Pulse transit time (PTT) and blood pressure (BP) are widely used to quantify arterial characteristics. Arm position influences arterial BP and peripheral PTT. This study aims to quantify the relationship between PTT changes with internal vascular pressure variations induced by the arm moving. With left arm at horizontal position as reference and the right arm moving from 90 to 45, 0, −45, and −90° respectively, PTT difference was calculated by the difference of the pulse foot between right arm and left arm within the same heartbeat. The change in the BP was calculated from the gravitational effect with the measured arm length. Our results showed that the change in PTT with arm elevating is more obvious than that with arm lowering, indicating the different relationship between PTT changes due to the internal BP changes. This can help in understanding the inherent physiological/pathological mechanism of cardiovascular system. A common method to reflect the performance of the cardiovascular system includes extraction of the information contained in radial artery pressure waveforms  by the World Medical Association, 22 healthy volunteers (13 men and 9 women) aged between 21 and 46 years were recruited from Shandong Jiaotong University, Jinan, China. The study received ethical permission from the Research Ethics Committee of the Affiliated Hospital of Shandong First Medical University, China (No. 2022001). All subjects provided their written informed consent.The design of this study has been described in detail in our previous study  and 10 cm (the distance from the clavicle to the shoulder) was considered as each subject's midpoint of the arm. The actual changes in blood pressure induced by the arm movements were calculated individually for each subject by using the lowering/lifting vertical distance from the midpoint of the arm and the hydrostatic principle , and the variations of MAP were large with the arm below the horizontal level while small with the arm above the horizontal level , which implies that the PTT differences were large with the right arm above the horizontal level while small with the right arm below the horizontal level.al level . Figure o and from −45 to −90°).The changes in the PTT were calculated from the PTT differences of the right arm at positions 90, 45, −45, and −90° min those at 0°, respectively. The relationship between the changes in the PTT and a corresponding MAP with the arm positioned at 90, 45, −45, and −90° are depicted in We investigated the relationship between the changes in the PTT and the changes in the MAP induced by the right arm lifting and lowering, and we found that (1) when the arm was positioned at 45 and 90°, the changes in the PTT increased while the BP decreased and (2) when the arm was positioned at −45 and −90°, the changes in the PTT increased and the BP increased. These results indicated that there were different relationships between PTT variations and MAP changes induced by different right arm positions. At 90° and 45°, the changes in the PTT were 17.1 and 11.4 with a rate of −1.19 ± 0.60 and −0.79 ± 0.39, respectively, while, at −45° and −90°, the changes in the PTT were −3.0 and −3.3 with the rate of −0.21 ± 0.23 and −0.06 ± 0.27, respectively.Our results are consistent with the studies of Foo et al.  and Liu This distinct result indicates that the effects of the physiological structure on PTT are different when lifting or lowering the arm. The reason may be partly due to different muscle states corresponding to different movements (Siu et al., This study has several limitations. First, the sample involved only 22 subjects. The small sample size limits obtaining statistically significant results for a wide population. Second, when calculating the length of the midpoint of the arm, it was not accurate that 10 cm is considered to be the distance from the clavicle to the shoulder for all subjects, and the values of MBP with the arm positioned at 90, 45, −45, and −90° were estimated by the linear hydrostatic principle using the midpoint of the arm but not to the direct measuring. These values will cause some errors in calculating the changes in MBP. Finally, this study only involved healthy people and did not involve the diseased population.This study demonstrated that there are different relationships between changes in PTT and changes in BP induced by right arm lifting or lowering at the same height relative to the level of the right atrium. Changes in PTT were larger during the arm lifting than the arm lowering with the approximate linear change in MBP. Future research should focus on the relationship between changes in PTT and changes in BP induced by arm movement for patients with a certain disease, which may thus be potentially useful for clinical applications.The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.The studies involving human participants were reviewed and approved by the Medical Ethics Committee of Jinshoulder, Lumbar, and Leg Pain Hospital Affiliated to Shandong First-Medical University. The patients/participants provided their written informed consent to participate in this study.ZS is responsible for data acquisition, programming, and thesis writing. XJ is responsible for experimental scheme design, data sorting, and paper modification. HW is responsible for the design of experimental equipment and the revision of papers. FL is responsible for guiding the experimental procedure. All authors contributed to the article and approved the submitted version.


Tasks measuring the sense of agency often manipulate the predictability of action outcomes by introducing spatial deviation. However, the extent to which spatial predictability of an outcome influences the sense of agency when spatial deviation is controlled for remains untested. We used a novel task to investigate the effect of several factors  on the sense of agency. We also investigated trait predictors of metacognition of agency—the degree to which participants’ confidence in their agency judgements corresponds to the accuracy of those judgements. Initial and replication samples completed contingency, deviation, and predictability versions of the task. Across samples, participants’ sense of agency was impacted by action–outcome contingency and spatial deviation of action outcomes. Manipulation of the spatial predictability of action outcomes did not reliably impact the sense of agency. Metacognition of agency was related to alexithymic traits—higher alexithymia scores were associated with reduced metacognition of agency.The online version contains supplementary material available at 10.1007/s00221-022-06339-1. The sense of agency is defined as one’s awareness that one is initiating, executing and controlling one’s own actions and their consequences .Two distinct forms of the sense of agency have been investigated, an implicit and explicit form. The implicit sense of agency is typically measured using indirect markers to agency such as the perceived temporal compression between a voluntary action and its consequence relative to that of an involuntary action  and with each of the studies detailed in “Introduction” which assessed the impact of action–outcome contingency on the sense of agency. Sample size for the replication sample was sufficient to detect effects of an equivalent size to those seen for significant effects in the initial samples in our study with an alpha level of 0.05 and 80% power. Significant effects in the original samples in the current study were large (d ranging from 0.95–1.68) and, thus, sample sizes of N = 23  and N = 26  were sufficient to replicate these effects .All sample sizes in the current study are sufficient to detect medium to large effects with an alpha level of 0.05 and with 80% power. Effects of this size would be consistent with previous research investigating metacognition of agency  with the Cogent 2000 toolbox (http://www.vislab.ucl.ac.uk/Cogent).One task with three versions was used to assess the impact of contingency, predictability, and deviation on the sense of agency. Each version manipulated the relationship between the participant’s movements and the movement of an on-screen cursor. These manipulations are described in further detail below. The experimental task was created and presented using Matlab 8.0 . The trial time was equally split between green and black snake colours. Each colour had 10, 600 ms segments assigned to it and these were randomly dispersed throughout the trial. Cases where the participants were required to remain still and where participants were required to move were necessary to manipulate action–outcome contingency (i.e. the probability of the outcome occurring both when the participant was moving and when they were still). Specifically, 600 ms ‘freeze’ periods (cursor remains static when participant is moving when the snake is black) and 600 ms ‘jitter’ periods (cursor moves when the participant is still when the snake is green) were introduced randomly into trials. The amount of freeze and jitter periods in a given trial dictated the level of control the participant had over the cursor . Four levels of contingency were utilised, corresponding to 1200, 2400, 3600, and 4800 ms of freeze/jitter. Thus, the movements of the cursor were not contingent on the participant’s movements for 10%, 20%, 30% or 40% of the total trial time.Forty-five participants completed the contingency version (see results for demographics). Participants completed 40 trials at each of the three difficulty levels . This version of the task took approximately 1 h to complete. Participants were given the opportunity for a break at the end of each block of 40 trials.Each trial lasted 6 s. In this version, the number of possible locations that the cursor could appear was manipulated to influence how predictable the cursor position was. The possible locations in which the cursor could appear were always governed by the X and Y coordinate, which would be reached by the participant’s movement were it veridically represented by the cursor. The Y coordinate was always veridically represented (i.e. was not subject to manipulation). The position of the cursor in the X plane was governed by a matrix of positions of 60 pixels wide centred on the cursor’s veridical X coordinate. Where the cursor appeared within the matrix was determined randomly from a subset of positions within the matrix, where the number of possible positions varied according to the four levels of the predictability manipulation . The cursor position was updated every 10 ms.Thirty-five participants completed the predictability version. Participants completed 40 trials at each of the three difficulty levels . These participants also completed the deviation version (see below) in the same session . The session took approximately 1 h to complete (the predictability version took approximately 30 min). Due to a technical issue, data from two participants were not recorded, thus data from 33 participants were analysed. Participants were given the opportunity for a break at the end of each block of 40 trials.Each trial lasted 6 s. In this version, the degree of spatial deviation between the participant’s movement and the movement of the cursor was manipulated. Deviation was manipulated in the X plane only, and was achieved by calculating the difference between the cursor’s last position and where it would appear currently if the participant’s movement was veridically represented. This difference was multiplied by 2, 4, 6 or 8 to create the four levels of deviation manipulation, with the result used to determine the cursor’s position in the X plane. The cursor position was updated every 10 ms.Thirty-five participants completed the deviance version. Participants completed 40 trials in each of the three difficulty blocks . Participants also completed the predictability version in the same session in a counterbalanced order. The deviation version took approximately 30 min to complete. Participants were given the opportunity for a break at the end of each block of 40 trials, and in between the two versions of the task .In a follow-up study, 28 new participants completed the third difficulty block only of each of the three versions of the task (see “Results” for demographics). The order of the three versions of the task was randomised across participants. Only the most difficult block was used to avoid ceiling effects on performance seen in some of the easier blocks in the initial samples. The contingency version of the task took approximately 30 min to complete whilst both the deviation and predictability versions