TL Measurements Research Articles

Thermoluminescence and Kinetic Parameters of Beta Rays Irradiated Egyptian Muscovite.

The current work was going to study the dosimetric properties of Egyptian muscovite minerals irradiated with β-rays using the thermoluminescence technique (TL). The analysis of the TL glow curves was done using the (Tm - Tstop) and the initial rise methods. The deconvolution of the muscovite glow curves was analyzed to have eight superimposed trapping peaks. These trapes were located at 0.72, 0.80, 0.98, 1.09, 1.19, 1.30, 1.50, and 1.59 eV. Muscovite samples were studied at doses up to 330 Gy and exhibited good linearity in relation to beta radiation. The kinetic parameters, sensitivity, and dosimetric characteristics were evaluated. High accuracy was achieved through the repeatability of TL measurements.

Study of non-exponential OSL decay curve within critical physical conditions of synthetic quartz material and their resolution by selection of suitable protocol

Researchers had reported that synthetic quartz which was annealed either at 400 °C irradiated by 75.6 Gy beta doses or at 600 °C irradiated by 25.2 Gy beta doses showed better rise in OSL intensity at room temperature depicting the change from non-exponential to exponential shape of the decay curve. Under these conditions, the non-exponential shape of decay curve with weaker OSL intensity was observed. It was due to re-trapping of optically released electrons by shallow traps corresponding to 110 °C TL glow peak and it was later verified by ESR spectra.In order to eliminate the non-exponential behaviour of decay curve, the researchers suggested OSL measurement at elevated temperature so as to further remove the contribution of shallow traps. However, in the present work, the OSL decay curves are recorded at 160 °C for 400 °C and 600 °C annealed samples irradiated by 2.52 Gy, 5.04 Gy, 25.2 Gy and 75.6 Gy beta doses. Both the samples show non-exponential shape of OSL decay curve up to 25.2 Gy beta doses. However, it gradually changes to exponential shape with better OSL intensity at higher beta doses. Additionally, few attempts were made to examine the non-exponential pattern of OSL decay at room temperature as well as elevated temperature within respective critical conditions by using fitting equations. It reports that various mode of non-exponential patterns of curve and their changes were influenced by strength of physical conditions. Further, a new protocol of cyclic sequence of doses, pre-heat up to 200 °C, test dose and stimulation at 125 °C for 40 s stimulation time was implemented to identical treated samples. It shows disappearance of non-exponential shape of OSL decay by growth in OSL intensity. These changes in OSL pattern were further justified by the contribution of annealing, irradiation, thermal transfer and thermal assistance process and TL measurements before and after OSL.

Telomere length in relation to fecundability and use of assisted reproductive technologies: the Norwegian Mother, Father, and Child Cohort Study.

In women, shorter telomeres have been reported to be associated with conditions such as endometriosis and polycystic ovary syndrome, whereas other studies have reported the opposite. In men, studies mostly report associations between shorter telomeres and sperm quality. To our knowledge, no studies have thus far investigated the associations between TL and fecundability or the use of ART. This study is based on the Norwegian Mother, Father, and Child Cohort (MoBa) Study and uses data from the Medical Birth Registry of Norway (MBRN). We included women (24,645 with genotype data and 1,054 with TL measurements) and men (18,339 with genotype data and 965 with TL measurements) participating between 1998 and 2008. We investigated the associations between leukocyte TL and fecundability, infertility, and the use of ART. We also repeated the analyses using instrumental variables for TL, including genetic risk scores for TL and genetically predicted TL. Approximately 11% of couples had experienced infertility and 4% had used ART. TL was not associated with fecundability among women (fecundability ratio [FR], 0.98; 95% confidence interval [CI], 0.92-1.04) or men (FR, 0.99; CI, 0.93-1.06), nor with infertility among women (odds ratio [OR], 1.03; CI, 0.85-1.24) or men (OR, 1.05; CI, 0.87-1.28). We observed an increased likelihood of using ART with increasing TL among men (OR, 1.22; CI, 1.03-1.46), but not among women (OR, 1.10; CI, 0.92-1.31). No significant associations were observed using the instrumental variables. Our results indicate that TL is a poor biomarker of fecundability, infertility and use of ART in MoBa. Additional studies are required to replicate the association observed between TL and ART in men.

