Edge Spread Function Research Articles

Measuring PET Spatial Resolution Using a Cylinder Phantom Positioned at an Oblique Angle

A cylinder phantom positioned at a slightly oblique angle with respect to the z-axis of a PET scanner allows for fine sampling of the edge-spread function. We show how this technique can be used to measure the spatial resolution that can be expected with clinical PET protocols, potentially providing more relevant estimates than are typically obtained with established experimental procedures. Methods: A 20-cm-diameter water-filled cylinder phantom containing a uniform 18F solution was centrally positioned at a small angle with respect to the z-axis of a clinical PET/CT system. The oblique angle ensures that the phantom edge intersects the image matrix differently in different slices. Combining line profiles from multiple slices results in a composite profile with fine sampling. Spatial resolution was measured as the full width at half maximum (FWHM) by fitting a model to the finely sampled edge-spread functions in both radial and axial directions. The technique was validated by controlled modulation of image reconstruction parameters and by comparison with extended phantoms with fillable inserts. Separate experiments with uniform cylinders containing 18F, 11C, 13N, 68Ga, and 124I were used to further assess the proposed method. Results: Controlled adjustment of a gaussian postreconstruction filter was accurately reflected in the measured FWHM values. Recovery coefficients derived using the cylinder FWHM values agreed closely with recovery coefficients derived from physical phantoms over a range of insert-to-background ratios, phantom geometries, and reconstruction protocols. The effect of increasing positron energy was clearly reflected in the FWHM values measured with different isotopes. Conclusion: A method has been developed for measuring the spatial resolution that is achieved with clinical PET protocols, providing more relevant estimates than are typically obtained with established procedures. The proposed method requires no special equipment and is versatile, being capable of measuring resolution for different isotopes as well as for different reconstruction protocols. The new technique promises to aid standardization of PET data acquisition by allowing a more informed selection of reconstruction parameters.

Deferred slanted-edge analysis: a unified approach to spatial frequency response measurement on distorted images and color filter array subsets.

The slanted-edge method of spatial frequency response (SFR) measurement is usually applied to grayscale images under the assumption that any distortion of the expected straight edge is negligible. By decoupling the edge orientation and position estimation step from the edge spread function construction step, it is shown in this paper that the slanted-edge method can be extended to allow it to be applied to images suffering from significant geometric distortion, such as produced by equiangular fisheye lenses. This same decoupling also allows the slanted-edge method to be applied directly to Bayer-mosaicked images so that the SFR of the color filter array subsets can be measured directly without the unwanted influence of demosaicking artifacts. Numerical simulation results are presented to demonstrate the efficacy of the proposed deferred slanted-edge method in relation to existing methods.

On the quantification of spatial resolution for three-dimensional computed tomography of chemiluminescence: erratum.

This erratum clarifies an accidental omission of a citation.

Modified slanted-edge method for camera modulation transfer function measurement using nonuniform fast Fourier transform technique

ISO 12233 slanted-edge method experiences errors using fast Fourier transform (FFT) in the camera modulation transfer function (MTF) measurement due to tilt angle errors in the knife-edge resulting in nonuniform sampling of the edge spread function (ESF). In order to resolve this problem, a modified slanted-edge method using nonuniform fast Fourier transform (NUFFT) for camera MTF measurement is proposed. Theoretical simulations for images with noise at a different nonuniform sampling rate of ESF are performed using the proposed modified slanted-edge method. It is shown that the proposed method successfully eliminates the error due to the nonuniform sampling of the ESF. An experimental setup for camera MTF measurement is established to verify the accuracy of the proposed method. The experiment results show that under different nonuniform sampling rates of ESF, the proposed modified slanted-edge method has improved accuracy for the camera MTF measurement compared to the ISO 12233 slanted-edge method.