of the task took 15 min to complete.In addition to the computer-based tasks, participants who completed the contingency task also completed four questionnaires to assess individual differences in autistic traits , for the cursor staying within the boundaries of the snake  and, in the case of the contingency version, the cursor staying still during snake colour changes . These percentages were averaged to create an overall percentage accuracy score for each trial. Control and certainty judgements were also expressed as percentages.lowest degree of manipulation, 4 = highest degree of manipulation; hereafter ‘manipulation level’). Additionally, for the predictability version, the discrepancy between the veridical cursor position and where it was displayed was calculated along the x plane. This additional measure was calculated for the predictability version to allow for the removal of variance associated with deviation (i.e. so that the influence of predictability could be identified unconfounded by deviation).To calculate the effect of each of the three manipulations  a categorical value of 1–4 was assigned to each trial to indicate the degree of manipulation . These values were calculated during the contingency version only, as this is the only version where control objectively varies, and therefore where the accuracy of control judgements can be calculated , and during the deviation version the cursor’s location is controlled by the participant’s movements entirely). The individual differences variables were used to predict metacognitive values in separate regression models which either did, or did not, control for perceived performance.The degree of actual control was calculated by determining the amount of time the participant was in control during a given trial. This was calculated by summing the durations of 600 ms freezes and jitters introduced to each trial and dividing this by the total trial time. This was then multiplied by 100 to get a percentage score representing the amount of time the participant was out of control. This value was then taken from 100 to get a percentage score reflecting the amount of time the participant was in control .To calculate metacognition of agency, the absolute difference between perceived control and actual control  was calculated. Higher scores indicate greater discrepancy between perceived and actual control and therefore indicate worse performance. These were then entered into a regression with certainty judgements to see the extent to which certainty judgements could predict accuracy of perceived control judgements. More negative betas indicate better metacognitive sensitivity for the sense of agency.F = 82.841, p < 0.001, ƞp2 = 0.664].Forty-five participants completed all three difficulty blocks. Two participants were removed for outlying data (performing three times the interquartile range below the median). Thus, data for 43 participants were included in the analyses . Mean accuracy for each block is presented in Table t tests were conducted at the group level to test whether beta coefficients were significantly different from 0. The contingency beta was significantly different from 0 in all three blocks (block 1 , block 2 , block 3 ). The contingency beta remained significantly different from 0 in all three blocks when controlling for perceived performance (block 1 , block 2 , block 3 ).One-sample Twenty-eight new participants completed the third difficulty block only. Data for five participants were not recorded due to a technical issue. Therefore, data for 23 participants were included in subsequent analyses .t(64) = 5.108, p < 0.001, d = 1.37]. This was due to a reduced accuracy in the replication sample relative to the initial sample  and when it was controlled for  . This suggests that in both samples of participants, contingency affected the sense of agency to a similar extent.As with the initial data, the contingency regressors were significantly different from 0, both when perceived performance was not controlled for   but not in the more difficult blocks . No betas from any of the difficulty blocks were significant after controlling for deviation and perceived performance ; ;   . However, in contrast to the initial data, the predictability beta was significantly different from zero after controlling for deviation and perceived performance . However, in this case, the predictability beta was positive, indicating that participants perceive themselves as having more control as predictability was reduced (i.e. the opposite pattern of results to what would be expected if participants were using predictability as a cue to agency).As with the initial data, the predictability beta (prior to controlling for deviation and performance) was not significantly different from zero ; however, a significant difference between the two groups was found when controlling for deviation and perceived performance . This reflects the fact that the second group had positive betas, while the first group had negative, but non-significant, betas.No significant sample difference in beta size was observed for the predictability beta prior to controlling for spatial deviation and perceived performance  , block 2 , block 3 }. The deviation manipulation beta remained significantly different from 0 in all blocks after controlling for perceived performance {block 1 , block 2 , block 3 }.One-sample t(54) = 2.968, p = 0.004, d = 0.79] , and remained significant when controlling for perceived performance .As with the initial sample, the deviation regressor was significantly different from zero . However, a significant group difference in beta was observed after controlling for perceived performance . This was due to a stronger effect in the replication sample relative to the initial sample  of the contingency version of the task. One participant was removed from the analysis for outlying data . Therefore, 67 participants were included in this analysis .Data were pooled from the third block of the initial sample and the replication sample . At the group level, the beta was significantly different from zero for metacognition of agency . A positive beta was observed for the relationship between perceived control and perceived performance . The relationship between perceived control and perceived performance was also significantly different from zero .As expected, negative betas were observed for the metacognition of agency regression . One outlier was removed (as above). Additionally, not all participants completed all of the questionnaires. Sixty-one participants were included in the analyses investigating the ASQ and AQ . Sixty participants were included in the analysis investigating the TAS-20 , and 60 were included in the analysis investigating the PDI . Note, one participant who completed the TAS-20 did not complete the PDI and vice versa. . This suggests that predictability, when controlling for deviation between intended and actual target location, may not be used when determining the sense of agency. In fact, in the case of the replication sample, spatial predictability may impair one’s ability to determine one’s sense of agency over the cursor. This highlights the need to account for the differential contribution of cues to agency—specifically to disambiguate spatial deviation and predictability.During the deviation version of the task, participants reported less of a sense of agency when the spatial deviation between the veridical and actual outcome of their action increased. This is in line with previous research showing that deviation between where the participant moves and the visual feedback associated with that movement impacts the sense of agency Below is the link to the electronic supplementary material.


Inside the eye light can be reflected multiple times due to light-tissue interactions and the spherical geometry of the eye. Due to these optical properties, a defined retinal area is not only illuminated by direct light but also by indirect, reflected light from the inner side of the eyewall. During illumination for ophthalmic surgery, this could lead to an unintended increase in intraocular retinal irradiance, which was already discussed in previous studies but without a detailed consideration of spectral differences and a potential influence of pigmentation. In this study this effect is investigated wavelength-dependent to see if different wavelengths lead to different increase in irradiance, with a special focus on the raise in photochemical and thermal hazard to the retina. It is also examined whether this effect is dependent on the pigmentation of the eye.M of porcine eyes can be calculated, which represents the increase of radiance due to multiple reflections inside a sphere compared to a planar diffuser of the same size. Based on measurements of the emitted irradiance of ophthalmic illumination fibers the increase in photochemical and thermal retinal hazard due to these multiple reflections is calculated for eyes with small and high amounts of pigmentation.The reflectance properties of either less or highly pigmented porcine eyes are measured in the wavelength range between 350 and 1100 nm with an integrating sphere and a spectrometer. With these reflectance spectra the wavelength-dependent Sphere Multiplier The reflectance of the inner eyewall in the range between 350 and 1100 nm is significantly higher for eyes with low pigmentation (between 4.90% and 37.44% reflectance) in comparison to eyes with a high amount of pigmentation (between 4.30% and 28.88% reflectance). The Sphere Multiplier for the inner side of the eyewall  ranges between 1.13 and 1.59 and between 1.13 and 1.48 for eyes with low and high pigmentation, respectively, in the range between 350 and 1100 nm. The reflectance, as well as the Sphere Multiplier, is strongly wavelength-dependent due to the absorption spectra of melanin and hemoglobin, which are located in the eye. With increasing wavelength, the reflection properties and the Sphere Multiplier also increases. With this, the photochemical retinal hazard of highly pigmented eyes increases by (14.11 ± 0.09)% and of lightly pigmented eyes by (16.75 ± 0.35)% compared to if the reflection properties are not considered. The thermal retinal hazard increases by (14.30 ± 0.07)% for highly pigmented eyes and by (19.65 ± 0.17)% for low pigmented eyes.This study demonstrates that the anatomy and pigmentation of the eye plays an important role for the reflectance properties of the eye and for the photochemical and thermal hazard to the retina. A-R and EVIR-R, are given A-R is exceeded, the maximal exposition time has to be considered. This time indicates the point at which a potential photochemical hazard to the retina is reached due to irradiation. The calculation of this period is also given in For pars plana vitrectomy and for visualisation of structures inside the eye a bright illumination of the ocular fundus is essential. Therefore, an endoillumination fiber is inserted into the eye and illuminates it from the inside The eyewall consists of three main layers, the sclera (outermost layer), the choroid (median layer) and the retina (innermost layer). These layers contribute to the reflectance properties inside the eye. Preece and Claridge (2002) defined the ILM (inner limiting membrane), RPE , choroid and sclera as reflective structures within the eyewall The eyewall contains a high amount of pigments, such as melanin and haemoglobin Another influence on the reflection properties of the eye is caused by hemoglobin. Hemoglobin is mainly located in the choroid of the eye to provide nourishment to the retina and for thermal regulation of the eye M of an integrating sphere given in M is also wavelength-dependent. It is necessary to know the wavelength-dependence of the Sphere Multiplier as it plays an important role in increasing photochemical and thermal retinal hazard. Photochemical hazard to the retina is caused by short-wavelength blue and ultraviolet light Due to the reflection properties of the ocular fundus and its spherical shape the intraocular irradiance may increase compared to if the eye would be unfolded. With the spherical geometry of the eye light can often hit the same part of the retina and therefore increase its hazard. Koelbl et al. (2019) supported this hypothesis and demonstrated that the spherical geometry of the porcine eye increases the irradiance on the surface of up to 1.5 compared to a reference measurement, where no multiple reflections are possible To determine the wavelength-dependence of the effect of increasing intraocular irradiance in this