Measurements of the neutron and gamma dose via TL/OSL in LiF:Mg,Ti and activation methods analysis of aluminum foils

The measurement of beta/gamma and neutron dose components in mixed radiation fields is described involving combined OSL and TL measurements. The accuracy of the technique is investigated by irradiation of LiF:Mg,Ti samples with 14.1 MeV neutrons and a comparison of the OSL/TL results with the neutron fluence determined by Al activation. The precision of the measurements is 6.1 to 6.7 % (1 SD) for the OSL/TL technique compared to 7.3 % for the Al foils. The advantage of the technique is the simultaneous determination of the two dose components on the same samples of 7LiF:Mg,Ti in a single dedicated TL/OSL reader.

Radiological or nuclear emergency OSL dosimetry using commonplace salt

During recovery phases following a nuclear or radiological incident, it is crucial to assess the radiation exposure of both the general public and responders. This assessment is vital for directing protective actions and for conducting subsequent analyses of the incident's impact. Several methods have been employed at different timescales after an incident, including assessments based on measurements of materials present at the time of the incident. Common salt has previously been shown to have potential for retrospective dosimetry in the μGy-mGy dose range using portable OSL instruments. This study aims to explore the effects of sample storage under light and dark conditions on OSL signals. The OSL signals indicate a brief decrease in luminescence during the initial days after irradiation, followed by a gradual rise with extended storage. The period from 8 days to 64 days is characterized by relatively stable results, which encompass a significant portion of the timeframe relevant for dose estimation during both the early and later phases of responding to radiological emergencies. Light exposure (simulated daylight) results in an extremely rapid loss of OSL signals. Results are discussed with reference to TL measurements of associated trapping systems which provide insight into potential zeroing mechanisms and the observed fading behaviour. The results are sufficiently favourable to conclude that these characteristics, together with the widespread availability and low cost of household salt, support its use for prompt emergency assessment and as a retrospective dosimeter, below 100 μGy.

Assessing whether a thermoluminescence peak at ∼100 °C in calcitic opercula can be used to monitor thermal reproducibility

The opercula of the gastropod Bithynia tentaculata is composed of calcite and exhibits three main thermoluminescence peaks at ∼100, 280 and 360 °C when heated at 0.5 °C.s−1. The two higher temperature peaks can be used for geological and archaeological dating, whilst the lower temperature peak has a lifetime of hours and is only seen after laboratory irradiation. This study explores whether this lower temperature TL peak can be used to assess the reproducibility of laboratory heating of opercula. As found in previous studies, the TL peak at ∼100 °C is seen to consist of at least two signals which have different lifetimes at room temperature. By fixing the interval between irradiation and measurement of the TL signal, the impact of these different lifetimes on the temperature at which the TL peak occurs (Tm) can be reduced, and replicate measurements on a single operculum using the same radiation dose yield values of Tm within 1 °C. Comparison of different opercula shows variation in Tm of 9 °C when heating at 5 °C.s−1, interpreted as primarily arising from variation in thermal lag between the hotplate and the different samples assessed. Reducing the heating rate to 0.5 °C.s−1 reduces the variation in Tm between opercula to 2 °C. Imaging the TL emission from opercula using an EMCCD shows spatial variation in heating, and also demonstrates the reduction in variability that can be achieved by using a slower heating rate. Thus, monitoring the position of the TL peak at ∼100 °C can be used to assess thermal reproducibility of TL measurements on calcitic opercula.

Optical properties of pure and Sn-doped β-Ga2O3 single crystals grown by optical float zone technique

High-quality single crystals of both pure and Sn:β-Ga2O3 single crystals weregrown using the optical floating zone technique and a comprehensive study of its luminescence and scintillation properties was carried out. The pure and Sn:β-Ga2O3 grown crystals were oriented along (100) by Laue diffraction pattern and its monoclinic structure was confirmed using a single crystal XRD. X-ray induced luminescence spectrum shows a maximum emission peak at 365 nm. The cut off wavelength was observed around 258 nm and the optical band gap was calculated to be 4.64 eV from UV–Vis-NIR transmission spectroscopy. The room temperature Raman spectra were recorded and the various vibration modes were investigated. Low temperature (10 to 300 K) and high temperature (325 to 675 K) TL measurements were carried out on X-ray irradiated crystals and its TL kinetic parameters such as activation energy (eV) and frequency factor (S) were calculated. Scintillation decay time profiles were measured for both pure and Sn-doped crystals under 137Cs γ-ray excitation. The calculated scintillation light output is 2300 Ph/5.5 Mev for Sn:β-Ga2O3 crystal under α-particle excitation from 241Am radiation source.

