Study of correlation between MTF and extended source encircled energy through Monte-Carlo simulation and measured data

Several methods are available to measuring the presampled modulation transfer function (MTF) of a digital radiography system by using a slit camera, a slanted edge test device or a bar phantom. Many studies demonstrated the advantages of the edge method compared to the slit method. However, the method of processing to estimate the MTF is slightly different for each publication. The purpose of this study is to compare the effects of various processing steps with an edge image on estimating the presampled MTF. A digital image of a slanted edge test device was acquired and then examined using different image processing such as windowing the edge spread function (ESF), determining a region of interest (ROI) and locally smoothing the ESF data. The results of this study indicated that the impact of determining a ROI on the MTF is relatively modest and that the truncation of the ESF due to a finite window width causes an incorrect inflation error in the MTF estimate and loss of detail at high frequency. Moreover, the influence of ESF smoothing on the MTF is demonstrated, and more rigorous smoothing of the ESF produces a less noisy MTF and, consequently, a high data loss at high-frequency. In conclusion, an ESF processing technique can moderately impact the MTF estimates, and an adequate ROI and window width without a smoothing process is suggested.

The presampling modulation transfer function (MTF) of a digital imaging system is commonly determined by measuring the system’s line spread function (LSF) using a narrow slit or differentiating the detector’s edge spread function (ESF) with an edge device. The slit method requires precise fabrication and alignment of a slit as well as a high radiation exposure. The edge method [3] is a complicated image processing procedure, requiring determination of the edge angle, reprojection, sub-binning, smoothing and differentiating the ESF, and spectral estimation. In this paper, a simple method is employed to evaluate the MTF using an edge device. The image processing procedures required by this method involve simply the determination of the over-sampling rate and the Fourier transform of the modified ESF. Differentiation and signal to noise ratio (SNR) improvement are jointly applied in the Fourier domain. The MTFs obtained by this simple method are compared to the theoretical MTF and the previously proposed more complicated edge method. The experimental results show that the proposed method provides a simple, accurate and convenient measurement of the presampling MTF for digital imaging systems.

Purpose: To demonstrate a method of measuring the modulation transfer function (MTF) of digital imaging systems using the common star pattern test tool. The goal of this research is to develop a technique that brings precise and objective evaluation of spatial resolution to routine quality control in radiography and fluoroscopy. Method and Materials: Images of a 2‐degree star pattern were obtained on a variety of digital radiographic imaging systems, spanning a range of spatial resolution performance levels. One‐dimensional profiles from concentric circles around the center of the star were obtained from each star image. The circular profiles were unwrapped to produce a series of square waves, which were analyzed to produce the square wave response function (SWRF). Droege's method was used to compute the MTF from the SWRF. The MTF determined using the star pattern method was compared to published and quality control measurements of the MTF for several digital mammography and digital radiography systems. In implementing this method, important parameters that must be considered include the radial and angular sampling rates, the method for determining the zero‐frequency normalization and correction for beam nonuniformity. Results: The MTF computed from star pattern profile measurements closely matched the MTF obtained using other methods over the range of spatial frequencies between the Nyquist frequency and 1/3 of the Nyquist frequency. The star pattern MTF, which is a system measurement and includes the effects of detector and geometric unsharpness, was within 6–8% of reference values obtained from the scientific literature for two models digital mammography equipment. Conclusion: Images of a 2‐degree star pattern can produce estimates of the two‐dimensional system MTF. This method may offer a convenient means of assessing the spatial resolution of digital imaging systems for acceptance testing and quality control.

To derive a theoretical model for the modulation transfer function (MTF) of the complete imaging chain of a cardiovascular x-ray system. A sufficiently accurate MTF model may be used in quantitative coronary arteriographic applications to decrease the systematic overestimation of small coronary vessels. The model could be used to restore blurred images in image restoration applications and also may be used for image quality assurance measurements. Digital images of a step wedge phantom were acquired at different modes (5-, 7-, and 9-inch) of the image intensifier and at different kilovolt levels of the x-ray generator. From these images the MTFs that were used to estimate the parameters of the model were assessed. The total MTF of the cardiovascular x-ray imaging chain consisting of image intensifier, video camera, optical elements, and analog/digital converter can be modeled by the simple formula MTF = e-(w/f)R, where w is the frequency in linepairs per millimeter. The constants frequency f and the device index n are parameters that can be derived for an individual x-ray system using the phantom. In this formula, the contribution from the focus of the x-ray source has been excluded. The mean square error (MSE) between the measured values and those assessed from the theoretical model of the MTF for the horizontal direction was found to be equal to 0.00003 for the 5-inch mode of image intensifier, and for the vertical resolution at the 9-inch mode this MSE was equal to 0.00038. In addition, we have demonstrated that the contributions of the video camera and the image intensifier to the total MTF can be replaced by an imaginary electron-optical device. An accurate representation for the MTF of a cardiovascular x-ray system has been derived. This MTF model can be used in x-ray image quality assurance measurements and in quantitative image processing applications.