study, the reflection properties of the inner eyewall of ex-vivo porcine eyes are investigated directly with an integrating sphere, without prior absorption, reflection or scattering of the light beam by other ocular tissue. The measurements are performed in the wavelength range between 350 – 1100 nm. This range is chosen because ophthalmic laser for therapeutic applications do not only emit light in the visible region but also in the near infrared region > 780 nm for example in laser photocoagulation with 810 nm In this study, porcine eyes are used as tissue specimens. They are a good alternative to human eyes as they have many similarities in anatomy and physiology Fresh porcine blood is obtained from the same local slaughterhouse as the porcine eyes. According to Faber et al. the absorption spectrum of blood is mainly dominated by the hemoglobin absorption spectrum Synthetic melanin is obtained from Sigma Aldrich in a powder form  and stored at -20 °C.3 of Mountain Photonics, Landsberg am Lech (Germany)) is applied and placed onto the aperture, which diffusely reflects the incident light.To measure the reflectance of the inner side of the eyewall an integrating sphere is used A. The inP, where the probe is placed just below the aperture, a reference spectrum R, where the reflection standard is placed just below the aperture, and a halo spectrum H. The halo spectrum is the spectrum of the scattered light that remains in the integrating sphere and could not exit through its aperture. During these three measurements, the light stays on. With these spectra, the reflectance ρ can be calculated as shown in equation (1).To determine the amount of reflected light of the specimen three different spectra are necessary. The spectrum To measure the relative absorbance of porcine hemoglobin and melanin the samples are diluted in distilled water and put in a 1 ml UV-cuvette, respectively. As reference 1 ml pure distilled water is used. The absorbance is measured using a spectrometer ) in the wavelength range between 350 and 1100 nm.M of an integrating sphere is given by Parretta and Calabrese (2013) The Sphere Multiplier f is the ratio of the open ports to the overall area of the sphere. In case of the eye f is the fraction of the size of the iris and pupil together divided by the surface of the eye: f = AIris/AEye = 0.075, with different radii of 6 and 7.2 mm of the elliptic iris and with a diameter of the eye of 23.9 mm ρ and f the Sphere Multiplier is calculated.The reflectance of the sample is ρ and A-R and the thermal weighted irradiance EVIR-R on the retina (equation 3 and 4) Due to these multiple reflections inside the eye, caused by its spherical shape, the irradiance inside the eye increases, compared to the irradiance that would be observed if there wouldn’t be this spherical shape. In ophthalmologic surgery the illumination of the ocular fundus is performed with either hand-held endoillumination fibers or chandeliers To measure the emission of these different illumination fibers they are combined with either a halogen lamp ) or a xenon light source ) depending on the illumination fiber. Some fibers can only be connected to the halogen lamp and some can only be used in combination with the xenon lamp, depending on which type of adapter they have. These two light sources are typically used in ophthalmic surgery and emit light in the region between 380 and 780 nm. The emitted irradiances of these fibers were measured with another integrating sphere ) and an array spectrometer ) in the range between 380 and 780 nm. The intensities of the light sources are set to the maximum possible intensity in combination with the used fibers.A-R and E*VIR-R, due to multiple reflections, are calculated by weighting equation (3) and (4) with M(λ), given in equation (5) and (6), where M(λ) is the Sphere Multiplier depending on the wavelength and Eλ is the irradiance of the fiber without reflections.The irradiances E*A-R and ΔEVIR-R, respectively, and is calculated according to equation (7) and (8).The increase of the photochemical and thermal hazard for the retina is given by ΔETo illustrate the resulting reduction in operation time, the exposure time is calculated for the illumination fiber ) in combination with the xenon light source ).To perform a statistical analysis SPSS Statistics ) is used. To determine the difference in reflection between eyes with blue and brown irises the area under the curve (AUC) between 350 and 1100 nm and between 380 and 500 nm is calculated for each sample The AUC between 350 and 1100 nm is calculated to get an overall impression of the reflectance properties of the tissue, whereas the AUC between 380 and 500 nm is calculated due to the fact that this range is the most important one for the calculation of the photochemical retinal hazard. For these AUCs a Mann Whitney-U-Test is performed. P < 0.05 is considered as statistically significant.SCR(R) = Rblue/Rbrown, is given for wavelengths between 350 and 1100 nm. In The reflectance is calculated for the sclera, S A, scleraTo determine the influence of hemoglobin and melanin to the reflectance of the inner eyewall the absorbance spectra of porcine hemoglobin and synthetic melanin are recorded. The relative absorbance of hemoglobin (black solid line) and melanin (black dashed line) in the range from 350 to 1100 nm are plotted in M for eyes with blue and brown irises equation f = 0.075. The results are shown in For determining the Sphere Multiplier M of blue and brown eyes, QSCR (M) = Mblue/Mbrown, is given for wavelengths between 350 and 1100 nm. The Sphere Multiplier, and therefore the increase in irradiance, in blue eyes is higher than in brown eyes by a factor between 1.003 and 1.151.It is observed that the sphere Multiplier not only depends on the wavelength but also on the pigmentation of the eye. The Sphere Multiplier is larger for eyes with blue irises compared to brown irises. The increase of the Sphere Multiplier for blue eyes compared to brown eyes is shown in The measured irradiances of various typical used illumination fibers in ophthalmology according to the standard ISO 15752:2010 With this Sphere Multiplier the increase in potential retinal hazard can be calculated according to equation The reflectance measurements of the inner side of the porcine eyewall resulted in a significant higher reflectance for less pigmented eyes compared to strong pigmented eyes between 350 and 1100 nm. Here, the reflectance of the sclera is the largest. The sclera also contains some blood Considering all layers of the eyewall, the reflectance becomes smaller, due to hemoglobin and melanin absorption, which are located in the choroid and retina. The reflectance of the inner side of the eyewall is between 4.85 and 34.77% for eyes with blue irises and between 4.24 and 30.37% for eyes with brown irises. Additionally, the reflectance increases with increasing wavelength. Considering the pigmentation of the eye our data reveals significant higher reflectance values for eyes with blue irises compared to eyes with brown irises in the range between 350 and 1100 nm.The differences in the reflection spectra for different pigmented eyes are partly due to the melanin content in the eye. Melanin absorbs more light in the short-wavelength range compared to longer wavelengths . TherefoAnother influence of the increase in reflection of the ocular fundus for larger wavelengths is the strong decrease in hemoglobin absorption in this range. In our study we performed an absorbance measurement of porcine blood, which is mainly dominated by hemoglobin absorption, and covered the complete spectral range between 350 and 1100 nm, which extends the spectral range of porcine hemoglobin absorption in the literature Due to the reflection properties of the ocular fundus and its spherical shape the intraocular irradiance increases compared to if the eye would be unfolded. With the spherical geometry of the eye light can often hit the same part of the retina and therefore increase its hazard. The Sphere Multiplier of the ocular fundus reaches values between 1.13 and 1.58 for a wavelength range between 350 – 1100 nm. Our study expands the results of Koelbl et al. (2019) Another method to reduce the hazard to the retina could be the use of light sources with a non-continuous spectrum. By reducing the portion of wavelengths in the spectrum that are not necessary for imaging in the eye, the radiation in the eye is reduced. Especially the reduction of the short-wavelength part of the spectrum can lead to a reduction of the photochemical ability. For example, white LEDs with relatively narrow blue emission peaks are less dangerous than xenon light sources which consists of the same blue emission peak and an additional portion of shorter and longer wavelength light When performing ophthalmic procedures with light sources, which emit light in the wavelength range around 960-980 nm, the absorption properties of the vitreous body should be included in the hazard evaluation, as it has a high absorption in this wavelength range, which is due to its high water content. Based on to these absorption properties, light in this spectral range would be attenuated and thus contribute less to the retinal hazard than without considering the vitreous body. In our evaluation, the vitreous body was not considered, since the light sources used in our study only emit light in the wavelength range between 380 and 780 nm. Another reason, for not considering the absorption properties of the vitreous body, is that some surgical procedures are performed after a vitrectomy, when no vitreous body is present in the eye.In this study, the reflectance properties of the porcine eyewall are determined in the equatorial region of the porcine eye. The reflectance properties in the region of the optic nerve, the fovea or the pars plana may differ from the results presented in this study. This is because the thickness of the eyewall and the pigment concentration vary in different parts of the eye. Two additional factors influencing the reflection properties of the eyewall could be the angle of incidence and the polarization of the light. The latter plays only a minor role, since most ophthalmological light sources emit non-polarized light. In case of laser applications in the eye, the reflection properties of the eyewall depend on the polarization angle, following the Fresnel equations. However, the effect of polarization on the reflection of the eyewall and the incident angle of the light on the retina were not investigated in this study. In our measurements the light fell on the retina at approximately the same angle as it usually does during eye surgery. To measure the angular dependence of the reflection in the eye was not possible with our set-up, but is a task which could be investigated in the future.Our study proves that the pigmentation of the eye has an influence on the Sphere Multiplier M. In less pigmented eyes the Sphere Multiplier of the eyeball is higher as for highly pigmented eyes. However, this effect is very strongly dependent on the wavelength. This is illustrated clearly in In the literature, unexplained vision loss after eye surgery is often reported. Despite a good understanding of eye physiology and diagnostic capabilities, there are still cases of unexplained vision loss Our study reveals that the reflection properties of porcine eyes depend strongly on the wavelength and on the pigmentation of the eye. The wavelength- and pigmentation-dependency can be explained by the absorption spectrum of hemoglobin and melanin located in the eyewall. The reflection of the eyewall has a great influence on the Sphere Multiplier, which represents the increase of irradiance due to multiple reflections inside a sphere compared to a plane of the same size and reflection properties. Due to these multiple reflections and their wavelength-dependency, the photochemical and thermal hazard for the retina increases in comparison to if no reflections would be considered. The anatomy and pigmentation of the eye plays an important role for the intraocular irradiance on the retina and for the maximum exposition time during vitreoretinal surgery. These results indicate that the limit values specified in the standard DIN EN ISO 15004-2:2007 This work was financially supported by the German Federal Ministry of Economics and Technology within the ZIM joint project “Safe Light” (grant number ZF4137902AK9). This article does not contain any studies with human participants or animals performed by any of the authors.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.


