True Modulation Transfer Function Research Articles

Technical Note: Accuracy of MTF measurements with an edge phantom at megavoltage x-ray energies.

Measurement of the modulation transfer function (MTF) is performed by evaluating the response of an imaging system to a predefined input. To obtain accurate results when using an edge phantom, the detector input signal must resemble an ideal step function. The MTF of megavoltage (MV) imagers used in radiotherapy has been measured with highly absorbing edge phantoms fabricated from thick metal blocks. This study investigates the influence of the edge phantom design on the accuracy of the resulting MTF. The MTF of an electronic portal imaging device (EPID) was measured at 6MV beam quality with four edge phantoms made of lead with 1.3, 3.3, 5.0, and 10.0cm thickness. Monte Carlo simulations were carried out for these and a selection of tungsten phantoms to determine the photon fluence at the imaging plane and quantify the systematic error in the MTF introduced by the edge phantom design. The measured MTF depends on the design of the edge phantom. The detector input signal of a thin phantom is affected by secondary radiation from the phantom itself, causing an overestimation of the MTF. The amount of secondary radiation can be reduced by increasing the phantom thickness or introducing an air gap between the phantom and the detector. Both methods introduce geometric unsharpness, which can result in an underestimation of the true MTF. Edge phantoms made from 4.0cm thick tungsten or 5.0cm thick lead induce comparatively small systematic errors of below 3% or 5%, respectively. When MTF measurements are conducted at MV energies, even a highly absorbing edge phantom will introduce a systematic error of several percent. Direct comparison of MTFs obtained with different edge phantoms should therefore be treated with caution.

Application of a variable filter for presampled modulation transfer function analysis with the edge method.

We devised a new noise filtering method to reduce the noise in the line spread function (LSF) for presampled modulation transfer function (MTF) analysis with the edge method. A filter was designed to reduce noise effectively using a position-dependent filter controlled by the boundary frequency b for low-pass filtering, which is calculated by 1/2d (d: distance from the LSF center). In this filtering process, strong filters with very low b can be applied to regions distant from the LSF center, and the region near the LSF center can be maintained simultaneously by a correspondingly high b. Presampled MTF accuracies derived by use of the proposed method and an edge spread function (ESF)-fitting method were compared by use of simulated ESFs with and without noise, resembling a computed radiography (CR) and an indirect-type flat panel detector (FPD), respectively. In addition, the edge images of clinical CR, indirect-type FPD, and direct-type FPD systems were examined. For a simulated ESF without noise, the calculated MTFs of the variable filtering method agreed precisely with the true MTFs. The excellent noise-reduction ability of the variable filter was demonstrated for all simulated noisy ESFs and those of three clinical systems. Although the ESF-fitting method provided excellent noise reduction only for the CR-like simulated ESF with noise, its noise elimination performance could not be demonstrated due to the lesser robustness of the fitting.

Monotone spline regression for accurate MTF measurement at low frequencies

The modulation transfer function (MTF) of radiographic systems is frequently evaluated by the system's line spread function (LSF) using narrow slits. The conventional slit method requires LSF tail approximation, which is achieved by exponentially extrapolating the LSF tails beyond 1% of peak value. However, the estimated MTF at low frequencies from extrapolation may not reflect the true performance of the system. In this study, a monotone spline regression technique for LSF tail approximation is developed to improve the accuracy of MTF estimation at low frequencies. This technique is based on the underlying physical principles of the system response. The advantages of this technique are demonstrated with simulated examples of which the true MTFs are known. The application of this measurement technique is also demonstrated.

WE-C-304A-07: A Method for Measuring the MTF of Digital Radiography Systems Using Noise Response

