of the involved dyes and from the intrinsic properties of the photo-polymerizing medium has been demonstrated.® HX film can be successfully described by a simple non-local reaction diffusion model. Having investigated in n1 and mechanical stiffness (measured as storage shear modulus photo curedG).We have shown in the previous A. A will then be converted to its excited triplet state Dye* with a rate constant ak. The dye A can be recovered from its excited triplet state Dye* with a decay constant rk. rk is the inverse of the lifetime τr of the excited triplet state Dye*.As outlined in  the descR• the excited triplet state Dye* reacts with a co-initiator CI with a rate constant dk. Besides R• a protonated dye molecule HDye is formed too.For the formation of the primary radical molecule HDye with the co-initiator CI. An intermediate co-initiator state CIint is also formed.A finally bleached dye is generated by the reaction of the protonated dye molecule M1• the primary radicals R• react with a monomer u with a rate constant ik. There may not be only a single type of monomer present but a mixture of monomers with for example different functionalities could be used. Monomers with higher functionality will form an interpenetrating network with the matrix network. Different monomer types are not further distinguished from the chain initiator state on. Also all mobility of the resulting chain and network molecules is assumed to be lost from this state on within our model.For the initiation of a chain initiator molecule f > 1 it might be reasonable to assume that the initiation rate constant ik scales with f.For monomers with functionalities pk.After the initiation process the chain propagation has to be described by the rate constant pk is independent of the functionality of the monomer type. If several types of monomers are used they should have the same chemical type of functional group  to keep the latter assumption valid.The driving force for monomer diffusion is generated by the assumed local immobilization of the polymerized monomers. Therefore it might be reasonable to assume that the propagation rate constant After chain growth chain termination has to be described. Combination or disproportionation is a consequence of bimolecular termination as depicted below.tk:It is common to combine the two respective rate constants in one bimolecular termination rate constant A terminated polymer is also achieved by the termination of a growing chain radical with a primary radical.Primary radical recombination will be neglected in this study. For high recording powers especially in the case of mono pulse recording (~ns pulse time) this assumption has to be revised again.Z) usually governs inhibition. Oxygene (Z) is able to react with the excited triplet state of the dye, the primary radical or the macro radical.Besides initiation, growth and termination the inhibition as a non-ideal effect has to be included. For free radical polymerization oxygen . Z0 is denoted as the equilibrium concentration of oxygen in the photopolymer layer. Within the photopolymer layer Z diffuses too. Mobile components are considered to be monomers u, the primary radical R• and all other components of the photo-initiator system. Within this model we consider as immobile components all chain radicals  and the cross linked matrix. A non-reactive contrast agent B is introduced to compensate the mass flow of monomers from the dark fringe towards the bright fringe during the holographic recording and by this equalizing the osmotic pressure. By the counter-diffusion of the contrast agent B to the monomers u the incompressibility is given at any time at any location. The contributions to incompressibility violation by the initiator system components are neglected as they are only present in very dilute concentrations. Still neglected for incompressibility violation is volume shrinkage that occur for example in free radical polymerization of acrylic monomers. In Bayfol® HX film photopolymers for example the volume shrinkage is below 3%, depending on the composition.The following assumptions can be made considering the mass transport of the different mobile species in the photopolymer. K = 2π/Λ.In the presence of a spatially sinusoidal variation of the intensity during recording of a plane-wave grating the reactions described above have to be translated into a set of integro-differential equations. In order to solve the set of integro-differential equations it is straightforward to expand them into a Fourier series of the grating period Λ of the respective grating vector length ak that describes the excitation rate of the dye A to its excited triplet state Dye* is expressed as:d is the traversed thickness of the light according to the recording conditions given in cm. ε is the molar extinction coefficient given in cm2/mol. Φ being identical to φT0 from Dye* per photon that traverses the photopolymer. T0 is the transmission at the recording wavelength before illumination and sfT is the final transmission after recording and is set to 0.9. A0 is the initial zero-order spatial Fourier component of the dye concentration, given in mol/cm3. AN is the Avogadro’s constant, h the Planck’s constant and c the vacuum speed of light. Θ denotes the Heaviside function. The average number of absorbed mol photons per second and per unit volume through the photopolymer layer during the full recording interval  is described by Equation (29). A0(t) denotes the transient zero order Fourier component of the dye distribution. By A0(t) also the transient bleaching during the recording interval  is taken into account within this model.In  we furthA. All concentrations are given in mol/cm3.Rate equations for the extensive variables were formulated and the details are given in . One exau.Another example is the rate equation for the monomer 2 again [2 was set to 100 nm2.The non-local parameter is denoted as σ2 again . As repo2 again , σ2 was N the following rate equation