Tangential Distortion Research Articles

A Novel Approach to Calibrating Multifunctional Binocular Stereovision Sensor

We present a novel multifunctional binocular stereovision sensor for various threedimensional (3D) inspection tasks. It not only avoids the so-called correspondence problem of passive stereo vision, but also possesses the uniform mathematical model. We also propose a novel approach to estimating all the sensor parameters with free-position planar reference object. In this technique, the planar pattern can be moved freely by hand. All the camera intrinsic and extrinsic parameters with coefficient of lens radial and tangential distortion are estimated, and sensor parameters are calibrated based on the 3D measurement model and optimized with the feature point constraint algorithm using the same views in the camera calibration stage. The proposed approach greatly reduces the cost of the calibration equipment, and it is flexible and practical for the vision measurement. It shows that this method has high precision by experiment, and the sensor measured relative error of space length excels 0.3%.

Complete calibration of a structure-uniform stereovision sensor with free-position planar pattern

We present a novel structure-uniform stereovision sensor for variable 3D inspection tasks. In this paper, the mathematical model of the stereovision sensor is established. A flexible approach to estimate all the primitive parameters of the stereovision sensor with free-position planar pattern is proposed. In this technique, without restriction to the moving of the planar reference object, all the camera parameters with coefficient of lens radial and tangential distortion can be readily calibrated, and based on the 3D measurement model of stereovision sensor, the sensor parameters can be optimized with the feature points constraint algorithm simultaneously. The proposed approach greatly reduces the cost of the calibration equipment, and it is flexible and practical for the vision measurement. It shows that this method has high precision by experiment, and the measured relative error of space length excels 0.3%.

Lensing by galaxies in CNOC2 fields

We have observed two blank fields of approximately 30 × 23 arcmin2 using the William Herschel Telescope. The fields have been studied as part of the Canadian Network for Observational Cosmology Field Galaxy Redshift Survey (CNOC2), and spectroscopic redshifts are available for 1125 galaxies in the two fields. We measured the lensing signal caused by large-scale structure, and found that the result is consistent with current, more accurate measurements. We study the galaxy—galaxy lensing signal of three overlapping samples of lenses (one with and two without redshift information), and detect a significant signal in all cases. The estimates for the velocity dispersion of an galaxy agree well for the various samples. The best-fitting singular isothermal sphere model to the ensemble-averaged tangential distortion around the galaxies with redshifts yields a velocity dispersion of σ*= 130+15−17 km s−1, or a circular velocity of V*c= 184+22−25 km s−1 for an L*B galaxy, in good agreement with other studies. We use a maximum-likelihood analysis, where a parametrized mass model is compared with the data, to study the extent of galaxy dark matter haloes. Making use of all available data, we find σ*= 111 ± 12 km s−1 (68.3 per cent confidence, marginalized over the truncation parameter s) for a truncated isothermal sphere model in which all galaxies have the same mass-to-light ratio. The value of the truncation parameter s is not constrained that well, and we find s*= 260+124−73h−1 kpc (68.3 per cent confidence, marginalized over σ*), with a 99.7 per cent confidence lower limit of 80 h−1 kpc. Interestingly, our results provide a 95 per cent confidence upper limit of 556 h−1 kpc. The galaxy—galaxy lensing analysis allows us to estimate the average mass-to-light ratio of the field, which can be used to estimate Ωm. The current result, however, depends strongly on the assumed scaling relation for s.

Weak Gravitational Lensing by a Sample of X‐Ray–luminous Clusters of Galaxies. II. Comparison with Virial Masses

Dynamic velocity dispersion and mass estimates are given for a sample of five X-ray-luminous rich clusters of galaxies at intermediate redshifts (z ~ 0.3) drawn from a sample of 39 clusters for which we have obtained gravitational lens mass estimates. The velocity dispersions are determined from between nine and 20 redshifts measured with the low-dispersion survey spectrograph (LDSS) of the William Herschel Telescope, and virial radii are determined from imaging using the UH8K mosaic CCD camera on the University of Hawaii 2.24 m telescope. Including clusters with velocity dispersions taken from the literature, we have velocity dispersion estimates for 12 clusters in our gravitational lensing sample. For this sample we compare the dynamic velocity dispersion estimates with our estimates of the velocity dispersions made from gravitational lensing by fitting a singular isothermal sphere profile to the observed tangential weak lensing distortion as a function of radius. In all but two clusters, we find a good agreement between the velocity dispersion estimates based on spectroscopy and those based on weak lensing.

