A Multi-Segments Stitching Method for Profile Measurement of Large Scale Aspheric Surface within Submicrometer Accuracy

Aspheric surfaces are important to the optical systems and need high precision surface metrology. Stylus profilometry is currently the most common approach to measure axially symmetric elements. However, if the asphere has the rotational alignment errors, the wrong cresting point would be located deducing the significantly incorrect surface errors. This paper studied the simulated results of an asphere with rotational angles around X-axis and Y-axis, and the stylus tip shift in X, Y and Z direction. Experimental results show that the same absolute value of rotational errors around X-axis would cause the same profile errors and different value of rotational errors around Y-axis would cause profile errors with different title angle. Moreover, the greater the rotational errors, the bigger the peak-to-valley value of profile errors. To identify the rotational angles in X-axis and Y-axis, the algorithms are performed to analyze the X-axis and Y-axis rotational angles respectively. Then the actual profile errors with multiple profile measurement around X-axis are calculated according to the proposed analysis flow chart. The aim of the multiple measurements strategy is to achieve the zero position of X-axis rotational errors. Finally, experimental results prove the proposed algorithms achieve accurate profile errors for aspheric surfaces avoiding both X-axis and Y-axis rotational errors. Finally, a measurement strategy for aspheric surface is presented systematically.

Objective To evaluate the effect of setup errors on the 2D image projection and image registration, and then propose an improved registration method based on mutual information. Methods An anthropomorphic head phantom was used to simulate the rotational and translational setup errors. The geometric disparities were reflected by the changes of mutual information. Known setup errors were intentionally introduced to twenty cases divided into two groups demarcated by 3 mm translation error and 3° rotation error: ten cases with larger errors and ten with smaller errors. Then the anterior-posterior and lateral portal images were captured by the electronic portal imaging device (EPID), based on which the setup errors were calculated using two mutual information registration method respectively: the vender provided one, and the improved method as proposed. The calculated errors were compared with the actual setup errors to evaluate robustness of the method. Results For the ten cases with smaller setup errors, the average translational registration disparities using the conventional method were 0.3, 0.4, and 0.3 mm in x, y and z directions respectively. The rotational disagreements were 0.4° in both x and z directions. The average time consumption was 28.7 s. The corresponding discrepancies analyzed using the improved method were 0.3, 0.4, 0.3 mm, 0.5° and 0.4°, respectively. On average, 31.1 s was needed for registration. For the ten cases with larger setup errors, the mean disparities of the conventional method were 0.9, 0.7, 0.8 mm, 0.9° and 0.8°, 29.9 s taken on average. The corresponding result of the improved method was 0.5, 0.4, 0.5 mm, 0.6° and 0.5°, 33.2 s taken on average. Conclusions Regarding smaller setup errors, the two methods showed little difference and both had good performance in image registration accuracy. For larger setup errors, however, the improved mutual information registration method exhibited significantly higher accuracy than the conventional method, at cost of clinically acceptable registration time. Key words: Setup errors; Electronic portal imaging device; Portal image; Image registration

Real-time 3D optical tracking of free-hand imaging devices or surgical tools has been studied and employed for object localization in many minimally invasive interventions. However, the surgical workspace for many interventional procedures is often sub-dermal with tool access through ports from surgical incisions or anatomical orifices. To maintain the optical line-of-sight criterion, external extensions of inserted imaging devices and rigid surgical tools must be tracked to localize the internal tool tips. Unfortunately, tracking by this form of correspondence is very susceptible to noise as orientation errors on the external tracked end compound into both rotational and translational errors on the internal, workspace position. These translational errors are proportional to the length of the probe and the sine of the angulation error, so small angulation errors can quickly compromise the accuracy of the tool tip localization. We propose a real-time tracking correction technique that uses the rotational fulcrum created by the device entry port to minimize the effect of translational and rotational noise errors for tool tip localization. Our technique could apply to many types of interventions, but we focus on the application to the prostate biopsy procedure for tracking a transrectal ultrasound (TRUS) probe commonly used for prostate biopsies. In vitro studies were performed using the Claron Technology MicronTracker 2 to track a TRUS probe in a fixed rotational device. Our experimental results showed an order of magnitude improvement in RMS localization of the internal TRUS probe tip using fulcrum correction over the raw tracking information.