can be formulated:For the polymerized monomer units B has to account for the incompressibility and as a consequence has to be written as:The rate equation for the non-polymerizable contrast agent u and the contrast agent B is denoted as VF.The ratio of molar volumes of the monomer N0, which is a measure of the spatially averaged monomer conversion and by this a measure for the increasing internal viscosity, was used in [D are scaled down linearly in N0(t) via:The zero-order Fourier component of the polymerized monomer units  used in  to descrG0 versus the shear modulus in the fully cured state photo curedG the scaling constant α can be deduced. Due to the possible large concentrations and concentration gradients of the monomers uD has the character of an inter-diffusion coefficient. Due to small concentrations of the initiator system components in the photopolymer formulation AD, HDyeD, CID and RD● have the character of tracer diffusion coefficients. From rheological properties like the ratio of the shear modulus of the unrecorded state D0 of the various mobile components to that of the monomer unit in a rubbery network (Equation (29) in [Further we relate the diffusion coefficients  (29) in ) by the AD = HDyeD and CID = RD●.For further simplification we set By Fourier-series expansion with respect to the basic grating period Λ the above mentioned set of integro-differential equations under appropriate initial conditions can be solved.k of the monomers u, the polymerized monomers N, the contrast agent B and the matrix b as background and their different refractive indices, the refractive index profile ∆n can be calculated using the Lorentz-Lorenz relation and the incompressibility condition. In n profile is depicted with the inhibition period clearly visible.With all the respective volume fraction profiles φn1 of the refractive index profile ∆n is of interest. At each time t we can therefore write for ∆n1, which is then identical to the index modulation of the holographic grating: In the two wave approximation outlined in Kogelnik’s work  for the darkn denotes the refractive index of the unrecorded photopolymer, un the refractive index of the monomer, Bn the refractive index of the contrast agent, Nn the refractive index of the polymerized monomers and bn the refractive index of the matrix. These refractive indices were measured independently in our case. φ1k is the first-order Fourier component of the volume-fraction profile φk of the component k of the photopolymer. Extension to a multi-component monomer mixture is straightforward.Here ® HX film grade at two different spatial frequencies. Independently measured refractive indices of all relevant components were used. Also experimental data for pk [dk and rk for the formulation components were set as starting values for the fit procedure. dk and rk were deduced from respective experiments as described in r of the excited triplet state of the dye was found to be of the order of 10 µs, therefore rk is of the order of 1/10 µs−1. According to qk = dk∙CI0 (t = 0) from the experimentally accessible quenching constant qk of the excited triplet state Dye*. As the whole set of rate equations can be scaled by an arbitrary factor in time it is important to know at least a few of the above mentioned rate constants. This then leads to a consistent set of physically reasonable model parameters. In In  we descra for kp  and for ik, pk, tk, tpk, zk2, zk3, σ2) and mass transport of monomer and oxygen  depicted in rk, dk, bk, AD, CID) could be kept fixed for the different SF for reflection and transmission geometry for each recording wavelength. Only for the blue recording in transmission geometry φ, rk, dk, bk and ik had to be chosen significantly different from the other cases (~50%).After parameter value optimization the simulations show a very good fit quality to the experiments. The good fit quality is underlined by the fact that the parameters for the polymerization  were keIn sum we can state that the fully detailed non-local reaction-diffusion model is able to describe our photopolymer recording behavior very well in a wide variety of recording conditions and also in wide variations of spatial frequencies.n1 for transmission holograms in saturation recording is only about half the value of ∆n1 for reflection holograms at comparable power densities. This fact can be easily rationalized by the picture that at large grating spacing Λ  the diffusing monomers already react on their travel to the bright fringe before reaching the bright fringe’s center. By that higher harmonic orders in the refractive index profile ∆n are built up. Therefore only part of the complete dynamic range of the photopolymer is transformed into the desired first Fourier component ∆n1. From the model predictions we can expect that increasing the monomer mobility, by changing the composition of photopolymer formulation should improve the ∆n1 at large grating spacing.As we reported previously in The monomers can be selected as a mixture of monofunctional and multifunctional species. Upon photo-polymerization the multifunctional species together with the monofunctional species generate a rigid cross linked polymer network. Multifunctional monomers will generate a very rigid network that gives the hologram long term stability. A too high amount of multifunctional species however vitrifies this photopolymer network already at low monomer conversion and decreases monomer mobility at an early stage. On the other hand a high amount of small, monofunctional monomers generates flexible linear segments in the network and allows the monomer mobility to be kept high even at elevated monomer conversion.n1 caused by varying the monomer mixing ratio can be attributed to the change in monomer mobility, the monofunctional and the multifunctional monomers were chosen such that they have almost the same double-bond density per volume , the same chemical type of double bond (acrylate) and almost identical