The use of BAS-TR imaging plates calibration in determining the resolving power of Fuji BAS-1800II image plate reader

The importance of this work lies in assuring the reliability of the results obtained from both imaging plates type BAS-TR and Fuji Image Reader BAS-1800II as they are widely used in calculating essential x-ray sources parameters such as the source size, x-ray flux and brilliance, hence, the calibration presented in this work. For such quantitative analysis, a common practice used by many researchers, where Gold resolution meshes are utilised for such purpose, however not quite successful due to the transmission effect of high energy photons at their edges as well as the pixeling effect while magnifying the scanned image to secure the edge spread function (ESF) data. In contrast, the use of resolution test target (RTT) and wire mesh grid together with a set of test samples i.e. Stanley blades, Ta, Ti and Si wafer of 100, 300, 15, and 490 micron thickness respectively appeared to be efficient in determining IP pixel size and the resolution of the reader. Two different experiments were conducted using two different targets and lasers of very different performance. The first, was a 15 μm VHS video tape composed of Mylar as carrier film with Fe2O3 and CrO2 powder. Nd:YAG laser of long pulse 800 ps, 50 Hz repetition rate and single shot were utilised. Whereas, the second experiment were conducted on a 9μm C wire and a short pulse 500fs Cerberus single shot laser was used. The results obtained from both experiments were pretty much similar. The imaging plate spatial resolution was measured to be: 3.4 ± 0.2 pixels and a pixel size of 41.26 ± 1.4 μm, whereas the smallest resolvable object visible to the reader (1:1 imaging with magnification factor) was of order 140.3 ± 0.3 microns. This appeared to be worse by a factor of three which indicates the importance of the reader's calibration on a regular basis, and at the same time one has to reconsider any related work and calculation based upon the previous nominal values.

Towards the enhancement of medical imaging with non-destructive testing (NDT) CMOS sensors. Evaluation following IEC 62220-1-1:2015 international standard

The aim of the current work was to investigate the modulation transfer function (MTF) of a non-destructive testing (NDT)/ industrial inspection CMOS sensor in conjunction with a calcium tungstate (CaWO4) thin screen, following both the IEC 62220-1:2003 and IEC 62220-1-1:2015 methods. Thin screen samples, with dimensions of 2.7x3.6 cm2 and mean coating thickness of 36.26 mg/cm2 (actual thickness: 118.9 μm estimated from scanning electron microscopy-SEM images) were extracted from an Agfa Curix universal screen and were manually coupled to the active area of a high resolution, active pixel (APS), complementary metal oxide semiconductor (CMOS) sensor. Experiments were performed using the RQA-5 beam quality, as described in the IEC series. Modulation transfer function was assessed using the slanted-edge method. The final MTF, following IEC 62220-1-1:2015 was obtained through averaging the oversampled edge spread function (ESF), using a custom-made software developed in our laboratory. MTF values were found with close agreement in the low and medium spatial frequency ranges, for both methods. Thereafter, MTFs calculated following the 62220-1:2003 protocol, were found overestimated for spatial frequencies higher than 5.7 cycles/mm. The combination of the thin calcium tungstate screen and the CMOS sensor provided very promising image resolution properties and thus could be also considered for use in CMOS based X-ray imaging devices, for various applications.

Accuracy and Precision of Edge-Based Modulation Transfer Function Measurement for Sampled Imaging Systems

The real-time, edge-based, multidirectional modulation transfer function (MTF) measurement system has elucidated the MTF characteristics of sampled imaging systems. However, the accuracy and precision of edge-based MTF measurements are not well understood quantitatively because of the complicated shift-variant nature of the sampling process by the image sensor and the binning process in the edge-based method for producing a supersampled edge spread function. The edge-based MTF measurement is valid only when the edge positions imaged are assumed to be distributed uniformly relative to the sampling sites. This study demonstrates that precision, which is dependent on the edge angle, is counterintuitively high at a higher oversampling ratio of the binning regardless of the smaller pixel counts per bin even with camera noise, and that significantly high precision can be achieved by taking an ensemble average of MTFs computed over a single cycle of the binning phase, even at low oversampling ratios, with high accuracy through proper corrections to compensate for the attenuation of the MTF values due to the discrete processing of the edge-based method.