Purpose: The purpose is to evaluate the rotational setup errors in SBRTtreatment for lungtumors using cone beam CT(CBCT), to investigate the dosimetric impact of rotational setup error, and to determine if translational shifts can compensate the rotation. Methods: Online setup CBCT (n=38) from ten lung patients treated with SBRT were re‐evaluated offline by matching with reference CT using adjustment to 3 rotational angles (pitch, roll and yaw). To investigate the dosimetric impact, planning CTimages were rotated using the actual magnitudes obtained from offline match and the dosimetric changes were quantified by comparing the recalculated dose distribution to the original plans. Translational corrections were simulated by manual translational registration of the target volumes on the rotated images to the original CT. The correction efficacy was evaluated by comparing the recalculated plans to the original treatment plan. Results: The systematic and random setup errors in rotational angles were −0.01±0.50, − 0.57±1.08, −0.11±0.42 degrees for pitch, roll and yaw, respectively. Out of 38 acquired CBCTimages, 57.9% had rotational error >1 degree in any axis, 15.7% had error >2 degree in any axis and only 5.3% had error >3 degree in any axis of rotation. Our previous simulation study using various degrees of rotations showed that target coverage reduced significantly for rotation greater than 3 degrees. Plans recalculated using actual patient roll motions obtained from offline match showed similar reduction in tumor coverage. Translational correction resulted in a fairly good recovery of target coverage except it may result in increased dose to organs at risk (OAR). Conclusions: Rotational setup errors for lungSBRT are relatively small in magnitude and not likely to affect GTV coverage significantly. Translational corrections can be optimized to compensate for rotational setup errors; however, caution needs to be paid regarding dose increase to OAR.

If 3D rigid motion is estimated with some error a distorted version of the scene structure will in turn be computed. Of computational interest are these regions in space where the distortions are such that the depths become negative, because in order to be visible the scene has to lie in front of the image. The stability analysis for the structure-from-motion problem presented in this paper investigates the optimal relationship between the errors in the estimated translational and rotational parameters of a rigid motion, that results in the estimation of a minimum number of negative depth values. The input used is the value of the flow along some direction, which is more general than optic flow or correspondence. For a planar retina it is shown that the optimal configuration is achieved when the projections of the translational and rotational errors on the image plane are perpendicular. Furthermore, the projection of the actual and the estimated translation lie on a line passing through the image center. For a spherical retina given a rotational error, the optimal translation is the correct one, while given a translational error. The optimal rotational error is normal to the translational one at an equal distance from the real and estimated translations. The proofs, besides illuminating the confounding of translation and rotation in structure from motion, have an important application to ecological optics, explaining differences of planar and spherical eye or camera designs in motion and shape estimation.

If 3D rigid motion can be correctly estimated from image sequences, the structure of the scene can be correctly derived using the equations for image formation. However, an error in the estimation of 3D motion will result in the computation of a distorted version of the scene structure. Of computational interest are these regions in space where the distortions are such that the depths become negative, because in order for the scene to be visible it has to lie in front of the image, and thus the corresponding depth estimates have to be positive. The stability analysis for the structure from motion problem presented in this paper investigates the optimal relationship between the errors in the estimated translational and rotational parameters of a rigid motion that results in the estimation of a minimum number of negative depth values. The input used is the value of the flow along some direction, which is more general than optic flow or correspondence. For a planar retina it is shown that the optimal configuration is achieved when the projections of the translational and rotational errors on the image plane are perpendicular. Furthermore, the projection of the actual and the estimated translation lie on a line through the center. For a spherical retina, given a rotational error, the optimal translation is the correct one; given a translational error, the optimal rotational negative deptherror depends both in direction and value on the actual and estimated translation as well as the scene in view. The proofs, besides illuminating the confounding of translation and rotation in structure from motion, have an important application to ecological optics. The same analysis provides a computational explanation of why it is easier to estimate self-motion in the case of a spherical retina and why shape can be estimated easily in the case of a planar retina, thus suggesting that nature‘s design of compound eyes (or panoramic vision) for flying systems and camera-type eyes for primates (and other systems that perform manipulation) is optimal.

High-accuracy aspherical mirrors and lenses with large dimensions are widely used in large telescopes and other industry fields. However, the measurement methods for large aspherical optical surfaces are not well established. Scanning deflectometry is used for measuring optical signals near flat surfaces with uncertainties on subnanometer scales. A critical issue regarding scanning deflectometry is that high-accuracy autocollimators (AC) have narrow angular measuring ranges and are not suitable for measuring surfaces with large slopes and angular changes. The goal of our study is to measure the profile of large aspherical optical surfaces with an accuracy of approximately 10 nm. We have proposed a new method to measure optical surfaces with large aspherical dimensions and large angular changes by using a scanning deflectometry method. A rotating AC was used to increase the allowable measuring range. Error analysis showed that the rotating AC reduces the accuracy of the measurements. In this study, we developed a new AC with complementary metal-oxide semiconductor (CMOS) as a light-receiving element (CMOS-type AC). The CMOS-type AC can measure wider ranges of angular changes, with a maximum range of 21 500 µrad (4500 arcsec) and a stability (standard deviation) of 0.1 µrad (0.02 arcsec). We conducted an experiment to verify the effectivity of the wide measuring range AC by the measurement of a spherical mirror with a curvature radius of 500 mm. Furthermore, we conducted an experiment to measure an aspherical optical surface (an off-axis parabolic mirror) and found an angular change of 0.07 rad (4 arcdegrees). The repeatability (average standard deviation) for ten measurements of the off-axis parabolic mirror was less than 4 nm.

