The image‐guided radiotherapy technique (IGRT) makes use of imaging devices to verify the positions of the target volume and organs at risk during the treatment sessions. In this work we evaluate the image quality provided by an imaging system based on a kilovoltage cone‐beam CT, and explore its ability to perform IGRT and adaptive radiotherapy. We analyze the accuracy of the image slice width, the spatial resolution using the MTF function, the image uniformity, the signal‐to‐noise ratio, the contrast‐to‐noise ratio, the low‐contrast sensitivity, and the HU linearity with density. The studied parameters are evaluated in an objective and quantitative way, allowing for a direct comparison with other imaging devices. We conclude that the analyzed cone‐beam imaging system is adequate to accurately perform IGRT within its clinical use, despite the high level of noise present in a cone beam caused by scatter. We also point out the presence of a bowtie wobble artifact in the reconstructed images. Nevertheless, we conclude that these features do not limit the capability of the system to perform adaptive radiotherapy in most cases.PACS number: 87.57.‐s Successful external radiotherapy requires the ability to reproduce in the treatment room the patient setup used in the simulation. The employment of imaging devices to verify the patient position is known as image‐guided radiotherapy technique (IGRT). Therefore, an image of the patient at the time of treatment is acquired and registered with the reference image obtained in the simulation. Once the best match between both sets of images is achieved and the proper setup of the patient is checked, it is possible to correct the patient position by shifting the treatment table. The comparison between these images and the digitally reconstructed radiographs (DRR) leads to an anatomic registration based on high‐contrast areas such as bony structures. However, this method does not discriminate soft tissue. Some modern imaging systems, such as those based on a kilovoltage cone beam (kV CBCT) allow obtaining tomographic images of the patient that can be directly compared with the CT planning study. Moreover, they also provide information of low‐contrast structures, which make possible the registration based on areas with soft tissue.Thus, IGRT imaging systems are designed to detect and correct positioning errors in every treatment session. The conventional method consists in the acquisition of two orthogonal planar megavoltage images (2D) with an electronic portal imaging device (EPID).1 The  Reliable contouring of organs at risk and treatment volumes requires an appropriate image quality, as well as accurate and reproducible HU if dose calculations are going to be performed.Another possibility is to use these tomographic images in the monitoring of patients which may present significant changes in the treatment volume or anatomical changes that could modify their outer contour. Such modifications of the initial conditions would in turn alter the dose distribution both within the treatment volume itself and the organs at risk. kV CBCT images may also be used to perform adaptive radiotherapy (ART), a computation of the treatment dose distribution, and/or contouring structures and treatment replanning.,,,,  In general, the tests to be performed can be classified in the following groups: functional and safety, geometric, and image quality. It is also important to know the calibration procedures, which directly affect the behavior of the system and aim to reduce possible artifacts or improve the quality of the acquired images.Clearly, imaging systems play an increasingly relevant role in radiotherapy. As a consequence, it becomes necessary to understand their characteristics and limitations, as well as to implement a quality assurance program that includes these imaging systems.,,11The system analyzed in this study is the Varian on‐board imager (OBI) in the mode cone‐beam computed tomography (CBCT). The manufacturer provides a set of calibration procedures that include the system geometric calibration and image detector calibration itself. Geometric calibration aims to correct errors associated with the non‐rigid nature of the system . The imaging system detector calibration includes several tasks: creation of a defective pixel correction map, acquisition of a dark field, measurement of the detector response to a uniform radiation field, measurement of the charge trapping effect, creation of normalization maps over a homogeneous phantom to consider scattered radiation and beam hardening effect, and HU calibration. These calibration procedures define corrections that are directly applied to the acquired images and contribute to improve the quality of the reconstructed images. For instance, the presence of defective pixels can lead to the appearance of ring artifacts, which can be minimized with a proper calibration of the imaging system. The calibration should be performed for each acquisition protocol under the following circumstances: when changes that may affect the imaging system occur, and when a decrease in image quality is observed which, according to manufacturer's instructions, should be checked monthly. Although the manufacturer provides a calibration for all acquisition modes, the user can also perform them, if necessary. determined the OBI's mechanical precision to be 1.5 mm for the isocenter localization and less than 1 mm for the arms positioning accuracy, with time stability below 1 mm in both cases on a follow‐up period of 8 months. In relation to image quality, low‐ and high‐contrast resolutions have been studied in a qualitative way.Safety and functional tests, as well as geometric tests, have been already described in the literature. Yoo et al.10 detIn order to avoid subjectivity in image quality tests, it is possible to determine physical parameters that characterize the system objectively — namely, the modulation transfer function for spatial resolution, and the contrast detail ratio, calculated based on statistical criteria, for low‐contrast resolution.In this paper, we present a study of the volumetric CBCT image quality obtained with the OBI system to test its capability to perform both IGRT and ART. Among other parameters, system spatial resolution and low‐contrast resolution are analyzed. A comparison with the results obtained with a multislice CT scanner dedicated to simulation is also included.Image quality tests have been performed on the tomographic CBCT images provided by the OBI (software Version 1.5). The OBI system  consists of an X‐ray tube and an amorphous silicon flat‐panel detector, both mounted on the robotic arms  and orthogonally coupled to the MV beam of the CLINAC 21EX  linear accelerator. It provides an X‐ray cone beam that allows obtaining volumetric images using a filtered back‐projection reconstruction algorithm.397 mm×298 mm active area, and consists of a 2048×1536 detector matrix with a distance between detectors of 194 μm. The system has a 10:1 ratio focused antiscatter grid to reduce the amount of scattered radiation reaching the detector.The flat panel, composed by an amorphous silicon detector coupled to a CsI:Tb scintillator, has a The OBI system has two working modes: full‐fan and half‐fan. In the full‐fan mode the detector is centered on the axis of rotation and is used to visualize regions with a small diameter or small soft tissue organs, such as the prostate. In the half‐fan mode, the detector is shifted in a direction perpendicular to the kilovoltage X‐ray beam, increasing the scanned area, hence enlarging the diameter of the field of view from 25 cm, as in the full‐fan mode, to 45 cm. In both cases, a filter must be placed at the exit of the X‐ray tube. The full‐fan filter (the one used in the full‐fan mode) is symmetric with respect to the beam axis in the axial plane, being narrower at the center. The half‐fan filter is asymmetric, narrow in the central part with increasing thickness towards the edge of the X‐ray beam. These filters absorb part of the incident radiation, and they are used to compensate for the difference in the thickness traversed by the beam on the patient, so that the photon fluence that reaches the detector is as uniform as possible. In addition, the absorption of low energy X‐rays reduces the dose received by the patient and the noise generated in the detector. An image artifact known as bowtie wobble, related to the movement of these filters with gantry rotation, has been reported in the literature.130.8 mm×1.1 mm. The radiation field as measured at the isocenter is 27.2 cm×20.6 cm, and the reconstruction matrix is 512 × 512. The field of view chosen for this study is 256 mm × 256 mm, smaller than the one used in the clinical practice, so that the Nyquist frequency (1 line pair per mm) lies beyond the cut‐off frequency . The reconstructed image slice width is set to 2 mm with a Ram‐Lak convolution filter and medium ring artifact suppression filter. The standard reconstruction filter is employed, although results obtained using other filters (sharp and smooth) are also discussed. Finally, the results obtained for the Pelvis Spot Light protocol with full‐fan filter, used for prostate treatment in clinical practice, are briefly discussed. In this case, gantry rotates 200° and acquires 375 projections with a pulse width of 25 ms.The CBCT images are acquired with the Pelvis clinical protocol. This protocol acquires 650 projections in a 364° gantry rotation with the detector placed at 150 cm from the source and acquisition technique of 125 kVp, 80 mA, 13 ms pulse width (1 projection per pulse) and half‐fan filter. The focal spot size used is 2 mm × 16 acquisition channels, gantry rotation period of 1 s, and focal spot size of 0.9 mm×0.8 mm. The reconstructed images are 2 mm wide, with a 512 × 512 pixel matrix and a field of view of 256 mm . In clinical practice, a modulated tube current is used, with a tuning based on the scanograms acquired prior to helical scan. In the present study, a fixed tube current set to 80 mA is used to match the one used by OBI in Pelvis protocol. It is worthwhile to comment that this value is similar on average to the one obtained in real patients.Regarding the simulation CT Aquilion LB , it is a multislice CT scanner with a detector matrix consisting of 40 detector rows and 16 acquisition channels. The detectors located in the 16 central rows are 0.5 mm wide as measured at isocenter, while the other 24 rows, 12 on each side, are 1 mm wide. The detectors are separated by septa that absorb part of the scattered radiation reaching the detector. The analyzed images were obtained using the routine clinical protocol for pelvis, adapting some parameters to match the ones used by the OBI in order to make a comparison between both systems in conditions as similar as possible. Therefore we used the following protocol: helical technique with 120 kV, pitch 0.938, a detector configuration of Therefore, the technique described above is employed to obtain the CT images used for contouring and treatment planning with IMRT in pelvic regions. They are also used as reference for comparison with CBCT images acquired in the treatment unit. The IGRT protocol followed in our hospital for this kind of treatment consists in performing a CBCT in all treatment sessions prior to irradiation. Thus, it is an online protocol, which implies daily correction of systematic and random errors. Additionally, patient preparation is verified .2 mm × 16 channels (3.2 cm fan‐beam width) to 0.5 × 16 (0.8 cm fan‐beam width) has been analyzed.Apart from the geometric differences between both systems , one of their main differences is the fan beam size along the z‐axis. The maximum fan‐beam size available in the CBCT is 20.6 cm as measured at isocenter, while the largest fan‐beam width for the CT is 3.2 cm. As a consequence, the amount of scattered radiation is much higher in the CBCT. Both systems incorporate an antiscatter grid and correction algorithms to minimize its effect. The CBCT larger coverage in the z‐axis allows obtaining the data in a single X‐ray tube rotation, being the acquisition