refractive indices.Different photopolymer formulations were evaluated in red laser (633 nm) reflection hologram recording to test this assumption . The totn1 versus the monomer mixing ratio is depicted (right y-axis) in G, measured with an optical Rheometer . It is very obvious that if the multifunctional monomers are the majority component ∆n1 drops significantly. This drop in ∆n1 by increasing amount of multifunctional monomers can be attributed to the early densification of the photopolymer network and therefore strong attenuation of the monomer diffusion constant. Note that G0 does not change with the monomer mixing ratio. This suggests identical rheological conditions for the monomers to diffuse in the very initial state of exposure.As a result of this experimental test the index modulation ∆cribe in ) is showSF. Therefore the diffusion time scale τD in the early stage of recording is still small. This holds even for the samples with multifunctional monomer species only. The results in n1 can be attributed to different diffusion attenuation due to the different emerging photopolymer network densities (rigidities) at different monomer mixing ratios.Reflection hologram recording shows a high spatial frequency From the experimental results described above we decided for subsequent simulations to identify the diffusion attenuation factor α as: As we now know the relation of the diffusion attenuation factor α versus the mixing ratio of mono- and multifunctional monomers via the relation shown in ® HX film, we identified and rationalized a formulation design strategy to tune spatial frequency response of the photopolymer to a desired property profile.The model almost quantitatively predicts the experimental values as can be clearly seen from G0 in the unrecorded state should be reasonably large to guarantee sufficient mechanical stability for recording and web-coating [n1 over wide range of SF can be realized  a rather homogeneous illumination; (ii) a control of the UV wavelength and (iii) a control of UV dosage and VIS dosage separately. Furthermore, the UV LED and VIS LED combination can be switched on and off as required by the step-and-repeat process whereas such a cycling would dramatically decrease the lifetime of a metal halide bulb or mercury bulb.2 and UV: 52 mW/cm2) is shown in The spectrum of a standard metal halide bulb  and the dosage is too high yellowing of the material starts and yellowing increases with increasing UV dosage.The intensity itself and the dosage, i.e., the exposure time times the intensity, govern the bleaching result. A better bleaching result is defined as a higher transmission in the visible spectral region (~400–800 nm) as measured in a spectrometer with the film laminated onto a glass slide. Even though both parameters may be carefully optimized for each BayfolThis is exemplarily shown in ® HX film grade with a TAC substrate using both curing systems. As can be seen in To illustrate the yellowing effect we bleached a certain Bayfol® HX film is laminated to this master vHOE. A single scanning laser line copies the phase hologram of the master vHOE into the copy film. The copy film is moved in a step and repeat process through the replication line. To record a master vHOE in Bayfol® HX film without being bound to size limitations by laser power limits we described in [For the commercialization of vHOEs simple and robust mass production schemes are of utmost importance. Therefore at the end of this review we would like to touch on this aspect too. In ,56 we reribed in  a hologr® HX film.First we review the main topics of computer generated volume holographic optical elements generated in a printer and which can be used as master vHOEs. Second we outline the main topics of the replication procedure indicated above for BayfolA major bottleneck for applications using large size vHOEs has been the master hologram recording which, if recorded in traditional full aperture mode, needs expensive, large and high precision optical equipment and high power laser with long coherence length to achieve the minimum needed intensities in the plane of the recording medium. Furthermore, the recording setup, especially the object path needs to be rearranged.x, y-translation stage [® HX film, both given in [A large master vHOE can be recorded alternatively using only standard size and off the shelf optics and low power lasers, if they are combined with an on stage ,59. Smalgiven in .x, y translation stage that we used allows the recording of vHOE sizes up to 600 mm × 600 mm. The holographic printing system described here records functional transmission type vHOEs. The One example for a functional vHOE is a holographic off-axis transmission lens.On the other hand it is also possible to “stitch” such a vHOE of an off axis lens sequentially. The phase function needed in the object beam is generated by starting the design algorithm with a small circle. On the left side of To reconstruct a single focal point, for each Hogel a deflecting phase function has to be added to the phase function of the small circle. The deflection has to be chosen with respect to the position of the Hogel on the vHOE and the desired focal length  with a plane wave with a diameter larger than the size of the vHOE  to avoid complex and costly lens surface shapes corrected for spherical aberrations. Detailed specifications of the optics are listed in [The module transforms the circular output laser beam of diameter 2 × 954.5 mm . Along tisted in ,56.The bleaching module has to provide a suitable spectrum and intensity see  to irrev® films, i.e., the relative diffraction efficiency η of the copy as function of the applied dosage D during recording. In a static exposure this is usually done by varying the exposure time at a constant intensity I0 during recording. In our machine this can be implemented by using the computer controlled shutter. The impinging intensity for any specific position on the copy recording plate can be measured, e.g., by using a power detector head with a circular mask having a 1 mm diameter pinhole .In order to compare the scanning contact copy process with a static exposure, we measured dosage response curves of vHOE copies recorded in Bayfol HXD on the scanning speed v needs to be derived from the machine parameters. Details can be found in [For the scanning copy process a dependency of dosage found in .BR for the copy is 0.67. We applied scanning speeds stagev between 2 mm/s and 55 mm/s in the scanning case and used 0.52 to 14.19 s for the static exposure. measuredI was 11.5 mW/cm² in both cases.As an example we show in As we used the contact copy process the dosage response for the scanning process indeed follows that of the static exposure case. This proves the viability of the presented contact copy process and its suitability for mass production of vHOEs.