Practical Considerations and Limitations of Using Leaf and Canopy Temperature Measurements as a Stomatal Conductance Proxy: Sensitivity across Environmental Conditions, Scale, and Sample Size.

Stomatal conductance (gs) is a crucial component of plant physiology, as it links plant productivity and water loss through transpiration. Estimating gs indirectly through leaf temperature (Tl) measurement is common for reducing the high labor cost associated with direct gs measurement. However, the relationship between observed Tl and gs can be notably affected by local environmental conditions, canopy structure, measurement scale, sample size, and gs itself. To better understand and quantify the variation in the relationship between Tl measurements to gs, this study analyzed the sensitivity of Tl to gs using a high-resolution three-dimensional model that resolves interactions between microclimate and canopy structure. The model was used to simulate the sensitivity of Tl to gs across different environmental conditions, aggregation scales (point measurement, infrared thermometer, and thermographic image), and sample sizes. Results showed that leaf-level sensitivity of Tl to gs was highest under conditions of high net radiation flux, high vapor pressure deficit, and low boundary layer conductance. The study findings also highlighted the trade-off between measurement scale and sample size to maximize sensitivity. Smaller scale measurements (e.g., thermocouple) provided maximal sensitivity because they allow for exclusion of shaded leaves and the ground, which have low sensitivity. However, large sample sizes (up to 50 to 75) may be needed to differentiate genotypes. Larger-scale measurements (e.g., thermal camera) reduced sample size requirements but include low-sensitivity elements in the measurement. This work provides a means of estimating leaf-level sensitivity and offers quantitative guidance for balancing scale and sample size issues.

Thermoluminescence glow curve analysis of Ca3Y2B4O12 phosphor prepared using combustion method

Ca3Y2B4O12 (CBYO) phosphor was synthesized using a gel combustion method. X-ray diffraction (XRD) measurement confirmed a single-phase structure (space group Pnma (62)) of synthesized compound. TL measurements were conducted between room temperature (RT) and 450 °C at a heating rate of 2 °Cs−1. Significant glow peaks were observed at 64, 116, and 242 °C in CYBO phosphor sample exposed to different beta doses. In the range of 0.1–100 Gy, the TL intensity of the glow peak displayed good linearity. Different methods were employed to determine the number of peaks, the trap structure, and the kinetic parameters of the thermoluminescence glow curve of CBYO; the Hoogenstraaten method, various heating rates (VHR), and glow curve deconvolution method (CGCD) implemented through tgcd:An R package. Currently available findings confirm that CYBO host is a promising candidate for environmental studies because one exhibits adequate TL dose response coupled with a good sensitivity and linearity.

Anomalous fading in thermoluminescence signal of ten different K-feldspar samples and correlation to structural state characteristics

The present work reports an extended study of anomalous fading (AF) in the TL signal of ten different pure K-feldspar samples from North Greece. A fading protocol was applied, including a standard series of TL measurements undertaken following a variety of storage times after irradiation, in order to plot the luminescence output as a function of storage time. Anomalous fading was found to be ubiquitous for the TL signal of all feldspars. The remnant signals are defined as the ratio of the TL signal remaining after storage time t, over the corresponding signal promptly measured. Two different fading rates were calculated, namely the value of g-factor which describes the luminescence signal loss in terms of percentage per decade of time as well as the g50-factor which describes the fading rate when the signal has been reduced to 50% of the prompt value measured after irradiation due to AF. Both aforementioned fading factors were calculated over the entire TL glow curves in step intervals of 10 °C and were eventually plotted versus glow curve temperature. The analysis indicated that fading factors yield maximum values within the temperature range between 200 and 350 °C, with a tendency to decrease with increasing temperature along the rest glow curve. As the 10 K-feldspar samples belong to three different groups (microclines, sanidines and orthoclases), possible correlation is studied between the fading factors and specific structural parameters of alkali feldspars, such as the probability of Al-cation to occupy specific sites in the forming tetrahedra and the volume of the unit cell.