HSTlarge-field weak lensing analysis of MS 2053−04: study of the mass distribution and mass-to-light ratio of X-ray luminous clusters at 0.22<z<0.83

We have detected the weak lensing signal induced by the cluster of galaxies MS 2053-04 (z =0.58) from a two-colour mosaic of six Hubble Space Telescope (HST ) WFPC2 images. The best-fitting singular isothermal sphere model to the observed tangential distortion yields an Einstein radius r (E) =6.2+/-1.8 arcsec, which corresponds to a velocity dispersion of (Omega (m) =0.3, Omega(Lambda) =0.0). This result is in good agreement with the observed velocity dispersion of 817+/-80 km s(-1) from cluster members. The observed average rest-frame mass-to-light ratio within a radius aperture is 184+/-56 h (50) M-./L (B.). After correction for luminosity evolution to z =0, this value changes to 291+/-89+/-19 h (50) M-. /L (B .) (where the first error indicates the statistical uncertainty in the measurement of the mass-to-light ratio, and the second error is due to the uncertainty in luminosity evolution). MS 2053 is the third cluster we have studied using mosaics of deep WFPC2 images. For all three clusters we find good agreement between dynamical and weak lensing velocity dispersions, in contrast to weak lensing studies based on single WFPC2 pointings on cluster cores. This result demonstrates the importance of wide-field data. We have compared the ensemble-averaged cluster profile of the clusters in our sample with the predicted Navarro, Frenk & White (NFW) profile, and find that an NFW profile can fit the observed lensing signal well. The best-fitting concentration parameter is found to be (68 per cent confidence) times the predicted value from an open cold dark matter (CDM) model. The observed mass-to-light ratios of the clusters in our sample evolve with redshift, and are inconsistent with a constant, non-evolving, mass-to-light ratio at the 99 per cent confidence level. The evolution is consistent with the results derived from the evolution of the fundamental plane of early-type galaxies. The resulting average mass-to-light ratio for massive clusters at z =0 is found to be 239+/-18+/-9 h (50) M-. /L (B .).

Lens distortion in optically coupled digital x-ray imaging.

The objectives of this research are to analyze geometrical distortions introduced by relay lenses in optically coupled digital x-ray imaging systems and to introduce an algorithm to correct such distortions. The radial and tangential errors introduced by a relay lens in digital x-ray imaging were experimentally measured, using a lens-coupled CCD (charge coupled device) prototype. An algorithm was introduced to correct these distortions. Based on an x-ray image of a standard calibration grid, the algorithm first identified the location of the optical axis, then corrected the radial and tangential distortions using polynomial transformation technique. Lens distortions were classified and both radial and tangential distortions introduced by lenses were corrected using polynomial transformation. For the specific lens-CCD prototype investigated, the mean positional error caused by the relay lens was reduced by the correction algorithm from about eight pixels (0.69 mm) to less than 1.8 pixels (0.15 mm). Our investigation also shows that the fourth order of polynomial for the correction algorithm provided the best correction result. Lens distortions should be considered in position-dependent, quantitative x-ray imaging and such distortions can be minimized in CCD x-ray imaging by appropriate algorithm, as demonstrated in this paper.

Galaxy‐Galaxy Lensing in the Hubble Deep Field: The Halo Tully‐Fisher Relation at Intermediate Redshift

