Calculation Of Modulation Transfer Function Research Articles

Validating computer applications for calculating spatial resolution and noise property in CT using simulated images with known properties.

The purpose of this study was to evaluate, using simulated images with known property values, how accurately some computer applications for calculating modulation transfer function (MTF), task transfer function (TTF), or noise power spectrum (NPS) in computed tomography (CT) based on widely known techniques produce their results. Specifically, they were three applications applicable to the wire method for MTF calculation, two applications corresponding to the circular edge (CE) and linear edge (LE) methods for TTF, and one application using a two-dimensional Fourier transform for NPS, which are collectively integrated with the software 'CTmeasure' provided by the Japanese Society of CT Technology. Images for the calculation with radial symmetry were generated based on a roll-off type filter function. The accuracy of each application was evaluated by comparing the calculated property with the true one. The calculated MTFs for the wire method accurately matched the true ones with percentage errors of smaller than 1.0%. In contrast, the CE and LE methods presented relatively large errors of up to 50% at high frequencies, whereas the NPS's errors were up to 30%. A closer investigation revealed, however, that these errors were attributable not to the applications but to the insufficiencies in the measurement techniques commonly employed. By improving the measurement conditions to minimize the effects of the insufficiencies, the errors notably decreased, whichvalidated the calculation techniques in the applications we used.

Analysis of the Slanted-Edge Measurement Method for the Modulation Transfer Function of Remote Sensing Cameras

The modulation transfer function (MTF) serves as a crucial technical index for assessing the imaging quality of remote sensing cameras, which is integral throughout their entire operational cycle. Currently, the MTF evaluation of remote sensing cameras primarily relies on the slanted-edge method. The factors influencing the slanted-edge method’s effectiveness are broadly classified into two categories: algorithmic factors and image factors. This paper innovatively comprehensively analyzes the influencing factors of the slanted-edge method and proposes an improved slanted-edge method to calculate the MTF testing method of remote sensing cameras, which is applied to the MTF testing of remote sensing cameras. Since the traditional algorithm can only be applied in the small angle situation, this paper proposes a new method of slanted-edge method test calculation based on the optimal oversampling rate (OSR) adaptive model of the slanted edge and uses simulation experiments to verify the reliability of the algorithm model through the deviation of the slanted-edge angle calculation and MTF measurement, and the results show that the algorithm improves the accuracy of the MTF measurement compared with the ISO-cos and OMINI-sine methods. Then, the effects of the slanted-edge angle, image region of interest (ROI), as well as image contrast and signal-to-noise ratio (SNR) on the accuracy of the MTF calculation by the slanted-edge method were quantitatively analyzed as the constraints of the slanted-edge method test. Based on the laboratory target experiment, the algorithm flow and various influencing factors obtained in the simulation stage are verified, and the experimental results are more consistent with the various test results obtained in the simulation stage. Consequently, the slanted-edge method introduced in this paper is applicable for future remote sensing camera MTF testing. This approach offers a valuable reference for on-orbit focusing, satellite operational condition monitoring, lifespan estimation, and image restoration.

Rectangular and radial region of interests on the edge of cylindrical phantom for spatial resolution measurement

<span lang="EN-US">The purpose of this study was to evaluate the effect of rectangular region of interest (ROI) size on modulation transfer function (MTF), to develop the radial ROI, and to compare both ROIs performances for MTF measurement using a cylindrical polymethyl methacrylate (PMMA) phantom. The PMMA phantom used in this study was rotated 45°. Four rectangular ROIs and a radial ROI were created to measure the MTF value. The rectangular ROI sizes were 3×41, 21×41, 41×41, and 61×41 pixels; each was placed at upper phantom edge. The radial ROI’s length was 41 pixels and placed at several points in phantom edge. The MTF calculation was automatically conducted using MATLAB. The MTFs from rectangular ROIs and radial ROI were then compared. The comparison of the MTF measurement was also conducted using three different filters. The MTF which used radial ROI was smoother than those of rectangular ROI for all filters. This indicated that radial ROI was more resistant to noise than rectangular ROI. Rectangular ROI with the 41×41 pixels had similar 50% and 10% MTF values with the radial ROI. The MTF value which was obtained using radial ROI is more accurate and robust than those obtained using rectangular ROI.</span>