Strong light–matter interaction plays a central role in realizing quantum photonic technologies. The entanglement state, which results from the hybridization of excitons and cavity photons, forms the foundation of quantum information science. In this work, an entanglement state is achieved by manipulating the mode coupling between surface lattice resonance and quantum emitter into the strong coupling regime. At the same time, a Rabi splitting of 40 meV is observed. A full quantum model based on the Heisenberg picture is used to describe this unclassical phenomenon, and it perfectly explains the interaction and dissipation process. In addition, the observed concurrency degree of the entanglement state is 0.5, presenting the quantum nonlocality. This work effectively contributes to the understanding of nonclassical quantum effects arising from strong coupling and will intrigue more interesting potential applications in quantum optics. Recently, the study of strong coupling between optical microcavities and quantum emitters has attracted great attention . Strong κ2+γ2)/2 , the intκ2+γ2)/2  has attrκ2+γ2)/2 . FurtherE2 is the energy stored in the cavity and E1 is the stored energy lost per oscillation cycle [Since the strong coupling could reach the limit of quantum optics , it shouon cycle .Vmode of the optical cavity represents the localization ability of the optical mode in space, and a smaller Vmode presents higher optical field confinement and better photon localization in the nanostructure. Hence, both Vmode are important indicators to describe the cavity properties in CQED [Vmode are highly demanded.Generally,  in CQED , and coh5–107 [Vmode of Various optical microcavities are widely designed to increase the ery mode  could re 105–107  and option limit , 17.Vmode as well as an enhanced and localized electric field, further increasing the value of Compared to conventional optical microcavities, the plasmonic structure has the ability of subwavelength optical field confinement , causingcument}V . For exacument}V  and silvcument}V  are usedanoarray  is propoanoarray  mode tha3 [Vmode of the surface plasmon and effectively reduces the radiative loss, it is attractive to be a subsystem in the strong coupling system and is expected to enhance the coupling coefficient 2 is more prominent due to its single-layer direct band gap with high electron mobility, and it also possesses a long carrier lifetime and excellent nonlinear properties. As a result, WS2 is a great candidate to achieve strong coupling among quantum emitters. The material of metal plasmon is based on two points: It should be a relatively economical and manipulatable material, and should exhibit high plasmon density. From the band structure and optical properties, Al exhibits higher density of free electron, with three electrons per atom (Au and Ag has one electron per atom), and this could lead to a higher n is the density of free electrons, The line width of SLR mode reduces remarkably and the each 103  when come moment , where t broader . Besides2 film to obtain a strong coupling between the SLR and excitons. The generated strong coupling phenomenon with a Rabi splitting of 40 meV was investigated by using numerical simulation and theoretical calculation. A full quantum model was established to reveal the temporal dynamics of SLR–exciton entanglement. Concurrence [This work proposes a composite system that consists of the plasmonic periodic nanoarray and a quantum emitter of WScurrence , the noncurrence . The simFirst of all, the optical modes in a bare plasmonic lattice without emitters are characterized, and then, they are regulated to interact with the exciton of quantum emitters to reach the strong coupling regime. The Al columns with a radius of 50 nm and height of 50 nm are arranged in a square lattice with a period of 400 nm to generate SLR modes.n. A typically schematic diagram of the Al periodical nanocolumns array that could generate SLR mode is displayed in Fig. The SLR caused by the radiative coupling of periodic nanoparticles is generated through regulating the shape and size of the LSPR mode to interact with the DOs. LSPR is manipulated by thickness T, radius R and the ambient refractive index Vmode and greater field enhancement. Therefore, the radius of the columns is set to 50 nm which is small enough compared with the whole system. DOs are influenced by the period P and the surrounding refractive index n, which are geometry parameters from the periodic columns.A smaller R and T will result in smaller E is the photon energy, c is the speed of the light, n is the refractive index, k is the absolute value of the wave vector and the component in the  axis is kx, ky and kz, respectively. If k|| is constant, then kz is 0, the dispersion relation defines a cone surface in the three-dimensional space known as a light cone, and plane waves can propagate freely inside the cone which is usually called in-plane mode. But outside the light cone, at least one wave number must become imaginary to satisfy the dispersion relation in the above equation, and this is the case for evanescent waves.Thus, the coupling strength depends on the interdistance between the spectral center wavelength of two modes and the generated SLR closely follows the dispersion of DOs, which can be described by the empty lattice approximation (ELA). The dispersion relation of the light in free space:px in the x-direction and py in the y-direction is assumed in this work. The reciprocal lattice vectors are px is as 400 nm. After vector composition, the dispersion relation is expressed as:Then, the periodical boundary condition should be considered, and a 2D infinite lattice with a periodicity of x–y and forms the array in Fig. The light cone is duplicated and shifted in-plane Gy = 0 and ky = 0 in the dispersion. The / diffraction mode  mode and transverse magnetic (TM) mode. Under these two different polarization directions, nanoparticles would behave distinctive characters. The 0, 1)/ mode excited by the TM is shown in Fig. / n = 1.2 is chosen to match the energy of the quantum emitter. This also shows the refractive index is one of the important freedom degrees to regulate the SLR mode.After determining the incidence angle, as mentioned above, the refractive index n of different dielectric layers will have an impact on the energy matching of SLR mode and the quantum emitter. When the structural parameters are fixed, the refractive index n is changed from 1.0 to 1.4. The transmission spectra reveal the dispersion of the SLR mode in Fig. Besides, there are also some other free degrees in regulating, such as the radius, height of the Al columns and incident angle for further using a real dielectric material practically.2 to satisfy the strong coupling generation condition.Figure mentclass2pt{minim2 is added between the metal column array and the dielectric layer to offer excitons in this system as presented in Fig. A monolayer of WSFor the definition of strong coupling, two common conditions are used: 2 overlaps the energy of the SLR pattern, an anti-crossing of the two modes is observed. This could be considered as a mode splitting and strong coupling of the SLR with the quantum emitter. In this paper, When the transmission peak of WSThe coupling constant obtains from the dispersion of the simulation is entclass1pt{minima2 and SLR modes are indicated by black and blue solid lines, respectively. The splitting between the UP and LP is depicted using the red line, further demonstrating the generation of strong coupling.The spectral features of the newly formed polariton modes at 0° are extracted to analyze the optical response of the coupled system as shown in Fig. 2 quantum emitter. Though the interaction increases, the intrinsic loss of WS2 still cannot be ignored. The theoretical energy level diagram of the strong coupling system is illustrated in Fig. The transmission intensity of the UP and the LP is reduced compared to the two subsystems without the interaction. This could be explained by the dissipation of WSΩR forms .The coherent coupling energy of UP and LP is 2, and the electric dipole mode mainly participates in the interaction. The maximum intensities of UP (3) and LP (11) are slightly weaker than that of the SLR pattern . By using the Jaynes–Cummings model, the mode can be used to calculate the time evolution of a quantum state and for a quantized bosonic field interacting with a two-level atom. And here the excitonic mode is quantized as a two-level atom by the two-level approximate approach. Herein, the SLR mode and excitonic mode are quantized as bosonic mode and fermionic mode.z-axis, the electric field component can be expressed as nth standing wave mode.Considering the electromagnetic field within a one-dimensional confined cavity of length According the Maxwell equations, the magnetic field is y-polarized and is expressed as:The energy of electromagnetic field is ing Eqs.  and 4)  \documenNext, the following operators are introduced:Substituting Eqs.  and 8)  8) into The matter–classical field interaction and the matter–quantum field interaction can be understood in a consistent way as follows: In the both cases, the energy oscillates periodically between its ground state and excited state. In the case of matter–classical field interaction, only the matter is quantized; therefore, the phenomena related to the quantization of the field cannot be explained well, such as the spontaneous emission. And this phenomenon can be explained well in the view of matter–quantum field interaction.H of the established quantum mechanical model includes the following terms:The total Hamiltonian The first term is the system Hamiltonian,The second term is the reservoir Hamiltonian,The reservoir follows the Bose–Einstein distribution at thermal equilibrium, where The next term that describes the interactions between the coupling system and the reservoir is the radiative and nonradiative damping of the subsystems:The last term is the driven field Hamiltonian that describes the driven field with a Gauss wave packet:The total Hamiltonian is Figure With the purpose of analyzing the photon entanglement induced by the strong coupling, the concurrence is employed to justify entanglement states between two subsystems , as illuThe highest concurrence has reaches to 0.5 at 27.2 fs which is a big boost. Though the concurrence from the plasmonic lattice exhibits a fast decay process about 600 fs, the study of this ultrafast dynamics of physical processes could still be measured by applying the fs transient absorption spectroscopy technology.x, p), which is real-valued and dimensionless. It is equivalent to the wave function or density matrix when describing the quantum states; besides, it contains all the information of quantum states and can be described by the following formula:To get further valuable insight into the nature of the quantum states of UP and LP modes within the strong coupling system, the Wigner functions of the corresponding modes are also investigated under the quantum mechanical model. The Wigner function is the quasi-probability distribution function defined in the phase space of (t = 0 fs, and there is no entanglement states existing in the two subsystems. At t = 27.2 fs, the concurrences reach to the maximum in Fig. As illustrated in Fig. We proposed a composite structure consisting of a periodic nanoarray and a quantum emitter to achieve strong coupling between SLR and excitons. In this work, the strong coupling occurred at the degenerate point, due to the large density of states at the degenerate point and the strong local electric field characteristics of the SLR mode. It greatly promoted the coupling between the SLR mode and the exciton, and realized the Rabi splitting of