Modified slanted-edge method to measure the modulation transfer function of camera

The slanted-edge method specified in ISO Standard 12223, which experiences large errors in the camera modulation transfer function(MTF) due to tilt angle error in the knife-edge resulting in non-uniform sampling of the edge spread function. In order to resolve this problem, a modified slanted-edge method for camera MTF measurement is proposed. By applying a simple direct calculation of the Fourier transform of the derivative for the non-uniform sampling data, the camera super-sampled MTF results are obtained. Theoretical simulations for images with and without noise under different tilt angle errors are run using the proposed method. It is demonstrated that the MTF results are insensitive to tilt angle errors. To verify the accuracy of the proposed method, an experimental setup for camera MTF measurement is established. Measurement results show that the proposed method is superior to traditional methods, and improves the universality of the slanted knife-edge method for camera MTF measurement.

Laser scanning laser diode photoacoustic microscopy system

The development of low-cost and fast photoacoustic microscopy systems enhances the clinical applicability of photoacoustic imaging systems. To this end, we present a laser scanning laser diode-based photoacoustic microscopy system. In this system, a 905nm, 325W maximum output peak power pulsed laser diode with 50ns pulsewidth is utilized as the light source. A combination of aspheric and cylindrical lenses is used for collimation of the laser diode beam. Two galvanometer scanning mirrors steer the beam across a focusing aspheric lens. The lateral resolution of the system was measured to be ∼21μm using edge spread function estimation. No averaging was performed during data acquisition. The imaging speed is ∼370 A-lines per second. Photoacoustic microscopy images of human hairs, ex vivo mouse ear, and ex vivo porcine ovary are presented to demonstrate the feasibility and potentials of the proposed system.

Resolution Properties of a Calcium Tungstate (CaWO4) Screen Coupled to a CMOS Imaging Detector

The aim of the current work was to assess the resolution properties of a calcium tungstate (CaWO4) screen (screen coating thickness: 50.09 mg/cm2, actual thickness: 167.2 μm) coupled to a high resolution complementary metal oxide semiconductor (CMOS) digital imaging sensor. A 2.7x3.6 cm2 CaWO4 sample was extracted from an Agfa Curix universal screen and was coupled directly with the active area of the active pixel sensor (APS) CMOS sensor. Experiments were performed following the new IEC 62220-1-1:2015 International Standard, using an RQA-5 beam quality. Resolution was assessed in terms of the Modulation Transfer Function (MTF), using the slanted-edge method. The CaWO4/CMOS detector configuration was found with linear response, in the exposure range under investigation. The final MTF was obtained through averaging the oversampled edge spread function (ESF), using a custom-made software developed by our team, according to the IEC 62220-1-1:2015. Considering the renewed interest in calcium tungstate for various applications, along with the resolution results of this work, CaWO4 could be also considered for use in X-ray imaging devices such as charged-coupled devices (CCD) and CMOS.

Analytical transmission cross-coefficients for pink beam X-ray microscopy based on compound refractive lenses

Analytical expressions for the transmission cross-coefficients for x-ray microscopes based on compound refractive lenses are derived based on Gaussian approximations of the source shape and energy spectrum. The effects of partial coherence, defocus, beam convergence, as well as lateral and longitudinal chromatic aberrations are accounted for and discussed. Taking the incoherent limit of the transmission cross-coefficients, a compact analytical expression for the modulation transfer function of the system is obtained, and the resulting point, line and edge spread functions are presented. Finally, analytical expressions for optimal numerical aperture, coherence ratio, and bandwidth are given.

On the quantification of spatial resolution for three-dimensional computed tomography of chemiluminescence.