® HX film) that allow a pure photonic processing to manufacture volume holographic optical elements (vHOEs). Holographic recording is done by laser interference recording. Several variants of recording schemes are shown including digital master hologram recording and mass photonic replication. The photochemistry to build a light sensitive material is explained in detail and the chemical response is based on the reaction driven diffusion process. Consequences on the recording conditions are explained.We describe the Chemistry and the Physics of a new class of holographic photopolymers (BayfolvHOEs in photopolymers are a key enabler to many new applications. While vHOEs do not represent a standalone product and need to work in conjunction with other components, including light source, spatial light modulators and alike, they need to be customized towards specific optical properties. This film media technology is an enabler towards those needs and links itself to classic film processing. Major consumer applications are in development like augmented reality glasses and head-up displays that will change the way we interact with the world in the future. The combination of Physics and Chemistry has been the driver for the development of these materials, which now will bridge towards consumer electronics, the automotive industry and beyond.


Following publication of the original article , the autIn Table 3, the values in the fourth column (% population with access to an ITN within their own HH) and some values in the fifth column (% population that used an ITN the previous night) are incorrect. The corrected Table In addition, consequent of the errors in Table 3, please be advised of these corrections to the second paragraph under subsection ‘General knowledge on Malaria’ :72.6 to 90.3%. The proportion of the population that used an ITN the previous night varied from 65.7 to 87.8% (Table The proportion of the population with access to an ITN within their household varied from The authors apologize for this error.


The data presented in this article are related to the research article ‘Chemical and biological monitoring of the load of plant protection products and of zoocoenoses in ditches of the orchard region Altes Land’ , which is only available in the German language. The zooplankton data presented here were acquired from four ditches  between 2001 and 2003 . This article describes the methods used to determine zooplankton species in the samples. The field data set is publicly available at the OpenAgrar repository under . It is related to the field data set of Lorenz et al. (2018) where pesticide monitoring data from the same ditches and time period were presented. Three ditches were located in an apple orchard, and one ditch was located in a grassland region. The site characteristics of the four studied ditches are presented in Lorenz et al. (2018) This research did not receive any specific grant from funding agencies in the public, commercial or not-for-profit sectors.


A novel design for the classical microfluidic device known as T-junction is proposed with the purpose of obtaining a simultaneous measurement of the in-plane velocity components in two orthogonal planes. A crucial feature of the proposed configuration is that all three velocity components are available along the intersection of the two planes. A dedicated optical set-up is developed to convey the two simultaneous views from the orthogonal planes into the sensor of a single camera, where a compound image is formed showing on either half one of the two views. A commercial micro-particle image velocimetry system is used to measure the velocity in the two planes. Feeding the T-junction with a liquid continuous phase and a dispersed gas phase, the velocity is measured by phase averaging along the bubble formation and break-up process showing the potentialities of the new design. The accuracy analysis shows that the error is dominated by a systematic component due to the thickness of the measurement slice. The error can be reduced by applying confocal microscopy to the present system with no further modifications so as to reduce the thickness of the measurement slab thereby reducing the error. Moreover, by sweeping the planes across the region of interest, a full three-dimensional reconstruction of the velocity field can be readily obtained. Finally, the simultaneous views offer the possibility to extract the principal curvatures of the bubble meniscus thereby providing access to the Laplace pressure. In microfluidics, different methods are used to produce microbubbles, exploiting laminar flow conditions to allow for high reproducibility and high production rate at relatively low energy and mass transfer rates  with a mass flow rate in the range We report here a brief description of the assembly procedure of the novel microdevice. The detailed fabrication process is reported in Appendix Microchannels with rectangular cross-sections and different aspect ratio, height and width can be fabricated using calibrated glass spacers of different thickness, highlighted in yellow