Effects of processing steps with an edge image on determining the presampled modulation transfer function

In order to evaluate and characterize the spatial resolution properties of a direct digital radiography (DDR) system based on a four CCD array detector, we measure the modulation transfer function (MTF) of the imaging system from its edge spread function (ESF). Different from the traditional algorithm for fine sampling of the ESF of an edge or a slit image with a slight angle to the image coordinate, in this paper we propose a new iterative algorithm. The novel algorithm finely samples the ESF along the column almost parallel to the edge, but not the row perpendicular to the edge. The samples of the first column and the second column are combined and averaged to get a segment of fine-sampled ESF. Then the segment of fine-sampled ESF is further combined with the next column and averaged to get a slight longer segment of ESF, and so forth. A complete fine-sampled ESF can be obtained after repeating the procedure for all columns of the edge image. An adaptive filtering is used for smoothing the ESF so that the sharpness at the edge of ESF can be protected. The MTF of the DDR is obtained from a series of image processing and data processing. The image processing includes the automatic determination of the angle of the edge to the pixel array of the edge image and fine sampling of edge spread function (ESF); data processing includes smooth filtering of ESF, numerical differential and fast Fourier transformation (FFT).

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.

Calculation of the modulation transfer function (MTF) is a multi-step procedure. At each step in the calculation, the algorithms can have intrinsic errors which are independent of the imaging system or physics. We designed a software tool with a graphical user interface to facilitate calculation of MTF and the analysis of accuracy in those calculations. To minimize the source of errors, simulated edge images without any noise or artifacts were used. We first examined the accuracy of a commonly used edge-slope estimation algorithm; namely line-by-line differentiation followed by a linear regression fit. The influence of edge length and edge phase on the linear regression algorithm is demonstrated. Furthermore, the relationship of edge-slope estimation error and MTF error are illustrated. We compared the performance of two kernels, [-1,1] and [-1,0,1], in the computation of the line spread function (LSF) from finite element differentiation of the edge spread function (ESF). We found that there is no practical advantage in choosing the [-1,0,1] kernel, as recommended by IEC. However, a correction for finite element differentiation should be applied; otherwise, there is a measurable error in the MTF. Finally, we added noise into the edge images and compared the performance of two noise reduction methods on the ESF; convolution with a boxcar kernel and a monotonicity constraint. The former method always produces MTF error higher than 4% up to the sampling frequency, while the latter was consistently less than 1%.

The modulation transfer function (MTF) of an amorphous silicon (aSi) sensor array was measured using proper sampling techniques to determine the edge spread function (ESF). The detector under study was a area detector (EG&G Heimann, RTM128) consisting of aSi photodiodes arranged in a square array. Two independent methods for calculating the presampling MTF were implemented, based on finely sampling the ESF measurements produced using 40 kV x-rays from a Faxitron microfocal spot x-ray tube. The two calculations of the detector's presampling MTF are in excellent agreement, and are within 20% at the Nyquist frequency when compared with the ideal MTF based only on the size of the detector elements. ESF measurements were also made at 6 MV on a Siemens MD-2 linear accelerator. A calculation of the system presampling MTF was performed which included effects from the linear accelerator source, the lead block used to create the high contrast edge, and the aSi detector response.

The authors describe a new technique to determine the system presampled modulation transfer function (MTF) in digital radiography using only the detector noise response. A cascaded-linear systems analysis was used to develop an exact relationship between the two-dimensional noise power spectrum (NPS) and the presampled MTF for a generalized detector system. This relationship was then utilized to determine the two-dimensional presampled MTF. For simplicity, aliasing of the correlated noise component of the NPS was assumed to be negligible. Accuracy of this method was investigated using simulated images from a simple detector model in which the "true" MTF was known exactly. Measurements were also performed on three detector technologies (an x-ray image intensifier, an indirect flat panel detector, and a solid state x-ray image intensifier), and the results were compared using the standard edge-response method. Flat-field and edge images were acquired and analyzed according to guidelines set forth by the International Electrotechnical Commission, using the RQA 5 spectrum. The presampled MTF determined using the noise-response method for the simulated detector system was in close agreement with the true MTF with an averaged percent difference of 0.3% and a maximum difference of 1.1% observed at the Nyquist frequency (fN). The edge-response method of the simulated detector system also showed very good agreement at lower spatial frequencies (less than 0.5 fN) with an averaged percent difference of 1.6% but showed significant discrepancies at higher spatial frequencies (greater than 0.5 fN) with an averaged percent difference of 17%. Discrepancies were in part a result of noise in the edge image and phasing errors. For all three detector systems, the MTFs obtained using the two methods were found to be in good agreement at spatial frequencies less than 0.5 fN with an averaged percent difference of 3.4%. Above 0.5 fN, differences increased to an average of 20%. Deviations of the experimental results largely followed the trend seen in the simulation results, suggesting that differences between the two methods could be explained as resulting from the inherent inaccuracies of the edge-response measurement technique used in this study. Aliasing of the correlated noise component was shown to have a minimal effect on the measured MTF for the three detectors studied. Systems with significant aliasing of the correlated noise component (e.g., a-Se based detectors) would likely require a more sophisticated fitting scheme to provide accurate results. Results indicate that the noise-response method, a simple technique, can be used to accurately measure the MTF of digital x-ray detectors, while alleviating the problems and inaccuracies associated with use of precision test objects, such as a slit or an edge.