A tangential distortion of background source galaxies around foreground lens galaxies in the Hubble Deep Field is detected at the 99.3% confidence level. An important element of our analysis is the use of photometric redshifts to determine distances of lens and source galaxies and rest-frame B-band luminosities of the lens galaxies. The lens galaxy halos obey a Tully-Fisher relation between halo circular velocity and luminosity; the typical lens galaxy, at a redshift z = 0.6, has a circular velocity of 210 +/-40 km/s at M_B = -18.5, if q_0 = 0.5. Control tests, in which lens and source positions and source ellipticities are randomized, confirm the significance level of the detection quoted above. Furthermore, a marginal signal is also detected from an independent, fainter sample of source galaxies without photometric redshifts. Potential systematic effects, such as contamination by aligned satellite galaxies, the distortion of source shapes by the light of the foreground galaxies, PSF anisotropies, and contributions from mass distributed on the scale of galaxy groups are shown to be negligible. A comparison of our result with the local Tully-Fisher relation indicates that intermediate-redshift galaxies are fainter than local spirals by 1.0 +/- 0.6 B mag at a fixed circular velocity. This is consistent with some spectroscopic studies of the rotation curves of intermediate-redshift galaxies. This result suggests that the strong increase in the global luminosity density with redshift is dominated by evolution in the galaxy number density.

Weak Gravitational Lensing by Galaxies

We report a significant detection of weak, tangential distortion of the images of cosmologically distant, faint galaxies due to gravitational lensing by foreground galaxies. A mean image polarisation of $ =0.011\pm 0.006$ is measured for 3202 pairs of source galaxies with magnitudes $23< r \le 24$ and lens galaxies with magnitudes $20\le r\le 23$. The signal remains strong for lens-source separations $\lo 90''$, consistent with quasi-isothermal galaxy halos extending to large radii ($\go 100h^{-1}$ kpc). Our observations thus provide the first evidence from weak gravitational lensing of large scale dark halos associated with individual galaxies. The observed polarisation is also consistent with the signal expected on the basis of simulations incorporating measured properties of local galaxies and modest extrapolations of the observed redshift distribution of faint galaxies. From the simulations we derive a best-fit halo circular velocity of $V\sim 220$ km/s and characteristic radial extent of $s \go 100h^{-1}$ kpc. Our best-fit halo parameters imply typical masses for the lens galaxies within a radius of $100h^{-1}$ kpc on the order of $1.0^{+1.1}_{-0.7}\times 10^{12}h^{-1} M_\odot$, in good agreement with recent dynamical estimates of the masses of local spiral galaxies. This is particularly encouraging as the lensing and dynamical mass estimators rely on different sets of assumptions. Contamination of the gravitational lensing signal by a population of tidally distorted satellite galaxies can be ruled out with reasonable confidence. The prospects for corroborating and improving this measurement seem good, especially using deep HST archival data.

Lensing from the light-traces-mass map of MS 1224+20

The MS1224+20 cluster of galaxies is a high luminosity X-ray source at z=0.325. To compare the lensing mass to the virial mass we have completed a uniform, high precision redshift survey over a field of $7\arcm\times9\arcm$, obtaining 75 redshifts. The velocity dispersion of 30 cluster galaxies is $775$ \kms and the projected harmonic radius is 0.32 \hmpc. The virial mass is $2.1\times 10^{14} h^{-1} \msun$. Correcting for faint cluster galaxies without redshifts and allowing for a modest evolution in the galaxy luminosity function gives a current epoch mass-to-light ratio $M/L_V(0)=255h \msun/\lsun$. The same field contains a $z=0.225$ cluster with $\sigma_v\simeq 500$ \kms, and a group at $z=0.412$ with $\sigma_v\simeq 400$ \kms. The clusters' gravitational field induces image ellipticities that are calculated from the light-traces-mass density distribution and compared to the observed average tangential distortions from Fahlman \et (1994). Between 1.5 and 3 virial radii, the observed lensing distortions are $4\pm2$ times stronger than the light-traces-mass model and the virial M/L predict.

Dual camera calibration for 3-D machine vision metrology

A dual-camera calibration algorithm and procedure are presented. The algorithm is based on the method of direct linear transformation and results in an overdetermined set of linear algebraic equations that can be utilized in determining the coordinate position of some identifiable feature in a scene relative to any set of orthogonal axes. Both radial and tangential lens distortions are considered in a second step of the calibration algorithm to improve the accuracy of the position sensor. Since the algorithm incorporates both types of lens distortions, it can be applied to a camera with any combinations of lenses, e.g. a lens system with a supplementary lens for close-up observations. >