in sketches of Figs. x–y) and (z–x), respectively,  view, hereafter called direct view, is directly captured by the objective. The (z–x) view is instead first reflected on the mirror, reflected view. To simultaneously focus both views, the two optical paths should be identical. This requires the interposition of an optical adapter, here a simple calibrated glass spacer. From the geometry of the optical system, the refraction indices of the materials and the desired positions of the focal planes as well as the thickness of the glass spacer can be easily evaluated, see Appendix The double optical access through orthogonal planes allows to visualize the bubble formation and break-up in the two planar views,  in the channel symmetry plane, x–z, reflected image), now in the symmetry plane The left panel of Fig. entclass1pt{minimaFigure The positions of the two orthogonal planes can be independently varied by changing the objective focus and the thickness of the optical path adapter with an accuracy related to the correlation depth. Since, in principle, the coordinates x along the intersection line of the two views, illustrating the possibility to simultaneously measure all three velocity components.The left panel of Fig. x–y plane at nominal spanwise location The right panel of Fig. Let us now focus on the T-junction configuration described in Sect. At variance with the simpler case of the straight channel, for the T-junction configuration the a priori estimate of the confidence interval is much harder to achieve. The reason is that, due to the geometrically complex and time-dependent flow domain, it is difficult to accurately evaluate the occupancy fraction of the interrogation volume. To circumvent this difficulty, the occupancy fraction was directly evaluated from the raw data. Its typical value turned out to be x–y) view and the blue one corresponds to the reflected (z–x) view. As for the case of the rectilinear channel, the confidence interval is x–y) view and the blue line providing z–x) view.The right panel of Fig. Figure x–y) plane. The other half captures the orthogonal view in the (z–x) plane which is conveyed to the camera objective through an inclined mirror and a suitable optical adapter. The device is used together with a traditional, single camera, An important issue in microfluidics is accessing the three-dimensional structure of the velocity field. For the specific case of a T-junction, the three-dimensional field can be reconstructed using stereo n et al. . Here weThe analysed data were obtained for channels with typical size of For a


I read with great interest, the work of Jean-Louis Vincent and colleagues ‘Mean Arterial Pressure and Mortality in Patients with Distributive Shock: A Retrospective Analysis of the MIMIC-III Database’ . I congrThere are several merits of the authors work. Firstly, the database in question—the Medical Information Mart for Intensive Care (MIMIC-III) is a well validated, robust dataset with about 50,000 ICU admissions and related variables. Secondly, the authors work is novel—while we all believe that we know that hypotension in the ICU is bad and we think that we are doing a good job defending a MAP of 65 mmHg, the results reported here make it clear that we are not. As reported by Jean-Louis Vincent’s group, more than 60% of this population in question had a continuous MAP of less than 65 mmHg of at least 2 h to up to 4 h of duration. (This was after being exposed to a minimum of 6 h of preceding vasopressor therapy to stabilize blood pressure). The story is not very different when lower thresholds of defending MAPS are analyzed as well. In addition, the authors elegantly show a progressive increase in ICU mortality as the duration of exposure to MAPS less than 65, 60 and 55 mmHg is lengthened.Where does this work take us next? What MAP should I defend in the ICU, and how should I best do it? This analysis of MIMIC-III does have its own limitations. The biggest one is the lack of granularity of blood pressure data that were recorded about once per hour. This is something that most hemodynamic analytics in the ICU are faced with currently, as we report only nurse-verified ICU blood pressures which may be few and far between, and indeed may be more for only the perceived sicker patients. We as a critical care research community need to develop an effective system of conserving continuously generated hemodynamic data (or monitor data) with an inherent mechanism to filter out the noise and artifacts. This is the only way that we will be able to effectively report associations with outcomes with some degree of certainty. The other opportunities in this work concern vasopressors, and maybe something that the authors would want to reconsider for the future. It would be fascinating to analyze a MAP of 65 mmHg and even higher and lower thresholds, in the context of increasing vasopressors, specifically the use of catecholamines only versus a more multi-modal balanced approach using vasopressin and other newer analogs as well. Furthermore, the utilization of high-dose vasopressors has been associated with 50–80% 30-day and 90-day mortality, and balance of adequacy of blood pressure versus the necessity of loading vasopressors is an evolving argument [The need of the hour is larger, more granular hemodynamic datasets such as these that can allow us to precisely see what we are doing with our defense of blood pressures in the ICU. Outcomes such as mortality are important and serious; however, other critical outcomes such as myocardial injury after non-cardiac surgery also need to be considered. Clearly, if the perceived ‘magic number’ is a mean arterial pressure of 65 mmHg, we are not quite there yet, and we are not doing a good job in terms of defending it. If the number is higher than 65 mmHg, then the situation may be even more worrisome. There remain several unanswered questions in religiously defining and appropriately defending a blood pressure in the ICU.