Computational phantoms for investigating impact of noise magnitude on modulation transfer function

Accurate measurement of spatial resolution in terms of modulation transfer function (MTF) is essential in computed tomography (CT) images. The purpose of this study was to developed a computational phantom that can be used to evaluate the effect of noise on the MTF in CT images. Our computational phantoms for measuring MTF in CT were developed with MATLAB software. The phantom image was blurred by a point spread function of a certain standard deviation. Subsequently, different noise levels were added to the phantoms. Next, an automatic MTF calculation was implemented. The first step of the MTF calculation was to determine the region of interest (ROI). Profile was generated from the ROI, and a line spread function (LSF) curve was formed. The LSF curve was Fourier transformed to produce a MTF curve. Greater noise added to phantom image, it yields greater effect of standard deviation on the measured MTF. The greater noise makes the MTF curve increases differently than MTF with 0 HU noise. The 10% MTF values at the 25% noise reach more than 2.0 cycle/mm. By the developed computational phantoms, the spatial resolution and the amount of noise can be determined independently.

Resolution Analysis of Fast Neutron Imaging Based on D-T Neutron Source

Fast neutron radiography (FNR) has a great potential as a nondestructive technique for testing large objects. A FNR system developed based on a deuterium-tritium neutron generator is presented. Resolution of the FNR system is analyzed using the modulation transfer function (MTF). FNR experiments based on film and charge-coupled device imaging are carried out, respectively. The experimental results of image resolution are compared with the results of MTF calculation. Moreover, the impacts of various system components on signal degradation are discussed in this paper.

RAD_IQ: A free software for characterization of digital X-ray imaging devices based on the novel IEC 62220-1-1:2015 International Standard

Characterization of digital X-ray imaging devices is very important because it can be used to measure and compare the performance of detectors used in Diagnostic Radiology. This characterization is usually made through the calculation of Modulation Transfer Function (MTF), Noise Power Spectrum (NPS) and Detective Quantum Efficiency (DQE). These parameters, especially the DQE, are very important because they quantify the effect of spatial resolution, contrast and noise on Radiographic image quality (IQ). The IEC 62220-1-1:2015 International Standard provides comprehensive guidelines how to capture and analyze X-ray images to characterize digital X-ray detectors. A novel, fast and free MATLAB-based software was developed, named RAD_IQ, to calculate the Signal Transfer Property (STP), perform Noise Component Analysis (NCA), and calculate the parameters MTF, NPS & DQE of X-ray detectors based on the novel IEC 62220-1-1:2015 International Standard for General Radiography and IEC 62220-1-1:2007 for Digital Mammography. Our results were validated against well-established software products used for quantitative image analysis of digital X-ray detectors. The calculated parameters were within 5% difference compared to available software products. The conclusion of our study was that RAD_IQ can be easily used from Medical Physicists, Biomedical Engineers and researchers without any programming experience to characterize the performance of digital X-ray detectors used in Diagnostic Radiology.

Three-dimensional transfer function of optical microscopes in reflection mode.

Three-dimensional (3D) transfer functions build the basis for a comprehensive characterization of optical imaging systems in the spatial frequency domain. Utilizing the projection-slice theorem, the 2D modulation transfer function of an incoherent imaging system can be derived from a 3D transfer function by integration with respect to the axial spatial frequency. For a diffraction limited microscope with homogeneous incoherent pupil illumination, the modulation transfer function equals the 2D autocorrelation function of a circular disc. However, until now to the best of our knowledge no 3D transfer function has been published, which exactly leads to the 2D modulation transfer function of a diffraction limited microscope in reflection mode. In this article, we derive a formula, which after integration with respect to the axial spatial frequency coordinate perfectly fits to the diffraction limited 2D modulation transfer function. The inverse three-dimensional Fourier transform of the 3D transfer function results in a complex-valued 3D point spread function, from which the depth of field, the lateral resolution and, in addition, the corresponding 3D point spread function of both, a conventional and an interference microscope, can beobtained.