Purpose: To provide a new method for measurement of the modulation transfer function(MTF) using the noise response of digital radiographysystems.Method and Materials: Cascaded linear system methods have been used for several decades to accurately predict the signal and noise performance of a wide variety of digital x‐ray imaging technologies including x‐ray image intensifiers, direct and indirect flat‐panel detectors(FPDs), and CCD/EMCCD‐based detectors. The noise response of such imagers inherently incorporates the detector resolution response, i.e. the detectorMTF. In this work, a generalized linear systems analysis was used to derive an exact relationship. The two‐dimensional noise power spectrum (NPS) was plotted versus the mean signal level, for all spatial‐frequencies. A linear regression was fitted to this data to isolate the quantum‐noise component, the shape of which depends in part on the system resolution. The spatial‐frequency response of the resulting slopes was then used to obtain the MTF. The accuracy of this method was investigated using simulated images from a simple detector model, based on high‐resolution EMCCD detectors, in which the MTF was known exactly. Measurements were also done on a FPD and the results were compared using the standard edge response method. Results: The MTF measured from the noise response of the simulated detectorsystem showed exceptional agreement with the “true MTF” at both low and high spatial‐frequencies. Differences of 0.3%, 1.8% and 6.1% were observed at 5, 10 and 15cycles/mm, respectively. The FPDMTF obtained using the noise and edge response methods were also shown to agree within experimental uncertainty. Conclusions: Initial results indicate that the noise response method is a simple technique which can be used to accurately measure the MTF (in all directions simultaneously) of digital x‐ray imagers, alleviating the burdens of development and implementation of precision edge or slit devices. (Support: NIH‐R01‐EB008425; NIH‐R01‐EB002873)

Sci-Sat AM(1): Imaging-07: Open field normalization: How to avoid inflation to MTF and DQE values caused by zero-frequency normalization.

To show that the novel open-field normalization technique prevents a common error in calculation of the detective quantum efficiency (DQE) caused by zero-frequency normalization of the modulation transfer function (MTF). Models describing zero-frequency and open-field normalization were used to derive the resulting measured MTF, noise power spectrum (NPS) and DQE using a finite region of interest (ROI) of image data. Simulated one-dimensional images containing Gaussian blur were used to model a deterministic system and to calculate the resultant values. Measurements were made using both zero-frequency and open-field normalization with ROIs ranging in size from 1-10 cm. Use of a finite ROI results in truncation of the system line-spread function (LSF) causing the zero-frequency value of the measured MTF to be less than the true MTF value of unity, and causes spectral leakage in both the MTF and NPS. Zero-frequency normalization of the MTF inflates values at all non-zero frequencies. Since no zero-frequency normalization is performed on the NPS, this causes inflated DQE values. Simulated results show a 6% inflation of DQE values for a ROI of 10 cm, which increases as the ROI is reduced. Open-field normalization accurately determines MTF and NPS (and thus DQE) values at all frequencies away from zero frequency. Open-field normalization measurements provide a good estimate of the true MTF and DQE. This approach should be used to avoid a common error in DQE calculations that is not obvious and inflates DQE calculations by 5-20%.

WE-C-332-03: Open Field Normalization Prevents a Common Error in MTF Measurements

Purpose: To show that open‐field normalization prevents a common error in measurements of the modulation transfer function(MTF) caused by zero‐frequency normalization. Method and Materials: Models describing zero‐frequency and open‐field normalization are used to derive the resulting measured MTF obtained from a finite region of interest (ROI) of an edge image in terms of the true system MTF. Simulated edge images containing Gaussian blur, as well as images of a tungsten sheet acquired on a GE flat‐panel detector in clinical use were used to calculate the MTF. Measurements were made using both zero‐frequency and open‐field normalization with ROIs ranging in size from 1–15 cm × 10 cm and 1–15 cm × 5 cm. Results: Use of a finite ROI results in truncation of the system line‐spread function (LSF) causing the zero‐frequency value of the measured MTF to be less than the true MTF value of unity. Subsequent zero‐frequency normalization results in inflation of the MTF values at all non‐zero frequencies. Data from the clinical system shows a 5% inflation of values for an ROI of 10 cm, increasing to 14% for an ROI of 1 cm. Open‐field normalization accurately determines MTF values at all frequencies away from zero frequency. The open‐field normalized zero‐frequency value is equal to the area of the truncated system LSF, and is less than unity. Conclusion: Open‐field normalization measurements provide a good estimate of the true MTF if the zero‐frequency value is disregarded with the understanding that it is expected to have a value less than unity. This work should be used in MTF‐measurement guidelines and recommendations on acceptable ROI sizes and normalization techniques.