The development of peripheral acuity

This paper proposes a high-accuracy distortion correction method for optical imaging distortion mapping and computational image predistortion. Due to the establishment of the predistortion is based on the distortion evaluation in the common optical design software CODE V, it can be used in the broad field of optical imaging system. Two distortion correction methods considering radial and tangential distortion rates which defined by optical design are introduced to perform distortion correction, and the forward and inverse image warping interpolation methods are adopted, separately. Simulations are conducted to verify the effectiveness in correcting complex distortion for freeform off-axis optical system. Furthermore, we implement a distortion correction experiment for an augmented reality head-mounted display that suffers from an asymmetric distortion with the maximum tangential distortion over 7%. For the first method, fast and high-accuracy image warping is achieved, and the RMS error of the approximation predistortion image is less than 1 pixel. Meanwhile, the RMS errors of the corrected imaging points are approximately 1.93 pixels vertically and 2.16 pixels horizontally when using a 5-megapixel camera. The second method considers the additional influence of the actual machining and assembly errors of the optical system, and the RMS errors of 0.89 pixels vertically and 0.85 pixels horizontally are achieved.

A method of presenting full-field images with minimal distortion

A method of presenting an image covering the total monocular visual field is described. The geometry of distortion in this full-field image is analysed. Computations demonstrate that local tangential and radial distortion can be minimised by selection of the surface shape, projection and viewing distances. Image luminance distribution can be computed and appears tolerable for most experimental purposes. A unidirectional grating can be presented with the local magnification varying by less than 3% from the central value over the total monocular visual field. For projection of images or gratings with multiple orientations distortion of up to + or − 25% may need to be tolerated. Such systems could have many applications in vision research where unrestricted fields are necessary. A miniature prototype diffusing surface has been generated to produce a full-field grating image with tolerable distortion. An experiment is described to demonstrate the feasibility of plotting a full-field contrast sensitivity function.

Improvement of the optical properties of an aerial lens type

This paper considers the improvement of the optical properties of the aerial wide-angle lenses used in Wild RC-8 and RC-10 cameras over a period of 20 years. The lens types 15Ag, 15UAg, 15UAg II and 15/4 UAg are compared. All determinations were made with the horizontal goniometer of the Helsinki University of Technology (HUT) between 1975 and 1979. The prototype of the 15/4 UAg lens was in the HUT for measurements in 1977. The characteristics then determined were the radial distortion and its asymmetry, calibrated focal length, tangential distortion, lateral colour, resolving power and MTF. The image quality of the first three lenses mentioned was about the same, but the 15/4 UAg was considerably better.

Iristorsion bei akutem Primärglaukom*

In acute primary glaucoma tangential distortion of the iris in the pupillary zones are often seen. The reason for these iris changes has not yet been satisfactorily explained.

Determination of radial and tangential distortion of reseau cameras with the Helsinki University of Technology horizontal goniometer

The radial distortion and its asymmetry, the tangential distortion, the mutual positions of the fiducial centre, principal point of autocollimation and point of best symmetry, and the calibrated focal length have been determined from two Canadian réseau cameras, Zeiss RMK AR 15/23 No. 21197 and Wild RC-8 15U Ag. R 10 No. 107 with a horizontal goniometer in the Helsinki University of Technology in 1974. The radial distortion was determined from the two diagonals and two diameters parallel to the frame sides in all in 124 points for both cameras. The tangential distortion was calculated from bending observations of 12 diameters of the frame plane. In the Zeiss réseau camera there was a great asymmetry in radial distortion (PPA-PBS was 45 μm) and its maximum azimuth in the frame plane was the same as the 0-axis of tangential distortion, which had the maximum values of 14 μm. In the Wild camera, the asymmetry of the radial distortion was very small and the values measured for the tangential distortion were below 1 μm. Some results have also been compared with those measured by Carl Zeiss Oberkochen and Wild Heerburg. In all 10 wide-angle aerial cameras (6 from Carl Zeiss Oberkochen and 4 from Wild Heerbrugg) were measured with the Helsinki University of Technology horizontal goniometer in 1974–1975.

