Magnification Correction Research Articles

Influence of Correction of Ocular Magnification on Spectral-Domain OCT Retinal Nerve Fiber Layer Measurement Variability and Performance

To analyze the influence of ocular magnification on the peripapillary retinal nerve fiber layer (RNFL) thickness measurement and its performance as acquired with spectral-domain optical coherence tomography (SD-OCT). Spectral domain OCT measurements from 108 normal eyes (59 subjects) and 72 glaucoma eyes (58 patients) were exported and custom software was used to correct RNFL measurements for ocular magnification. Retinal nerve fiber layer prediction limits in normal subjects, structure-function relationships, and RNFL performance for detection of glaucoma were compared before and after correction for ocular magnification (Bennett's formula). Association of disc area with cross-sectional RNFL area was explored. The median (interquartile range, [IQR]) visual field mean deviation and scaling factor were 0 (-0.85 to 0.73) dB and 0.96 (0.93-1.00) in normal eyes and -4.0 (-6.0 to -2.2) dB and 0.99 (0.95-1.03) in the glaucoma group (P < 0.001 and P = 0.003, respectively; average correction 3%). Correction for ocular magnification caused a reversal of the negative relationship between the cross-sectional RNFL area and axial length (slope = -0.022 mm(2)/mm, P = 0.015 vs. = 0.22 mm(2)/mm, P = 0.007). However, such correction did not change RNFL prediction limits (except in superior and nasal quadrants), improve global or regional structure-function relationships, or enhance the ability of RNFL measurements to discriminate glaucoma from normal eyes (P > 0.05). The cross-sectional RNFL area was not correlated with optic disc area (P = 0.325). Correction of RNFL measurements for ocular magnification did not improve prediction limits in normal subjects or enhance the performance of SD-OCT in this group of eyes in which the axial length did not deviate significantly from average values. The cross-sectional area of the RNFL was not related to the optic disc area.

Radiographic measurements of front feet of the sound Akhal-Teke horses

BACKGROUND: The Akhal-Teke is an ancient horse originat- ing from Asia where it was used by nomadic tribes and used as a warhorse. Lameness examinations require proper interpretation of clinical and radiographic findings. Therefore, understanding of normal radiographic findings of the foot is necessary. Although the radiographic appearance of the normal foot must be understood to recognize abnormalities ,there are no studies examining the normal hoof and digital soft tissues in Akhal-Teke horses. OBJECTIVES:The purpose of the study reported here was to determine a normal radiographic appearance and morpho- metry of the distal phalanx and its related soft tissue in mature Akhal-Teke racehorses without any clinical signs of lameness and foot problems. METHODS: Radiography of the distal phalanx and associated soft-tissue structures of the front feet of 10 healthy pure Akhal-Teke horses were performed to determine normal radiographic appearance and morphometry. Lateromedial radiographic views of each front distal phalanx were used to measure important distances, angles and ratios of the hoof wall. All the measurements from lateromedial radiographs were multiplied by the magnification correction factor to gain the actual distances. RESULTS: Mean ± SD thickness of the soft tissues dorsal to the middle aspect of distal phalanx was 18.3 ± 1.22 mm. There was not any significant difference between left and right digits for any radiographic determination. CONCLUSIONS: This study introduced S-Founder and CF-Founder as important criteria in evaluating laminitis and sinking of P3.

Spatial Light Modulator Microscopy

The use of spatial light modulators (SLMs) for two-photon laser microscopy is described. SLM phase modulation can be used to generate nearly any spatiotemporal pattern of light, enabling simultaneous illumination of any number of selected regions of interest. We take advantage of this flexibility to perform fast two-photon imaging or uncaging experiments on dendritic spines and neocortical neurons. By operating in the spatial Fourier plane, an SLM can effectively mimic any arbitrary optical transfer function and thus replace, in software, many of the functions provided by hardware in standard microscopes, such as focusing, magnification, and aberration correction.