Electron beam irradiation studies of ZnGa2O4:Mn2+ green phosphor

The surface composition and stability of ZnGa2O4:Mn2+ green phosphor were evaluated using Auger electron spectroscopy (AES) under electron beam irradiation in vacuum and oxygen (4.0 × 10−7 mbar). The surface chemistry was monitored while measuring the cathodoluminescence (CL) intensity. The Auger peak-to-peak heights (APPHs) of Zn and Ga were stable during irradiation in vacuum for a beam current of 1 μA, whereas the APPH of Ga initially slightly increased during irradiation in vacuum and oxygen for a beam current of 3 μA. This was accompanied with a slight initial decrease of C contamination. The APPH of O decreased during irradiation in vacuum for a beam current of 3 μA, whereas it slightly increased during irradiation in oxygen. In vacuum the CL intensity exhibited a slight initial decrease during irradiation, after which it recovered and stabilized, whereas in oxygen the CL intensity decreased initially and then stabilized. The profile of the CL spectra did not show noticeable changes as a result of irradiation. TL measurements showed that the ZnGa2O4:Mn2+ activated with UV or e-beam exhibited two broad peaks. The differences were attributed to the change in concentrations of Zn and O vacancies that could be caused by e-beam irradiation.

A Neural Network-Based Observation Operator for Coupled Ocean-Acoustic Variational Data Assimilation

AbstractVariational data assimilation requires implementing the tangent-linear and adjoint (TA/AD) version of any operator. This intrinsically hampers the use of complicated observations. Here, we assess a new data-driven approach to assimilate acoustic underwater propagation measurements (Transmission Loss, TL) into a regional ocean forecasting system. TL measurements depend on the underlying sound speed fields, mostly temperature, and their inversion would require heavy coding of the TA/AD of an acoustic underwater propagation model. In this study, the non-linear version of the acoustic model is applied to an ensemble of perturbed oceanic conditions. TL outputs are used to formulate both a statistical linear operator based on canonical correlation analysis (CCA), and a neural network-based (NN) operator. For the latter, two linearization strategies are compared, the best-performing one relying on reverse-mode automatic differentiation. The new observation operator is applied in data assimilation experiments over the Ligurian Sea (Mediterranean Sea), using the Observing System Simulation Experiments (OSSE) methodology to assess the impact of TL observations onto oceanic fields. TL observations are extracted from a nature run with perturbed surface boundary conditions and stochastic ocean physics. Sensitivity analyses indicate that the NN reconstruction of TL is significantly better than CCA. Both CCA and NN are able to improve the upper ocean skill scores in forecast experiments, with NN outperforming CCA on the average. The use of the NN observation operator is computationally affordable, and its general formulation appears promising for the adjoint-free assimilation of any remote sensing observing network.

On the use of silicon photomultipliers for thermoluminescence measurements

Abstract: In this work, we evaluate the use of silicon photomultipliers (SiPMs) as a suitable candidate for use as a photodetector for thermoluminescence measurements. The measurements were based on the Hamamatsu S13360-series with a pixel area of 3 × 3 mm2 and microcell pitches of 25 μm, 50 μm, and 75 μm, which were mounted on a Riso TL/OSL reader system with LiF:Mg,Cu,Si chosen as the reference TL material. Through the experiment, we showed that the typical TL glow curves can be obtained with SiPMs, despite their lower geometric efficiencies. We also demonstrated the dose response of SiPMs ranging from 6 to 66 mGy for three different photon threshold levels. The detection limit was approximately equal to 0.2 mSv, 0.08 mSv, and 0.17 mSv for 25 μm, 50 μm, and 75 μm SiPMs, respectively. More importantly, a sensitivity change and sensor temperature depending on a TL reading up to 260 °C was monitored on a sequential readout. Lastly, we discuss some of the possible benefits and limitations of SiPM-based TL measurements in comparison to PMT-based TL measurements.

