Small Systematic Errors Research Articles

Test-retest Reliability of Jump Execution Variables using Mechanography

Mechanography during the vertical jump test allows for evaluation of force-time variables reflecting jump execution, which may enhance screening for functional deficits that reduce physical performance and determining mechanistic causes underlying performance changes. However, utility of jump mechanography for evaluation is limited by scant test-retest reliability data of force-time variables. PURPOSE: To examine test-retest reliability of jump execution variables assessed from mechanography using two different protocols. METHODS: 32 women (mean ± SD: age = 20.8 ± 1.3 yr, height = 167.6 ± 6.3 cm, mass = 68.2 ± 12.7 kg) and 16 men (age = 22.1 ± 1.9 yr, height = 181.5 ± 5.0 cm, mass = 94.1 ± 24.6 kg) attended a familiarization session followed by two testing sessions, all one week apart, during which they performed the vertical jump test and had mechanography data recorded. Participants performed six squat jumps (SJ) per session, with squat depth self-selected for the first three jumps and controlled using a goniometer to 110° knee flexion for the remaining three jumps. Raw data were sampled at 1,000 Hz and filtered with a cutoff frequency of 90.9 Hz using Bertec Digital AcquireTM. Jump execution variables were calculated using a macro program in Microsoft Visual Basic. Eight force-time variables were assessed. Test-retest reliability was quantified as the systematic error (using %difference between jumps), random error (using coefficients of variation), and test-retest correlations (using intraclass correlation coefficients). RESULTS: Jump execution variables demonstrated good reliability, evidenced by very small systematic errors (mean ±95%CI: -1.2 ±2.3%), small random errors (mean ±95%CI: 17.8 ±3.7%), and very strong test-retest correlations (range: 0.73-0.97). Differences in random errors between controlled and self-selected protocols were negligible (mean ±95%CI: 1.3 ±2.3%). CONCLUSION: Jump execution variables demonstrated good reliability, with no meaningful differences between the controlled and self-selected SJ depth protocols. To simplify testing, a self-selected SJ depth protocol can be used to assess force-time variables with negligible impact on measurement error.

Bladder dose–surface maps and urinary toxicity: Robustness with respect to motion in assessing local dose effects

The purpose of this study was to quantify the impact of inter-fraction modifications of bladder during RT of prostate cancer on bladder dose surface maps (DSM).Eighteen patients treated with daily image-guided Tomotherapy and moderate hypofractionation (70–72.8Gy at 2.5–2.6Gy/fr in 28 fractions and full bladder) were considered. Bladder contours were delineated on co-registered daily Megavoltage CT (MVCT) by a single observer and copied on the planning CT to generate dose–volume/surface histograms (DVH/DSH) and bladder DSMs. Discrepancies between planned and daily absorbed doses were analyzed through the average of individual systematic errors, the population systematic errors and the population random errors for the DVH/DSHs and DSMs.In total, 477 DVH/DSH and 472 DSM were available. DSH and DVH showed small population systematic errors of absolute surfaces (<3.4cm2) and volumes (<8.4cm3) at the highest doses.The dose to the posterior bladder base assessed on DSMs showed a mean systematic error below 1Gy, with population systematic and random errors within 4 and 3Gy, respectively. The region surrounding this area shows higher mean systematic errors (1–3Gy), population systematic (8–11Gy) and random (5–7Gy) errors.In conclusion, DVH/DSH and DSMs are quite stable with respect to inter-fraction variations in the high-dose region, within about 2cm from bladder base. Larger systematic variations occur in the anterior portion and cranially 2.5–3.5cm from the base.Results suggest that dose predictors related to the high dose area (including the trigone dose) are likely to be sufficiently reliable with respect to the expected variations due to variable bladder filling.

Accuracy of image-plane holographic tomography with filtered backprojection: random and systematic errors.

This paper explores the concept of image-plane holographic tomography applied to the measurements of laser-induced thermal gradients in an aqueous solution of a photosensitizer with respect to the reconstruction accuracy of three-dimensional variations of the refractive index. It uses the least-squares estimation algorithm to reconstruct refractive index variations in each holographic projection. Along with the bitelecentric optical system, transferring focused projection to the sensor plane, it facilitates the elimination of diffraction artifacts and noise suppression. This work estimates the influence of typical random and systematic errors in experiments and concludes that random errors such as accidental measurement errors or noise presence can be significantly suppressed by increasing the number of recorded digital holograms. On the contrary, even comparatively small systematic errors such as a displacement of the rotation axis projection in the course of a reconstruction procedure can significantly distort the results.