Development of a Rat Schematic Eye From In Vivo Biometry and the Correction of Lateral Magnification in SD-OCT Imaging

Optical magnification in optical coherence tomography (OCT) depends on ocular biometric parameters (e.g., axial length). Biometric differences between eyes will influence scan location. A schematic model eye was developed to compensate for lateral magnification in OCT images of the healthy rat. Spectral-domain optical coherence tomography images were acquired in 19 eyes of 19 brown Norway rats. Images were scaled using the OCT instrument's built-in scaling function and by calculating the micron per degree from schematic model eyes developed from in vivo biometry (immersion A-scan and videokeratometry). Mean total retinal thickness was measured 500 μm away from the optic nerve head and optic nerve head diameter was measured. Corneal curvature, lens thickness, and axial length were modified to calculate their effects on OCT scan location and total retinal thickness. Mean total retinal thickness increased by 21 μm and the SD doubles when images were scaled with the Built-in scaling (222 ± 13 μm) compared with scaling with individual biometric parameters (201 ± 6 μm). Optic nerve head diameter was three times larger when images were scaled with the Built-in scaling (925 ± 97 μm) than the individual biometric parameters (300 ± 27 μm). Assuming no other change in biometric parameters, total retinal thickness would decrease by 37 μm for every millimeter increase in anterior chamber depth due to changes in ocular lateral magnification and associated change in scan location. Scaling SD-OCT images with schematic model eyes derived from individual biometric data is important. This approach produces estimates of retinal thickness and optic nerve head size that are in good agreement with previously reported measurements.

Influence of Axial Length on Peripapillary Retinal Nerve Fiber Layer Thickness in Children: A Study by RTVue Spectral-Domain Optical Coherence Tomography

Purpose: To evaluate the influence of axial length on peripapillary retinal nerve fiber layer (RNFL) thickness in myopic, hyperopic and emmetropic children eyes by RTVue optical coherence tomography (OCT).Methods: One hundred twenty eyes of 120 children including 40 myopic, 40 emmetropic and 40 hyperopic eyes were enrolled in the study. Peripapillary RNFL thickness measurements were performed using spectral-domain RTVue OCT (Optovue, Fremont, CA). RNFL thickness parameters were obtained from all octametric sections: upper temporal (TU), superotemporal (ST), superonasal (SN), upper nasal (NU), lower nasal (NL), inferonasal (IN), inferotemporal (IT) and lower temporal (TL). Spherical equivalent refractive error was determined via cycloplegic auto-refraction (Topcon, Tokyo, Japan). The axial length was measured using IOLMaster (Carl Zeiss MEDITEC). Littmann formula was used for correction of axial length-related ocular magnification effect.Results: Peripapillary RNFL thicknesses were significantly different among the three groups in all sectors except for NU and IT sectors. RNFL thicknesses in all sectors except for TU and TL sectors had significant negative correlations with axial length. However, these differences (excluding TU and TL sectors) and correlations disappeared after correction of magnification effect.Conclusion: In conclusion, axial length influences peripapillary RNFL thickness as measured by RTVue OCT. However, this appears to be due to the ocular magnification effects associated with axial length and can be corrected for with the application of the Littman formula.

Acrylic Customized X-Ray Positioning Stent for Prospective Bone Level Analysis in Long-Term Clinical Implant Studies

Objectives: This paper describes a technique to produce individualized X-ray positioning devices for intraoral digital imaging of dental implants with long-term stability. Materials and Methods: An X-ray positioning device was built for Gendex ® Visualix ® eHD sensor, using the Dentsply rinn XCP-DS ® system individualized by the incorporation of the bite piece within an acrylic stent to perform successive standardized radiographs to 16 patients. X-ray tube stabilization was achieved with polivinylsiloxane. Series of 3 radiographs were taken to each patient in different moments. Specific linear measurements as the implant diameter (mesio-distal width) and the height between consecutive threads (thread pitch) were made to all radiographs to determine the reproducibility and accuracy of the procedure. Results: The intraclass correlation coefficient for the mesio-distal width was 0.964 [(0.920 - 0.986) 95% CI] (p < 0.01) and 0.990 [(0.976 - 0.996) 95% CI] (p < 0.01) for the thread pitch. Bland-Altman plots comparing implant diameter showed mean bias of 0.01 ± 0.01975, 0.01 ± 0.02243 and 0.0006 ± 0.025 for groups 1 - 2, 1 - 3 and 2 - 3 respectively. Mean bias of 0.0024 ± 0.00552, 0.0027 ± 0.00552 and 0.0003 ± 0.0012 was found for the thread pitch analysis of groups 1 - 2, 1 - 3 and 2 - 3. One sample t-test for trueness of mesio-distal width, thread pitch and ratio showed mean difference of 0.00156 mm for the test value of 3.3 (p = 0.9), −0.00026 mm for 0.8 (p = 0.96) and 0.0124 for 4.125 (p = 0.72), respectively, after the application of a magnification correction factor. Conclusion: The device produced reproducible images in different moments and was suitable for comparative clinical examinations of marginal bone as it was convenient to perform reliable linear measurements.