time close to 1 min. In the case of the CT scanner, it is necessary to use several rotations around the patient over the moving table in order to cover the same range. However the acquisition time is smaller in this case (around 15 s) because of the faster tube rotation. Z‐axis resolution is limited by the fan‐beam width, determined by the detector configuration used. For this reason, the influence on the z‐axis resolution of the fan‐beam width, from  The phantom long axis (z‐axis) has to be placed longitudinal to the CT table, the modules are in transverse planes to the phantom z‐axis (x–y plane).Our study is based on images acquired with the Catphan 600 phantom . The phantom, cylindrical in shape, is constructed of PMMA and consists of 5 modules designed to perform various quality tests in tomographic images.14 The−1000, 990], so the linearity of the system (HU density) can be checked  macros specifically designed for this purpose. In the following we describe the performed image quality tests.Digital images, stored in DICOM format, are automatically analyzed by a set of ImageJ,16 m The correct phantom positioning is checked by defining a threshold pixel value to localize some reference points in the CTP404 module which are used to measure the phantom rotation angle around its long axis. Images rotated more than 1° are rejected, as described below. This criterion is relevant to estimate the uncertainty of our measurements. The regions of interest (ROI) used to perform the tests are generated automatically; therefore, a phantom rotation could cause an inappropriate ROI localization.The automatic analysis of the images requires a correct phantom positioning as well as an appropriate image quality, as recommended in the Catphan user manual.14 TheThe small air and tungsten inserts in CTP404, which separated a known distance of 50 mm  placed inside the CTP404 module. These ramps are rotated 23° around the x‐y plane. The slice width is given by FWHM·tan (23°), where FWHM is the full width at half maximum of the ramp profile. We report the average slice width value measured over the four ramps.2 mm × 16 channels (3.2 cm fan‐beam width) to 0.5 × 16 (0.8 cm fan‐beam width).Z‐axis spatial resolution is measured using the slice sensitivity profile (SSP). A profile of the tungsten insert from the CTP591 module is performed over a sagittal reconstruction plane. The FWHM of the generated profile is registered. In addition, the impact of the fan‐beam size on the z‐axis resolution has been analyzed, from The modulation transfer function (MTF) measures the system spatial resolution. The MTF will be obtained in two ways: from the image of a point object and from a bar pattern with different spatial frequencies. A spatially invariant linear system is assumed in both cases, implying that there is no overlap of system response in frequency space. This hypothesis has been experimentally verified both for the CBCT and the CT, measuring the system response to a point impulse at different image planes and at different locations within the same image plane. For each point we have studied the two directional components, radial (line between isocenter and point) and azimuthal , which may be affected by various design parameters.17u, v are the frequency space coordinates. The function H is the system transfer function, defined as the Fourier transform of the point spread function (PSF), which is the system response to a point‐like object (δ‐Dirac function):The MTF of a spatially invariant linear system is the modulus of the object transfer function (OTF): The CTP591 module contains a tungsten bead, which acts as a point object.Therefore, it is possible to extract the MTF from the system response to a point‐like object (δ‐Dirac).18 TheThe determination of the MTF function from the system response to a point object (PSF) will be carried out in two ways.MTFrad and MTFazim, respectively.Once the image of the point object (PSF) has been obtained, fluctuations present in the background nearby the point are removed. Then, the 2D Fourier transform of the resulting PSF is performed. Pixel values in radial and azimuthal directions are obtained from the generated frequency spectrum corresponding to  We analyze both point profiles , fit the obtained data to a Gaussian function and register the σrad,azim widths. Hence, the MTF is given by the Gaussian function centered at the origin with a width of 1/σ.The image system response to a point‐like object is a Gaussian function with width σ, the Fourier transform of which is another Gaussian with width 1/σ.18 We JI(x) is the first order Bessel function, u is the frequency, and d is the tungsten sphere diameter. The correction factors for each spatial frequency are shown in Table To account for the influence of the bead finite size in the MTF measurement with both methods, the following correction is applied:19(4)u frequency sinusoidal input. Therefore, if one has a sinusoidal pattern, the image modulation created by the system becomes a direct measurement of the MTF.The MTF can be understood as the image to object contrast ratio. In fact, it can be shown that MTF(u) represents the system modulation of a  The MTF written in terms of the system response to square waves with different spatial frequencies is:u is the line frequency, A(u) is the output amplitude of the u frequency square wave, and A0 is the amplitude of the input square wave.Phantoms providing a sinusoidal pattern are unusual, but phantoms with a square pattern of different spatial frequencies are quite common. According to Fourier's Theorem, a square wave can be expressed as a sum of sinusoidal waves; thus, the MTF can be calculated based on the system modulation of a square bar pattern.20 TheM2=A2/2. For a square wave, on the other hand, this relation becomes M=A. Therefore:The relation between amplitude and variance for a sinusoidal wave is given by As a consequence, the MTF is measured as the standard deviation (square root of variance) of a set of ROIs centered in the different inserts of the bar pattern present in the CTP528 module.As we already mentioned, in our case phantom positioning is important, as the ROIs are automatically generated assuming that the phantom is perfectly centered. We found that phantom rotations above 1° introduce an error in the MTF‐50% which is higher than 3%. This is why our program rejects images rotated more than 1°. To perform this test, we intentionally rotated the position of the ROIs used in the MTF calculation and compared the result with the one obtained with the correct ROI orientation.We evaluate image uniformity and the signal‐to‐noise ratio using the CTP486 module. Image uniformity has also been analyzed with the normalization phantoms provided by Varian to perform the CBCT image calibration. They are two cylindrical homogeneous phantoms, one of 25 cm in diameter made of polyethylene and the other of 45 cm in diameter made of polyurethane.mmax and mmin are the maximum and minimum ROI pixel mean values, respectively. Signal‐to‐noise ratio is measured over the same ROIs, and it is defined as the ratio between the ROI mean pixel value mi and its standard deviation σi:Image nonuniformity is analyzed in two ways. We study the profiles generated over the uniform section of the Catphan phantom and Varian normalization phantoms. In addition, we calculate the integral nonuniformity defined over 5 squared ROIs (side length of 15 mm) located in the center and the periphery of the image, in the four cardinal points i corresponds to the low contrast insert, b to the background measured in a region next to the insert, m denotes the mean value of the corresponding ROI, and σ its standard deviation.Contrast‐to‐noise ratio is measured in the largest insert with the highest nominal contrast (1%) provided by the low‐contrast test module CTP515  an object is distinguishable from its background if the object‐to‐background signal ratio exceeds some threshold. This threshold defines a contrast‐detail curve. Objects with size and contrast above the curve are distinguishable, while those below are indistinguishable from the surrounding background. In order to find the contrast‐detail curve, the contrast of the inserts present in the phantom must be evaluated, as well as the image noise measured in the phantom uniform section.Low‐contrast sensitivity is characterized using the contrast‐detail curve. According to Rose model,,24 aThe noise associated to an insert of certain size is measured as the standard deviation of the mean values of 28 ROIs of the same size defined in the Catphan uniform section. Since the phantom provides low‐contrast inserts of nine different sizes ranging from 2 to 15 mm in diameter, nine groups of 28 ROIs of the corresponding size are created. The contrast of each insert is obtained as the difference between the mean pixel values of the ROI centered in the insert and another ROI placed in the background next to the insert. The smaller the ROI, the higher the standard deviation, making it more complicated to distinguish an object with HU close to the background HU. In particular, they claim that a low‐contrast object with a mean pixel value which differs from its background mean pixel value in less than 3.29 standard deviations is undistinguishable with a 95% confidence level.Some references establish a statistical criterion to objectively decide whether the objects of a given size and contrast are distinguishable from the background.,25 IThe HU corresponding to different materials present in the CTP404 module are measured as the mean pixel value of a circular ROI with a 4 mm radius centered in those materials.The materials of the different inserts are made of commercial plastics. There are also two air inserts. In Table In this section we analyze the results obtained for the CBCT system and the CT scanner. The results presented correspond to five sets of images acquired the same day; this permits us to evaluate the reproducibility of the performed tests. We show the mean values and their corresponding standard deviations, unless otherwise stated. Furthermore, in order to analyze the temporal stability of the studied parameters, we have performed the proposed image quality assurance program weekly during three months.0.4±0.2mm for the CBCT and 0.1±0.1mm for the CT. In both cases, the error is smaller than the pixel size, 0.5 mm. No significant time variations were observed .Geometric distortion is not observed in the reconstructed tomographic images by any of the two systems. The mean value of the detected error in the measurement of known distances (50 mm) is 2.2±0.1mm. For the CT, with a detector configuration of 2 × 16, the measured slice width is 2.8±0.1mm. Table 0.5×16 or 1 × 16), a better slice width accuracy is achieved. No time trend was observed .The nominal slice width of the images is 2 mm, while the measured value using the ramp method over the CBCT images for the standard reconstruction filter is SSP function is characterized through the FWHM of a longitudinal profile defined over the tungsten insert in a sagittal slice; the results are shown in Table According to the results shown in Table Finally, we state that this parameter does not present significant changes over time .Both studied systems have been considered to be spatially invariant with a real input function, so the obtained MTF is symmetric. Hence we only present the results corresponding to the positive frequency axis.0,±2), , , and  cm. From Fig. 0,±2.5) and  are coincident within the experimental uncertainty, for each localization and between different positions within the same image plane. In other positions and for the OBI system, we obtained similar results; therefore, we do not show them.The spatial invariance has been tested by comparing the system response to a point object PSF 2D method) placed in several positions  of the FOV, namely: .Coinciding with published results,11 no  The reproducibility of the method based on the analytical fit of the PSF (PSF 1D) is poor because of the uncertainty of the method, mainly determined by the reduced number of points employed in the curve fitting. In