Assessment of Uncertainty Depending on Various Conditions in Modulation Transfer Function Calculation Using the Edge Method.

In medical X-ray imaging, to perform optimal operations, it is essential for the user to understand whether a required image quality level which depends on a diagnostic task can be achieved with the imaging system used. This study focuses on the effects of noise on the modulation transfer function (MTF) using the edge method, the most widely used to evaluate the task dependence property. The purpose is to verify the uncertainty of the MTF value at each spatial frequency and examine the conditions under which the accuracy is ensured. By using a Monte Carlo simulation, edge images with various contrast-to-noise ratio (CNR) are acquired. MTFs are then calculated with different edge spread function (ESF) lengths. The uncertainties for each spatial frequency are estimated based on the independent MTF calculations obtained from the five edge data. The uncertainty of the MTF is inversely proportional to the CNR. In the frequency range up to the Nyquist frequency, the uncertainty in five calculations is <0.01 when the CNR is more than 60. In addition, it is observed that the uncertainty increases as the ESF length increases. This relationship depends on the frequency range, but it is proportional to the 0.3–0.5 power of the ESF length. The results in which the uncertainty is most likely to be large in the MTF calculation are clearly shown. Therefore, it is expected to provide an important barometer and useful insights for a proper image quality measurement.

Performance of a new star-bar phantom designed for MTF calculations in x-ray imaging systems.

A new phantom, designed and manufactured for modulation transfer function (MTF) calculations is presented in this work. The phantom has a star-bar pattern and is manufactured in stainless steel. Modulation transfer function determinations are carried out with the new phantom and with an edge phantom to compare their performance and to compare them with previous theoretical predictions. The phantoms are imaged in an x-ray imaging system using different beam qualities and different entrance air KERMA. Methods, previously developed for synthetic images and simulations, are adapted to real measurements, solving practical implementation issues. In the case of the star-bar, in order to obtain optimal MTF determinations it is necessary to accurately determine the center of the pattern. Also, to avoid underestimates in MTF calculations, the length in pixels of each of the scanning circumferences must be an integer multiple of the number of cycles in the pattern. Both methods, star-bar and edge, give similar mean values of the MTF in all cases analyzed. Also, the dependence with frequency of the experimental MTF standard deviation (SD) agrees with the theoretical expressions presented in previous works. In this regard, the precision is better for the star-bar method than for the edge and differences in precision between both methods are higher for the lowest beam quality. The star-bar phantom can be used for MTF determinations with the advantage of having an improved precision. However, precision is reduced when the radiation quality increases. This fact suggests that, for the highest beam qualities, materials with an attenuation coefficient greater than that of steel should be used to manufacture the phantom.

Analysis of Dynamic Modulation Transfer Function for Complex Image Motion

In remote-sensing imaging, the modulation transfer function (MTF) for image motion relevant to the mixing of multiple forms of motions is hard to calculate because of the complicated image motion expression. In this paper, a new method for calculating the MTF for complex image motion is proposed. The presented method makes it possible to obtain an analytical MTF expression derived from the mixing of linear motion and sinusoidal motion at an arbitrary frequency. On this basis, we used the summation of infinitely many terms involving the Bessel function to simplify the MTF expression. The truncation error obtained by the use of finite order sum approximations instead of infinite sums is investigated in detail. In order to verify the MTF calculation method, we proposed a simulation method to calculate the variation of MTF in an actual optical system caused by image motion. The mean value of the relative error between the calculation method and the simulation method is less than 5%. The experimental results are consistent with the MTF curve calculated by our method.

Spatial Distortion Assessments of a Low-Cost Laboratory and Field Hyperspectral Imaging System.