LaAlO3:Pr3+ as photon radiotherapy dosimeter

The intention of radiotherapy is to control and cure tumor while avoiding late effects caused by radiation. High energy photon beam dose can be determined by different modalities. In this paper, dosimetric properties of praseodymium doped lanthanum aluminate exited by X-ray beams are reported. LaAlO3:Pr3+ powders samples were prepared using modified Pechinis’s method. The formations of the obtained samples were confirmed by an X-ray diffraction patterns. TL glow curve and dosimetric characteristics of LaAlO3:Pr3+ powder samples were investigated under X-ray irradiation effects. All TL measurements were made using an automated Harshaw TL reader 5500. TL glow curves were obtained using a constant heating rate 10 °C/s from room temperature up to 350°C in a nitrogen atmosphere. The dose response and minimum detectable dose (MDD) values of the samples were determined. Dosimetric characteristics of the samples were carefully analyzed. Experimental results of TL dosimetric characteristics of the powder samples appear to have potential application for high energy photon beam dose measurements.

Comparison of dose distributions in target areas and organs at risk in conformal and VMAT techniques and dose verifications with the use of thermoluminescence dosimetry

Abstract The aim of the present study is to compare dose distributions and their verification in target areas and organs at risk (OAR) in conformal and volumetric modulated arc therapy (VMAT) techniques. Proper verification procedures allow the removal of the major sources of errors, such as incorrect application of a planning system, its insufficient or cursory commissioning, as well as an erroneous interpretation of the obtained results. Three target areas (head and neck, chest, and pelvic) were selected and the treatment was delivered based on plans made using collapsed cone convolution and Monte Carlo algorithms with 6-MV photon beams, adopting conformal and VMAT techniques, respectively. All the plans were prepared for the anthropomorphic phantom. Dose measurements were performed with TL detectors made of LiF phosphor doped with magnesium and titanium (LiF:Mg,Ti). This paper presents the results of TL measurements and calculated doses, as well as their deviations from the treatment planning system (TPS) in the three planned target areas. It was established that the algorithms subject to analysis differ, particularly in dose calculations for highly inhomogeneous regions (OAR). Aside from the need to achieve the dose intended for the tumour, the choice of irradiation technique in teleradiotherapy should be dictated by the degree of exposure to individual critical organs during irradiation. While nothing deviated beyond the bounds of what is acceptable by international regulatory bodies in plans from TPS, clinically one must be more cautious with the OAR areas.

TL investigation of glasses from mobile phone screen protectors for radiation accident dosimetry

TL dosimetric characteristics of glass screen protectors were analyzed for radiation accident dosimetry. Radiation-induced TL signal and intrinsic background signal of these glasses were investigated. An attempt to categorize the glasses according to the shape of their radiation-induced TL glow curve was made. Then, the main dosimetric properties were studied for a category of glass. Radiation-induced TL signal was light sensitive and TL measurements were done on the hard-to-bleach component of the TL signal after bleaching with blue LEDs. The sensitization was negligible after 5 cycles “irradiation – pre-bleaching – TL measurement”. The dose response was linear up to 20 Gy. Fading was negligible up to 100 h and limited to ~20% for the investigated time range of 12 days. The results of a dose recovery test were promising. These preliminary results are interesting, but further studies on a larger set of screen protectors are needed to really appreciate the potential of glass extracted from mobile phone screen protectors to be used as fortuitous retrospective dosimeter in the event of a radiological accident.

Dosimetric properties of Li2B4O7:Cu,Ag,P solid detector

This work presents results obtained following the preparation of lithium borate by the chemical reaction between lithium carbonate (Li2CO3) and boric acid (H3BO3), doping the host salt of lithium borate (Li2B4O7) with ions of copper, silver and phosphorus. With the obtained material dosimeters were produced in sintered pellet form which were exposed by gamma radiation that emitted from 60Co source. The highest sensitivity was found for the sample of Li2B4O7:Cu,Ag,P (in pellet form) with 0.45, 0.45 and 12 mol% of Cu, Ag and P, respectively, subjected to a thermal treatment at 1123 K during 2 h. The TL response shows linearity in the dose range from 0.005 to 100 Gy. The lower detection limit (LDL) was equal to 6.10 μGy. The fading was found to be 3% in the first ten days and 9% at the end of thirty days. The repeatability of TL measurements for twenty cycles, showed a variability coefficient equal to 4.15%. The glow curve shape of Li2B4O7:Cu,Ag,P sintered pellet shows two peaks with general-kinetics order. This new material could be appropriate for dosimetry in clinical radiation applications.