Reliable non-destructive methods for verifying spent nuclear fuel are essential to draw credible nuclear safeguards conclusions from spent fuel. In Finland, spent fuel items are verified prior to the soon starting disposal in a geological repository with Passive Gamma Emission Tomography (PGET), a uniquely accurate method capable of rod-level detection of missing active material. The PGET device consists of two highly collimated detector banks, collecting gamma emission data from a 360° rotation around a fuel assembly. 2D cross-sectional activity and attenuation images are simultaneously computed. We present methods for improving reconstructed image quality in the central parts of the fuel. The results are based on data collected from 2017 to 2021 at the Finnish nuclear power plants with 10 fuel assembly types of varying characteristics, for example burnups from 5.7 to 55 GWd/tU and cooling times from 1.9 to 37 years. Data is acquired in different gamma energy windows, capturing the peaks of Cs-137 (at 662 keV) and Eu-154 (at 1274 keV), abundant isotopes in long-cooled spent nuclear fuel. Data from these gamma energy windows at well-chosen angles are used for higher-quality images, resulting in more accurate detection of empty rod positions. The method is shown to detect partial diversion of nuclear material also in the axial direction, demonstrated with a novel measurement series scanning over the edge of partial-length rods. Prior to the disposal, the spent fuel needs to be comprehensively verified to assure that nuclear safeguards objectives are met and that all nuclear material stays in declared use. This was a major driver for the work of designing a Passive Gamma Emission Tomography (PGET) device that was approved by the International Atomic Energy Agency (IAEA) for nuclear fuel inspections. This Non-destructive Assay (NDA) method detects gamma emission from the spent fuel assembly from all angles with two linear arrays of highly collimated CdZnTe gamma detectors2. With modern inverse problems techniques, a 2D cross-sectional image is reconstructed3. Both the attenuation and the gamma activity of the fuel are simultaneusly computed, and based on the images, even rod-level anomalies in the fuel can be detected. Together with the neutron multiplication verifying method PNAR (Passive Neutron Albedo Reactivity)7, the fuel material can be verified with very high confidence.Finland is constructing a first-of-its-kind underground geological repository for spent nuclear fuel disposal in Olkiluoto, Eurajoki. The start of operations at the new facility is scheduled for 20258 have studied iterative reconstruction methods and automated rod identification from simulated fuel data. Shiba et al.10 have simulated data with Poisson noise and compared different iterative reconstructions methods. Eldaly et al.11 have estimated fuel rod activities and their uncertainties with Bayesian approaches. Most authors have limited access to real measurement data, and therefore simulated data is often used. The IAEA has also released a PGET dataset measured with mockup fuel consisting of neutron-irradiated cobalt rods containing Co-60, and this mockup data has been used widely9.Recent studies on the image reconstruction methods and analysis of PGET data have been conducted worldwide. Fang et al.13 and the results presented here build upon them. The results show that the visibility of empty fuel grid positions in the central parts of the fuel is enhanced with our proposed novel method. The results are compared to measurement data from 2017 to 2020 in general terms to see overarching trends in image quality.During 2021 and 2022, PGET measurement data was acquired at the Finnish nuclear power plants. A unique series of measurements was conducted on BWR (Boiling Water Reactor) fuel to test the ability of the PGET method to detect partial diversion also in the axial direction of the fuel. For VVER (Water-Water Energetic Reactor) fuel, new methods were used to enhance the reconstructed image qualities in the central parts of the fuel, both with data acquisition changes as well as with data post-processing tools. Image quality matters were investigated previously in14.The Passive Gamma Emission Tomography (PGET) device is an NDA instrument that gathers data from spent nuclear fuel assemblies for tomographic image reconstruction. The PGET device houses two detector banks on opposite sides of a torus. Each detector bank consists of a linear multi-slit tungsten collimator backed by a row of CdZnTe gamma detectors. In this arrangement, only gamma rays travelling in a very specific transaxial direction can be detected, providing transaxial imaging information. A spent fuel assembly is placed in the central hole of the device and tomographic data acquisition is performed by rotating the detector banks a full 360° around it, gathering gamma emission data from all angles. The collimator slits of the device are trapezoidal in shape towards the axial direction, opening up the axial view of a fuel assembly, increasing the gamma ray count rate and allowing for shorter data acquisition times. The axial field of view of the detectors into the fuel is around 20–30 cm, depending on the fuel dimensions. The axial field of view increases from the front to the back of the assembly. The device is described in more detail in15, and it was approved in 2017 by the IAEA for NDA inspections16.The PGET device has been designed and developed jointly with experts from the IAEA, STUK in Finland and othersFrom 2017 to 2021, the PGET device has been used in collaboration with the IAEA and the European Comission at the Finnish nuclear power plants in altogether seven measurement campaigns. In total 101 individual fuel assemblies have been measured, out of which 12 included fuel grid positions with missing rods. The initial enrichments have ranged from 1.9 to 4.4 %, average burnups (BU) from 5.7 to 55 GWd/tU and cooling times (CT) from 1.9 to 37 a. Campaigns have been conducted at the Loviisa nuclear power plant in 2017, 2018, 2020 and 2021 and at the Olkiluoto nuclear power plant in 2017, 2019 and 2021. The nine Olkiluoto BWR fuel types measured are 9x9-1AB, 8x8-1, ATRIUM 10, SVEA-64, SVEA-100, SVEA-96 OPTIMA, SVEA-96 OPTIMA2, GE-12 and GE-14. At Loviisa, all fuel is of the VVER-440 type. All relevant fuel parameters for the assemblies presented in this work can be found as Supplementary Table 13.The gamma emission data acquired from the measurements is preprocessed first. Misbehaving detectors resulting in abnormalities in the data are removed and an interleaved value from the neighboring detectors is used instead. The profile of the detector counts integrated over the 360° rotation is also smoothed to account for individual differences in the detector responses. After preprocessing, a Filtered Back-projection (FBP) is performed to provide a quick initial reconstruction. Based on this FBP image, the fuel type is deduced and a pre-defined fuel grid based on the declared information of the fuel geometry is fitted onto the FBP image. This will act as a base for the reconstruction of activity and attenuation images, where the grid is used as a prior. Solutions where rod-shaped areas are at the predefined positions are favoured in the reconstruction process, but nothing about the content of these positions is assumed . Activity and attenuation images are then reconstructed by solving a constrained regularised problem with an iterative scheme. The mathematical details of the approach used can be found in3. The end result of the analysis is a reconstructed 2D image of the fuel and a conclusion about each grid position either being classified empty or filled.Average activity values for each fuel grid position are calculated from the activity images by averaging the pixel values over the area of each rod. These values are then used for classifying the grid positions into empty and filled positions. In this classification, each grid position is compared to its immediate neighbors and a classification border is computed using support vector machines. The support vector machines are trained on the reconstructions of training data sets from varied assemblies including mock-up fuel and real spent fuel assemblies with different rod placements and intensities. The classification process is described in more detail inThe quality of the reconstructed gamma activity images is assessed with a tailor-made image quality index, which enables quantitative comparison between different images. The index helps evaluating the effects of different data processing approaches or settings on the end result. It looks into the most important quality of the images: how much the empty fuel grid positions differ from the filled positions.The image quality index is based on comparing the fuel grid positions where a fuel rod is known to be present to such positions which include only water . Activity average values of each position are used for the comparison.Figure In an ideal case, the separation between the full-length fuel rods and the empty grid positions in the axial field of view , but from a methodological point of view, the water positions can also be treated as empty rod positions in the fuel grid and they act as good substitutes for “missing” fuel rods in the method development.In image quality plots shown for different measurement results  to find out the sensitivity of the PGET method to detect a possible diversion of nuclear material in the axial direction. The geometry of the device  causes the field of view of the device to be rather broad in the axial direction. Thus, changes in the fuel rods in the approximately 20–30 cm axial field of view area will be seen as differences in the activity of the rods in the reconstructed images. If part of a fuel rod is missing and some of that empty space is present in the field of view, the resulting image will show a lower activity of that rod in question.An axial scan over the partial-length fuel rod edge was performed with seven steps of 2 cm increments. The aim was to estimate how much of the fuel rod needs to be missing before the reconstruction results will differ from the baseline result acquired at a height where the partial-length fuel rods are covering the full field of view of the device.Figure x is the axial position and b and c are free parameters in the fit, b representing the axial position where c indicating the steepness of the slope. The fit is obtained by a least-squares minimizing algorithm.The sigmoid curve used is of the form:If the halfway point of the sigmoid curve represents the edge of the partial-length fuel rod, based on the fit the edge would be at Figure Figure The location of water channel positions might have a minor influence on the results. For the BWR assemblies, there is a varying number of water channel positions in the grid and in the VVER-440 fuel there is only the one position in the center. For the image quality index, these positions are treated equally and if the assembly has multiple water positions, a mean value is used. For BWR assemblies, which often have water channel positions a bit further out from the very center, the visibility of these positions for the gamma ray detectors is better. The VVER-440 assemblies thus have a disadvantage due to their geometry, when they are compared with the image quality index of BWR assemblies.Based on this comparison it is clear that the quality of the images especially in the central region needs to be enhanced. In the remainder of this section we describe data acquisition changes implemented