Patient dose estimation in cardiac computed tomography with a 320 detector row scanner based on Monte Carlo simulation

In this work, the effect of noise on the precision in the modulation transfer function (MTF) calculation using different phantoms is investigated. Three different techniques are studied, based on three different phantoms: edge, bar, and star bar. For each technique, theoretical expressions for the standard deviation and the signal to noise ratio (SNR) of the MTF are derived. In addition, Monte Carlo simulations are carried out to study the accuracy and precision of all the three techniques. Using the analytic expressions for the MTF calculation, statistical fluctuations of noise in the phantom images are propagated to MTF values. Then, for each frequency the standard deviation and the SNR of the MTF are calculated. Monte Carlo simulations are carried out for each phantom image and for different noise level. Images are artificially generated following a procedure that simulates sampling, blurring, and noise present in a real phantom image and takes into account the attenuation of each phantom. Then, oversampling procedures are applied to these images to obtain presampled MTFs. In all three techniques the standard deviation of the MTF is proportional to that of the noise in the image. For the edge image, the standard deviation is proportional to the frequency f, whereas for the bar and star bar techniques it is proportional to the square root of f. Regarding the precision, theoretical expressions and simulations results agree that the bar technique shows the best precision for all the frequencies and all the noise levels analyzed in this study. In addition, simulation results show how, for large levels of noise, the edge technique gives rise to large bias errors at high and medium frequencies. Finally, the precision of the star bar technique is similar to that of the bar technique for isotropic systems, but worse for nonisotropic ones. The uncertainties in the MTF calculation with the edge technique are larger than with the bar technique, and the differences increase with the frequency. On the one hand, the stronger dependency on the frequency shown by the standard deviation of the MTF makes the precision gets worse faster in the edge technique. On the other hand, in the case of the edge and for high levels of noise, differentiation produces line spread functions (LSF) with a poor SNR, increasing erroneously the MTF and worsening accuracy.

The Modulation Transfer Function (MTF) of any system is the frequency response to a delta signal. This response is degraded by several factors such as the inherent veiling glare of the detector and the focal spot size among others. Consequently, the MTF has been one of the physical characteristics that are commonly used to quantitatively measure the physical performance of a system. In this article, the MTF of two flat panel detectors (FPD) and of two Cone Beam CT systems is evaluated. First, the MTF of PaxScan 2520 and of PaxScan 4030CB is evaluated. One of the standard techniques to evaluate the MTF of a FPD is by using an edge of a metal with high atomic number. For instance, it has been suggested by IEC 62220-1 to use an opaque edge to evaluate the MTF of a FPD. Yet, it was found that different metals yield slightly different MTF. In this study, the effects on the MTF evaluation of different metals and exposure parameters was studied and analyzed. First, the MTF was evaluated using different kVps and exposures levels. Second, the MTF was evaluated using aluminum edges of different thickness. Third, the MTF was evaluated using the following four different metals: Aluminum, Copper, Steel and Lead. Finally, the MTF obtained previously were compared to the MTF obtained by using a pinhole. In the second part of this study, the MTF of two systems using these two FPDs were also evaluated using different wires, filters and acquisition modes. The preliminary results demonstrate that the MTF is independent of kVp and exposure level. Yet, it is dependent on the material used to evaluate it.