Photogrammetric calibration of a scanning electron microscope

Since the invention of the SEM (Scanning Electron Microscope), researchers have used 2-dimensional measurements on micrographs. Stereo-pairs of micrographs are used to some extent for limited 3-dimensional analyses. This is done primarily for qualitative analyses. With the growing need for serious quantitative investigations, more attention is presently drawn to statistically sound metric calibration of the SEM. A procedure of analytical calibration of SEM developed in the Ohio State University department of Geodetic Science is discussed. The concept of system calibration is used. This procedure used advanced photogrammetric self-calibration techniques to solve for the tilt and rotation angles, also magnification and systematic distortion parameters which define the trajectory of light rays and electron beams in the SEM system. Utilizing multiple micrographs made of a diffraction-granting replica calibration standard tilted at angles up to 45°, with four 90° differential rotation angles for each tilt, hundreds of photogrammetric comparator measurements made on each micrograph were combined in a least-squares adjustment, which determines the calibration parameters and their variances and covariances. The sample test SEM (Materials Analysis Co. Model 700) was calibrated separately for magnifications of 2000 ×, 5000 ×, and 10,000 ×. In addition to an affine deformation plus radial and tangential distortions, as found in other photographic systems, a new “spiral” distortion was mathematically modelled which accounted for more than 300 μm of systematic distortion at photo scale for each image throughout the format of the micrographs.

THE CALIBRATION OF AERIAL SURVEY CAMERAS

AbstractTwo experimental procedures for aerial survey camera calibration using respectively a Wild TA theodolite and a modified Cooke, Trough ton and Simms geodetic theodolite are described. The procedures determine radial distortion only; tangential distortion is assumed to be negligible. Details of a graphical method of computing the results are given in an appendix.

Physical Limitations of Photogrammetry

Several physical sources of errors have been neglected in photogrammetry because of their negligible effects compared to the required accuracy, for example, the minimum size of sensitized particle of film, tangential distortion of lens, irregular film shrinkage, image movement due to the motion of aircraftetc.But several of them should not be ignored if the higher accuracy is considered, and some of them often produce larger errors than commonly believed.They shall be pointed out, criticized, and estimated about their effects and correlations, some of them such as colour abberation, and image movement, result the error greater than 30cm, which can not be reduced by simple change of photo-scale.As the conclusion, reduction of errors beyond 30cm can not be obtained for any photoscale, unless necessary physical considerations are given to those physicalphenomena.

A New Catalogue of Hα Emission Objects in the Southern Hemisphere.

view Abstract Citations (4) References Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS A New Catalogue of Hα Emission Objects in the Southern Hemisphere. Wray, James D. Abstract Henize at the Lamont Hussey Observatory have been searched for Ha emission objects, S stars, and carbon stars. A previous search by Henize of medium-exposure plates covering the entire southern hemisphere to +10.5 m~ at a dispersion of 450 A/mm at Ha has yielded 1100 stars tentatively classified as early-type Ha emission stars. The recent search by the author of long-exposure plates covering the southern Milky Way from 240~100 galactic longitude to + 13.0 m~ has revealed an additional 800 probable early-type emission stars, and a few new objects of type P, C, and S. Coordinates (a, ~) accurate to H*~1511 p.e. have been computed for all obj ects found on the long exposure plates by means of a 12 constant-plate reduction theory modified to account for tangential distortion introduced by the objective prism. All standard stars were of spectral type A0, providing a well-defined absorption line at Ha for measurement. Plate measures were obtained on a fully digitized Mann 621 comparator with punched card output. Use of a digital x,y plotter for identification of comparison stars, evaluation of plate reduction residuals, and measure data confirmation greatly facilitated the data reduction. A preliminary analysis of the surface distribution of southern hemisphere early-type emission stars reveals the strong concentration of the galactic plane and the irregular distribution in longitude similar in nature to that found in the northern hemisphere by Merrill. The relatively high surface concentration in the Carina-Crux region previously examined by Bok is fully confirmed by this survey. Publication: The Astronomical Journal Pub Date: 1966 DOI: 10.1086/110160 Bibcode: 1966AJ.....71S.403W full text sources ADS |

High-Precision, Strain-Free Mounting of Large Lens Elements

This paper explains how the eight lens elements of a 600 mm, f/2.0 ballistic camera are mounted and retained in almost perfect alignment. The total weight of the glass in this lens is 107 kg, the largest element weighing 21.1 kg. The lens is aligned to less than 3 μ of tangential distortion and the elements are supported in the mount in such a way that they are completely free of any strains. The near perfect alignment of the lens is maintained by soldering the lens elements into the supporting cells.