BackgroundDry eye syndrome has been recently reported in patients who underwent whole brain radiotherapy (WBRT). WBRT based on a couch with three‐degrees of freedom (3D) can occasionally be performed in which the rotational head motion is not corrected. This study assessed the dependency of the rotational errors on the mask and the dose variation of the lens and lacrimal gland in WBRT patients.MethodsTranslational and rotational setup errors were obtained at the first treatment with cone‐beam CT (CBCT) for patients under WBRT and frameless stereotactic radiosurgery (SRS) (n = 20 each) immobilized using a conventional WB mask and an SRS mask with a bite block, respectively. For the CT sets of SRS cases, WBRT plans were generated for the study. To simulate the rotational error, rotated CT images were created with each rotational error, on which initial WBRT plans were copied and doses were recalculated. The lens and lacrimal gland doses with and without rotation errors were compared.ResultsDespite similar translational setup errors for the two masks, the SRS mask showed a dramatic reduction in rotational errors compared to those of the WB mask. The errors varied within −2.9° to 2.9° and −1.2° to 0.7° for the WB and SRS masks, respectively. Accordingly, the SRS mask confined the change in the maximum lens dose, mean dose of the lacrimal gland, and lacrimal volume receiving 15 Gy to one‐third of those using the WB mask.ConclusionWhen the six‐degrees of freedom (6D) couch is not available, the frameless SRS mask is beneficial to WBRT for the faithful treatment as it was planned.

This paper presents a non-nulling absolute interferometric method for fast and full-area measurement of aspheric surfaces without the necessity of any mechanical movement. Several single frequency laser diodes with some degree of laser tunability are used to achieve an absolute interferometric measurement. The virtual interconnection of three different wavelengths makes it possible to accurately measure the geometrical path difference between the measured aspheric surface and the reference Fizeau surface independently for each pixel of the camera sensor. It is thus possible to measure even in undersampled areas of the high fringe density interferogram. After measuring the geometrical path difference, the retrace error associated with the non-nulling mode of the interferometer is compensated for using a calibrated numerical model (numerical twin) of the interferometer. A height map representing the normal deviation of the aspheric surface from its nominal shape is obtained. The principle of absolute interferometric measurement and numerical error compensation are described in this paper. The method was experimentally verified by measuring an aspheric surface with a measurement uncertainty of λ/20, and the results were in good agreement with the results of a single-point scanning interferometer.

Point diffraction interferometry (PDI) combined with annular subaperture stitching is proposed for ultrahigh-accuracy measurements of aspheric surfaces. By adding an axial movement to the test optics in the PDI system, aspheric surfaces with large departures can be measured with high accuracy by stitching the annular measurement data of different axial positions. We examine the principle of PDI-based annular subaperture stitching and the stitching algorithm. Simulations and experiments demonstrate the feasibility and effectiveness of our proposed method. Our method retains the ultra-high accuracy of PDI while extending the vertical dynamic range of the interferometer, enabling nanometer or even subnanometer accuracy measurements of large-departure rotationally symmetric aspheric surfaces.

Evaluation of the dosimetric influence of interfractional 6D setup error in hypofractionated prostate cancer treated with IMRT and VMAT using daily kV-CBCT

We present a proof of principle, experimental validation of the potential of proton ‘Range Probes’ (RP) for patient positioning verification in proton therapy. In this work, we have evaluated experimentally the accuracy of RP by using tissue-like samples and an in-house developed multilayer ionization chamber (MLIC). In addition we build on our previous, simulation based work to present first experimental measurements of RP through anthropomorphic phantoms to detect either rotational or translational positioning errors. For this, a technique has been proposed to characterize the residual integral depth dose curve (RIDDC) after range mixing. This parametrization has been used to evaluate the similarity between Monte Carlo calculated error scenarios of the database and the measured RIDDC, while considering the intrinsic uncertainties of both modalities in order to deduce the positioning error. Finally, the additional dose applied to the patient when using clinical RP with known fluence has been estimated by measuring the local dose of a single RP. In tissue phantoms, the prediction accuracy of the water equivalent path length was 0.70%, with the highest deviations being found in low density samples (up to 5.67%). In addition, the results of the patient positioning verification measurements demonstrated that using carefully selected RPs, 1D translational or rotational errors could be detected with an accuracy of 1 mm and 2°, respectively, and that these would be associated with a low additional dose burden to the patient. In summary, these promising results suggest that the RP method could be a simple, fast and low-dose tool for verifying patient set-up during proton therapy treatment.