This paper concerns an experimental method to quantify the spatial resolution of an experimental DPC-CT system via modulation transfer function (MTF) measurement. Note that conventional metal wire-based MTF measurement methods are no long applicable to DPC-CT, because: (i) The refractive signal generated by the high density metal is out of the dynamic range of DPC-CT, and (ii) A DPC-CT system is not sensitive to input pulse finer than a detector pixel. These technical challenges were overcome by a new experimental design, in which a graphite rod was used as the probe to simultaneously measure the MTFs of the DPC-CT and the associated absorption CT. An appreciable difference in MTFs between DPC-CT and absorption CT was observed in our experimental benchtop system: At the 10% MTF level, the MTFs of the DPC-CT and the absorption CT are 4.7 cycles/mm and 5.2 cycles/mm, respectively. Such a difference in MTF leads to the conclusion that the grating interferometer used by the DPC-CT system has a frequency-dependent response to input DPC-CT signals.

We use aberration theory to derive a generalized pupil function of the Golay3 imaging system when astigmatisms exist in its submirrors. Theoretical analysis and numerical simulation using ZEMAX show that the point spread function (PSF) and the modulation transfer function (MTF) of the Golay3 sparse aperture system have a periodic change when there are piston errors. When the peak-valley value of the wavefront (PV(tilt)) due to the tilt error increases from zero to λ, the PSF and the MTF change significantly, and the change direction is determined by the location of the submirror with the tilt error. When PV(tilt) becomes larger than λ, the PSF and the MTF remain unvaried. We calculate the peaks of the signal-to-noise ratio (PSNR) resulting from the piston and tilt errors according to the Strehl ratio, and show that the PSNR decreases when the errors increase.

The multiple light scattering in a turbid medium degrades imaging through the medium. The degradation can be quantitatively described by the modulation transfer function (MTF). Knowledge of the MTF of a turbid medium is important for imaging system design, imaging processing, and related areas The MTF of a turbid medium is equivalent to the transmitted radiance distribution from the medium under isotropic diffuse illumination with unit intensity. By solving the radiative transfer problem we could obtain the MTF in full spatial frequency range and investigate effects of any kind of scattering parameters on the MTF. The radiative transfer problem in a typical turbid medium could only be solved numerically, and an explicit analytical expression of the MTF is impossible to be given in a general manner. A convenient analytical MTF expression is useful and necessary for application. The widely used MTF expression is obtained from the small-angle-approximation (SAA) analysis The SAA approximation is valid only for a rather narrow frequency range. Though the MTF is affected by the whole scattering properties of the turbid medium the SAA MTF expression depends only on the scattering and absorption optical thickness. An analytical MTF expression for a turbid medium is obtained as a function of some main scattering parameters. It is found that the analytical expression of MTF is with high accuracy at practical frequencies for a typical optical thickness.

: The end-to-end performance achieved by an adaptive optical (AO) imaging system is determined by a combination of the residual time-varying phase distortions associated with atmospheric turbulence, and the quasi-static unsensed and uncorrectable aberrations in the optical system itself. Although the effects of these two errors on the time averaged Strehl ratio and the time averaged optical transfer function (OTF) of the AO system are not formally separable, such an approximation is found to be accurate to within a few per cent for a range of representative residual wave-front errors. In these calculations, we have combined static optical system aberrations and time-varying residual phase distortion characteristic of deformable mirror (DM) fitting error, wave-front sensor (WFS) noise, and anisoplanatism. The static aberrations consist of focus errors of varying magnitudes as well as a combination of unsensed and uncorrectable mirror figure errors derived from modeling by the Gemini beta-meter Telescopes project. The overall Strehl ratios and OTF's due to the combined effect of these error sources are well approximated as products of separate factors for the static and time-varying aberrations, as long as the overall Strehl ratio due to both errors is greater than about 0.1. For lower Strehl ratios the products provide lower bounds on the actual values of the Strehl ratio and OTF. The speckle transfer function (STF) is also well approximated by a product of two functions, but only where AO compensation is sufficiently good that speckle imaging techniques are usually not required.