Three-dimensional computed tomography of chemiluminescence (CTC) for combustion diagnostics is attracting a surged research interest due to recent progress in sensor technologies and reduced costs of high-speed cameras. For example, it has been applied to recover the 3D distributions of intermediate chemical species such as CH* and OH*, heat release rate, and flame topology. Although these applications were demonstrated to be successful, there are still a few drawbacks of this technique that have not be cured. For example, to the best of the authors' knowledge, all the imaging models that have been developed so far ignore the imperfections of cameras such as lens distortion and skewness. However, this will unavoidably introduce errors into the weight matrix. In addition, spatial resolution of a CTC system is a critical performance parameter. However, it has only been studied qualitatively and no quantitative quantification method is reported so far. This work aims to solve these problems by improving the imaging model and developing a method based on edge spread function for the quantification of spatial resolution. Although this work is conducted under the context of CTC for combustion diagnostics, it also provides useful insights for other tomographic modalities such as volumetric laser-induced fluorescence and tomographic laser-induced incandescence.

Bias-variance tradeoff in anticorrelated noise reduction for spectral CT.

In spectral CT, basis material decomposition is commonly used to generate a set of basis images showing the material composition at each point in the field of view. The noise in these images typically contains anticorrelations between the different basis images, which leads to increased noise in each basis image. These anticorrelations can be removed by changing the basis functions used in the material decomposition, but the resulting basis images can then no longer be used for quantitative measurements. Recent studies have demonstrated that reconstruction methods which take the anticorrelations into account give reduced noise in the reconstructed image. The purpose of this work is to analyze an analytically solvable denoising model problem and investigate its effect on the noise level and bias in the image as a function of spatial frequency. A denoising problem with a quadratic regularization term is studied as a mathematically tractable model for such a reconstruction method. An analytic formula for the resulting image in the spatial frequency domain is presented, and this formula is applied to a simple mathematical phantom consisting of an iodinated contrast agent insert embedded in soft tissue. We study the effect of the denoising on the image in terms of its transfer function and the visual appearance, the noise power spectrum and the Fourier component correlation coefficient of the resulting image, and compare the result to a denoising problem which does not model the anticorrelations in the image. Including the anticorrelations in the noise model of the denoising method gives 3-40% lower noise standard deviation in the soft-tissue image while leaving the iodine standard deviation nearly unchanged (0-1% difference). It also gives a sharper edge-spread function. The studied denoising method preserves the noise level and the anticorrelated structure at low spatial frequencies but suppresses the noise and removes the anticorrelations at higher spatial frequencies. Cross-talk between images gives rise to artifacts at high spatial frequencies. Modeling anticorrelations in a denoising problem can decrease the noise level in the basis images by removing anticorrelations at high spatial frequencies while leaving low spatial frequencies unchanged. In this way, basis image cross-talk does not lead to low spatial frequency bias but it may cause artifacts at edges in the image. This theoretical insight will be useful for researchers analyzing and designing reconstruction algorithms for spectral CT.

Characterization of Makrofol [formula omitted] DE 1-1 for alpha particle radiography

Makrofol ® DE 1-1 (bisphenol-A polycarbonate) was investigated for alpha particle radiography. The edge spread function (ESF) was measured by razor-blade's edge. Makrofol ® DE 1-1 detectors were irradiated with perpendicular incident alpha particles of energy 2.5, 4 and 5.4MeV, thereafter they were etched in 75% 6N KOH+25% C2H5OH at a temperature of 50°C for different durations. The etched Makrofol®DE 1-1 detectors were imaged with an optical microscope equipped with a CCD camera. The results revealed that the green channel of the original RGB image provides the highest contrast comparing with red and blue channel by a factor of 27.6% of the original RGB image. The image contrast of alpha particle-irradiated Makrofol®DE 1-1 detector was found to be inversely related to the etching time since the alpha particle tracks proceed from a conical phase to spherical phase. The spatial resolution of alpha particle-irradiated Makrofol®DE 1-1 detector, in terms of line spread function, was found to deteriorate as the etching time increases for all examined alpha particle energies. The results revealed the potential capability of Makrofol®DE 1-1 detector as an efficient detector for alpha particle radiography such as autoradiography.