THE $z\lt 1.2$ OPTICAL LUMINOSITY FUNCTION FROM A SAMPLE OF ∼410,000 GALAXIES IN BOÖTES

Using a sample of ~410 000 galaxies to depth I_AB = 24 over 8.26 deg^2 in the Bootes field (~10 times larger than z~1 luminosity function studies in the prior literature), we have accurately measured the evolving B-band luminosity function of red galaxies at z<1.2 and blue galaxies at z<1.0. In addition to the large sample size, we utilise photometry that accounts for the varying angular sizes of galaxies, photometric redshifts verified with spectroscopy, and absolute magnitudes that should have very small random and systematic errors. Our results are consistent with the migration of galaxies from the blue cloud to the red sequence as they cease to form stars, and with downsizing in which more massive and luminous blue galaxies cease star formation earlier than fainter less massive ones. Comparing the observed fading of red galaxies with that to be expected from passive evolution alone, we find that the stellar mass contained within the red galaxy population has increased by a factor of ~3.6 from z~1.1 to z~0.1. The bright end of the red galaxy luminosity function fades with decreasing redshift, the rate of fading increasing from ~0.2 mag per unit redshift at z = 1.0 to ~0.8 at z = 0.2. The overall decrease in luminosity implies that the stellar mass in individual highly luminous red galaxies increased by a factor of ~2.2 from z = 1.1 to z = 0.1.

Scattering cluster wave functions on the lattice using the adiabatic projection method

The adiabatic projection method is a general framework for studying scattering and reactions on the lattice. It provides a low-energy effective theory for clusters which becomes exact in the limit of large Euclidean projection time. Previous studies have used the adiabatic projection method to extract scattering phase shifts from finite periodic-box energy levels using L\"uschers method. In this paper we demonstrate that scattering observables can be computed directly from asymptotic cluster wave functions. For a variety of examples in one and three spatial dimensions, we extract elastic phase shifts from asymptotic cluster standing waves corresponding to spherical wall boundary conditions. We find that this approach of extracting scattering wave functions from the adiabatic Hamiltonian to be less sensitive to small stochastic and systematic errors as compared with using periodic-box energy levels.

Are published ESR dose assessments on fossil tooth enamel reliable?

We performed dose recovery tests on proto-historic enamel samples that were dosed to approximately 200 Gy to present equivalents of Middle to Late Pleistocene fossil teeth. The experimental results confirmed that the ESR dose response of fossil tooth enamel can be best described by a double saturating exponential (DSE) function. When using a DSE for dose evaluation, it is necessary to irradiate samples to very high doses (at least 20 kGy, ideally up to 50 kGy) and use at least 15 additive dose steps.In past studies, dose estimations were mostly carried out using a single saturating exponential (SSE) function and maximum doses (Dmax) in the range of around five to ten times the equivalent dose, usually less than 5 kGy. To address the question whether older dose estimations have to be disregarded as unreliable, we carried out computer simulations using DSE dose response curves which were then fitted with SSEs. Artificial data sets were generated for a wide range of preset dose values between 10 and 5000 Gy. The results indicate a strong correlation between the magnitude of the DE value with systematic and random errors. Reliable doses can be obtained with SSEs for preset dose values of <1000 Gy using 10 exponentially distributed dose points with maximum dose values in the range of up to ten times the DE value. Higher preset doses (>1 kGy) require modified Dmax values. Although here the application of DSEs is preferable, the use of SSEs can nevertheless provide reliable results with reasonably small systematic errors for doses of up to 2000 Gy, provided Dmax is adjusted to about 1*Dset and measurement precision is better than 0.3%. The overall uncertainty remains acceptable (∼10%) using DSEs for DE values of up to 5000 Gy, provided the measurement precision is better than 0.5% and up to 20 dose steps are used. 5000 Gy is apparently the maximum dose than can be reliably assessed with ESR.Finally, we provide some detailed recommendations to ensure reliable dose evaluations with either the SSE or DSE functions. These recommendations can also be used to evaluate the reliability of previously published ESR dose assessments.