To investigate the modulation transfer function (MTF) behavior of compressed sensing (CS) MR spectroscopic imaging (MRSI) with regard to CS reconstruction weights and the acquired peak signal-to-noise ratio (SNR); which may have an effect on MTF due to the nonlinear nature of the CS reconstruction process. A specially designed phantom consisting of wedges arranged in a fan pattern was used to calculate the MTF of the MRSI scans. Arc profiles of the phantom yield a square wave with a spatial frequency inversely proportional to the radius of the profile. The MTF was derived by considering the amplitude ratio of the fundamental frequency between the ideal square wave and the reconstructed output. As compressed sensing relies on nonlinear reconstruction and a minimization algorithm that requires the definition of reconstruction weights, the behavior of the MTF with respect to the choice of reconstruction weights and peak SNR is not intuitive. As such, simulations were used to investigate the response of the MTF to CS reconstruction weights at varying peak SNRs. The resulting optimized reconstruction weight was used to reconstruct an experimental CS-MRSI scan of the phantom and compare the corresponding MTF to those of a fully sampled dataset, and a time-equivalent Nyquist-sampled low-resolution dataset. Simulations showed that MTFs of CS-MRSI datasets varied widely with different reconstruction weights. Moreover, the response of the MTF to peak SNR was not consistent across the range of reconstruction weights. An optimized reconstruction weight was derived from the simulations and used in reconstructing the experimental dataset. The MTF of the experimental CS-MRSI dataset showed improvement over the equivalent Nyquist sampled dataset at the resolution limit of 0.1 MTF, while it suffered from reduced response at low resolutions between 0.4 and 0.8 lp/cm. The authors have shown that in certain cases small variations in the reconstruction weights yield a measureable effect on the CS reconstructed images, particularly with regard to MTF. Furthermore, it was found that peak SNR affects CS-MRSI MTF especially at higher wavelet reconstruction weights. Accordingly, prior knowledge of the expected peak SNR is essential to optimize the CS reconstruction process. Their phantom-MTF technique provides a quantitative performance measure of MRSI sequences, through which they were able to quantify a loss of 32.4% in spatial resolution for CS-MRSI at 0.1 MTF compared to a loss of 48.6% for the time-equivalent Nyquist-sampled low-resolution scans. They also showed that CS-MRSI suffered decreased low-resolution response as opposed to the equivalent low-resolution datasets.

A recent study has shown that the double-pass method provides a good estimate of the ocular modulation transfer function (MTF) but that it does not yield the phase transfer function (PTF) [J. Opt. Soc. Am. A 12, 195 (1995)]. Therefore, one cannot recover the true retinal point-spread function (PSF). We present a modification of the double-pass method to overcome this problem. The key is to break the symmetry between the two passes. By using an unexpanded Gaussian input beam, we produce a diffraction-limited PSF for the first passes. Then, by using a large exit pupil, we get an aberrated PSF for the second pass. The double-pass aerial image is the cross correlation of both PSF's, so that the Fourier transform of such an aerial image directly provides the true retinal PTF, up to the cutoff frequency of the effective (small), diffraction-limited entrance pupil. The resulting double-pass aerial image is a blurred version of the true retinal PSF. Thus it shows the effect not only of even symmetric aberrations but also of odd and irregular aberrations such as coma. We have explored two different ways to retrieve the true retinal PSF: (a) deblurring of the aerial image and (b) PSF reconstruction combining PTF data with conventional double-pass MTF. We present promising initial results with both artificial and real eyes.

This paper proposes a simple method to achieve the optical transfer function of a circular pupil wavefront coding system with a separable phase mask in Cartesian coordinates. Based on the stationary phase method, the optical transfer function of the circular pupil system can be easily obtained from the optical transfer function of the rectangular pupil system by modifying the cut-off frequency and the on-axial modulation transfer function. Finally, a system with a cubic phase mask is used as an example to illustrate the way to achieve the optical transfer function of the circular pupil system from the rectangular pupil system.

The pixel array of BSI CMOS image sensor is a kind of photoelectric device to obtain 2D image information. The image quality was evaluated by the modulation transfer function (MTF) of BSI CMOS image sensor pixel at Nyquist frequency. With the decreasing pixel size of BSI CMOS image sensor and the increasing spatial resolution, it is more and more difficult to improve the MTF at Nyquist frequency. According to the theoretical analysis, MTF is composed of aperture MTF and diffusion MTF, the comprehensive MTF function is usually obtained by the multiplication relationship between the two MTFs in the frequency domain. Aperture MTF and diffusion MTF have different influence factors and calculation functions, but they are related to the size of the opening. The opening here represents the sensitivity aperture and photo-sense region respectively. The smaller the opening of the detector pixel, the larger MTF will be. In this paper, the theoretical mechanism of MTF function is analyzed in detail, and the calculation results of MTF of BSI CMOS image sensor pixel under 8 typical optical wavelengths in 300nm-1000nm spectral band are listed.