New earth system model for optical performance evaluation of space instruments.

In this study, a new global earth system model is introduced for evaluating the optical performance of space instruments. Simultaneous imaging and spectroscopic results are provided using this global earth system model with fully resolved spatial, spectral, and temporal coverage of sub-models of the Earth. The sun sub-model is a Lambertian scattering sphere with a 6-h scale and 295 lines of solar spectral irradiance. The atmospheric sub-model has a 15-layer three-dimensional (3D) ellipsoid structure. The land sub-model uses spectral bidirectional reflectance distribution functions (BRDF) defined by a semi-empirical parametric kernel model. The ocean is modeled with the ocean spectral albedo after subtracting the total integrated scattering of the sun-glint scatter model. A hypothetical two-mirror Cassegrain telescope with a 300-mm-diameter aperture and 21.504 mm × 21.504-mm focal plane imaging instrument is designed. The simulated image results are compared with observational data from HRI-VIS measurements during the EPOXI mission for approximately 24 h from UTC Mar. 18, 2008. Next, the defocus mapping result and edge spread function (ESF) measuring result show that the distance between the primary and secondary mirror increases by 55.498 μm from the diffraction-limited condition. The shift of the focal plane is determined to be 5.813 mm shorter than that of the defocused focal plane, and this result is confirmed through the estimation of point spread function (PSF) measurements. This study shows that the earth system model combined with an instrument model is a powerful tool that can greatly help the development phase of instrument missions.

A method to measure the modulation transfer function of Bayer filter color camera

With the development of optoelectronic technologies, color cameras have been widely exploited in space remote sensing, earth observations from space, environmental monitoring, urban construction, and many other fields. Currently, most commercial color cameras use a single charge coupled device (CCD) or complementary metal-oxide-semiconductor (CMOS) sensor that has a Bayer color filter array (CFA) on its pixel surface to obtain red (R), green (G), or blue (B) samples. As a way of evaluating imaging quality, modulation transfer function (MTF) can provide a comprehensive and objective metric for camera imaging performance. In the conventional knife-edge method for color camera MTF measurement, a linear uniform sampling of the edge spread function (ESF) must be completed before a fast Fourier transform (FFT) can be applied. As the sampling rate becomes large, the number of pixel points on the line which is parallel to the knife-edge become less. So taking average of the pixel points to obtain ESF can be strongly affected by the noise of sensor. Therefore it is necessary to balance the influences of sampling rate and sensor noise on the MTF measurement, and the recommended sampling rate is 4-6. When the tilt angle of knife-edge has an error, the non-uniform sampling ESF can be obtained by the slanted knife-edge method. This leads to a variation in the results of the camera MTF on a spatial frequency scale and early cut-off. The best MTF results of camera can be obtained by rotating knife-edge, calculating MTF power under different tilt angles of knife-edge, and finding the maximum MTF power. And we propose an algorithm for Bayer filter color camera MTF measurement. The algorithm processing includes extracting R, G, B colors of knife-edge images; projection; differential operation; Hanning window filtration; FFT; correction; weighting combination of R, G, B colors MTF; MTF power calculation; optimal tilt angle of knife-edge estimation. To verify the accuracy of the proposed method, the weighting response factors of R, G, B colors are calibrated and an experimental setup for color camera MTF measurement is established. The knife-edge target is rotated in angle steps of 0.02, and the MTF results are calculated under different tilt angles of knife-edge within0.1 surrounding the estimate position by the proposed algorithm. The maximum differences of MTF results between the proposed method and fringe target method are 0.061 (Nyquist frequency fc) and 0.043 (fc/2), respectively. The results show that by searching the optimal tilt angle of knife-edge, the effect of non-uniform sampling on MTF result of color camera can be eliminated. Compared with the conventional method, the proposed method is superior for the measurement of the super-sampled MTF of color camera. Meanwhile, this method can also be applied to MTF measurements of radiographic systems, such as X-ray imaging system and other systems.