The prototype imaging motional Stark effect diagnostic for ASDEX upgrade

This paper presents the development and testing of the prototype Imaging Motional Stark-Effect (IMSE) diagnostic, designed for ASDEX upgrade. A detailed description of the core hardware, theory of operation, and application to complex MSE spectra are presented and analytical evaluation methods suitable for the required accuracy are developed. The diagnostic is tested with a MSE-like polarised spectrum to assess the accuracy of different modulation modes suggested in previous works. Each is found to have small systematic errors due to non-ideal effects of the components, which must be carefully examined. In particular, the effect of intrinsic contrast that results from imperfect parallelism of the birefringent plates is found to have a strong effect. Methods to mitigate and correct for this are discussed. With the necessary corrections and calibrations, the accuracy of polarisation orientation is shown to be within ±0.2°. The effect of finite ellipticity is examined and the possibility to measure this to an accuracy of ±2.0° is demonstrated. The system is shown to be insensitive to broadband polarised background light, temperature variations, and critically to variations in the details of the MSE spectrum.

Observed secular gravity trend at Onsala station with the FG5 gravimeter from Hannover

Abstract Annual absolute gravity measurements with a FG5 instrument were performed in Onsala Space Observatory by the Institute of Geodesy of the Leibniz Universität Hannover from 2003 to 2011 and have been continued with the upgraded meter FG5X in 2014. Lantmäteriet, Gävle, with their FG5 absolute gravimeter have visited Onsala since 2007. Because small systematic errors may be inherent in each absolute gravimeter, their measuring level and a resulting bias (offset) between the instruments must be controlled over time by means of inter-comparison. From 2007 to 2014, 8 direct comparisons took place well distributed over the time span. A complete re-processing of the absolute gravity observations with the Hannover instrument has been conducted to improve the reduction of unwanted gravity effects. A new tidal model is based on continuous time series recorded with the GWR superconducting gravimeter at Onsala since 2009. The loading effect of the Kattegat is described with a varying sea bottom pressure (water and air mass load) and has been validated with the continuous gravity measurements. For the land uplift,which is a result of the still ongoing glacial isostatic adjustment in Fennoscandia, a secular gravity trend of −0.22 μGal/yr was obtained with a standard deviation of 0.17 μGal/yr. That indicates a slight uplift but is still not significantly different from zero.

Recall accuracy of mobile phone calls among Japanese young people.

This study aimed to elucidate the recall accuracy of mobile phone calls among young people using new software-modified phone (SMP) technology. A total of 198 Japanese students aged between 10 and 24 years were instructed to use a SMP for 1 month to record their actual call statuses. Ten to 12 months after this period, face-to-face interviews were conducted to obtain the self-reported call statuses during the monitoring period. Using the SMP record as the gold standard of validation, the recall accuracy of phone calls was evaluated. A total of 19% of the participants (34/177) misclassified their laterality (i.e., the dominant side of ear used while making calls), with the level of agreement being moderate (κ-statistics, 0.449). The level of agreement between the self-reports and SMP records was relatively good for the duration of calls (Pearson's r, 0.620), as compared with the number of calls (Pearson's r, 0.561). The recall was prone to small systematic and large random errors for both the number and duration of calls. Such a large random recall error for the amount of calls and misclassification of laterality suggest that the results of epidemiological studies of mobile phone use based on self-assessment should be interpreted cautiously.

Validation of self-reported start year of mobile phone use in a Swedish case-control study on radiofrequency fields and acoustic neuroma risk.

The possible effect of radiofrequency exposure from mobile phones on tumor risk has been studied since the late 1990s. Yet, empirical information about recall of the start of mobile phone use among adult cases and controls has never been reported. Limited knowledge about recall errors hampers interpretations of the epidemiological evidence. We used network operator data to validate the self-reported start year of mobile phone use in a case-control study of mobile phone use and acoustic neuroma risk. The answers of 96 (29%) cases and 111 (22%) controls could be included in the validation. The larger proportion of cases reflects a more complete and detailed reporting of subscription history. Misclassification was substantial, with large random errors, small systematic errors, and no significant differences between cases and controls. The average difference between self-reported and operator start year was -0.62 (95% confidence interval: -1.42, 0.17) years for cases and -0.71 (-1.50, 0.07) years for controls, standard deviations were 3.92 and 4.17 years, respectively. Agreement between self-reported and operator-recorded data categorized into short, intermediate and long-term use was moderate (kappa statistic: 0.42). Should an association exist, dilution of risk estimates and distortion of exposure-response patterns for time since first mobile phone use could result from the large random errors in self-reported start year. Retrospective collection of operator data likely leads to a selection of "good reporters", with a higher proportion of cases. Thus, differential recall cannot be entirely excluded.