We present an infrared microscopy technique, capable of measuring the temperature of both the bounding surfaces and the oil film in an elastohydrodynamic contact. This technique can, for the first time, spatially resolve the oil film temperature in three dimensions. The contact is produced by loading a steel ball against a sapphire disc, and the film is viewed using an infrared microscope focussing through the disc. Two band pass filters are used to isolate the radiation from the oil film, and Planck’s law is applied to data obtained at a known temperature as part of the calibration procedure. The proposed technique requires the emissivity of the oil film to be measured, which is acquired in situ and is shown to vary strongly as a function of thickness and temperature. The technique is validated under pure rolling conditions, when the temperature of the oil film is equal to the controlled lubricant reservoir temperature, and also compared to an equation commonly used to predict average film temperatures, confirming the value of the unknown constant. The technique is then used to gain insights into the thermal/rheological behaviour within a contact. This is important since the temperature of elastohydrodynamic contacts is critical in determining friction and hence the efficiency of machine components and this technique enables much needed validation and provides input data for CFD and numerical simulations. Frictional heat generation in lubricated contacts has been a major area of research during the last 50 years as it affects the performance of materials in industrial applications. The resulting temperature rise can lead to materials melting , crackinAn area where detailed interfacial temperature measurements are particularly needed is elastohydrodynamic (EHD) lubrication, which occurs in the contacts between, e.g. rolling element bearings, gears and cams. Under normal operating conditions, the energy efficiency of these components is largely determined by shearing of the lubricant film that separates the sliding surfaces. However, this is difficult to predict and hence optimise, since the non-conformal nature of component surfaces results in contact widths of around 100 µm and pressures that can reach several gigapascals (GPa), which, combined with film thickness less than 1 µm, lead to highly non-Newtonian behaviour. The situation is further complicated by thermal feedback whereby lubricant rheology dissipates heat causing an increase in temperature, which in turn affects the rheological properties of the fluid. Despite the importance of being able to reliably predict and optimise such behaviour, there is a lack of experimental data to support the modelling efforts in this area and, to the best of the authors’ knowledge, there is no effective method to accurately measure the distribution of temperature three-dimensionally within the oil film. This information would be useful in validating the disputed rheological models being used to predict friction . The aimInfrared thermography or so-called infrared thermal imaging is a spectroscopic technique based on the acquisition of electromagnetic infrared radiation. Experimental approaches typically involve an infrared camera with a microscope lens sensitive to IR radiation used to collect radiation emitted from samples, which is then processed to convert the radiation to temperature according to Planck’s law. The advantages of this infrared approach are accurate spatially resolved measurements, with high thermal resolution, and the ability to obtain transient variations and separate radiation components from the different components that make up the interface.In 1950s, Bowden and Thomas  used a lIn 1995, Spikes and co-workers  used theReddyhoff and co-workers , 28, 29 both contact surfaces and oil film in an EHD contact configuration. The detailed information of the proposed methodology is presented in Sect. Despite these experimental studies and a number of thermal models built on different methods, such as multi-grid multi-level , to showIt has so far not been possible to use the IR technique to obtain oil film temperature distributions in EHD contacts accurately since variations in emissivity, which links the measured radiation to the temperature, have not been accounted for. The emissivity of a material is defined as the ratio of emissive power of a nonblack body at the surface to the emissive power of a black body at the same temperature , 33, whiUdisc and Uball are the surface speed of the disc and ball, respectively). The AISI 52,100 steel ball was 19.05 mm in diameter with roughness lower than 10 nm in each test. The transparent disc  has a diameter of 100 mm and a thickness of 3.5 mm. The roughness of the sapphire disc was lower than 10 nm, and similar to that of the steel ball. Santotrac 50 was used as the lubricant, which has a low viscosity and high traction coefficient under normal conditions (the dynamic viscosity of Santotrac 50 at 40 °C is 24.973 mPa s). This lubricant filled the reservoir to half-immerse the ball specimen in all tests, so that it was entrained into the contact by the rotation of the ball. The oil inlet temperature was monitored and controlled by a thermocouple probe located in the reservoir. This is acceptable since, according to .)