addition, if the system does not show a Gaussian response to a point object, one should find an appropriate fitting function and analytically solve the Fourier transform integral, which is time consuming and implies an additional computational cost. For these reasons, and since the PSF 2D method presents a better reproducibility (lower standard deviation), it is taken as the reference method.The MTF obtained using the three different methods described in the previous section, for both the CBCT and the CT, are shown in Fig. 20 TheWe consider that the agreement shown by the different methods is good for the CT see Fig. , the MTFFinally, in Fig. No time trend was observed from the data.The image uniformity and SNR of the CBCT images for any of the studied reconstruction filters is significantly lower than that obtained with the simulation CT scanner. This is due to the increased presence of noise, since a cone beam generates more scatter. In Fig. C=−16±1, while C=0.4±0.6 for the CT. The cupping effect is related to the beam hardening correction, which is partly corrected by the system software, and the significant presence of scatter (which can be corrected with an antiscatter grid). As a consequence, and also due to ring artifacts, the OBI images are less uniform than the CT images, as reveals the UI parameter. The presence of ring artifacts in the reconstructed images may be due to differences in the detector gains or to charge trapping effects. The OBI system incorporates a correction to mitigate this effect, as well as a processing filter that reduces these kinds of artifacts. We have used the medium ring artifact suppression filter, as recommended by the manufacturer.The CBCT images present cupping effect, meaning that the central part of the image is hypodense compared to the periphery. For instance, for the CBCT system with the standard reconstruction filter In Fig.  The artifact appears always in the same position, coinciding with the projection of the filter on the image detector. In the Catphan phantom, the artifact remains unnoticed because this phantom is smaller (radius of 20 cm) and the ring is beyond its outer edge. The image quality tests performed with the Catphan phantom are restricted to the center of the FOV. The obtained results could change in the periphery of the FOV due to the artifacts mentioned above.The uniformity of the CBCT images was also analyzed with the normalization phantoms provided by Varian, which have the advantage of being larger than the Catphan. We obtained similar results in both normalization phantoms, therefore we only discuss the results obtained with the larger one. In Fig. 13 The This artifact is a ring with an increase of signal at one end of the ring and a decrease in the opposite end.Finally, we have studied the image uniformity obtained with the CBCT in the full‐fan mode with the Pelvis Spot Light protocol, which is the one used in the prostate IGRT clinical protocol in our hospital. There is a reduction in the SNR value from east to west due to the bowtie wobble artifact related to the movement of the filter with gantry rotation.13 ThiNo significant time variations were observed.The CNR Eq.  has been2 × 16. The CBCT system exhibits a lower CNR value, CNR=0.7±0.1 for the CBCT versus CNR=1.3±0.1 for the CT. Probably this difference is due to the higher presence of noise caused by the scattered radiation. This result is consistent with the contrast‐detail curve .Compared to a narrow beam CT system, the CBCT presents a less favorable geometry: larger source–detector distance and higher presence of scatter. As a consequence, one expects the appearance of a larger number of artifacts (such as cupping artifact or rings) due to the larger influence of charge trapping in the detector. In patients, one also expects streaking pattern artifacts near high‐density regions  and movement artifact. The OBI system attempts to correct these artifacts by hardware devices or appropriate software corrections. Hence, the system incorporates a bowtie filter, antiscatter grid, nonlinear scatter correction, beam hardening correction, and ring artifact suppression algorithms. However, the resulting 3D images are not entirely free from the presence of artifacts. In fact, the images obtained from various homogeneous phantoms with different diameters have a circular band centered on isocenter with a fixed diameter of approximately 22 cm. This artifact presents a uniform intensity if the half‐fan filter is used, while it is asymmetrical in the full‐fan mode. It may be due to the vibration of the bowtie filter13 witTo avoid the observer dependence in the implementation of resolution tests, we have used two physical parameters that characterize the imaging system in an objective way. Namely, the modulation transfer function for spatial resolution and the contrast‐detail ratio, calculated from statistical criteria, in the case of low‐contrast sensitivity. for a half‐fan protocol is 6 line pairs per centimeter (1p/cm), 6.2±0.4 lp/cm for Yoo et al., and 4 lp/cm for Cheng et al. The minimum size visible group can be approximated by the 10% of the MTF curve. Therefore, according to Bissonnette et al., the frequency at which the MTF reaches the 10% value is 8.4 lp/cm. With our protocol, the 10% MTF value is located approximately at 8 lp/cm.The spatial resolution, calculated as the minimum size group visible in a bar pattern, reported by Kim et al.9 for We note that, under the conditions adopted in our study and for the same pixel size, the OBI spatial resolution is higher than that of the Aquilion, despite the smaller number of projections and the less favorable geometry. We interpret this result as a consequence of the smaller size of the detectors present in the OBI flat panel, around 194 microns, compared to the size of the detectors used by the Aquilion CT, 500 or 1000 microns. found that the total number of discs visible with a nominal contrast level of 1% was 7, while targets with 0.5 and 0.3% nominal contrast were all invisible regardless of their size. Yoo et al. put the number of visible disc inserts in 4.2±0.4, and Kim et al. in 5.Regarding the low‐contrast sensitivity, Cheng et al.12 fouAccording to our results, the OBI provides a low‐contrast sensitivity good enough to distinguish soft tissue. For example, the prostate usually shows a contrast level with respect to its surrounding tissue which is between 1% and 4%. The contrast‐detail curve that we have obtained indicates that the OBI is able to distinguish objects with that contrast and with a size as small as 3.3 mm. However, the correlation between the results obtained with the statistical method and those based on observers is not clear.In summary, we conclude that the image quality is good enough to perform IGRT verifications. The implementation of ART requires a better image quality, mainly regarding the low‐contrast sensitivity. In our case, the images do seem to present an adequate visualization of the soft tissues for reliable contouring, in agreement with the clinical results published in the literature.,6± 35 HU with respect to the reference values.Furthermore, in order to use the CBCT images to calculate dose distributions, it is essential that the patient contour is completely imaged. In a pelvic treatment this can only be achieved with the half‐fan mode (FOV up to 45 cm). A strict image quality control is also mandatory, especially to monitor the HU density relation, which directly affects the dose calculation. Our results suggest that this relation has a good reproducibility over time. As for the accuracy of the measured values, they are within  which makes the measured HU to be lower than real bone HU. This will affect the HU density curve. In addition, the insert size (1.2 cm diameter) seems to be too small to provide the correct HU when the amount of scattered radiation is high, as in the case of a CBCT.However, the Catphan phantom, used to measure HU, seems to present a number of drawbacks. The composition of the highest density insert, Teflon, generates a photoelectric attenuation behavior different from that of real bone,8 whic and Hatton et al. A variation in the scatter volume length from 5 to 26 cm can cause errors in the measurement of HU values up to 260 HU, but this seems to have an insignificant dosimetric impact. In addition, the calibration curve is dependent on the length of the scan — an increased z coverage will lead to more scattered radiation and, therefore, lower HU in high‐density regions. In our case, the patient scanned length will be the maximum achievable by the system (20.6 cm) in order to completely scan the treatment volume and the organs at risk. On the other hand, the radial scatter seems to present an important impact on the HU values. Differences up to 1000 HU have been found by Hatton et al. when varying the phantom diameter from 18 to 40 cm. Therefore, a HU density calibration with a phantom sized for each patient should be performed. However this is certainly difficult to implement in clinical practice. Another option is to perform the dose calculation with the HU density curve obtained in the narrow‐beam CT (Aquilion), which in our hospital was determined with a phantom that contained inserts with tissue‐equivalent materials. This choice has been shown to provide a good accuracy in the calculation of dose distributions on both phantoms and patients, although the degree of accuracy depends on the patient's radial diameter.Moreover, the diameter of the Catphan phantom is 20 cm, smaller than that commonly found in clinical conditions (standard patient thickness 25–35 cm). Thus, in a real patient we expect to have more scattered radiation which, together with the presence of heterogeneities, can lead to inconsistencies in the final calculation of the dose distribution. The influence of scattered radiation on the HU density curve has been studied by Guan and Dong7 and In any case, the HU density curve obtained with the Catphan phantom is adequate to monitor the constancy of the HU density ratio in periodic quality controls.The OBI imaging system used as a CBCT provides volumetric images acquired with a kilovoltage cone beam. In this paper we have analyzed the image quality obtained within the Pelvis protocol, studying, in addition, its reproducibility over time. Similarly, we have analyzed the image quality provided by a simulation CT with the acquisition technique usually employed for the pelvis site in our hospital. In order to test the ability of OBI to perform IGRT and ART, we have studied some parameters that define image quality in an objective way. The analysis was automatically performed using macros implemented with the program ImageJ.We conclude that the images obtained with the OBI system present an image quality adequate to accurately perform IGRT. However, the OBI images are noisy due to the scattered radiation present in a cone beam, and they also show some artifacts. On the one hand, we find a slight cupping effect and some ring artifacts which do not compromise the image quality. On the other hand, and of greater importance, we point out the presence of the bowtie wobble artifact. This artifact appears as a bright ring centered on the isocenter with a diameter of 22 cm. In order to carry out ART, the impact of this artifact on volume definition should be assessed. The criticality of the artifact on volume contouring will depend on the anatomical region to be imaged. The influence of the bowtie wobble artifact on dose calculation will be less important, since it involves minor changes in HU. However, before using the OBI images to perform ART, the special case of very thick patients should be considered since, in this situation, a poor choice of the HU density calibration curve could cause significant errors in dose calculation.Finally, we stress the importance of carrying out a periodic quality control of the image used in IGRT. In addition, our experience reveals the need to calibrate the imaging system after major interventions, and then check the quality of the obtained images. This becomes more important if we intend to use the OBI to perform ART.