Optic Disc Imaging with Spectral-Domain Optical Coherence Tomography: Variability and Agreement Study with Heidelberg Retinal Tomograph

To evaluate the agreement of optic disc measurements obtained with the Cirrus high-density optical coherence tomography (HD-OCT) and the Heidelberg retina tomograph (HRT) and compare the intervisit, test-retest variability between the instruments. Prospective, cross-sectional study. Two hundred seven subjects (109 glaucoma and 98 normal subjects). One eye from each individual was selected randomly for optic disc imaging by the Cirrus HD-OCT and the HRT. Areas of the optic disc and the cup, cup volume, vertical cup-to-disc ratio and cup-to-disc area ratio were compared between the instruments. The OCT measurements were corrected for ocular magnification using the Littman's formula. The measurement agreement was evaluated with the Bland-Altman plots. The intervisit test-retest variability was examined in 17 randomly selected glaucoma patients who underwent optic disc imaging weekly for 8 consecutive weeks. The intraclass correlation coefficients (ICC) and the reproducibility coefficients of the optic disc parameters were computed. Measurement agreement, reproducibility coefficients, and ICCs of optic disc parameters. The OCT measured smaller optic disc and rim areas and greater cup volume, vertical cup-to-disc ratio and cup-to-disc area ratio than the HRT did (all with P<0.001). There were proportional biases in the Bland-Altman plots between OCT and HRT optic disc measurements except for rim area and cup-to-disc area ratio. The 95% limits of agreement of rim area ranged between -0.28 and 0.88 mm(2) before, and between -0.22 and 0.92 mm(2) after correction for ocular magnification. Both OCT and HRT showed high test-retest reproducibility with ICCs ≥ 0.921. Although the reproducibility coefficient of OCT rim area (0.093 mm(2); 95% confidence interval [CI], 0.081-0.105 mm(2)) was significantly smaller than that of the HRT (0.186 mm(2); 95% CI, 0.163-0.210 mm(2); P = .018), there were no differences in the ICCs between the instruments. Optic disc assessment by spectral-domain OCT and confocal scanning laser ophthalmoscopy demonstrates poor agreement but similarly low test-retest variability. The source of their disagreement and its effects on the detection of progression require further study.

Computerized scheme for evaluating mammographic phantom images

The authors developed a computer algorithm to automatically evaluate images of the American College of Radiology (ACR) mammography accreditation phantom. The developed algorithm consist of the edge detection of wax insert, nonuniformity correction of background, and correction for magnification and also calculate the cross-correlation coefficient by image matching technique. The algorithm additionally evaluates target shape for fibers, target contrast for speck groups, and target circularity for masses. To obtain an ideal template image without noise and spatial resolution loss, the wax insert containing the embedded test pattern was extracted from the phantom and radiographed. Two template images and ten test phantom images were prepared for this study. The results of evaluation using the algorithm outputs were compared with the averaged results of observer studies by six skilled observers. In comparing the results from the algorithm outputs with the results of observers, the authors found that the computer outputs were well correlated with the evaluations by observers, and they indicate the quality of the phantom image. The correlation coefficients between results of observer studies and two outputs of computer algorithm, i.e., the cross-correlation coefficient by template matching and indices of target shape for fibers, were 0.89 (95% confidence interval, 0.82-0.93; hereinafter the same) and 0.85 (0.76-0.91). The correlation coefficients between observer's results and two outputs: the cross-correlation coefficient and indices of target contrast for speck groups, were 0.83 (0.79-0.86) and 0.85 (0.81-0.88) and between observer's results and two outputs: the cross-correlation coefficient and indices of target circularity for masses, were 0.90 (0.84-0.94) and 0.87 (0.77-0.92). Image evaluation using the ACR phantom is indispensable in quality control of a mammography system. The proposed algorithm is useful for quality control and image evaluation of mammography units.