This paper describes the use of a rotating test pattern or reticle to measure the Modulation Transfer Function (MTF) of a staring array sensor. The method finds the Edge Spread Function (ESF) from which the MTF can be calculated. The rotating reticle method of finding the ESF of a sensor has several advantages over the static tilted edge method. The need for precise edge alignment is removed. Motion blur is used to simultaneously average out the effect of undersampling and to oversample the edge. The improved oversampling allows reduction of the noise in the generated ESF while keeping a high resolution. A unique data readout technique reads edge data perpendicular to the edge. Perpendicular readout eliminates the need to know or estimate the slope of the tilted edge. This MTF measurement method is validated using simulation and actual data captured by a digital camera. The resulting ESF plots agree well with expected results.

In this chapter, we consider the imaging properties of a system with a circular exit pupil by applying the general formulas derived in Chapter 1. We derive expressions for its point-spread function (PSF), optical transfer function (OTF), and encircled, ensquared, and excluded powers. The effect of aberrations on a PSF is first studied in terms of its central value, i.e., its Strehl ratio. An exact expression is obtained for the Strehl ratio and the results for primary aberrations are compared with those obtained from the approximate expressions based on the phase variance of the aberration across the pupil derived in Chapter 1. The tolerances for primary aberrations are given for a certain value of the Strehl ratio. Balanced primary aberrations are also discussed and they are identified with the Zernike circle polynomials. A defocused PSF is considered next, and it is shown that systems with large Fresnel numbers, such as photographic systems, have a very small depth of focus. However, systems with small Fresnel numbers, e.g., a laser transmitter, have a large depth of focus. Focused and collimated beams are discussed, and the concept of near- and far-field distances is introduced. It is shown that if the Fresnel number of the beam focused on a target is small, the axial irradiance is maximum at a point that is closer to the focusing optics. However, maximum central irradiance on a target at a given distance is obtained when a beam is focused on it, even though a larger irradiance is obtained at a closer point. Aberrated PSFs for rotationally symmetric aberrations are considered, and numerical results are obtained that show that the size of their central spot is practically independent of the aberration. Symmetry properties of the aberrated PSFs are considered next. Full PSFs for primary aberrations are shown graphically and pictorially. A brief comparison of the diffraction and geometrical PSFs is also given. The line of sight of an optical system is identified with the centroid of its PSF and discussed for aberrated systems. It is shown that only coma-type aberrations change the line of sight. The OTFs for primary aberrations are discussed, and the concept of contrast reversal is described. The OTF aberrated by coma is complex, and we give its real and imaginary parts as well as its modulus and phase. Aberration tolerances are given for a certain value of the Hopkins ratio. The geometrical OTF is also discussed and approximate expressions for it are obtained for the primary aberrations. It gives reasonably accurate results in the region of very low spatial frequencies, a region of practical interest when the MTF of an aberrated system at high frequencies is practically negligible. It is shown that the MTF averaged over all angular orientations of a spatial frequency vector is maximum when the standard deviation of the ray aberration [i.e., the root mean square (rms) radius of the spot diagram with respect to its centroid] is minimum. The diffraction OTF is shown to approach the geometrical OTF in the limit of zero wavelength. The differences between the diffraction and geometrical OTFs are summarized. The incoherent line- and edge-spread functions are discussed, and numerical results for both the aberration-free and the aberrated systems are given. The aberration tolerances for a certain value of the Struve ratio are also given.