Asynchrony among synaptic inputs may prevent a neuron from responding to behaviorally relevant sensory stimuli. For example, “octopus cells” are monaural neurons in the auditory brainstem of mammals that receive input from auditory nerve fibers (ANFs) representing a broad band of sound frequencies. Octopus cells are known to respond with finely timed action potentials at the onset of sounds despite the fact that due to the traveling wave delay in the cochlea, synaptic input from the auditory nerve is temporally diffuse. This paper provides a proof of principle that the octopus cells' dendritic delay may provide compensation for this input asynchrony, and that synaptic weights may be adjusted by a spike-timing dependent plasticity (STDP) learning rule. This paper used a leaky integrate and fire model of an octopus cell modified to include a “rate threshold,” a property that is known to create the appropriate onset response in octopus cells. Repeated audio click stimuli were passed to a realistic auditory nerve model which provided the synaptic input to the octopus cell model. A genetic algorithm was used to find the parameters of the STDP learning rule that reproduced the microscopically observed synaptic connectivity. With these selected parameter values it was shown that the STDP learning rule was capable of adjusting the values of a large number of input synaptic weights, creating a configuration that compensated the traveling wave delay of the cochlea. A singular sensory event such as a flash of light, the sound of a clap, or the onset of a glottal pulse in speech may create a neural response that is temporally diffuse. In the auditory domain this happens as a result of the traveling wave delay in the cochlea for example   model of the octopus cell used to recreate the firing behavior of octopus cells. This is simpler than a Hodgkin-Huxley model, but adequate to capture the relevant dynamics.A conventional STDP model of synaptic weight adjustments used to adjust the weights of the connections between the periphery model, and the octopus cell model.A model was established consisting of the following components:Some parameters of the combined LIF/STDP system were selected using experimental evidence. Those parameters without sufficient basis in evidence were selected using a genetic search algorithm. The genetic algorithm was not intended to replicate any biological process. It was intended to find any set of parameters for the STDP algorithm that: (a) conformed to a physiologically plausible range of values and (b) recreated the correct known connectivity of octopus cells. These two requirements were sufficient to provide proof of principle that STDP can play the hypothesized role in octopus cells. It was not necessary to converge on a single unique set of optimal parameters. The genetic algorithm may not converge to a local or global optimum, however it was sufficient to meet the above requirements.Synaptic input to the octopus cell was simulated by a realistic model of the auditory periphery, the Zilany-Bruce model  over one time step then a spike is triggered and the membrane potential is reset to the leak reversal value. The value of κ was chosen to approximate the known value measured from octopus cells  and R was set to 4 to match the number of expected spikes during each 50 ms epoch. The rule increments the total synaptic drive if the cell is producing spikes at a rate below the nominated rate, R, and reduces the total synaptic drive if it is above the nominated rate. Note that, in the absence of post-synaptic activity, the change in synaptic weight due to homeostasis is positive. and so initiates post-synaptic activity in the cell, which is something that is necessary for STDP.where The specific components of the homeostatic plasticity rule are not intended to represent particular physiological processes. Rather, the rule is meant to be a phenomenological recreation of the effect of homeostatic regulation of the total synaptic input to the cell.The total learning equation combines homeostasis and STDP:W ∈ . These adjustments to synaptic weight were not made continuously during learning, but once at the end of each 50 ms epoch.where Given that there is no experimental evidence of the particular parameter values of STDP mechanisms in octopus cells it was necessary to constrain the parameters of the STDP model by selecting values that resulted in the expected final synaptic configuration of the octopus cell. A metric was established that was used to quantify the configuration of synapses after a period of STDP learning. The metric was designed to return a high value when the dendritic delay matched and compensated for cochlear traveling wave delay.basic form of the metric was chosen to be a sum of Gaussians xn is the sum of the traveling wave delay and the dendritic delay for each individual synapse, and T is a constant (0.5 ms) and is the target delay of the combined dendritic delay and traveling wave delay. So, if xn = 0.5 ms then that particular synapse will contribute the maximum value to the metric. Wn is the weight of each synapse. The value of σ was chosen to penalize synapses for which traveling wave delay did not compensate for dendritic delay (70 μs).The Wn increase the value of the metric. However, a synapse with value of |T − xn| close to 0, leading to a high value of T − xn|. A large value of |T − xn| indicates that the dendritic delay is not optimally compensating for the traveling wave delay.With this metric, synapses that increase their value of If total synaptic weight remained constant over time and across models, as did connectivity, then this metric would be sufficient. However this is not the case, and so it was necessary to introduce normalization to compare models with different total synaptic input and delay configurations. The normalization factor had the same Gaussian form, with the mean weight and the mean difference in the traveling wave delay and dendritic delay. This final normalized metric η was:tTW, n is the cochlear traveling wave delay for synapse n, and tD, n is the dendritic delay for synapse n.where This metric allows comparison across different epochs and models. In practice, a homogenous weight distribution, whether the synapses are strong or weak, was observed to produce a metric value of approximately 0.40. A value of η higher than this represents a synaptic configuration in which the dendritic delay is compensating for the traveling wave delay.In order to perform a multi-dimensional search efficiently a simple genetic algorithm was used. This rule was not meant to represent any real process in the animal, but simply to discover values for the parameters of the STDP learning rule and homeostatic rule that lead to the predicted final configuration of synapses.Initially a population of 15 models was instantiated with random parameter values and evaluated. The two which produced the highest values of η were copied without modification to the next generation. Each parameter value of a further 15 models was selected randomly from the 2 “parents.” In addition, random variation was applied to each value (see below for details). The process was repeated again with the next generation, each time following the same process. In total 100 generations were completed, each consisting of 15 models each of which were evaluated over 10 epochs of sound stimulus. Each epoch consisting of 4 click sounds over the course of 50 ms, with STDP applied at the end of each stimulus and the final value of η is recorded.x−0.5)3)+0.5 to make frequent small changes, and infrequent large changes.As described, 15 “child” models were created by selecting parameter values from one of the two “parent” models. Random variation was then imposed on each value. This was done by creating a random change from the inherited value. The variation used white noise values between 0 and 1, and compressed by: .The results of 4 separate parameter searches Figure  show thaWmax) reduced to a level that did intervene in synaptic weight growth but was not highly restrictive . This result is explored in a further parameter exploration later in the paper.The most notable feature of the parameter search was the fact that in all 4 searches the temporal width of the positive part of the STDP window, τThe cellular dynamics of a 100th generation cell before and after 10 epochs of STDP learning show the effect of synaptic selection Figure . After t+) approached the value considered to be the physiological minimum (20 μs).In the previous parameter exploration Figure  the valu+ was systematically varied . This left 4 STDP parameters available for exploration (Figure In order to examine the effect of different physiological minimums on the outcome of the STDP learning the value of τd Figure . In addin Figure . In addih Figure .+ other parameters were allowed to vary to “compensate” for the value of τ+. This was a deliberate decision to discover the effect of τ+ in the presence of other compensating changes, which is most like the situation in vivo.Note that while varying τ+ (Figure + are associated with lower values of the metric η indicating a less realistic anatomical arrangement of synapses. There is also a dependence of the value of Wmax upon the value of τ+. Apparently, smaller values of τ+ led to a compensating effect in the form of a higher “choice” of value for Wmax.The results of the search Figure  show an + Figure . Higher + lead to less selectivity of synaptic weights than a cell model with the lower value of τ+ (Figure By examining the final synaptic profile of 100th generation cell models after 10 epochs of learning it can be seen that the longer duration of the positive STDP window has predictable effects Figure . The lon+ Figure . This laThis study demonstrates that it is possible for a spike-timing based synaptic plasticity mechanism to select synapses such that their dendritic delays compensate for input asynchrony. This was shown in a realistic model of the auditory nerve's synapses onto octopus cells in the ventral cochlear nucleus. Parameters associated with a standard STDP window were selected to allow the STDP to guide the selection of the correct subset of synapses. Parameter selection of the STDP learning process was achieved with a simple genetic search. The fitness function for this search was developed to be maximum when the synaptic configuration matched that known to occur in the cochlear nucleus.Previously published experimental studies on the arrangement of synaptic connections from ANFs to octopus cells include detailed descriptions of their anatomical structures (Oertel et al., Evidence suggests that it is dendritic back-propagation or dendritic spikes of the post-synaptic neuron's action potential that provides the learning signal to individual synapses (Golding et al., This investigation hypothesizes that developmental plasticity can provide synaptic tuning that allows for the detection of simulated clicks. However, there is also evidence that plasticity is maintained in the auditory brainstem of adult maternal mice (Miranda et al., dV/dt (Ferragamo and Oertel, In the present investigation it was found that STDP windows were required to be very brief. It has been shown that, in theory, learning is optimum when the time constant τ for the STDP window matched the time constant τ for the LIF synapse (Kennedy et al., The number of synapses initially provided to the cell is important. In particular, if there are too few then there will be insufficient numbers of synapses for the final selected subset. In this investigation we chose to provide 1,200 synapses from 400 different ANFs. A more thorough analysis of the exact numbers may be a useful target of future work and may reveal a minimum number beyond which convergence is not possible.The results suggest that a large number of synapses will be silent during selection using STDP. However, it is possible that these synapses are present only during a critical period after which structural plasticity would lead to their removal.Like the theory of evolution through natural selection, STDP is a simple rule that can create complex and sophisticated results adapted to local circumstances. While evolution works at the level of the gene Dawkins,  and timeMS undertook the computational work and preparation of the manuscript. All authors contributed to the development of the hypothesis and the analysis of the data.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