UV-CONTINUUM SLOPES OF &gt;4000z∼ 4-8 GALAXIES FROM THE HUDF/XDF, HUDF09, ERS, CANDELS-SOUTH, AND CANDELS-NORTH FIELDS

We measure the UV-continuum slope beta for over 4000 high-redshift galaxies over a wide range of redshifts z~4-8 and luminosities from the HST HUDF/XDF, HUDF09-1, HUDF09-2, ERS, CANDELS-N, and CANDELS-S data sets. Our new beta results reach very faint levels at z~4 (-15.5 mag: 0.006 L*(z=3)), z~5 (-16.5 mag: 0.014L*(z=3)), and z~6 and z~7 (-17 mag: 0.025 L*(z=3)). Inconsistencies between previous studies led us to conduct a comprehensive review of systematic errors and develop a new technique for measuring beta that is robust against biases that arise from the impact of noise. We demonstrate, by object-by-object comparisons, that all previous studies, including our own and those done on the latest HUDF12 dataset, suffer from small systematic errors in beta. We find that after correcting for the systematic errors (typically d(beta) ~0.1-0.2) all beta results at z~7 from different groups are in excellent agreement. The mean beta we measure for faint (-18 mag: 0.1L*(z=3)) z~4, z~5, z~6, and z~7 galaxies is -2.03+/-0.03+/-0.06 (random and systematic errors), -2.14+/-0.06+/-0.06, -2.24+/-0.11+/-0.08, and -2.30+/-0.18+/-0.13, respectively. Our new beta values are redder than we have reported in the past, but bluer than other recent results. Our previously reported trend of bluer beta's at lower luminosities is confirmed, as is the evolution to bluer beta's at high redshifts. beta appears to show only a mild luminosity dependence faintward of M(UV,AB) ~ -19 mag, suggesting that the mean beta asymptotes to ~ -2.2 to -2.4 for faint z>~4 galaxies. At z~7, the observed beta's suggest non-zero, but low dust extinction, and they agree well with values predicted in cosmological hydrodynamical simulations.

Evaluation of a laser scanner for large volume coordinate metrology: a comparison of results before and after factory calibration

Large volume laser scanners are increasingly being used for a variety of dimensional metrology applications. Methods to evaluate the performance of these scanners are still under development and there are currently no documentary standards available. This paper describes the results of extensive ranging and volumetric performance tests conducted on a large volume laser scanner. The results demonstrated small but clear systematic errors that are explained in the context of a geometric error model for the instrument. The instrument was subsequently returned to the manufacturer for factory calibration. The ranging and volumetric tests were performed again and the results are compared against those obtained prior to the factory calibration.

A smart device inertial-sensing method for gait analysis

The purpose of this study was to establish and cross-validate a method for analyzing gait patterns determined by the center of mass (COM) through inertial sensors embedded in smart devices. The method employed an extended Kalman filter in conjunction with a quaternion rotation matrix approach to transform accelerations from the object onto the global frame. Derived by double integration, peak-to-trough changes in vertical COM position captured by a motion capture system, inertial measurement unit, and smart device were compared in terms of averaged and individual steps. The inter-rater reliability and levels of agreement for systems were discerned through intraclass correlation coefficients (ICC) and Bland–Altman plots. ICCs corresponding to inter-rater reliability were good-to-excellent for position data (ICCs,.80–.95) and acceleration data (ICCs,.54–.81). Levels of agreements were moderate for position data (LOA, 3.1–19.3%) and poor for acceleration data (LOA, 6.8%–17.8%). The Bland–Altman plots, however, revealed a small systematic error, in which peak-to-trough changes in vertical COM position were underestimated by 2.2mm; the Kalman filter׳s accuracy requires further investigation to minimize this oversight. More importantly, however, the study׳s preliminary results indicate that the smart device allows for reliable COM measurements, opening up a cost-effective, user-friendly, and popular solution for remotely monitoring movement. The long-term impact of the smart device method on patient rehabilitation and therapy cannot be underestimated: not only could healthcare expenditures be curbed (smart devices being more affordable than today‘s motion sensors), but a more refined grasp of individual functioning, activity, and participation within everyday life could be attained.

A planning target volume margin formula for hypofractionated intracranial stereotactic radiotherapy under cone beam CT image guidance with a six-degrees-of-freedom robotic couch and a mouthpiece-assisted mask system: a preliminary study.