Tip Apex Distance: a useful method to assess extra-capsular neck of femur fixation?

Introduction: Fixation of trochanteric femoral neck fractures can be problematic. The tip apex distance (TAD) is a simple measurement that predicts screw cut-out in the femoral head from fractures treated with a fixed angle sliding hip screw device. By assessing whether the measurements in our centre were comparable to published results, we wanted to assess our proficiency in fixing these injuries as well as the general usefulness of this measurement in day to day practice. Methods: A retrospective review was conducted of 102 consecutively treated trochanteric fractures over a 12 month period, with 11 patients excluded. Three observers (n=3) used a standardised method to measure the TAD (from 2 orthogonal projections with a correction for magnification). The stability of the fracture patterns with the accuracy of reduction were measured according to published criteria. Results: 91 fractures were sustained in 90 patients, with one patient being treated for bilateral hip fractures. The mean tip apex distance was 19.06 mm ±0.77 mm (±95% CI). Assessing the inter-observer variability, the standard deviation between the 3 observers was 1.99mm, equivalent to 10% of the mean TAD. 12 out of 91 sliding hip screw devices (13.1%) had a TAD greater then 25mm, predictive of a higher extrusion rate. Conclusions: Measurement of the TAD can provide a reliable method to examine the adequacy of screw placement in the femoral head. Our results compare favourably to those published and we have found a similar level of inter-observer variability, confirming the usefulness of this measurement in assessing the quality of fixation and its reproducibility. By determining which patients have an increased risk of failure of fixation by screw cut-out we have been able to offer targeted surveillance rather than routinely following up all patients: bringing back those with a high TAD for x-ray follow up.

Detection of an ultrabright submillimetre galaxy in the Subaru/XMM-Newton Deep Field using AzTEC/ASTE

We report the detection of an extremely bright ($\sim$37 mJy at 1100 $\mu$m and $\sim$91 mJy at 880 $\mu$m) submillimeter galaxy (SMG), AzTEC-ASTE-SXDF1100.001 (hereafter referred to as SXDF1100.001 or Orochi), discovered in 1100 $\mu$m observations of the Subaru/XMM-Newton Deep Field using AzTEC on ASTE. Subsequent CARMA 1300 $\mu$m and SMA 880 $\mu$m observations successfully pinpoint the location of Orochi and suggest that it has two components, one extended (FWHM of $\sim$ 4$^{\prime\prime}$) and one compact (unresolved). Z-Spec on CSO has also been used to obtain a wide band spectrum from 190 to 308 GHz, although no significant emission/absorption lines are found. The derived upper limit to the line-to-continuum flux ratio is 0.1--0.3 (2 $\sigma$) across the Z-Spec band. Based on the analysis of the derived spectral energy distribution from optical to radio wavelengths of possible counterparts near the SMA/CARMA peak position, we suggest that Orochi is a lensed, optically dark SMG lying at $z \sim 3.4$ behind a foreground, optically visible (but red) galaxy at $z \sim 1.4$. The deduced apparent (i.e., no correction for magnification) infrared luminosity ($L_{\rm IR}$) and star formation rate (SFR) are $6 \times 10^{13}$ $L_{\odot}$ and 11000 $M_{\odot}$ yr$^{-1}$, respectively, assuming that the $L_{\rm IR}$ is dominated by star formation. These values suggest that Orochi will consume its gas reservoir within a short time scale ($3 \times 10^{7}$ yr), which is indeed comparable to those in extreme starbursts like the centres of local ULIRGs.