This article describes the adaptation of an existing aerial hyperspectral imaging system in a low-cost setup for collecting hyperspectral data in laboratory and field environment and spatial distortion assessments. The imaging spectrometer system consists of an ImSpector V9 hyperspectral pushbroom scanner, PixelFly high performance digital CCD camera, and a subsystem for navigation, position determination and orientation of the system in space, a sensor bracket and control system. The main objective of the paper is to present the system, with all its limitations, and a spatial calibration method. The results of spatial calibration and calculation of modulation transfer function (MTF) are reported along with examples of images collected and potential uses in agronomy. The distortion value rises drastically at the edges of the image in the near-infrared segment, while the results of MTF calculation showed that the image sharpness was equal for the bands from the visible part of the spectrum, and approached Nyquist’s theory of digitalization. In the near-infrared part of the spectrum, the MTF values showed a less sharp decrease in comparison with the visible part. Preliminary image acquisition indicates that this hyperspectral system has potential in agronomic applications.

Modulation transfer function of the thermal imaging monocular

The modulation transfer function (MTF) of thermal imaging monocular (TIM) was investigated in this article. TIM consists of a lens, a microbolometric matrix (MBM), an electronic system of video signal amplification and processing, a micro display and an eyepiece. The monocular is considered as a linear invariant incoherent system. It’s MTF is equal to the product of the modulation transfer functions of the components. For the convenience of practical application, it is proposed that all MTFs are considered as a function of the angular spatial frequency in the space of objects. An example of TIM MTF calculation with given characteristics was considered. The study of the MTF showed that the spatial impact of the MBM, which is determined by matrix structure, has the greatest influence on the deterioration of this function.

Validation of the tail replacement method in MTF calculations using the homogeneous and non-homogeneous edges of a phantom

We validated the tail replacement technique in the modulation transfer function (MTF) calculation of CT images using edges of homogeneous and non-homogeneous phantom using an automated method. The algorithm for the automated MTF calculation consists of several steps. The upper edge of the phantom was detected from its axial image and pixel values was taken to create an edge spread function (ESF). The left tail of the ESF was flipped horizontally to replace the right tail. Differentiating the ESF produced a line spread function (LSF) which was Fourier transformed to produce the MTF. To validate the result for the non-homogeneous phantom was compared with that for a homogeneous phantom. Results showed that in the homogeneous module, the MTF curve generated without tail replacement corresponded to its shape in use. However for the non-homogeneous module, the MTF obtained without tail replacement differed considerably from its shape in use. The 50% value of MTF (MTF-50) without tail replacement was 0.44 cycles/mm compared to 0.33 cycles/mm in use. Using the tail replacement, the MTFs in the homogeneous and non-homogeneous modules were comparable, with MTF-50 values of 0.33 cycles/mm for both. In summary, the MTF cannot be conventionally measured from the edge of the non-homogeneous module, but it can be resolved using the tail replacement technique on the ESF curve.

Optimization of digital radiography system using in-house phantom: preliminary study

The purpose of this study was to obtain information on optimum exposure parameter combination on simulated thorax and abdomen examinations using Direct-Digital Radiography (DR) and Computed Radiography (CR) systems. An in-house phantom dedicated for quick QC was utilized as an image quality quantification tool in term of contrast. The optimization was performed on Philips Essenta DR, CR Fuji Profect CS, and CR Agfa 10-X. Exposures were performed using corresponding clinical setting with combinations of kVp, mAs, filters, and a variation of simulated patient thicknesses. The Figure of Merit (FOM) was employed as optimization parameter, calculated as ratio of squared Signal Difference to Noise Ratio (SDNR) and surface dose for every measurement. The image quality was evaluated using Modulation Transfer Function (MTF) and Contrast Consistency (CV). Based on FOM, MTF, and CV calculations, acquisitions optimization for thorax examination using DR was obtained on 55-63 kVp, 5-8 mAs, with additional filter 1 mm Al + 0.1 mm Cu. For abdomen examination, the optimized results were 81-102 kVp, 8-12.5 mAs, with additional filters 1 mm Al+0.1 mm Cu and 1 mm Al+0.2 mm Cu. On the other hand, the optimized results using CR on thorax examination were on the range of 55-63 kV, 4-8 mAs, also with the same additional filters with DR. The results of optimization of abdomen examination were on the range of 85-102 kV, 8-20 mAs, and again with the same additional filters. This gave information that different receptors used on the same x-ray unit produced almost similar optimization conditions.