We have fabricated the multiple nanolayers impuritied on silicon pillars for Si solar cells to pick up photons in ultraviolet and infrared region of solar spectra, in which the localized states originated from nanosilicon doped with oxygen are built to avoid Auger recombination, and some interesting quantum phenomena in the localized states have been observed. The quantum effect of photo-generated carriers has been observed in I-V curve measurement on the photovoltaic sample prepared in oxygen by using nanosecond pulsed laser. More interesting, the twin states of quantum vibration are measured in the localized states originated from the impuritied nanosilicon, which provides a stable reservoir for electrons in the photovaltaic system. It should be noted that the amplitude change of the quantum vibration occurs under magnetic field with 0.33T on the sample prepared in oxygen, owing to the electron spin in the localized states. The photoluminescence (PL) spectra measured from 300 nm to 1700 nm exhibit the localized states in various regions in the photovoltaic system, in which the electrons can stand in the localized states with longer lifetime to be uneasy into Auger recombination. Micro-nanostructuring has been suggested as a promising method to find a new path to get an effective absorber for solar cells with higher efficiency in a photovoltaic system21. Recently, significant effort has been focused on enhancing the light absorption by nanoscale light trapping using nanowires, nanocones, nanodomes and nanoholes31. Despite the exciting success in light trapping, the power conversion efficiency of nano-structured Si solar cells, however, remain lower efficiency for the thick devices and the thin devices33. The Si solar cells with nanostructures are not efficient because of severe Auger recombination. In addition it is also needed for Si solar cells with higher efficiency to pick up photons in ultraviolet and infrared region of solar spectra.Surface-induced effects on micro-nanopattern and quantum confinement effect in Si nanostructures offer interesting features that could be used to boost the efficiency of photovoltaic energy conversion and to overcome some of the restraints that lead to the Shockley–Queisser limit31 are built from the impurities on the nanostructures for avoiding severe Auger recombination, which involve the electronic states due to impurities built on the smaller nanostructures doped with oxygen and the electronic states owing to impurities built on the defects doped with oxygen for improving photovoltaic conversion in ultraviolet and infrared regions.Here, we have found the new methods in which the localized electronic states with longer lifetime due to the Heisenberg principle related to Δt ~ h/ΔEIn the article, the quantum effect of photo-generated carriers in the localized states is observed in I-V curve measurement on the photovoltaic sample prepared in oxygen, which provides a stable reservoir for electrons. It is very interesting that the quantum vibration on the quantum platform of I-V curve is discovered on the Si quantum dots (QDs) doped with oxygen, and the quantum twin-state occurs in the localized states under irradiation of laser at 633 nm. The amplitude change of the quantum vibration occurring in the magnetic field with 0.33T should be related to the electron spin in the localized states. The quantum twin-state in the localized states originated from the QDs impuritied should have an application in quantum entangle and code.The photoluminescence (PL) spectra measured from 300 nm to 1700 nm exhibit the electronic states in various regions, especially the localized states for avoiding Auger recombination on the photovoltaic system, in which the electrons can stand in the localized states with longer lifetime originated from the impurities on the nanosilicon or on the defects of silicon to be uneasy into Auger recombination.2 surface of the pillars and the experimental result obeys the K-K relations34.We use the pulsed laser etching (PLE) device with a ns laser to fabricate the pillars structure, in which the spot diameter of laser beam is about 1 μm focused on the silicon wafers of P-type substrate with 10 Ωcm in vacuum (sample I) or in oxygen environment with 80 Pa (sample II). It can be assumed that the pure nanosilicon occurs in the sample I, and the sample II involves the nanosilicon doped with oxygen. It is interesting that the plasma lattice pattern occurs in the process of etching the pillars structure as shown in Fig. As shown in Fig. For confirmation of oxygen doping in nanosilicon, the comparison between the sample I prepared in vacuum and the sample II prepared in oxygen environment with 80 Pa has been taken in the TEM images. In Fig. The PL spectrum from 350 nm to 500 nm measured in the ultraviolet layer exhibits the localized states from the smaller nanosilicon doped with oxygen. Here, the localized states originated from impurities on nanosilicon effectively avoid the Auger recombination on the photovoltaic system. In Fig. The TEM image in Fig. It is interesting to make a comparison of electron states between the pillars samples prepared in vacuum and in oxygen of 80 Pa, whose PL spectra on the two kinds of samples are exhibited in Fig. In the photovoltaic measurement, much more photo-generated carriers under irradiation obviously occur on the sample II prepared in oxygen, as shown in Fig. In the experiments, the external quantum efficiency (EQE) was measured directly under laser radiation at 633 nm on the sample II and the sample I. The EQE on the sample II is about 70% which is ten times higher than the EQE on the sample I. The better inversion of photo-voltage on the sample II prepared in oxygen environment should be originated from the reservoir of carriers avoiding Auger recombination in the localized states due to the nanosilicon doped with oxygen.i (4п mKBT/h) ln{1 + exp[(Ef − Ei)/(KBT)]}ψiψi*, where Ef is the Fermi energy level, Ei and ψi is energy value and wave function of the carriers in the localized state, respectively35.It is very interesting that the localized states originated from impurities on nanosilicon is really the trap states with longer lifetime localizing under the opened conduction band of nanocrystals owing to the Heisenberg principle related to Δt ~ h/ΔE, in which the longer Δt can be obtained with the narrower ΔE in the localized states. The photo-generated electrons in the localized states flow out to form current, which has the quantum tunneling characteristic in the nanolayer doped with oxygen. The carriers density in the localized states can be described by the formula: N = ΣIt is amazed that the quantum vibration on the quantum platform of I-V curve is discovered on the pillars structure doped with oxygen, as shown in Fig. In the simulating calculation, the structure models of the Si quantum dot and the impuritied quantum dot have been built in order to simulate the experiment process, as shown in the inset of Fig. In conclusion, the multiple impuritied nanolayers on the pillars structure have been fabricated for Si solar cells to pick up photons in ultraviolet and infrared region of solar spectra. The localized states with longer lifetime originated from impurities on nanosilicon effectively avoid Auger recombination in the photovoltaic system. The calculation results indicate that the localized states occur in various regions on the pillars structure with the multiple impuritied nanolayers, which is demonstrated in the PL spectra measurement. The quantum effect of photo-generated carriers is observed in I-V curve measurement on the photovoltaic sample prepared in oxygen. The quantum vibration on the I-V quantum platform is discovered on the pillars structure doped with oxygen, and the quantum twin-state occurs in the localized states under irradiation of laser at 633 nm, in which the amplitude change of the quantum vibration appears in magnetic field related to the electron spin in the localized states. This kind of quantum twin-state in the localized states should have an application in quantum code and quantum entanglement in the photo-communication.A silicon wafer of P-type (100) oriented substrate with 1–10 Ωcm is taken on the sample stage in the fabrication system with nanosecond pulsed laser etching (ns-PLE) devices. A third harmonic of pulsed Nd:YAG laser at 355 nm with nanosecond pulsed width is used to etch Si surface by controlling with points and lines array scanning in vacuum or in various environment. For making a comparison between the samples prepared in different environment, we fabricate the pillars sample I prepared in vacuum to build the pure nanosilicon and the pillars sample II prepared in oxygen of 80 Pa to build the impurities structure on nanosilicon surface. After the etching process, in the amorphous layer on the pillars surface, the Si QDs can grow up through crystallizing in the irradiation of electron beam or the laser annealing and the furnace annealing process, in which their size range is narrower due to layer thickness confinement. The doping process with oxygen can be carried out through the gas tube in the chamber of the PLE combination fabrication system.On the pillars surface, the nanolayers can be prepared in the combination fabrication system with PLE and pulsed laser deposition (PLD) devices. A third harmonic of pulsed Nd:YAG laser at 355 nm is used to deposit nanolayers on the pillars in PLD process in various environment. The smaller QDs in the ultraviolet nanolayer (layer thickness: 2–3 nm) and the bigger QDs in the visible nanolayer (layer thickness: 3–5 nm) can be fabricated by using PLD method and controlling the annealing time. The defects in the infrared nanolayer (layer thickness: 8–10 nm) can be prepared by the faster annealing after PLD process. The doping process on the nanosilicon or on the defects can be carried out in the PLD method with oxygen environment for producing the localized states.PL spectra on the pillars samples are measured under the 266 nm or 488 nm excitation at room temperature (300 K) and lower temperature (10 K ~ 200 K) in sample chamber of 1 Pa. In the PL measurement system, The ultraviolet laser beam at 266 nm is used to measure the ultraviolet spectrum, and the light beam at 488 nm in Ar ion laser is focused on the pillars samples for excitation to detect the visible spectrum and the infrared spectrum for identifying the electronic states on the impuritied QDs or on the defects doped with oxygen.The construction of photovoltaic system is shown in Fig.