Subjective visual acuity with simulated defocus

Artificial degradation of vision by inducing dioptric blur is frequently used for evaluating diagnostic equipment. However, the use of lenses is prone to errors as it is adversely affected by eyelid squinting, pupil size, and imprecise lens position. The alternative is a degradation of the stimuli themselves based on a Fourier-optical mathematical model. With this, however, perceptual effects such as 'simultaneous blur' induced by the surround may affect acuity. We tested whether both methods, lens induced defocus and mathematical stimulus degradation, yield concordant results. We compared both methods in normal subjects, measuring Landolt C acuity at five different levels of defocus from 0 to 8 dioptres. The pupil size was determined individually, chromatic aberrations were avoided by using a monochromatic approach, and a correction for spectacle magnification was included. Otherwise, the experimental design was kept deliberately simple to remain comparable to typical applications. With the major sources of error associated with the use of lenses being accounted for, both methods yield similar mean results with differences in acuity ranging from <0.001 to 0.054 logMAR (0.2-13%). Using mathematically simulated defocus is a viable option if both reasonable accuracy and ease of use are required. The fact that the application of the mathematical model only blurs the stimulus itself, but not the surrounding environment, does not appear to be detrimental to the method.

A LABOCA survey of submillimeter galaxies behind galaxy clusters

Context: Submillimeter galaxies are a population of dusty star-forming galaxies at high redshift. Measuring their properties will help relate them to other types of galaxies, both at high and low redshift. This is needed in order to understand the formation and evolution of galaxies. Aims: We use gravitational lensing by galaxy clusters to probe the faint and abundant submillimeter galaxy population down to a lower flux density level than what can be achieved in blank-field observations. Methods: We use the LABOCA bolometer camera on the APEX telescope to observe five cluster of galaxies at a wavelength of 870 micron. The final maps have an angular resolution of 27.5 arcsec and a point source noise level of 1.2-2.2 mJy. We model the mass distribution in the clusters as superpositions of spherical NFW halos and derive magnification maps that we use to calculate intrinsic flux densities as well as area-weighted number counts. We also use the positions of Spitzer MIPS 24 micron sources in four of the fields for a stacking analysis. Results: We detected 37 submm sources, out of which 14 have not been previously reported. One source has a sub-mJy intrinsic flux density. The derived number counts are consistent with previous results, after correction for gravitational magnification and completeness levels. The stacking analysis reveals an intrinsic 870 micron signal of 390 \pm 27 microJy at 14.5 sigma significance. We study the S_{24 micron} - S_{870 micron} relation by stacking on subsamples of the 24 micron sources and find a linear relation at S_{24 micron} < 300 microJy, followed by a flattening at higher 24 micron flux densities. The signal from the significantly detected sources in the maps accounts for 13% of the Extragalactic Background Light discovered by COBE, and the stacked signal accounts for 11%.

From 2D to 3D: an algorithm to derive normal values for 3-dimensional computerized assessment

To test the accuracy of a mathematical model (algorithm) that corrects measurements made on conventional lateral head films to corresponding dimensions observed in a cone beam computed tomography (CBCT) scan in human subjects. Thirteen subjects had lateral cephalograms taken with a conventional cephalometric machine as well as a CBCT scan. Measurements of midface length, mandibular length, and lower anterior face height (LAFH) from both examinations were calculated. Two other groups of measurements were derived mathematically from the dimensions directly quantified on the lateral cephalogram: the magnification correction group and the algorithm correction group. The data were analyzed statistically, using repeated measures analysis of variance (ANOVA). All measurements from the lateral cephalogram were significantly different from the corresponding measurements derived from the CBCT. Simply taking into account the image magnification did not correct the 2-dimensional (2D) linear measurement obtained from a conventional cephalogram into a 3-dimensional (3D) linear measurement made on a CBCT scan, unless the structures from which the distance will be measured are located on the midsagittal plane. When the algorithm was used to correct the 2D measurements, however, there were no statistically significant differences between the CBCT group and the algorithm group. Using the mathematical formula presented herein, 2D cephalometric measurements from landmarks both on and off the midsagittal plane can be corrected into a 3D CBCT measurement with accuracy. By applying this algorithm to other existing cephalometric longitudinal growth studies, control groups and standards for CBCT images could be derived without exposing untreated subjects to radiation.