A planning target volume (PTV) margin formula for hypofractionated intracranial stereotactic radiotherapy (SRT) has been proposed under cone beam CT (CBCT) image guidance with a six-degrees-of-freedom (6-DOF) robotic couch. CBCT-based registration using a 6-DOF couch reportedly led to negligibly small systematic positioning errors, suggesting that each in-treatment positioning error during the treatment courses for the patients employing this combination was predominantly caused by a random gaussian process. Under this assumption, an anisotropic PTV margin for each axis was formulated based on a gaussian distribution model. 19 patients with intracranial lesions who underwent additional post-treatment CBCT were consecutively selected, to whom stereotactic hypofractionated radiotherapy was delivered by a linear accelerator equipped with a CBCT imager, a 6-DOF couch and a mouthpiece-assisted mask system. Time-averaged patient-positioning errors during treatment were estimated by comparing the post-treatment CBCT with the reference planning CT images. It was suggested that each histogram of the in-treatment positioning error in each axis would approach each single gaussian distribution with a mean of zero. The calculated PTV margins in the x, y and z directions were 0.97, 1.30 and 0.88 mm, respectively. The empirical isotropic PTV margin of 2 mm used in our facility for intracranial SRT was consistent with the margin calculated by the proposed gaussian model. We have proposed a PTV margin formula for hypofractionated intracranial SRT under CBCT image guidance with a 6-DOF robotic couch.

Absolute determination of the x-ray absorption coefficient of strontium in the K edge region

The x-ray absorption coefficient for strontium in the K edge region (15.6–17.6keV) is determined on aqueous solution of Sr(NO3)2 in a micrometer cell. A series of absorption spectra of the solution and of solvent is recorded for the thickness of the liquid layer varied stepwise between 1 and 2.5mm. The linear absorption coefficient of Sr and water is determined in a variational procedure whereby small systematic errors of the micrometer setting, of signal detection and of disclination of cell windows are eliminated in one step. The results confirm the data on Sr mass absorption coefficient in some recent tabulations in the smooth regions below the edge and further away from it, but show systematically higher values in the wider energy range above the edge. The tabulated data for water agree with the experiment within 4% in the entire range of measurement.

Evaluation of IL-ATPS and IL-MAE for Simultaneous Determination of Herbicides and Plant Growth Regulators in Sediment

Two analytical methods, an ionic liquid/salt aqueous two-phase system (IL-ATPS) and ionic liquid-based microwave-assisted extraction procedure (IL-MAE), were evaluated for simultaneous extraction and determination of herbicides (2,4-dichlorophenoxy acetic acid, bensulfuron) and plant growth regulators (kinetin, 6-benzylaminopurine, uniconazole) in sediment followed by high-performance liquid chromatography with the diode-array detector. The experimental parameters of two methods including the volume of ionic liquid (IL), pH, the extraction temperature and the amount of salt were studied. Under the optimum conditions, the limits of detection were in the range of 0.001–0.004 µg g−1 for IL-ATPS and 0.002–0.04 µg g−1 for IL-MAE procedure, respectively. Relative standard deviations (RSD, n = 5) and recoveries were in the range of 2.4–4.3 % and 95–98 %, respectively for IL-ATPS, 1.0–12.0 % and 83–127 % for IL-MAE procedure except for bensulfuron. The recoveries obtained by means of IL-ATPS were higher than that by means of other methods. In addition, the IL-ATPS has the advantages of small amount of IL consumption and small systematic errors, which was applied to the simultaneous determination of the above five target analytes in actual sediment samples.

SU‐E‐T‐257: Output Constancy: Reducing Measurement Variations in a Large Practice Group

Purpose:To standardize output constancy check procedures in a large medical physics practice group covering multiple sites, in order to identify and reduce small systematic errors caused by differences in equipment and the procedures of multiple physicists.Methods:A standardized machine output constancy check for both photons and electrons was instituted within the practice group in 2010. After conducting annual TG‐51 measurements in water and adjusting the linac to deliver 1.00 cGy/MU at Dmax, an acrylic phantom (comparable at all sites) and PTW farmer ion chamber are used to obtain monthly output constancy reference readings. From the collected charge reading, measurements of air pressure and temperature, and chamber Ndw and Pelec, a value we call the Kacrylic factor is determined, relating the chamber reading in acrylic to the dose in water with standard set‐up conditions. This procedure easily allows for multiple equipment combinations to be used at any site. The Kacrylic factors and output results from all sites and machines are logged monthly in a central database and used to monitor trends in calibration and output.Results:The practice group consists of 19 sites, currently with 34 Varian and 8 Elekta linacs (24 Varian and 5 Elekta linacs in 2010). Over the past three years, the standard deviation of Kacrylic factors measured on all machines decreased by 20% for photons and high energy electrons as systematic errors were found and reduced. Low energy electrons showed very little change in the distribution of Kacrylic values. Small errors in linac beam data were found by investigating outlier Kacrylic values.Conclusion:While the use of acrylic phantoms introduces an additional source of error through small differences in depth and effective depth, the new standardized procedure eliminates potential sources of error from using many different phantoms and results in more consistent output constancy measurements.