In contrast to global numbering which requires including all the previously computed eigenvectors in the search subspace, the proposed local numbering only requires a presence of one eigenvector in the search subspace. This effectively eliminates the search subspace growth and therewith the super-linear increase of the computational costs if a large number of eigenvalues or eigenvalues in the interior of the spectrum are to be computed. The new restart technique is integrated into nonlinear iterative projection methods like the Nonlinear Arnoldi and Jacobi-Davidson methods. The efficiency of our new restart framework is demonstrated on a range of nonlinear eigenvalue problems: quadratic, rational and exponential including an industrial real-life conservative gyroscopic eigenvalue problem modeling free vibrations of a rolling tire. We also present an extension of the method to problems without minmax property but with eigenvalues which have a dominant either real or imaginary part and test it on two quadratic eigenvalue problems.In this work we present a new restart technique for iterative projection methods for nonlinear eigenvalue problems admitting minmax characterization of their eigenvalues. Our technique makes use of the minmax induced  J can be characterized as minmax values of a Rayleigh functional ).mentclass2pt{minimMinmax induced numbering of eigenvalues) Let kth largest eigenvalue of the matrix kth eigenvalue of kth eigenvalue of problem kth eigenvalue of If T(·) and  holds.(iii)J contains the kth and the mth eigenvalue J contains all the eigenvalues Assume that for (iv)kth eigenvalue If mentclass2pt{minimThen the following assertions hold:For sparse linear eigenvalue problems, mentclass2pt{minimussed in , 32, 34.mentclasspt{minimaussed in . For nonussed in  it was pThere are many details that have to be considered when implementing an iterative projection method as outlined in Algorithm 1. The comprehensive review is out of scope of this work. Here, we restrict ourselves to only the essentials necessary for motivation and derivation of the local restart technique in Sect. V has to contain at least In order to preserve the numbering of the eigenvalues, the initial basis entclass1pt{minimaJ are minmax values of the restriction of the Rayleigh functional p of For nonlinear eigenvalue problem  let the kth eigenvalue of the nonlinear problem. There are many methods for solving small and dense nonlinear eigenvalue problems. For polynomial eigenvalue problems linearization is a natural choice, where the enumeration of eigenvalues in the sense of Sect. In general two approaches to subspace expansion can be found in the literature: Jacobi-Davidson  and NonlLet v we may choose as a new direction The Nonlinear Arnodi method uses the direction of the residual inverse iteration \documentσ|) (cf. ). For He=λ~ki-1,  the convAs the subspace expands in the course of the algorithm, the increasing storage and computational cost of the solution of the projected eigenvalue problem may make it necessary to restart the algorithm and purge some of the basis vectors. To be able to continue determining subsequent eigenpairs the correct enumeration has to be enforced at the restart.J contains the first eigenvalue jth eigenvalue of the projected problem : Initialization   Here, the only difference between the local and and global restarts is the initialization subspace, Lines –5: InitiLines (7–12): Computation of theth eigenpairj eigenvalues of J,v aiming at the Ritz pair If Line 13: Check if a new eigenpair has been computed   Ideally, the converged Ritz pair From the discussion in Sect. Lines (14–29): Restoring local numbering   For the sake of the following argument we assume that the algorithm returned a replicate eigenvalue q  ordering coincide on mentclass2pt{minima, b]. Then by assumption m, of the first eigenpair of a, b] is the number of the largest nonpositive eigenvalue, Let entclass1pt{minimam and after it converged, the eigenvalue with the local number mth local number converged this could be used as an anchor straight away. However, there is a danger of accepting a, b]) prematurely i.e. a, b] of the original problem  is the positive solution of the quadratic equationWe consider a conservative gyroscopic eigenvalue problemWe start with showing some qualitative behavior of our method on a small example of a wheel, composed of solid elements with Mooney-Rivlin material, see Fig. For the purpose of comparison we computed all the eigenpairs in the interval 0,16,820] by a globally restarted Nonlinear Arnoldi method. This corresponds to the smallest 200 eigenvalues. In all experiments an eigenvalue was regarded as converged if its relative residual norm was smaller than 0 by a glIn the next experiment we used the same global restart technique, but this time the restart was triggered whenever the dimension of the subspace exceeded the number of the last converged eigenvalue by 30, a relative threshold on the subspace dimension. In this way the average dimension of the search spaces and therefore the time for solving the projected problems were reduced, see Table Next, we computed the smallest 200 eigenvalues with Nonlinear Restarted Arnoldi. A restart was triggered whenever the search space dimension exceeded 80 or the convergence rate The outstanding advantage of the local restart strategy is its ability of computing eigenvalues in an interval in the interior of the spectrum without the need of computing all the preceding eigenpairs. Using the same local restart strategy we computed all the eigenpairs in The automated restart strategy described in Sect. Figures For the purpose of performance comparison of Nonlinear Arnoldi (NA) and Jacobi-Davidson (JD) type subspace expansions, we computed all the eigenpairs of the wheel problem in the interval The here used preconditioner  to find all 388 eigenvalues in this interval. Figure In this example we observed an increased occurrence of spurious values after the restarts. This leads us to believe that retaining some of the previously computed subspace after the restart may help to alleviate this effect, like for instance keeping further We believe that the key to the optimal performance is to balance the subspace growth with the occurrence of spurious eigenvalues. An optimal strategy may include adapting the number of eigenvectors kept in the local basis along with the anchor, The following two problems are non-quadratic nonlinear eigenvalue problems. Thus the projected problems are solved by the safeguarded iteration (Algorithm 2). For a general nonlinear function, we do not have an explicit formula for its zeros  as it was the case for the quadratic eigenvalue problem but we have to revert to Newton iteration.In both cases the method was initialized using the lower bound of the interval. The relative residual tolerance was B is a diagonal matrix corresponding to values of the function A is the negative sum of a diagonal matrix with entries corresponding to values of the function We consider the following delay differential equation on a square domain \documentDue to the symmetry of the problem in mentclass2pt{minimq, with consecutive local numbers, say For problems with double or higher multiplicity eigenvalues, it may be beneficial to consider extension of the restart strategy to block versions of the nonlinear Arnoldi and Jacobi-Davidson methods. Block methods by design are well suited for problems with multiple or clustered eigenvalues, as an entire subspace is iterated simultaneously. In principle, the local restarts can be used within block methods, when we simply iterate a number of eigenpairs, Our second problem is a rational eigenvalue problemle fluid .In each of the intervals  problem  satisfieThe considered matrix problem is a finite element discretization of an elliptic cavity with 9 emerged tubes with 36040 degrees of freedom, it has 9 poles, Using the search subspace with only the anchor locked i.e. The described local restart procedure hinges upon the minmax property of the nonlinear eigenvalue problem. However, observe that if We used such ordering to solve two quadratic eigenvalue problems from the NLEVP collection  which eiC and K are not sparse, hence the relatively small problem dimension. The real parts of the eigenvalues are approximately equal to the corresponding eigenvalues of the “wiresaw1” problem with the same dimension and value of the parameter v, and the imaginary part of all eigenvalues is a constant equal to 0.8.We consider a quadratic eigenvalue problem arising from the vibration analysis of a wiresaw including the effect of viscous damping, “wiresaw2” problem from NLEVP collection \documentAs for “wiresaw1” problem we computed all 100 eigenvalues with the real part in the interval  using the same initialization and solver parameters. Figure K, M are real symmetric and C is a low rank complex diagonal matrix dependent on the impedance parameter. For the formulation . All the examples in this paper were solved using MATLAB toolbox QARPACK  containi


It has been proposed that the visual system is able to estimate the refractive index of thick transparent objects from background distortions caused by them. More specifically, it was hypothesized that this is done based on a mid-level cue, the distortion field, whose computation from the input requires comparing the part of the background seen through the object with the part visible in plain view. We test two predictions derived from this hypothesis: (a) scene variables that do not change the distortion field, for instance, the density of the background texture, should not systematically influence the subjects’ settings in a material matching task. (b) The uncertainty of the estimates should increase sharply, if the part of the background texture in plain view is removed. Our results are not compatible with these two predictions but are completely in line with the alternative interpretation that the subjects maximized the similarity of the distorted background textures on the image level. Additional results indicate that subjects can take relations between the distorted and the undistorted background into account if this is encouraged by the experimental design, but they do this in a simplistic way that is inappropriate to estimate the refractive index. R of the object’s material and the angle of incidence θ. The reflected light leaves the surface in the mirror direction (specular reflection). The transmitted light is bend at the surface by an angle that is given by Snell’s law (refraction). The effects of refraction and specular reflection on the retinal projection of light-transmitting objects are especially apparent for thick, irregularly shaped objects like the ones shown in Light-transmitting materials often appear transparent. Previous investigations of perceived transparency that relate to such materials have mainly focussed