The burden of influenza in primary care is difficult to assess, since most patients with symptoms of a respiratory infection are not tested. The case definition of “medically attended acute respiratory infection” (MAARI) in the German physician sentinel is sensitive; however, it requires modelling techniques to derive estimates of disease attributable to influenza and respiratory syncytial virus (RSV).The objective of this paper was to review and extend our previously published model in order to estimate the burden of RSV and the differential burden of the two influenza B lineages  as well as both influenza A subtypes on primary care visits.Data on MAARI and virological results of respiratory samples  were available from 2010/11 until 2017/18. We updated the previously published generalized additive regression model to include RSV.We found that the proportion of MAARI due to RSV is substantial only in the 0‐1‐ and 2‐4‐year‐old age groups ; in the 0‐1 years old age group, RSV leads in almost all seasons to a higher burden than any influenza type or subtype, but this is reversed in the age group 2‐4 years old.We succeeded in rearranging our previously published model on MAARI to incorporate RSV as well as the two influenza B lineages  in the time period 2010 to 2018. Both viruses cause a similar syndrome , but influenza as well as RSV may also present without fever.The objective of this paper was to review and extend our previously published model in order to estimate the burden of RSV and the differential burden of the two influenza B lineages  as well as both influenza A subtypes on primary care visits.2Data from the German influenza sentinel system were used. Medically attended acute respiratory infections in age groups were weekly reported from around 500 primary care practices. The virological sentinel surveillance is performed by the German National Reference Laboratory for Influenza. From a subgroup of patients, systematic sampling by physicians is done according to the EU ILI case definition. Beside influenza virus detection and differentiation of A subtypes and B lineages, every sentinel sample was analysed also for RSV since 2010.We made three adaptations to the model: (a) we added RSV data, (b) we separated data on influenza B into the two lineages B(Vic) and B(Yam), and (c) we separated the age group 0‐4 years into 0‐1 and 2‐4 years old. Otherwise, we did not alter the model and estimated first the amount of [influenza + RSV] that exceeds the trend + baseline, and distributed this excess in a second step to the influenza subtypes A(H1), A(H3), B(Vic) and B(Yam) as well as RSV. Finally, we calculated age‐specific attack rates by season and subtype.3Between 20 and 791 positive samples per age group formed the basis for the modelling work , A(H3) and B, we present now estimates also for RSV and were able to separate B into B(Vic) and B(Yam). The estimated burden in primary care due to the two B lineages reveals that—between 2010/11 and 2017/18—B(Yam) leads to an approximately three times higher burden compared with B(Vic). In a global study with data from 2000 to 2013, Caini found that—among the B lineages—Victoria and Yamagata lineages predominated during 64% and 36% of seasons, respectively. The authors concluded also that the detection of influenza B was more associated with younger age than influenza A. In our analysis, we found that B(Yam) affects also older age groups. During the 2017/18 season in Germany, B(Yam) contributed to the burden of any influenza in an extraordinary manner.In addition, we were able to estimate the primary care burden due to RSV very well since the underlying data allowed us to analyse separately the 0‐1‐ and 2‐4‐year‐old age groups. Here, we made a number of important observations. First, RSV and influenza waves overlap widely; second, although there is a measurable impact of RSV in all age groups, the proportion of MAARI due to RSV is substantial only in the 0‐1‐ and 2‐4‐year‐old age groups; third, the RSV impact can be observed in these two age groups in all seasons analysed; and fourth, in the 0‐1‐year‐old age group RSV leads in almost all seasons to a higher burden than any influenza, but this is reversed in the age group 2‐4 years old. Because first RSV infection in life affects primarily children under two years of age, these results on RSV were expected and are consistent with study results of the burden of RSV and influenza in secondary care. In comparison with the results of the former model, adding RSV has led to a substantial decrease in the influenza estimate (only) in the 0‐1‐year‐old age group, and the geometrical form of the influenza incidence by age group would now be best described as a “skewed M” instead of a monotonous decline, see Figure Thus, the inclusion of RSV in the model not only showed the burden of the pathogen in the youngest age group but also improved our estimates for influenza. Opatowski et al stated the important role of considering cocirculating pathogens in mathematical modelling, and to our knowledge, only few studies included both influenza and RSV in burden estimates.Our model has still some limitations: we continue to have the difficulty that viral samples in the sentinel are taken from ILI patients while we are assessing the total burden of consultations to ARI. Thus, we have assumed that the distribution of INV subtypes/lineages and RSV among ARI cases is similar to that among ILI patients.We attempted to use the number of influenza and RSV‐positive samples separately in the model. However, we observed that in a couple of seasons the entire burden was taken of by either RSV or influenza in the two youngest age groups. One reason for this was that in seasons with a high MAARI activity already in autumn, this activity can typically not be fully explained by neither RSV nor influenza, and hence, the role of the virus that shows up first in autumn  is overestimated by the model and this is propagated also for the winter  of that season.We also considered using the positivity rate of influenza or RSV among all tested samples (data and results not shown) instead of the number of positive samples as explanatory variable in the model. However, although the general course was similar, data values of the positivity rate were more erratic, particularly because we considered the age groups separately.In summary, we extended our burden of disease model for the estimation of MAARI due to RSV in addition to influenza in primary care. This will allow us to monitor the effect of present and future prevention concepts such as vaccination for certain circulating respiratory viruses and to better understand interactions between influenza and RSV.