LBT/LUCIFER OBSERVATIONS OF THEz∼ 2 LENSED GALAXY J0900+2234

We present rest-frame optical images and spectra of the gravitationally lensed, star-forming galaxy J0900+2234 (z=2.03). The observations were performed with the newly commissioned LUCIFER1 near-infrared instrument mounted on the Large Binocular Telescope (LBT). We fit lens models to the rest-frame optical images and find the galaxy has an intrinsic effective radius of 7.4 kpc with a lens magnification factor of about 5 for the A and B components. We also discovered a new arc belonging to another lensed high-z source galaxy, which makes this lens system a potential double Einstein ring system. Using the high S/N rest-frame optical spectra covering H+K band, we detected Hbeta, OIII, Halpha, NII and SII emission lines. Detailed physical properties of this high-z galaxy were derived. The extinction towards the ionized HII regions (E_g(B-V)) is computed from the flux ratio of Halpha and Hbeta and appears to be much higher than that towards stellar continuum (E_s(B-V)), derived from the optical and NIR broad band photometry fitting. The metallicity was estimated using N2 and O3N2 indices. It is in the range of 1/5-1/3 solar abundance, which is much lower than the typical z~2 star-forming galaxies. From the flux ratio of SII 6717 and 6732, we found that the electron number density of the HII regions in the high-z galaxy were >1000 cm^-3, consistent with other z~2 galaxies but much higher than that in local HII regions. The star-formation rate was estimated via the Halpha luminosity, after correction for the lens magnification, to be about 365\pm69 Msun/yr. Combining the FWHM of Halpha emission lines and the half-light radius, we found the dynamical mass of the lensed galaxy is 5.8\pm0.9x10^10 Msun. The gas mass is 5.1\pm1.1x10^10~Msun from the H\alpha flux surface density by using global Kennicutt-Schmidt Law, indicating a very high gas fraction of 0.79\pm0.19 in J0900+2234.

Spatial relation between a rigid (digital) intraoral X-ray receptor and longitudinal axes of maxillary teeth

The purpose of this study was to quantify the existing (inevitable) angle which in intraoral radiology appears between tooth length axis and receptor caused by the anatomical situation. Especially in the upper jaw, due to its arched anatomy, a true "paralleling technique" is not achievable. The angulation necessarily causes distortion and a foreshortening of the image; hence, the foreshortened image leads to misinterpretations in diagnostics. We investigated the effects of the realistic angulation on these image deteriorating factors. Two hundred ninety-four plaster models of the upper jaw were collected, and the angles between a dummy receptor and the axes of the central incisor or the first molar were measured. For evaluation, a rigid dummy of an intraoral charge-coupled device (CCD) receptor (30 mm × 40 mm) was used. The mean angulation evaluated for central incisors was 36.7° (range 19-56°) and for first molars 42.5° (range 26-56°). This leads to a foreshortening of the tooth ranging from 5.4% to 44.1% in the image, when magnification is neglected. Large angles of up to 56°, in both incisor and molar region, result in a relevant underestimation of true tooth length up to 44%. It is important to note that this error cannot be simply corrected by means of local magnification correction. Techniques should be developed that allow for automated assessment of the effective angle to provide information for distortion correction.

Author's reply to comments on Shyam et al.: Leg lengthening by distraction osteogenesis using the Ilizarov apparatus: a novel concept of tibia callus subsidence and its influencing factors