on their transmission properties and correspondingly considered the color and luminance relations that lead to perceptual transparency . These iDue to the specular reflections, the environment is partly visible at the object’s surface. This suggests that previous investigations dealing with the perception of opaque mirror surfaces that specularly reflect all incoming light  are of sThe refraction, which is of primary importance to the present investigation, leads to distortions in the image. These are especially pronounced for thick irregularly shaped light-transmitting objects, like the blob of clear glass shown in Testing the RI hypothesis in this direct way is highly problematic for two reasons. A first problem is confounding variables. Physically correct stimuli as the ones used by displacement field D, a 2D vector field that “measures the displacement of all features in the background when seen through the transparent object” (p. 814): D = pr − pi, with pi =  being the image location of a feature in undistorted plain view and pr =  being the location of the same feature when refracted by the transparent object. Second, they consider the divergence d = ▽ · D of the vector field D, which they call the distortion field. The divergence is a scalar field that represents only a part of the information contained in the displacement field D. Its values are related to the “relative magnitude of compression” (p. 814) of the texture pattern. The core assumption of d from the input image and that this estimate could then be used in a second step to infer the refractive index. If both D and pi are completely unknown, it is obviously impossible to estimate pr alone. This implies that in order for this computational idea to work, constraints for pi are required. In the present article, we test two predictions derived from the computational ideas that In this article, we concentrate on empirical tests of the first step, the estimation of the distortion field. To this end, we derive two testable predictions from the RI hypothesis that do not require any knowledge about the second step that presumably uses the estimate We test both predictions and compare them with the predictions derived from the alternative explanation presented in Experiment 1 tests the first prediction derived from the RI hypothesis that changes in scene variables that do not influence the displacement field should have no systematic effect on the refractive index settings. This test is described in Experiment 1a. In Experiment 1b, we compare the results of Experiment 1a with the predictions from our alternative explanation.D and thus also the distortion field d depend on several variables, for example, the material and the shape of the object, its distance to the background, the viewing angle, but not on the background texture. In a scene that is geometrically fixed, D may be regarded as an operator that acts on arbitrary backgrounds and in each case yields the same distorted version of it. Thus, if the RI hypothesis is correct, then the refractive index estimate should be invariant against global changes in the background texture, as long as the texture contains enough structure to reflect the optical distortions truthfully.The displacement field To test this prediction, we performed an experiment similar to the ones conducted by RS ∈ {1.20, 1.50, 1.80}). The refractive index of the test object was adjusted by the subjects . The refractive index of the surrounding medium was set to 1.The stimulus material consisted of computer-generated images that were created with the Mitsuba renderer . They wex = .30, y = .32, L = 52.75 cd/m2) seams of .32 mm width. The faces were also achromatic , and their luminances were uniformly distributed between 4.43 and 47.43 cd/m2. The density of the background textures of the standard stimuli varied in three steps according to the experimental condition . It was computed with a different random seed than the texture of the same density used in the standard stimulus.The textured background plane (80 × 80 mm) was placed behind the transparent object at a distance of 60 mm. The background textures were random Voronoi patterns created with Matlab  that resSD = .5) and subsequently tonemapped to 8-bit low dynamic range images . The final image size was 370 × 370 px which corresponded to 100 × 100 mm on the screen.Image-based lighting with an infinitely distant spherical emitter was used as the sole illumination. The illumination texture was a high dynamic range image of a natural daylight outdoor scene with a partly cloudy sky. The camera settings (location and field of view) corresponded to the actual experimental setup. Thus, the stimuli appeared in nearly the same way as a corresponding real scene, except for the lack of binocular disparity. Stimuli were rendered as 16-bit high dynamic range images , which was located in a darkened room. The standard stimulus was presented in the upper half of the screen, the test stimulus in the lower half. The viewing distance was 40 cm. The subjects’ task was to adjust the test object until it appeared to be made of the same material as the fixed standard object. The refractive index of the test object was adjusted with the arrow keys of a standard computer keyboard. Each subject performed 27 trials in a pseudo-randomized order: 3 This and all following experiments were carried out in accordance with the relevant institutional and national regulations and legislation and with the World Medical Association Helsinki Declaration as revised in October 2008.Seven subjects, six of them female, participated in the experiment. Their age ranged from 20 to 27. All subjects were naïve as to the purpose of the experiment, except one, which was one of the authors (N. S.). They reported normal or corrected-to-normal visual acuity and showed no color vision deficiency, as tested by DS = “M”) are very similar to those found previously with a uniform gray background under otherwise identical conditions (cf. DS = “L”) and smaller for higher density . A two-way analysis of variance revealed a significant main effect of background texture density, F = 22.33, p < .001.The refractive indices obtained with different background texture densities in standard and test deviate systematically from those obtained with identical texture densities . The smaions cf.  that areThe results obtained in Experiment 1a contradict the prediction derived from the RI hypothesis. Even moderately different background densities in otherwise similar stimuli lead to significantly different refractive index settings. It is less the absolute amount of these deviations but their systematic nature that is diagnostic because systematic deviations are inexplicable if the subjects’ settings are based on the postulated distortion field. One cannot exclude the possibility that a manipulation of the texture density influences the accuracy of the distortion field estimation, but this should mainly affect the size of random errors. The random errors, however, are of comparable size in all conditions.The settings obtained in the condition with identical texture densities in standard and test closely replicate previous results with completely uniform backgrounds . This suCompared with the stimuli with a uniform background that were used in The alternative explanation presented in It is at present unclear which information is used in this type of match. The settings that would result under the conditions of Experiment 1a must therefore be determined empirically. To this end, we isolated the background distortions in the stimuli used in Experiment 1a by removing all specular reflections . In the second control condition “IsolSR,” fixed specular reflections were added to the inner object border by superimposing an image of an object with a constant refractive index (R = 1.5) in front of a uniform background texture . The inward transition to the original stimulus was blurred.The stimuli were the same as those used in Experiment 1a, except for the following differences: For the condition “Isol”, all specular reflections were omitted during the rendering process. The resulting darkening of the object area  was cancelled by correcting the average brightness of the object area to keep subjects from using it as a matching criterion. In the control condition “IsolMsk,” remnants of the specular reflections .The procedure was the same as in Experiment 1a. However, each subject performed 81 trials in a pseudo-randomized order (3 The subjects were the same as in Experiment 1a.DS = “L”), the refractive index settings are higher than the given ones (RT/RS > 1), while they are lower for a higher density in the standard . The deviations are comparatively small if standard and test have the same texture density . The size of the deviations in the two control conditions (“IsolMsk” and “IsolSR”) is similar and slightly larger than in the “Isol” condition.For all conditions, the refractive index settings deviate systematically from those given in the standard object . If the RS  backgrounds available for their matches. The similarity of the pattern of deviations found in Experiments 1a and 1b suggests that image-level matches of the distorted background textures had also played a critical role in Experiment 1a. The considerably smaller size of the deviations in Experiment 1a can be explained by assuming that the subjects also used information from specular reflections. Isolated matches of specular reflections have been found to lead to settings that are almost identical to the ones given in the standard .DS ∈ {#x0201C;L”, “M”, “H”}), while the test stimuli always had the same density  as depicted in The stimuli were similar to those used in Experiment 1a. Again, the background texture density of the standard stimuli was varied in three steps (RS × 3 DS × 2 surround conditions × 3 repetitions). In each half  of the conditions “Surr→NoSurr” and “NoSurr→Surr,” the trials were presented in random order.The procedure was the same as in Experiment 1a. However, each subject performed 54 trials , the refractive index settings are higher than the given ones (RT/RS > 1), for those with higher background texture densities (DS = “H”), the settings are lower (RT/RS < 1). The deviations are considerably smaller if standard and test stimuli have the same background texture density .The subjects’ settings do The prediction derived from the RI hypothesis that the errors of the refractive index settings will increase if the undistorted background texture in the surround is removed is not confirmed by our data. Instead, both the pattern of systematic deviations and the size of random errors are essentially identical for conditions with and without a textured surround. This suggests that the subjects referred solely to information within the object boundaries and ignored any information available in the surround.Furthermore, our