We develop a finite element method for the Laplace–Beltrami operator on a surface with boundary and nonhomogeneous Dirichlet boundary conditions. The method is based on a triangulation of the surface and the boundary conditions are enforced weakly using Nitsche’s method. We prove optimal order a priori error estimates for piecewise continuous polynomials of order  Finite element methods for problems on surfaces have been rapidly developed starting with the seminal work of Dziuk . Differek are used both in the interpolation of the surface and in the finite element space. Our theoretical approach is related to the recent work [In this contribution we develop a finite element method for the Laplace–Beltrami operator on a surface which has a boundary equipped with a nonhomogeneous Dirichlet boundary condition. The results may be readily extended to include Neumann conditions on part of the boundary, which we also comment on in a remark. The method is based on a triangulation of the surface together with a Nitsche formulation  for the ent work  where a ent work  is develthe work  where thk, we prove optimal order error estimates in the Provided the error in the position of the approximate surface and its boundary is (pointwise) of order The outline of the paper is as follows: In Sect. n be the exterior unit normal to x and the normal n(x) of Let, Clearly we may take Tangential calculus For each w, i.e. a mapping Model problem Find s on ·‖ω, see  for a deTo formulate our finite element method for the boundary value problem –2.4) in in2.4) iDiscrete surface Let h, that approximates k. We assume that the mesh is quasi-uniform. For each x and the normal Geometric approximation property We assume that Finite element spaces Let k defined on k defined on the reference triangle f is extended from The finite element method for the boundary value problem –2.4) ta ta2.4) tk we require Note that in order to prove optimal a priori error estimates for piecewise polynomials of order ude that  does notWe derive a priori error estimates that take both the approximation of the geometry and the solution into account. The main new feature is that our analysis also takes the approximation of the boundary into account.v defined on v defined on For each function B to denote a matrix representation of the operator dp with respect to an arbitrary choice of orthonormal bases in B is invertible.The derivative δ>0, see  for furtGradients of extensions and lifts are given by We have the following estimates B| denotes the absolute value of the determinant of B  and B to the one dimensional tangent space of the boundary curve. We then have the estimates Verification of  B, and the bounds . In  we thus : We have+1), see , and, th+1), see . Next weI) We have II) : Using tThe following estimates holdIn fact the estimate  holds alHowever,  is only and side –3.112)..\documenWe note that the estimates in Lemma Term–3.110)::3.110): estimate .TermsII and III have the same form and may be estimated as followsTerm  we used  and the Estimate  follows Estimate . and 3.1: We have we used , 3.94)  3.129\doWith the Strang Lemma u the solution of (With ution of –2.4) an anu the ution of  the follStarting from the Strang Lemma and using the interpolation estimate , the quahere, in  to estimu the solution of   Terms\doestimate  for the estimate  for the her with  for the her with . Thus weestimate , and the we used .Term Our results directly extends to the case of a Neumann or Robin conditionStrong implementations of the Dirichlet boundary condition may also be considered in our framework. In this remark we summarize the main modifications in the formulation of the method and in the analysis. To formulate a finite element method with strong Dirichlet boundary conditions we need to interpolate the Dirichlet data and construct a suitable interpolation operator. Then we formulate the method and finally we discuss the modifications in the theoretical results.Interpolation We recall that in the construction of the Scott–Zhang interpolation operator, see [i, then the nodal value N is the number of nodes and the nodal values are defined byp for the nodes in the interior. We have the interpolation error estimatetor, see , to eachify that  and the ify that , that thfined in , satisfiK with at least one vertex at the boundary Method To formulate the method we define the discrete Dirichlet dataError estimates In the analysis the following modifications are done:The energy norms are defined by In the Strang Lemma the lifted forms are simplified to For the consistency error we have the simplified expression The quadrature estimates in Lemma Combining these results we obtain energy and We next note that l values  and  and then the boundary is corrected such that the nodes on the discrete boundary mentclass2pt{minimNumerical study The numerical solution for the model problem with entclass1pt{minimaThe results for the convergence studies in energy norm and In the special case cription , illustr