Modulation Transfer Function of the Remote Sensing System when the Line of Sight Deviates From the Nadir

Background. Today, one of the main requirements, which relates to space optical-electronic viewing systems (OEVS) is shooting by a spacecraft (SC) of a requisite area at different angles of sighting. When the line of sight deviates from the nadir, the image quality gets worse. Primarily, the deformation of the projection of pixels on the Earth's surface (ES) and changing of the velocity and direction of vector of movement of the sub-satellite point of SC affect the image quality. Generally, the resulting image quality is estimated by the modulation transfer function (MTF) of OEVS. The evaluation of the MTF of OEVS by only two components, such as the MTF of a lens and detector is insufficient, since there is a high probability that the image will have significantly lower quality compared to theoretically calculated one. Therefore, it is necessary to take into account in the resulting MTF the effect of additional factors such as vibration, movement velocity of the sub-satellite point, detector reading frequency, height instability and position of the line of sight, the atmosphere, to name a few.Objective. The aim of the paper is to develop physico-mathematical model for determining MTF of space OEVS, that takes into account the deformation of the projection of pixels, the variation of velocity and movement vector direction of the SC sub-satellite point and the influence of additional factors at the different angles of sighting.Methods. In the basis of physico-mathematical model is proposed to use a Sun-synchronous orbit trajectory and to calculate the resulting MTF of OEVS in the direction and transverse to the direction of flight.Results. Practical results of the calculations confirm that the deformation of the projection of the pixels and the mentioned additional factors significantly affect the resulting MTF of space OEVS and also depending on the angles of sighting the MTF in the direction and transverse to the direction of flight differ.Conclusions. The analysis of the proposed physico-mathematical model for MTF calculation of the OEVS showed that when a scanner with a large number of pixels is deviated at the significant angles of sighting, heterogeneity appears on sensitive matrix of detector. Attention is drawn to the fact that when scanner deviates at the angles of sighting, the affect of the reading frequency of detector should also be reduced by negotiating it with the image movement velocity in the focal plane. In the process of the research, it was discovered that when use the slight additional turn of yaw angle it is possible to improve the MTF and reduce the difference between the MTF of in the direction and transverse to the direction of flight affecting the image perception efficiency.

An algorithm for automated modulation transfer function measurement using an edge of a PMMA phantom: Impact of field of view on spatial resolution of CT images.

PurposeThe purpose of this study was to introduce a new algorithm for automated measurement of the modulation transfer function (MTF) using an edge of a readily available phantom and to evaluate the effect of reconstruction filter and field of view (FOV) on the spatial resolution in the CT images.MethodsOur automated MTF measurement consisted of several steps. The center of the image was established and an appropriate region of interest (ROI) designated. The edge spread function (ESF) was determined, and a suitably interpolated ESF curve was differentiated to obtain the line spread function (LSF). The LSF was Fourier transformed to obtain the MTF. All these steps were accomplished automatically without user intervention. The results of the automated MTF from the edge phantom were validated by comparing them with a point image, and the results of the automated calculation were validated by the standard fitting method. The automated MTF calculation was then applied to the images of two polymethyl methacrylate (PMMA) phantoms and a wire phantom which had been scanned by a Toshiba Alexion 4‐slice CT scanner and reconstructed with various filter types and FOVs.ResultsThe difference in the 50% MTF values obtained from the edge and point phantoms were within ±4%. The values from the automated and fitted methods agreed to within ±2%, indicating that the automated MTF calculation was accurate. The automated MTF calculation was able to differentiate MTF curves for various filters. The spatial resolution values were 0.37 ± 0.00, 0.71 ± 0.01, and 0.78 ± 0.01 cycles/mm for FC13, FC30 and FC52 filters, respectively. The spatial resolution of the images decrease linearly (R 2 > 0.98) with increasing FOVs.ConclusionAn automated MTF method was successfully developed using an edge phantom, the PMMA phantom. The method is easy to implement in a clinical environment and is not influenced by user experience.