results show that the subjects did not ignore the remaining background texture completely, since their settings differ from those obtained with a uniform background .These observations do not seem to be compatible with the computational idea underlying the RI hypothesis.pattern of the deviations observed in Experiments 2a and 2b should be identical because the availability of the textured surround is then irrelevant for the settings. (b) The absolute size of the deviations should be larger in Experiment 2b than in 2a because the compensating effect of the reflection cue is no longer available (see discussion of Experiment 1b). (c) The results of Experiments 1b and 2b should be similar because under the above assumption the two conditions were equivalent.In Experiment 2b, we again isolated the background distortions to determine the settings resulting from image-level matches under the conditions realized in Experiment 2a. If the assumption is correct that the observed deviations in Experiments 1a, 1b, and 2a are the result of image-level matches of properties of the distorted textures, then the following results would be expected: (a) The We only used a single isolation condition , and the surround was manipulated in the same way as in Experiment 2a see .Figure x = .31, y = .32, L = 7.88 cd/m2).The stimuli were identical to those used in Experiment 2a, except that background distortions were isolated in the same way as in the “IsolMsk” condition of Experiment 1b, that is, any specular reflections were omitted during the rendering, the brightness of the object area was corrected for any refraction-dependent darkening, and a gray mask was added to the object boundary (RS × 3 DS × 2 surround conditions × 3 repetitions).The procedure was the same as in Experiment 2a. Again, each subject performed 54 trials (3 The subjects were the same as in Experiment 2a.n = 1”).The results of Experiment 2b are shown in In general, the pattern of deviations in this experiment is very similar to the one found in Experiment 2a. This suggests that image-level matches of background distortions had also played a critical role in Experiment 2a.An unexpected observation is the “collapse of the deviations” in the second half of the “NoSurr→Surr” condition. These settings are close to identity and one may therefore be tempted to interpret this as support for the RI hypothesis. However, several observations speak against this view: First, large systematic deviations from identity were found if the exact same stimuli were presented at the beginning of the experiment in the “Surr→NoSurr” condition. Second, the collapse of deviations was found in a physically inconsistent situation, in which the “objects” did not even appear transparent, whereas in Experiment 2a, in which the stimuli contained at least two consistent and physically correct cues and appeared transparent, no such collapse was observed. Third, not all subjects showed this collapse of deviations.relations between image attributes, for instance, the ratio of the mean element size within and outside of the object’s area, instead of image attributes within the object’s boundary directly, as in the other conditions. In the particular situation realized in the experiment, this can lead to settings near identity because these relations are presumably almost invariant against changes in the background texture density. The observed result is to be expected if three of the four subjects had deliberately switched their matching strategy from absolute to relational, when the surround suddenly changed from uniform to textured in the second half of the experiment. It is at present unclear, why such a switch did not occur in Experiment 2a, but it seems plausible to assume that the salient specular reflections that also influence the settings kept the subjects focussed on the object areas.A more plausible explanation is that the subjects in this case matched To test, whether the collapse of deviations in Experiment 2b could be explained by a match of relations between image-attributes, we explicitly instructed the subjects in a similar matching experiment to perform this kind of match.We also tried to address the question, whether such relational matches could constitute a viable strategy , while the thickness of the test object remained constant (TT = 6 mm). Different thicknesses were implemented by applying a directional scaling factor to the meshes of the objects. In contrast to Experiment 2b, only stimuli with a textured surround (“Surr”) were used, for which the “collapse of deviations” were found.The stimuli were similar to the ones used in Experiment 2b. However, the thickness of the standard object was varied in three steps (RS × 3 DS × 3 TS × 3 repetitions). The subjects were explicitly instructed to refer with their matches to the relations of distorted and undistorted background areas (“Your task is to adjust the test stimulus until the size ratio of the texture elements within the object area and its surround is the same as in the standard stimulus.”).The procedure was the same as in Experiment 2b. However, each subject performed 81 trials in randomized order . This explains the systematic deviations found with objects of different thicknesses. These latter results are in conflict with the assumption that referring to the relation of simple image criteria is generally sufficient to estimate the distortion field and the refractive index.In this article, we tested two predictions derived from the RI hypothesis of systematic and statistically significant effect on the subjects’ settings. both the distortion field and the relative scale of texture elements within the object and its surround. The observed systematic deviations from a perfect match may thus be explained by assuming that the visual system cannot completely distinguish between different influences on the distortion field. Our strategy to keep the distortion field and the relative scale of texture elements constant excludes this kind of explanation and therefore suggests that the deviations observed in Experiment 1a are not due to a bias in the estimation of the refractive index, but that the matches were performed without referring to the distortion field at all.Our strategy to test this computational idea was to derive predictions from it that could be tested without any knowledge about the exact nature of the putative processes. A first prediction is that the refractive index settings in a material matching task should not be influenced by isolated changes of a scene variable that is unrelated to the refractive index and does neither alter the relative scale of the texture elements inside the object and the surround nor the distortion field. In Experiment 1a, we tested this by asking subjects to match the material of two transparent objects across scenes that were identical apart from the density of their background texture. We found that even relatively small density differences had a highly not change when the texture in the surround was replaced by a uniform gray surface. Instead, we observed the same systematic deviations as in Experiment 1a. This suggests that the surround was completely ignored and that a comparison of distorted and undistorted background areas, as it has been proposed by absolute amount of the distortion. Such relative distortion information is insufficient to estimate the absolute value of the refractive index that uniquely characterizes a light-transmitting material. However, relative distortion information might be useful for other purposes, for example, to infer shape properties. Here, regions of relative magnification and compressions might serve as cues for convex or concave surface curvatures.The idea that the estimation of the distortion field involves a comparison of texture elements seen through the transparent object with elements seen directly leads to the further expectation that the uncertainty of refractive index settings that are based on this cue should increase sharply, if information about the undistorted background is removed. Contrary to this prediction, we found in Experiment 2a that the refractive index settings did relation of texture elements within and outside the objects’ boundary was confirmed in Experiment 2c. The results obtained in this experiment further indicate that such relational image-level matches are in general not a viable strategy to estimate refractive indices.The results of Experiments 1a and 2a are clearly not in line with basic assumptions underlying the general computational idea outlined earlier. In three additional experiments, we tested whether the pattern of results found in Experiments 1a and 2a is compatible with simple image-level matches of the distorted background texture. The procedures and stimuli used in Experiment 1b and 2b were essentially identical to those in Experiment 1a and 2a, respectively. The sole difference was that we removed specular reflections and in this way isolated the information contained in the background distortions. This manipulation had the side effect that the “objects” did no longer appear transparent, which is an advantage in that it increases the plausibility that the subjects actually performed image-level matches. In these experiments, we observed deviations from identity that are larger in absolute value but exhibit the same pattern as in the corresponding experiments with physically plausible transparent objects. This is compatible with the interpretation that such image-level matches were also made in Experiments 1a and 2a, but that the presence of specular reflections shifted the settings closer towards identity. In Experiment 2b, we unexpectedly found “perfect matches” in a condition, where a textured surround first appeared in the second half of the experiment. The conjecture that this resulted from image-level matches of the The results obtained in Experiments 1a and 2a seem not compatible with fundamental principles postulated in the RI hypothesis and thus confirm the results and conclusions reported in Our findings seem also instructive from a methodological point of view because they highlight potential pitfalls in “direct” tests of hypotheses. The available evidence suggests that subjects in the material matching task of The theoretical considerations and empirical findings presented in Whether the RI hypothesis can be confirmed in more complex scenes is an open empirical question. However, on theoretical grounds, we are not very optimistic about a positive outcome. In A serious problem for tests of the RI hypothesis in its present form is that the specification of putative mechanisms is rather vague. It would be desirable to develop proposals that are more specific and to investigate with the help of computer simulations, whether and, if so, under which conditions they are sufficient to solve the problem of estimating the refractive index.