We really appreciate the thoughtful and detailed comments by the readers in referencing our paper on subsidence in tibia lengthening [1]. In almost all our cases we used the 160 ring. Also, as seen in the figure in our article the patient is a child (as are most of our patients), and thus the first assumption in the comment is erroneous (although as stated below this will have minimal effect on the magnification). Also, as per the comments, for a 180 ring the plate bone distance will be 12.3 and not 13.3, and thus the magnification will be 11.9% (for standard plate focus distance of 115 cm as calculated from formula given below) and not 14.4% as mentioned. Beginning with these two comments on erroneous assumptions made by the readers, we need to take into account here that the subsidence is the difference between two readings. Thus, these magnifications are also subtracted to give us the final magnification of the subsidence fragment which, according to the authors' calculations, will be 14.4% minus 5.8%, which is 8.6%. If we consider the subsidence of mean 1.19 ± 0.78 cm (range 0.4–3.2 cm) to which if the magnification correction of 8.6% is applied (keeping in mind that if the distance is corrected from 14.4 to 11.9 as shown above, then this correction will be 6.1%), it becomes 1.09 ± 0.718 (range 0.36–2.94). Thus, although the reported figures definitely are erroneous in the original paper, we do not think they are completely off the mark. Now we will consider the more accurate assumption in terms of using a 160 ring as was the case in our series. Although the comments have used the centre of tibia as the reference point, we would like to point out that the distracted fragment is rarely at the centre. In our cases the position of the limb in the ring was determined by the posterior clearance of the calf; in fact, this is the point that dictates the use of various ring sizes. If we consider that 5.5 cm is the bone plate distance without ring, we can predict the bone plate distance with the ring. In the ring, the posterior clearance was ideally taken as 2 cm while the ring is 1.5 cm across; this sums to 9 cm bone plate distance [5.5 + 2 + 1.5]. Hence, the size of the ring will have minimal effect on the bone plate distance, which will remain constant irrespective of the ring used (as the breadth of the ring remains constant). To validate this point we made actual measurements in our current patients with similar profile and the distance from calf to the plate was indeed an average of 4.2 cm. Thus, from the examples, the two distances would be 5.5 and 9 cm with corresponding magnification calculated by the formula in Fig. 1 [2]. The standard film focus distance was 115 cm (1150 mm). Fig. 1 Formula for calculation of magnification [2] In this formula the standard film focus distance was taken as 1000 mm while in our case it was 1150 mm. Therefore, when the distance is 55 mm, magnification = 1150/1095 = 1.0502 (i.e. magnification of 5.02%) and when the distance is 90 mm, magnification = 1150/1160 = 1.084 (i.e. magnification of 8.4%). Thus, the respective magnifications would be 5.02% and 8.4% with final magnification of 3.36%, which is well within the 5% alpha error rate (p value 0.05). Once again, although there exists a measurement error in our paper, this was small and well within the acceptable error rates. Apart from mathematical calculations, we are required here to make an important point. Our paper was based on our observations that at two- to three-years follow-up, a few of our patients who underwent bilateral lengthening reported significant difficulties in walking barefoot (without the footwear correction) even though all patients were quite satisfied with the overall results. These patients also had a difference of more than 1 cm between the two lengthened legs, which were originally lengthened by the same amount. This led us to consider the presence of tibial subsidence as a factor, and we performed the investigation in question to study whether such a subsidence actually occurs and to what extent. With our measurements we did find differences in the follow-up lengthening from the final distraction in almost all patients and we tried to quantify this difference (although with error!). In effect, the aim of the paper was to introduce the concept of tibial subsidence, so that more and more of our colleagues would try and measure the subsidence in order to collectively devise a method to avoid this complication which led to unsatisfactory results in quite a few of our patients.

Correcting Fan-Beam Magnification in Clinical Densitometry Scans of Growing Subjects

As children grow, body and limb girths increase. For serial densitometric measurements, growth increases the distance between the bone region of interest and X-ray source over time, thereby increasing fan-beam magnification. To isolate bone accrual from magnification error in growing subjects, we developed a correction method based on waist girth, a common anthropometric measure. This correction was applied to dual-energy X-ray absorptiometry output obtained in a cohort of premenarcheal gymnasts and nongymnasts. After correcting for magnification, results for projected area and bone mineral content (BMC) increased by 0.4–1.1% at the lumbar spine and 8–16% at the femoral neck, decreasing areal bone mineral density (aBMD) by 0.4–2.3% at both sites. The effects of magnification correction were similar in magnitude to BMC and aBMD gains previously reported in longitudinal studies of normoactive children. Because of body size differences, the effect of correction for BMC and aBMD was 10–20% greater in nongymnasts than in gymnasts, which increased the observed aBMD differential between gymnasts and nongymnasts. Fan-beam magnification distorts true changes in bone mineral measures in growing premenarcheal girls and, therefore, may obscure additional activity-related changes during growth. Our correction technique may enhance detection of skeletal adaptation, particularly in pediatric populations.