Influence of ambient temperature on the modulation transfer function of an infrared membrane diffraction optical system.

In this paper, we present a model that analyzes the influence of the temperature on the modulation transfer function (MTF) of an infrared membrane diffraction optical system. Based on the physical imaging mechanism of diffractive optical systems, the imaging characteristics of the diffraction optical system are characterized by using diffraction efficiency. Then we establish the corresponding calculation model and MTF analysis model based on scalar diffraction theory. In particular, considering the material properties of flexible membrane optical elements and thermal environment effect, the Zernike polynomials are used to establish the thickness distribution model of the membrane diffractive optical components combined with the finite element analysis. After that, we modify the MTF calculation model of diffraction optical system and accordingly propose the model of the infrared membrane diffraction optical system. Finally, we present some experimental results for a 2-m infrared membrane diffraction optical system. The results show that when the temperature is -40°C and wavelength band is 80nm at the center field of view, the diffraction efficiency is reduced to 81%, and MTF at 75 lp/mm is reduced to 0.12. And when the temperature is -40°C at edge field of view, the efficiency at center wavelength is reduced to 71%, and MTF at 75 lp/mm is reduced to 0.02. The established model and method can be used to estimate the imaging performance of a space infrared membrane diffractive telescope and provide theoretical guidance for the processing algorithm and imaging system design.

Characterisation of Carestream 3543C/4343C digital detectors; experience with quantitative image quality techniques in digital radiography

Our department has recently commissioned four new Carestream DR imaging systems and the associated flat panel detectors (at least two per unit). The primary aim of this study was to characterise the performance of the detectors, primarily Carestream DRX Plus 3543C/4343C detectors, using quantitative measures. These were then compared with the results obtained from detectors of other vendors within our hospital group. Metrics used include the pre-sampled modulation transfer function (MTF), normalised noise power spectrum (NNPS) and detective quantum efficiency (DQE). These were calculated as per IEC 62220-1:2003, with any deviations from this documented. RQA5 beam quality was achieved using a 21 mm Al insert. A 1 mm thick 10 cm x 10 cm polished tungsten edge was used for the calculation of MTF. Initial analysis was performed using the analysis software IQworks. Results are displayed both graphically and in tabular format, allowing easy comparison of MTF, NNPS and DQE with other vendors. Commentary includes practical advice in achieving these results and discussion on the observed differences in detector performance. A brief discussion on the significance of varying some measurement techniques is included. In addition, a comparison of relevant analysis software is provided; namely IQWorks, ImageJ plugin:COQ and programs developed by the NCCPM, Royal Surrey County Hospital, UK.

Chirp phantom for MTF calculations. A study of its precision in noisy environments

Bar pattern phantoms are used to determine the maximum number of line-pairs per mm that an imaging system can resolve. In some cases, a numerical determination of the modulation transfer function (MTF) can also be carried out. However, calculations can only be performed in a relatively small number of frequencies because of the small number of bar groups in the phantom. In this work, a new bar pattern phantom has been simulated. This phantom consists of 66 pairs of lines of different periods and these periods vary exponentially with spatial position, like in a chirp wave. An oversampling procedure has been implemented to obtain the pre-sampled MTF of the system and the results obtained have been compared with those obtained with the edge method, recommended by the IEC. Monte Carlo simulations were carried out for three different levels of noise aimed at investigating the effect of noise on the uncertainties of the MTF determination. In addition, using the analytic expressions for the MTF calculation, statistical fluctuations of noise in phantom images were propagated to MTF values. Despite the smaller size of the chirp phantom, uncertainties in the chirp method are smaller than those of the edge method. For the edge image, the standard deviation of the MTF is proportional to the frequency f, whereas for the chirp method it is proportional to its square root. It is shown that applying an oversampling method allows the use of a single line pair per period without compromising the precision in noisy environments.

Effect of noise on MTF calculations using different phantoms.

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.