to better capture the desired gamma peaks and post-processing was fine-tuned for this specific application.In the past, data acquisition has usually been done in a standard energy window of 600–700 keV, capturing the 662 keV peak of Cs-137, the most intense gamma ray emitted by long-cooled fuel. This relatively wide window also captures a lot of photons scattered to lower energies, and while these photons contribute to the overall statistics, the information that they carry about the spatial position of the fuel rods is low. Thus, the energy window was cut narrower to test if the quality of the data could be improved by only including gamma rays in the photopeak.The energy resolution of the CdZnTe-semiconductor detectors used in the PGET device is 10.7 ± 0.4 keV FWHM  at 662 keV. This allows for a tighter gamma energy window around the 662 keV full-energy peak than the previously used 600–700 keV, but the resolution should be kept in mind when fine-tuning the window. The narrowest window which captures a very large fraction of the full-energy events is about 10 keV around 662 keV. We therefore chose a 650 keV lower limit for the window, eliminating as many scattered gamma rays as possible. The upper energy limit is not as critical, because there are much less counts at energies right above the 662 keV peak than right below it. We chose an upper limit of 700 keV in order to be compatible with the previously chosen upper limit for the Cs-137 energy window.The gamma energy spectra for two BWR assemblies are shown on the left in Fig. Figure The 650–700 keV window captures the 662 keV photopeak, representing unscattered Cs-137 photons and providing the sharpest image due to the excellent imaging information that the photons carry. The highest window 700–3000 keV contains the Eu-154 photopeak, which also represents unscattered photons, but with short data acquisition times as in this measurement, the Eu-154 does not produce enough counts for a high-quality image.The 600–650 keV window mostly captures 662 keV photons from Cs-137 which are scattered inside the fuel grid before entering the detector and thus carry very poor image information and do not contribute to the overall quality of the data in a positive way. The water channel is not visible in the image reconstructed from these counts. Leaving out this part of the data brings the overall counts down, the counts in this window being a third of the counts in the 600–700 keV window. The poor imaging information of these counts, however, causes the quality of 650–700 keV image to be even better than that of the image from the combined 600–700 keV window.The 400–600 keV window contains only scattered photons. The Compton edge at 478 keV, representing the escape from a detector of the backscattered photon, is most clearly seen in Fig. Figure The quality of images in the 400–600 keV and 700–3000 keV windows is surprisingly good, owing in the first case to the Compton edge and in the latter case to the high-energy full-energy peak from Eu-154. For the 600–650 keV window, the quality is very poor and the water channel position is actually showing as a higher-activity spot compared to the filled positions.In addition to the very abundant Cs-137 isotope, also Eu-154 has a significant intensity peak in long-cooled spent nuclear fuel. With a half-life of 8.6 a, this isotope is often seen next to the most abundant Cs-137 with a half-life of 30 a. As the energy of the Eu-154 gamma ray is 1274 keV, it has the potential of revealing the inner parts of the fuel assembly better than the lower energy 662 keV of Cs-137, since it has a bigger chance of not being absorbed in the fuel matrix and reaching the detector. The total attenuation coefficient in UOThis new approach for central part image quality enhancement was investigated during the Loviisa 2021 measurement campaign. The fuel was measured at a gamma energy window of 1200–1300 keV to capture the 1274 keV gamma peak of Eu-154. Data were also acquired at the 650–700 keV window for comparison. Data acquisition times needed to be lengthened significantly to account for the lower abundance of the Eu-154 isotope in the fuel.The gamma energy spectra for two VVER-440 fuel assemblies are shown in Fig. Figure Figure The average counts per sinogram pixel in the 650–700 keV window with the long data acquisition time is between 24000 and 32000 for the younger fuel assemblies with cooling times from 3 to 7 a and burnups from 44 to 55 GWd/tU. For the oldest and lowest-burnup assembly  the average counts per sinogram pixel is around 7600. In the 1200–1300 keV window, these averages are from 420 to 1800 counts per sinogram pixel for the younger fuel and 30 counts per sinogram pixel for the old fuel. For comparison, in the 650–700 keV window with usual data acquisition times the averages would be from 2900 to 3800 counts per sinogram pixel for the younger fuel and around 900 for the old fuel.The burnup and cooling time of the assemblies will have an effect on the quality of the images reconstructed from these two energy windows. For the outlier in Fig. Image quality indices of reconstructed images show that the quality of the Eu-154 window images is, for most assemblies, at roughly the same level as for the Cs-137 window, although the counts in the higher energy window are significantly lower than in the lower window. The data acquisition times could be further lengthened to get a better idea of whether the Eu-154 window really does bring more information from the center of the assembly. The matter requires further investigation with even longer data acquisition times. It is to be noted that the time required can be very long if similar counts per sinogram pixel are wanted as for the Cs-137 window. For example, for the bottom right assembly (d) in Fig. The reconstructed images are usually computed by using 120 equidistant projections from the total of 360 angles. Using all angles has sometimes shown worse results than using fewer angles.There are three ways to choose the 120 equidistant angles, and only some of these choices include the so-called see-through directions. These directions are such angles that the detector banks are perpendicular to a direction where there are no fuel rods back to back in some lines of sight, as illustrated in Fig. The image quality plot in Fig. The effect of burnup on the image quality is evident in Fig. See-through directions were studied further with the help of forward model calculations to understand their meaning for reconstructed image quality. The forward model used in the reconstructions was utilized for calculating different mock-up cases. For a test assembly with all fuel grid positions filled with fuel rods, but only one position housing an emitting spent nuclear fuel rod see Fig. , the effThe zoom-in inset in Fig. The results from the scan over the edge of partial-length fuel rods demonstrate that the PGET method is able to detect partial-length fuel material diversion also in the axial direction. For safeguards conclusions, especially in the Finnish geological disposal context, this is a useful ability, and it could be of use in other studies as well, for example in diagnostics of damaged fuel rods. The structure of fractured fuel rods could be investigated with the method in a non-destructive manner to find out details about the status of the fuel. With the current arrangement of collimators, the PGET device is not the most optimal to this use case, but it could be used in absence of more targeted instruments. With a slight modification of the collimators, the device could be tailored to this kind of use in the future. The highly tapered collimator slits could be narrowed to provide a tighter axial focus, but possibly requiring an increased data acquisition time.Investigations with the narrower energy windows capturing the Cs-137 gamma peak at 662 keV proved the usefulness of the photopeak. Despite the lower number of counts in the 650–700 keV window compared to the 600–700 keV window, the quality of the reconstructed images is similar or improved, especially in terms of detecting possible empty positions in the inner parts of the fuel grid. The energy window used could still be fine-tuned to be tighter around the desired 662 keV peak. However, one needs to bear in mind the accuracy and stability of the energy calibration and choose the energy window so that a small shift in the calibration would not result in a complete loss of the photopeak. Such shifts are known to sometimes occur in semiconductor detectors due to changes in temperature or count rate. The energy window used in the data acquisition is set for the whole device at once, and since there is a large number of detectors, the energy window has to be wide enough to take into consideration the energy resolution of the worst individual detector.Results from the higher-energy gamma window containing the Eu-154 show promise in possible image quality enhancements in the central parts of the fuel, because the higher energy of the Eu-154 gamma ray allows it to penetrate through the fuel matrix more efficiently. The linear attenuation coefficient for the Cs-137 gamma ray (662 keV) in uranium dioxide is around 0.16 mmIncluding the see-through directions in the set of projections used for the image reconstruction has shown promise to increase the image quality in the central parts of the fuel. Peeking from in-between the fuel rod rows is the only way to get a signal directly from the innermost parts of the fuel grid. When investigating the see-through directions for a specific arrangement of fuel rods in a grid imaged with the PGET device, the opening angle of the collimator slits needs to be taken into account. The collimator slits are 1.5 mm wide and 100 mm deep and the detectors are located behind them. Theoretically, the opening angle that each detector sees is 0.86°, and thus a bit smaller than the 1° effective rotation step. This affects which part of the fuel is seen at each direction. In real life, the manufacturing of the collimator slits  is never optimal and the collimators are not perfect. However, the scheme for choosing the projections might need to be further investigated and the equidistant angles approach might need to be reconsidered. In the future, measurements will be conducted with a finer angular resolution of 0.5° to investigate the effect.The sinogram calculations with one emitting fuel rod illustrate the fuel grid geometry effects on the data that is gathered. The minor but significant contribution to the sinogram that comes from the central parts of the fuel assembly shows the characteristics of the grid and the fundamentally important blocking by the fuel rods themselves. As the detectors rotate around the assembly, the view to the center is blocked by other fuel rods every 60°, but before and after these full blocks, the gamma signal is significantly enhanced. The maxima appear on both sides of each of the full signal blockages, but only very narrowly. Missing the optimal spot for the high signal within the selected angles will degrade the image quality significantly, and thus the projections for reconstruction need to be chosen with care. It is also noteworthy that in the sinogram constructed when the lone emitting rod is in the inner part of the fuel, no pixel is as bright as some pixels are in the sinogram where the emitting rod is at the outer edge of the assembly. This further emphasizes the need to capture the essential parts of the data from the inner region, because the rods at the outer edge have an even higher weight on the end result.The image quality index is a novel measure introduced for this work, mainly to allow