Purpose:The main purpose of this study was to investigate the impact of rotational (yaw, roll, and pitch) error on the planning target volume (PTV) coverage in lung cancer plans generated by intensity modulated proton therapy (IMPT).Methods:In this retrospective study, computed tomography (CT) dataset of previously treated lung case was used. IMPT plan were generated on the original CT dataset using left‐lateral (LL) and posterior‐anterior (PA) beams for a total dose of 74 Gy[RBE] with 2 Gy[RBE] per fraction. In order to investigate the dosimetric impact of rotational error, 12 new CT datasets were generated by re‐sampling the original CT dataset for rotational (roll, yaw, and pitch) angles ranged from −5° to +5°, with an increment of 2.5°. A total of 12 new IMPT plans were generated based on the re‐sampled CT datasets using beam parameters identical to the ones in the original IMPT plan. All treatment plans were generated in XiO treatment planning system. The PTV coverage (i.e., dose received by 95% of the PTV volume, D95) in new IMPT plans were then compared with the PTV coverage in the original IMPT plan.Results:Rotational errors caused the reduction in the PTV coverage in all 12 new IMPT plans when compared to the original IMPT lung plan. Specifically, the PTV coverage was reduced by 4.94% to 50.51% for yaw, by 4.04% to 23.74% for roll, and by 5.21% to 46.88% for pitch errors.Conclusion:Unacceptable dosimetric results were observed in new IMPT plans as the PTV coverage was reduced by up to 26.87% and 50.51% for rotational error of 2.5° and 5°, respectively. Further investigation is underway in evaluating the PTV coverage loss in the IMPT lung cancer plans for smaller rotational angle change.

White-light interferometric techniques and image processing techniques have been widely applied in measurement of surface profiles. A new method based on two technologies to achieve the optical non-contact shape measurement for spherical and aspherical surfaces is presented in this paper. This method utilizes the pixels of the image to locate the points of surface and obtains the surface height information by a vertical scanning white-light interferometric system. A set of a three-dimensional stage composed of a fine and coarse two-step vertical driver, and a two-dimensional horizontal driver is designed to enlarge the measurement area and the vertical scanning range. The measurement precision depends on the the performance of the interference microscope and the three-dimensional stage, so the influence of the interference microscope on the measurement result and the precision of the stage are analyzed. In the stage, a grating sensor is used to monitor the scanning process and the scanning information is fed to driving circuit to compensate for the errors. Additionally, experiments are carried out and correlative results are also shown.

The aim of this study is to calculate setup margin based on six-dimensional (6D) corrected residual positional errors from kV cone beam computed tomography (CBCT) and from intrafraction projection kV imaging in coplanar and in noncoplanar couch positions in stereotactic radiotherapy. Six dimensional positional corrections were carried out before patient treatments, using a robotic couch and CBCT matching. A CBCT and stereoscopic ExacTrac image were acquired post-table position correction. Further, a series of intrafraction ExacTrac images were obtained for the variable couch position. Translational and rotational errors were identified as lateral (X), longitudinal (Y), vertical (Z); roll (Ɵ°), pitch (Φ°) and yaw (Ψ°). A total of 699 intrafraction image sets (361 coplanar and 338 noncoplanar) for 51 SRS/SRT patients were analysed. Rotational errors were corrected in terms of translational coordinates. Residual set-up margins were calculated from CBCT shifts. ExacTrac shifts give residual+intrafraction setup margins as a function of coplanar and noncoplanar couchpositions. The average residual positional error obtained from CBCT in X, Y, Z, Ɵ, Φ, Ψ were 0.1±0.4mm, 0.0±0.6mm,0.0±0.5mm, 0.2±0.8°, 0.1±0.6° and -0.1±0.7° respectively. For ExacTrac, the shits were -0.5±0.9mm, -0.0±1mm, -0.6±1.0mm, 0.4±0.9°, -0.2±0.6°, and -0.0±0.8°. CBCT calculated linear setup margins in X, Y, Z direction were 0.5, 1.2, and 1mm respectively. ExacTrac yielded coplanar and noncoplanar linear setup margins were 1.2, 1.3, 1.5, 1.4, 1.5, and 2.1mm respectively. CBCT-based gross residual set-up margin is equal to 1mm. ExacTrac calculated residual plus intrafraction setup margin falls within a 2mm range; attributed to intrafraction patient movement, table position inaccuracies, and poor image fusion in noncoplanar geometry. There could be variations in the required additional margin between centers and between machines, which require further studies.