Samples to Determine the Resolution of Neutron Radiography and Tomography

Knowing the resolution and effective pixel size of an imaging system is essential for dimensional and quantitative measurements. A collection of test devices was developed for neutron imaging that can be used to quantify pixel and voxel size, resolution of the imaging system, and beam divergence. The first set of devices is intended for measurements with radiographs using test patterns or an absorbing edge. For tomography, Al vials were filled with Ti spheres of increasing dimensions in each vial. Ti was chosen since it provides sufficient contrast while the transmission is still guaranteed. The first resolution criterion was to determine from which vial that the spheres can be uniquely identified as spheres. More complex analysis would involve measuring the volume of the spheres or even to compute the edge spread function analogous to the method with the knife-edge for radiographs. For the edge analysis, a larger Ti sphere was considered. Using a sphere for the edge spread function analysis allowed for determination of the resolution in any direction. Images acquired using the different test items are included and methods to perform the analysis required to quantify the resolution from the images are proposed.

A New Method on Calibrating PSF of Remote Sensing Space Plane Arraycamera

Point spread function (PSF) of an imaging system is an important parameter to a remote sensing imaging system, and it is the important basis for image restoration [1]. The knife-edges method has been widely used to measure PSF because it provides a relatively easy way to get the point spread function. However, the location of the edge points in edge spread function (ESF) is difficult to determine of the knife-edges method, resulting in the inaccuracy of the point spread function. In this paper, we propose a new method to solve the problem of phase influence for calibrating PSF of space plane array camera. This method include: the design of target, the process of calibration and data processing. Then this method was used on calibrating PSF of GF-4 satellite panchromatic camera. The results showed that the new method could determine the PSF correctly.

Investigation of the Section Thickness Measurement in Tomosynthesis by Thin Metal Plate Edge Method.

When performing tomosynthesis, the section thickness needs to be set depending on a radiographic part and its diagnostic purpose. However, the section thickness in tomosynthesis has not been clearly defined and its measurement method has not been established yet. In this study, we devised the alternative measurement method to diagnose the section thickness using an edge of thin metal plate, and compared with the simulation results, the wire and bead method reported in the previous papers. The tomographic image of the thin metal plate positioned on the table top inclining 30 degrees, which showed the edge spread function (ESF) of each tomographic height, was taken, and then the line spread function (LSF) was obtained by differentiating the ESF image. For the next, a profile curve was plotted by maximum values of LSF of each tomographic height, and a section thickness was calculated using the full width at half maximum (FWHM) of the profile curve. The edge method derived the section thickness close to the simulation results than the other methods. Further, the section thickness depends on the thickness of the metal plate and not the material. The thickness of the metal plate suitable for the evaluation of section thickness is 0.3 mm that is equivalent to pixel size of the flat panel detector (FPD). We conducted quantitative verification to establish the measurement method of the section thickness. The edge method is a useful technique as well as the wire and bead method for grasping basic characteristics of an imaging system.

基于亚像素扫描的超分辨技术在高分辨X射线显微镜中的应用

Developing super-resolution scanning and reconstruction method on the existing hardware can improve imaging performance and saving the cost to upgrade hardware. In this paper, a super-resolution scanning mode based on sub-pixel scanning is designed and a series of low-resolution images of the sample is acquired through modulating the position of the sample. Then, the point spread function derived by processing the edge spread function is employed to the image restoration of the low-resolution image series. Finally, super-resolution reconstruction algorithm based on POCS is used to reconstruct super-resolution images. The experiments conducted on the high-resolution X-ray microscope equipped with a 10 times optical lens coupling detector show that the contrast-to-noise ratio increases about 20%, the spatial resolution has been improved about 0.2 μ m (about 15%), the detail resolution can exceed the limits of pixel size of the detector and more details are seen than low-resolution images. The experiment's results illustrate that the super-resolution technique has great potential in improving the spatial resolution of the high-resolution X-ray microscope. © 2017, Science Press. All right reserved.