comparison between reconstructed images of spent nuclear fuel. The focus of the index is to indicate how well the empty fuel grid positions are distinguished from the positions with fuel. The spent nuclear fuel rods have natural variations in their burnups that originate from varying conditions during operation in the reactor core. Intrinsic deviations in burnup are thus natural, and the activities of individual rods in an assembly are never perfectly homogeneous. The ground truth of the fuel activity is not known and thus there is no way of telling how good the reconstructed image is in absolute terms. In practice, separating the two groups of grid positions (“empty” and “filled”) is tricky due to intrinsically less active rods in the fuel or fluctuations in the images. To exclude effects from possible burnable absorber rods, the location of these rods should be known. Otherwise burnable absorber in the rods might bring the activity values unnecessarily down and interfere with the comparison. For the future, grid positions with burnable absorber material could be left out from the image quality computation.13, the results have improved, especially for the detection of empty grid positions in the VVER type of fuel . There is still room for improvement for VVER fuel, but the rates are much better than reported earlier. For BWR, the effect of burnable absorber rods cannot be excluded yet.The effect of the image quality enhancements on the misclassification frequency is noteworthy. For Olkiluoto 2021 data, a full The misclassifications often occur in certain parts of the fuel grid, pointing towards structural characteristics. For GE-12 and GE-14 types of assemblies, most of the misclassifications occur in two separate grid locations, and for SVEA assemblies there are also two separate grid locations where the majority of the misclassifications happen. This would point towards a possible burnable absorber rod in these locations.13. In this work, we demonstrate a further improvement for fuel rod-level detection of anomalies in the central parts of the spent fuel. This improvement was achieved by using well chosen parts of the collected data, taking into account the specifics of the geometry of the imaged object in question. The see-through directions are shown to have much promise for contributing to high-quality images and will be further investigated with simulations and measurements with finer angular resolution. Data acquisition in different energy windows, namely in a 1200–1300 keV window capturing the Eu-154 isotope abundant in long-cooled spent nuclear fuel, is also proven to have promise for better quality data from the central parts of the fuel. Narrowing the energy window tightly around a gamma peak is shown to improve the results also for the conventionally used 662 keV gamma peak of Cs-137. The PGET method was demonstrated to be able to detect partial diversion of fuel material in the axial direction. Despite the relatively broad field of view of the device in the axial direction, partial absence of fuel rod material was detected as lower activity. Future measurements will be conducted with 0.5° angular resolution to investigate the see-through directions in more detail. The gamma energy windows used in data collection will be further narrowed down and more tests in the Eu-154 window will be done with a longer data acquisition time.The PGET method has previously been demonstrated to be able to detect partial diversion of nuclear material in a spent nuclear fuel assembly with very high precisionSupplementary Information.Supplementary Information.Supplementary Information.


The package was created using the applications SolidWorks 2017 and AutoCAD Mechanical 2017. The ANSYS Mechanical Structural FEA Analysis program simulated all packages for mechanical stress to guarantee that all packages generated were resilient to high temperature conditions. All packages exhibit no abnormalities and are robust for various temperatures ranging from low to high. Therefore, these packaged 1 mm2 VCSEL chips with a diffuser on top provide an effective approach for the application of VCSEL suitable in high temperature conditions.Face recognition is one of the most sophisticated disciplines of biometric systems. The use of VCSEL in automotive applications is one of the most recent advances. The existing VCSEL package with a diffuser on top of a lens intended for automotive applications could not satisfy the criteria of the automotive TS16949: 2009 specification because the package was harmed and developed a lens fracture during 100 thermal cycle tests. In order to complete a cycle, the temperature rises from −40 °C to 150 °C and then rises again from 150 °C to 260 °C. The package then needs to be tested 500 times to ensure it fits the requirements without failing in terms of appearance or functionality. To this extent, the goal of this research is to develop packaging for 1 mm Vertical-cavity surface-emitting lasers (VCSELs) are high-performance semiconductor devices consisting of different epitaxial layers grown on n-type GaA or InP substrates. VCSEL technology was originally used for data transmission, but a large number of potential applications in other areas have recently been discovered . In contBiometric technologies will serve the same purpose for identification and verification. However, the technology and application elements will be distinct from those of others, such as traditional identification, e.g., a passport or identity card (IC). Implementation of VCSEL with packaging with diffuser was an innovation for recognition systems or biometrics with more accuracy compared with devices using infrared such as iris recognition. In previous research, VCSEL technology has been used in the automotive industry, such as for time of flight (ToF). ToF sensors are increasingly being employed for a number of in-cabin vehicle monitoring applications, including tracking the driver’s gaze direction and head position. A ToF device is a sensor that detects light wavelengths. Light waves are modified at high frequencies (in the lower to higher MHz range) and reflected by a target. The sensor receives and processes a portion of the original signal. Because of the time it takes for the signal to travel from the emitter to the object and back to the receiver, the reflected signal is phase-shifted with respect to the modulation signal. The phase shift is proportional to the distance, allowing the distance between the ToF sensor and the object to be calculated . Previou2 and 0.75 mm2. The package was designed based on manufacturing capability using Six Sigma rules [2 that can fulfill the requirements of automotive specifications where the package must qualify for thermal cycle testing between −40 °C and 260 °C for 1000 cycles. The package’s design and dimensions were based on the present packaging for chip size of 0.5 mmma rules  and it w2 VCSEL package was developed with the diffuser attached to the lens. The package was made using ceramic, lens, and supportive materials including potting, lens-attached glue, and die-attached glue. The VCSEL package with a diffuser on the lens was subjected to a thermal cycle from −40 °C to 260 °C to fulfill the requirements of automotive reliability. The current 1 mmAn optical diffuser diffuses light by shuffling its wavefront and reducing its spatial coherence. It acquires random or pseudo-random fluctuations in the optical phase for different parts of a given incoming light profile . When a The package must undergo and pass the thermal cycle test with −40 °C to 260 °C at 500 h for industrial and 1000 h for automotive needs to meet the criteria of the reliability specification. During this, the package was examined, and it was discovered that the lens had a break towards the beginning of the thermal cycle test, which was less than 100 h. Based on the thermal cycle test shown, the package did not meet the requirements of the reliability specification for automotive specifications. Thus, new research and ideas have been filed to address all of the issues raised by the current VCSEL package diffuser on the lens. In this investigation, a new concept and packages were presented, where the implementation of microlenses and VCSEL array chips  used wer2 or Pa or MPa. The mechanical stress in the simulation was presented based on the hook equation, as shown in Equation (1).E is the modulus and ϵ the mechanical strain from thermal loading. The package was simulated under mechanical stress during the resistance to soldering heat (RTSH) process. Three different materials were introduced: ceramic, lead frame, and printed circuit board (PCB). All of the packages are identical, and the diffuser was grown or formed on top of the chip rather than the lens as in the prior packaging. Supporting other materials, including epoxy for the lens and adhesive, are classified as conductive or nonconductive. The whole package, including the diffuser, was generated by using SolidWorks 2017 and AutoCAD 2017. The dimensions of all packages were ensured to meet the manufacturing capabilities for semiconductor backend processes such as die-attached (DA), wire- bond (WB), lens-attached, and potting with requirements for measurement within a Six Sigma process specification. According to automotive specifications, the maximum temperature stain for the inner component as a dashboard component is only 200 °C [Stress can be interpreted as an internal resistance force produced in a component as a result of deformation under the action of loading. Due to this load, an internal resisting force (IRF) is formed, and the body tends to restore its original shape if deformation reaches the elastic limit ,16. All The diffuser was developed on the top chip for the first time, rather than using the lens as a medium for a diffuser or separate component. This novel design was developed to avoid any cracks or damage during the thermal cycle test, specifically to fulfill the high demands of the automobile sector, which demanded that all components remain undamaged at temperatures as high as 200 °C and as low as −40 °C. The diffuser was created and designed to have a diameter of 0.03 m and a height of 0.01 m. It is shown in During the RSTH process, the whole VCSEL package was placed in extreme conditions of cold at −40 °C to a normal temperature of 25 °C, then to 150 °C, the standard temperature in oven conditions, and finally to a high temperature of 260 °C. Each package consists of different components that were attached to three types of VCSEL packages, as seen in 2 chip and the novel. 