Comparison of edge analysis techniques for the determination of the MTF of digital radiographic systems

The modulation transfer function (MTF) is well established as a metric to characterize the resolution performance of a digital radiographic system. Implemented by various laboratories, the edge technique is currently the most widespread approach to measure the MTF. However, there can be differences in the results attributed to differences in the analysis technique employed. The objective of this study was to determine whether comparable results can be obtained from different algorithms processing identical images representative of those of current digital radiographic systems. Five laboratories participated in a round-robin evaluation of six different algorithms including one prescribed in the International Electrotechnical Commission (IEC) 62220-1 standard. The algorithms were applied to two synthetic and 12 real edge images from different digital radiographic systems including CR, and direct- and indirect-conversion detector systems. The results were analysed in terms of variability as well as accuracy of the resulting presampled MTFs. The results indicated that differences between the individual MTFs and the mean MTF were largely below 0.02. In the case of the two simulated edge images, all algorithms yielded similar results within 0.01 of the expected true MTF. The findings indicated that all algorithms tested in this round-robin evaluation, including the IEC-prescribed algorithm, were suitable for accurate MTF determination from edge images, provided the images are not excessively noisy. The agreement of the MTF results was judged sufficient for the measurement of the MTF necessary for the determination of the DQE.

Validation of MTF measurement for digital mammography quality control

The modulation transfer function (MTF) describes the spatial resolution properties of imaging systems. In this work, the accuracy of our implementation of the edge method for calculating the presampled MTF was examined. Synthetic edge images with known MTF were used as gold standards for determining the robustness of the edge method. These images simulated realistic data from clinical digital mammography systems, and contained intrinsic system factors that could affect the MTF accuracy, such as noise, scatter, and flat-field nonuniformities. Our algorithm is not influenced by detector dose variations for MTF accuracy up to 1/2 the sampling frequency. We investigated several methods for noise reduction, including truncating the supersampled line spread function (LSF), windowing the LSF, applying a local exponential fit to the LSF, and applying a monotonic constraint to the supersampled edge spread function. Only the monotonic constraint did not introduce a systematic error; the other methods could result in MTF underestimation. Overall, our edge method consistently computed MTFs which were in good agreement with the true MTF. The edge method was then applied to images from a commercial storage-phosphor based digital mammography system. The calculated MTF was affected by the size (sides of 2.5, 5, or 10 cm) and the composition (lead or tungsten) of the edge device. However, the effects on the MTF were observed only with regard to the low frequency drop (LFD). Scatter nonuniformity was dependent on edge size, and could lead to slight underestimation of LFD. Nevertheless, this negative effect could be minimized by using an edge of 5 cm or larger. An edge composed of lead is susceptible to L-fluorescence, which causes overestimation of the LFD. The results of this work are intended to underline the need for clear guidelines if the MTF is to be given a more crucial role in acceptance tests and routine assessment of digital mammography systems: the MTF algorithm and edge object test tool need to be publicly validated.

Conditioning data for calculation of the modulation transfer function.

A method for conditioning data used in the measurement of the modulation transfer function (MTF) is discussed. This method is based upon imposing the constraint that the edge spread function (ESF) is monotonic. The advantages of this technique, when applicable, are demonstrated with simulated examples for which the true MTF is known. The application of this technique in the measurement of the MTF of a digital detector in clinical use is also demonstrated.

The effects of electron and photon scattering on signal and noise transfer properties of scintillators in CCD cameras used for electron detection

The detection properties of scintillators used in charge-coupled device cameras suitable for electron microscopy are examined with particular emphasis on the statistics of electron scattering and photon generation in the scintillator. We show that the root of the power spectrum of an evenly illuminated white noise image is in general not equal to the modulation transfer function (MTF) of the scintillator, as the former corresponds to the statistical properties of the detectable light intensity caused by single incident electrons while the latter corresponds to the statistical properties of the detected intensity caused by many electrons incident on the same point. A difference between these statistical properties leads to over-optimistic estimations of the MTF when the noise method is used and furthermore deteriorates the detection quantum efficiency (DQE) at high spatial frequencies. Monte Carlo simulations are used to calculate the true MTF, the expected outcome of a noise method measurement (MTF noise) and the spatial frequency dependent DQE for various scintillator thicknesses and acceleration voltages.