AN EXPANDED VERY LARGE ARRAY SEARCH FOR WATER MEGAMASER EMISSION IN THE SUBMM GALAXY SMM J16359+6612 ATz= 2.5

Using the Expanded Very Large Array, we have conducted a search for 22.2 GHz H2O megamaser emission in the strongly lensed submm galaxy, SMM J16359+6612 at z = 2.517. This object is lensed into three components, and after a correction for magnification is applied to its submm-wavelength flux density, it is typical of the bulk of the high-redshift, submm galaxy population responsible for the 850 μm extragalactic background (S 850 μm~ 1 mJy). We do not detect any H2O megamaser emission, but the lensing allows us to place an interesting constraint on the luminosity of any megamasers present, 5305 L ☉ for an assumed linewidth of 80 km s–1. Because the far-infrared luminosity in submm galaxies is mainly powered by star formation, and very luminous H2O megamasers are more commonly associated with quasar activity, it could be that blind searches for H2O megamasers will not be an effective means of determining redshifts for less-luminous members of the submm galaxy population.

Retinal Area and Optic Disc Rim Area in Amblyopic, Fellow, and Normal Hyperopic Eyes: A Hypothesis for Decreased Acuity in Amblyopia

Defects in visual functions in amblyopic eyes may have a neuroretinal explanation. The retinal area to optic disc rim area ratios of hyperopic normal, amblyopic, and fellow eyes were evaluated. Case-controlled study. A total of 293 patients with amblyopia and bilateral hyperopia and 77 non-amblyopic bilaterally hyperopic patients without strabismus. Disc areas were measured using magnification correction formulas developed by Bengtsson and Krakau. Axial lengths were determined by ultrasound biometry or laser interferometry with a Zeiss AOL Master (Carl Zeiss Co., Oberkochen, Germany). The visual area of the retina was calculated using axial length measurements. Optic disc rim areas, corrected for magnification, retinal areas, and a derived ratio, retinal area/disc rim area (RetA/DRimA). The RetA/DRimA for the amblyopic eyes was significantly greater than that of the fellow and normal eyes, indicating that amblyopic eyes have larger retinal receptor areas than fellow or normal eyes. The RetA/DRimA of the fellow eyes was smaller than for the amblyopic but larger than that of the normal eyes. These differences were due to smaller optic disc rim areas in the amblyopic and fellow eyes. Amblyopic and their fellow eyes, when compared with normal eyes, have reduced innervations of comparable retinal areas. These differences can be attributed to a paucity of nerve fibers, as indicated by the smaller neuroretinal rim areas. The authors have no proprietary or commercial interest in any materials discussed in this article.

Lensing corrections to features in the angular two-point correlation function and power spectrum

It is well known that magnification bias, the modulation of galaxy or quasar source counts by gravitational lensing, can change the observed angular correlation function. We investigate magnification-induced changes to the shape of the observed correlation function $w(\ensuremath{\theta})$, and the angular power spectrum ${C}_{\ensuremath{\ell}}$, paying special attention to the matter-radiation equality peak and the baryon wiggles. Lensing effectively mixes the correlation function of the source galaxies with that of the matter correlation at the lower redshifts of the lenses distorting the observed correlation function. We quantify how the lensing corrections depend on the width of the selection function, the galaxy bias $b$, and the number count slope $s$. The lensing correction increases with redshift and larger corrections are present for sources with steep number count slopes and/or broad redshift distributions. The most drastic changes to ${C}_{\ensuremath{\ell}}$ occur for measurements at high redshifts ($z\ensuremath{\gtrsim}1.5$) and low multipole moment ($\ensuremath{\ell}\ensuremath{\lesssim}100$). For the source distributions we consider, magnification bias can shift the location of the matter-radiation equality scale by 1%--6% at $z\ensuremath{\sim}1.5$ and by $z\ensuremath{\sim}3.5$ the shift can be as large as 30%. The baryon bump in ${\ensuremath{\theta}}^{2}w(\ensuremath{\theta})$ is shifted by $\ensuremath{\lesssim}1%$ and the width is typically increased by $\ensuremath{\sim}10%$. Shifts of $\ensuremath{\gtrsim}0.5%$ and broadening $\ensuremath{\gtrsim}20%$ occur only for very broad selection functions and/or galaxies with $(5s\ensuremath{-}2)/b\text{ }\ensuremath{\gtrsim}\text{ }2$. However, near the baryon bump the magnification correction is not constant but is a gently varying function which depends on the source population. Depending on how the $w(\ensuremath{\theta})$ data is fitted, this correction may need to be accounted for when using the baryon acoustic scale for precision cosmology.