1 and Dynamic Mechanical Analysis (DMA)2 are methods for measuring the properties of materials based on temperature and pressure changes, such as epoxy for die attachments, lens, diffusers, and dielectrics, as illustrated in The structural design and mechanical stress modeling, using various forms of packaging for VCSEL packaging utilized the 1 mmDuring the simulation procedure, the ANSYS Mechanical Structural FEA Analysis programme was utilized to simulate all package mechanical stress elements. The package was installed on a metal core print circuit board (MCPCB) with a dimension of 20 mm × 20 mm at the start of the simulation procedure, as illustrated in Tin Silver Copper (SAC) is a lead-free alloy with a composition of 96.5% Tin + 3.0% Silver and 0.5% Copper, capable of withstanding a temperature of 260 °C. The procedure employed the package temperature at 150 °C , and thermal loading was a homogeneous temperature application for the whole package (150 °C to 260 °C and 150 °C to −40 °C). The mechanical stress simulation methodology does not use cyclic simulation because material properties are linear, and the stress here represents the condition when the heating up from 150 °C to 260 °C at the maximum temperature for RTSH. The measured area is the die-attached surface, chip, and lens, which represents the full package structure for the identification of fractures or damage, as well as being able to deliver accurate results throughout the simulation process depending on the section or area indicated.There is no substantial difference between all the packages with a wide range of temperatures. At higher temperatures, the range of values for stress on all packages is 0 to 19.023 MPa, whereas at lower temperatures, it is 0 to 318.99 MPa. The stress values are uniform and homogenous throughout. The chip, which is considered the middle of the package, was the next area that was assessed. Similarly, the die-attached surface, chip, and lens were assessed for the principal stress for each type of package. At RSTH, none of these stress value differences were significant for all packages, as the range of stress values started from 0 to 31.673 MPa at higher temperatures, and at lower temperatures, the value of stress for all packages started from 0 to 211.42 MPa. In contrast to lead frame and PCB, ceramic packages have lower stress values of 2.567 MPa at higher temperatures. The lens is the final component to be analyzed, and it is the most crucial factor in evaluating the package’s durability since it is prone to breaking and destruction in the case of severe temperature and pressure changes. This will have a severe influence on the package’s durability. According to the simulation findings obtained on the lens area, the stress values obtained at high and low temperatures are uniform and do not indicate any aberrant stress results on the lens region. At higher temperatures, it ranges from 0 to 1.6045 MPa, whereas at lower temperatures, it ranges from 0 to 128.58 MPa for all packages. −5 whereas ceramic is 1.80 × 10−5 and lead frame is 2.35 × 10−5, as indicated in 2 with the diffuser package.According to the findings, all packages produced the same values and were standardized at each stage of the simulation. This proves that the proposed novel packaging design with the placement of the diffuser on the top of the chip prevents lens fractures during the heat cycles. The microstructure of the diffuser controls the efficacy of the optical qualities employed in biometric systems, but it is also a part that is easily broken and damaged if it is based on a weak-based material such as epoxy or glass. Therefore, the transfer of the microstructure on the diffuser from the lens to the top of the chip is beneficial because the chip has a strong base and is able to withstand significant changes in temperature and pressure. Overall, all of the proposed models produce uniform pressure values on each area  without a critical point that permits fractures to form throughout the heat cycles. The stress value of PCB is the lowest when compared to ceramic and lead frame because the CTE value on FR4 PCB is 1.20 × 10The primary purpose of this research is to discover VCSEL packages with a functioning diffuser that can endure high temperatures and pressure variations, allowing them to fulfill the automotive specifications outlined in the TS16949:2009 standard. This study looked at three different types of packaging models proposed for different materials: ceramic, lead frame, and PCB, all of which are capable of maintaining and providing equal stress values for each stage or area during stress simulation and providing the best impact on the entire package, particularly on the part or area with the microstructure, which is the chip. According to the model provided in this project, the pressure value given in all models, including low and high temperature, is the same in each packing model. Furthermore, there are no critical points in this packaging model that might induce cracking during the thermal cycle process, demonstrating that the suggested packaging model can withstand any temperature and condition. Identifying parts of the package that are prone to cracking and destruction is one of the major procedures necessary before the design and manufacturing processes are executed. It can save time, energy, and money throughout the packing process. As a result, mechanical stress simulation is a wise step that can discover areas or sections that require maintenance if there are fractures and damage. Furthermore, it may assess if the material used in the packing process is precise and can satisfy the standards, particularly if it can handle high temperatures and pressures. The three packages were designed to satisfy the demand for a thermal cycle that could accept heat and stress while also preventing lens cracking or damage.


The entropy of Tsallis is a different measure of uncertainty for the Shannon entropy. The present work aims to study some additional properties of this measure and then initiate its connection with the usual stochastic order. Some other properties of the dynamical version of this measure are also investigated. It is well known that systems having greater lifetimes and small uncertainty are preferred systems and that the reliability of a system usually decreases as its uncertainty increases. Since Tsallis entropy measures uncertainty, the above remark leads us to study the Tsallis entropy of the lifetime of coherent systems and also the lifetime of mixed systems where the components have lifetimes which are independent and further, identically distributed (the iid case). Finally, we give some bounds on the Tsallis entropy of the systems and clarify their applicability. X is a non-negative random variable (rv) with absolutely continuous cumulative distribution function (cdf) The Shannon entropy measure of a probability distribution has found critical applications in numerous areas described in Shannon’s seminal work . Informa by (see )(2)Hα.The following implications hold:[The] dispersive order is recognized to be the order of distributional variability.Below are other useful properties of the measure. First, another useful expression for the Tsallis entropy can be conveyed in terms of the proportional hazard rate (PH) function. For this purpose, if In X retains the identical differential entropy as It is worth noting that the pdf given in , is actui et al. )H(X2)=HNow, we recall the definition of Tsallis entropy which can be seen in  for greaDefinition 1. Suppose It is worth pointing out that Theorem 1. Let Proof. If This yields The following theorem develops the impact of a transformation on the Tsallis entropy of an rv. It is analogous to Theorem 1 in  and hencTheorem 2. Let The next theorem presents implications of the stochastic order under some aging constraints of the associated rv’s and the order Theorem 3. If (i) (ii) Proof. (i) Let x for all The first inequality in  is obtaielations , we havex for all The first inequality is obtained by mentioning that It is worth noting that Theorem 3 can be applied to several statistical models such as Weibull, Rayleigh, Pareto, Gamma, and Half Logistic, among others. The mentioned models involve the DFR aging property by choosing a suitable parameter.X is the life length of a new system. In this case, the Tsallis entropy Here we give an overview of the dynamical perspectives of the Tsallis entropy of order Based on the measure Definition 2. The rv X has increasing (decreasing) residual Tsallis entropy of order α  failure rates.Theorem 4. For any Proof. X is IFR and X is We shall prove it for IFR, while the DFR case can be derived similarly. Suppose ≥0, from  the resung again , we haveX is IFRA if There is a large class of monotonic density distributions to which the above theorem can be applied. Another important class of life distributions is those with an increasing failure rate in average (IFRA). In particular, Example 1. Consider the sf of a random lifetime asand henceThe plot of the residual Tsallis entropy in We now see how the residual Tsallis entropy and the hazard rate orders are related.Theorem 5. If Proof. Suppose 2). From , we obtahen from , we obtak-out-of-n system is a particular case of a coherent structure. Furthermore, a mixture of coherent systems is considered as a mixed system  structures. A coherent system is one in which all system components are relevant, and the structure-function of it is monotonic. The em . The resystem signature, such that The vector The order statistic Now, the pdf of Applying the above transformations, we find in the following theorem a formula for the Tsallis entropy of Proposition 1. The Tsallis entropy of T iswhere shown in .Proof. By using the change of x), from  and 11)v=F(x), fTo apply Proposition 1, consider the next example.Example 2. The vector for all The system signatures of orders 1–5 have been calculated in  and, theTheorem 6. The rv’s (i) If (ii) Assume If Proof. (i) By the assumption pression  gives(1(ii) If the condition Let us assumeThen, for all In , the secementing . The resLet us take the following example to demonstrate the above theorem.Example 3. Consider the lifetime and The signature is So, one can see that We show that the minimum of lifetimes in the iid case has lower or equal Tsallis entropy than all mixed systems under the property of decreasing failure rate of component lifetimes.Theorem 7. If T represents the mixed system’s lifetime in the iid case and the component lifetime is DFR, then Proof. Recalling , it is eWith the insights from the previous section, we can now find some inequalities and bounds on the Tsallis entropy of mixed systems. We note that it is usually difficult or sometimes impossible to determine the Tsallis entropy when the system is identified by a complex structure-function or when the components included in the system are immeasurable. This is why it is valuable to provide bounds on the measure. The following result provides bounds for the Tsallis entropy in the mixed system concerning the Tsallis entropy of its components.Theorem 8. If for all for Proof. Recall the relation , for allned from  and thisIf the amount of the components of a system is very big or the system has a very complicated design, the provided bounds in  and 22)22) are vTheorem 9. Underneath the requirements of the Theorem 8, we havewhere Proof. Recall the Jensen’s inequality for the convex function Since oth side  in 1/ an anα>1(0<relation  which arrelation  (dotted Extensions of Shannon entropy have been presented in the literature before. The Tsallis entropy, which can be considered as a different measure of uncertainty, is one of the extended entropy measures. We have described here some other properties of this measure. We first determined the Tsallis entropy of some known distributions and then proved that it is not invariant if a one-to-one transformation of the lifetime is taken in the continuous case. The connection to the usual stochastic order has been revealed. It is well known that systems having greater lifetimes and lower uncertainty are apposite systems, and that the reliability of a system usually decreases as its uncertainty increases. These findings led us to study the entropy of Tsallis for coherent structures and mixed systems in the iid case. Finally, we established some bounds on the Tsallis entropy of the systems and illustrated the usefulness of the given bounds.


The fifth and sixth images in the upper row of Figure 4C had overlapping fields of view. We apologize for this mistake. The fifth image in the upper row of Figure 4C has now been replaced in the corrected figure below, the other images within Figure 4C remain the same, and the interpretation of the results remains unchanged.