Thermoluminescence, elastic and dielectric investigations of calcium fluoro borophosphate glass composite materials doped by small concentrations of TiO2

The glasses of composition [(B2O3)10(P2O5)60]–[(CaF2)(30-x):(TiO2)x] (0 ≤ x ≤ 1 mol%) are synthesized. Prepared glasses are characterized by TL, elastic, and dielectric Techniques. The results obtained recommend that the TiO2 do exist in both divalent (Ti3+) (cm3 mol−1) and trivalent (Ti4+) states. The evaluations of refractive index (μ = 1.501), molar volume (V = 23.764 cm3 mol−1), Young’s and shear modulus (Y = 15.64 GPa and G = 15.04 GPa), and microhardness (H = 9.56 GPa) suggest that the sample of 0.6 mol% of TiO2 concentration (T6) exhibits covalently associated interlinked structure. TL measurements suggest that the sample of 0.6 mol% of TiO2 concentration (T6) exhibiting good shape symmetry factor (u = 0.247) and low AE’s ( $$ E_{\tau } $$ = 0.485 eV, $$ E_{\delta } $$ = 0.312 eV and $$ E_{\omega } $$ = 0.234 eV) under 20 min of UV irradiation might be good TL asset. Dielectric evaluations such as density of energy states (N(Ef) = 3.125 eV−1/cm3), temperature region of relaxation (149–167 °C), loss tangent (Tan δ = 0.0896), AC conductivity $$ \sigma_{\text{dc}} $$ = 4.52 × 10−8, Ω−1 cm−1), and activation energy (Ea = 1.703) of the sample (T6) suggest that good amounts of polaron hopping might be good dielectric asset.

Water deficit detection in sugarcane using canopy temperature from satellite images

Water deficit (WD) is the main yield gap for sugarcane in Midwest Brazil. Thus, WD detection is essential to quantify yield losses, but field detection requires measurement of soil water content over large areas. In this study, we tested leaf temperature (TL) and land surface temperature (TS) to detect WD in a commercial sugarcane area. The area is located in the central region of Goiás State, Brazil. According to Köppen classification, the climate of the region is Aw (humid tropical, with rainy summer and dry winter). The soil is a Ferralsol (clayey texture). TL was measured by a portable infrared thermometer, and TS was obtained using a spectral image from Landsat 8. Both TL and TS measurements occurred between 28 Jan and 24 Aug 2014 (298-506 DAP). The water balance identified periods of water deficit (WD) and surplus (WS). The difference between TL Ta was greater than zero (7.11 °C) in WD periods and lower than zero (-2.18 °C) in WS periods. The difference between TS-Ta, in turn, ranged from -0.66 °C to 4.06 °C, but not following the tendency of WD or WS, which is associated with a relative error between TL and TS near 20% for some date. The TS Ta difference detected soil WD or WS when the relative error was low (362 and 410 DAP) and under higher WD (506 DAP) and WS (394 DAP). This way, TL was able to detect WD and WS along sugarcane growth, while TS showed limited application, requiring improvement based on surface properties to reduce the error in relation to TL. Furthermore, bands 10 and 11 are recommended for surface temperature estimation. Calibration uncertainty increases when the band 11 is used alone, being this band more affected by the absorption of radiation by the atmospheric water vapor, which implies larger errors related to the atmospheric profile in the acquisition of surface temperature.

A deconvolution method for scintillator gamma-ray spectrum analysis based on convex optimization

A deconvolution method based on convex optimization is developed and applied to gamma-ray spectrum deconvolution of simulated complicated spectra of NaI(Tl) measurements. The gamma-ray deconvolution problem is transformed into a minimization problem with inequality constraints. Then the Lagrange dual method is applied to transform the primal Lagrange problem into the dual problem. The interior-point method is applied and the logarithm barrier function is applied to construct the Newton system for iteration search. PCG (Preconditioned Conjugate Gradient) is applied to do the inexact search of the Newton system. The proposed method is applied to deconvolution of 4 typical gamma-ray spectra: (a) characteristic gamma-ray spectrum of 137Cs; (b) characteristic gamma-ray spectrum of 60Co; (c) characteristic gamma-ray spectrum of 152Eu; (d) mixed fission products in the primary loop of PWR (Pressurized Water Reactor), including the isotopes of Kr, Xe, I and Cs. Compared with the ML-EM method, improved accuracies and high resolution can be obtained with the proposed method. Moreover, the proposed method costs about 1/3 computational time of the ML-EM method.