AN ATLAS OF GALAXY SPECTRAL ENERGY DISTRIBUTIONS FROM THE ULTRAVIOLET TO THE MID-INFRARED

We present an atlas of 129 spectral energy distributions for nearby galaxies, with wavelength coverage spanning from the UV to the mid-infrared. Our atlas spans a broad range of galaxy types, including ellipticals, spirals, merging galaxies, blue compact dwarfs and luminous infrared galaxies. We have combined ground-based optical drift-scan spectrophotometry with infrared spectroscopy from Spitzer and Akari, with gaps in spectral coverage being filled using MAGPHYS spectral energy distribution models. The spectroscopy and models were normalized, constrained and verified with matched-aperture photometry measured from Swift, GALEX, SDSS, 2MASS, Spitzer and WISE images. The availability of 26 photometric bands allowed us to identify and mitigate systematic errors present in the data. Comparison of our spectral energy distributions with other template libraries and the observed colors of galaxies indicates that we have smaller systematic errors than existing atlases, while spanning a broader range of galaxy types. Relative to the prior literature, our atlas will provide improved K-corrections, photometric redshifts and star-formation rate calibrations.

Mercury in compact fluorescent lamps (CFLs): European legislation introduces an avoidable analytical bias

European legislation has set a limit of 5 mg Hg per compact fluorescent lamp (CFL). Compliance with this regulation is tested with a method given in a European law from 2002 ("EU method"). According to the EU method, the arc tube has to be placed inside a fume cupboard and cut into segments. These pieces are collected and washed with HNO3, which is finally analyzed for Hg. In this study, we investigated the losses of Hg via the gas phase, which are ignored by the EU method, using a semiquantitative radiochemical neutron activation analysis (RNAA) technique developed at the TRIGA Mark II reactor in Vienna (Austria). Depending on the product, the losses range as high as approximately 2% at 20 °C. At higher ambient temperatures (hot summer days), the losses may increase by a factor of 4. Quality products generally suffer lower emission via the gas phase than cheap products, which is probably due to amalgam or other techniques that retain the Hg from broken CFLs. In any case, the EU method introduces a small but avoidable systematic error into the analysis and, in contrast to recommended practices, underestimates the Hg content of the CFL in question. Having technical alternatives at hand, we urge European lawmakers to adjust the law accordingly.

Astrometric calibration of the Xuyi Schmidt Telescope Photometric Survey of the Galactic Anti-center (XSTPS-GAC)

We present astrometric calibration of the Xuyi Schmidt Telescope Photometric Survey of the Galactic Anti-center (XSTPS-GAC). XSTPS-GAC is the photometric part of the Digital Sky Survey of the Galactic Anti-center (DSS-GAC), which is a photometric and spectroscopic sky survey, in combination with LAMOST. In order to select an astrometric reference catalog, we made comparisons between the four widely used astrometric catalogs, GSC2.3, USNO-B1.0, UCAC3 and PPMXL. PPMXL shows relatively small systematic errors in positions and more homogeneous proper motion distributions toward the Galactic Anti-center (GAC), and was selected as the reference catalog. Based on the high quality and bright reference stars that were picked out from PPMXL, we performed a 4th-order polynomial fitting in image units, to construct the transformation relation between coordinates used by XSTPS-GAC and standard coordinates, and to simultaneously correct the image distortions in the CCD. Then we applied the derived relation to all sources to obtain their mean celestial coordinates based on the International Celestial Reference System. For bright point sources with r < 17.0 mag, the accuracy of astrometric calibration could reach about 80 mas for each of the g, r, i bands, with systematic errors being less than 10 mas. But for the faint sources at the brightness limit of the survey, which was r ∼ 19.0 mag, the accuracy can still reach 200 mas. After combining all observations, the final weighted average coordinates could reach an accuracy of less than 70 mas for bright stars. For faint stars, the rms residuals of weighted coordinates decrease to ∼ 110 mas. The final combined XSTPS-GAC coordinates show a good consistency with the Sloan Digital Sky Survey.