Satellite imagery always has low-resolution causing poor application in practice because the serious degradation in imaging is resulted in many factors such as atmospheric turbulence, cloud, and aberration of optical system. To reconstruct the degraded remote sensing images with a high quality, we designed an algorithm to estimate the system modulation transfer function (MTF) accurately. Phase congruency is employed to detect the edges and corners of the image first, then the significant edges, which are utilized to estimate the edge spread function (ESF) using inclined edge method, are picked up from above features through a certain line detection measurement. An image restoration algorithm based on total variation (TV) is introduced to deconvolute the degraded image with the estimated MTF which is derived from the ESF. The experiments show that this method is adaptive and efficient to recover the remote sensing images taken from a Chinese Satellite. The restored images with a higher resolution and higher signal-to-noise ratio (SNR) will improve the applications greatly.

Our work is to investigate and understand the factors affecting the imaging performance of amorphous selenium (a-Se) flat-panel detectors for digital mammography. Both theoretical and experimental methods were developed to investigate the spatial frequency dependent detective quantum efficiency [DQE(f)] of a-Se flat-panel detectors for digital mammography. Since the k-edge of a-Se is 12.66 keV and within the energy range of a mammographic spectrum, a cascaded linear system model was developed which takes into account the effect of k-fluorescence on the modulation transfer function (MTF), noise power spectrum (NPS) and DQE(f) of the detector. This model was used to understand the performance of a prototype detector with 85 mm pixel size. The presampling MTF, NPS and DQE(f) of the prototype were measured, and compared to the theoretical calculation by the model. The calculation showed that k-fluorescence reduces the MTF by 15% at the Nyquist frequency (f<SUB>NY</SUB>) of the prototype detector, and the NPS at f<SUB>NY</SUB> was reduced to 82% of that at zero spatial frequency. Because of the decrease in both MTF and NPS at high spatial frequencies, k-fluorescence only has a small degradation effect on DQE(f) for mammography. The measurement of presampling MTF of the prototype detector revealed an additional source of blurring, which was attributed to the blocking layer at the interface between a-Se and the active matrix. This introduced high frequency drop in both presampling MTF and NPS, and reduced aliasing in the NPS. As a result, the DQE(f) of the prototype detector at f<SUB>NY</SUB> approaches 50% of that at zero spatial frequency.

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 (R2 > 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.

Modulation transfer function (MTF) is an important parameter for image quality evaluation of on-orbit optical image systems. Various methods have been proposed to determine the MTF of an imaging system which are based on images containing point, pulse and edge features. In this paper, the edge of the moon can be used as a high contrast target to measure on-orbit MTF of image systems based on knife-edge methods. The proposed method is an extension of the ISO 12233 Slanted-edge Spatial Frequency Response test, except that the shape of the edge is a circular arc instead of a straight line. In order to get more accurate edge locations and then obtain a more authentic edge spread function (ESF), we choose circular fitting method based on least square to fit lunar edge in sub-pixel edge detection process. At last, simulation results show that the MTF value at Nyquist frequency calculated using our lunar edge method is reliable and accurate with error less than 2% comparing with theoretical MTF value. © 2017 SPIE.

Purpose: To evaluate the efficacy of MTF measurement on digital mammography systems in the Ontario Breast Screening Program (OBSP). Methods: An MTF tool, composed of a copper square on a flexible printed circuit film is supported on top of a 40 mm PMMA slab and imaged with an x‐ray technique appropriate for this thickness. In‐house software, QuickQC, is used to review the image, define regions of interest (ROIs) over each copper edge and calculate the presampled MTF from the line spread function (LSF), by differentiating the edge spread functions (ESF). The noise in the LSF is zero at zero frequency, making the normalization of MTF(0) possible. Since implementing this test in the OBSP 5 years ago, over 180 digital mammography systems have been surveyed semi‐annually (∼ 800 reports). The physicist collects and analyzes the MTF images for all targets and focal spot sizes. MTF results for each digital mammography vendor were summarized to develop pass‐fail criteria. Results: Using appropriate x‐ray techniques, the MTF obtained in this way is similar to values published elsewhere. The noise in the MTF linearly increases to the cutoff spatial frequency, but doesnˈt seriously impair the ability to evaluate compliance. The effects of phosphor glare and extra focal radiation are evident in the low frequency region. Focal spot deterioration is observed as a decrease in MTF compared to the performance for other units of the same model. Underexposure of the phantom causes excessive noise in the MTF. The frequency at which the MTF drops to 50% is typically between 2.5 to 3.5 mm−1 for phosphor based systems with both 50 and 100 um pitch, and 4.0 to 5.0 mm−1 for Se systems with 74–85 um dels. Conclusions: This objective QC test is effective in identifying MTF degradation in a range of different digital mammography systems in the field.

Analysis of angular dependent spatial frequency response of Digital Coplanar Translational Laminography

The exact determination of the modulation transfer function (MTF) of a physical system is a persistent problem. We present a practical method of measuring numerically the MTF of linear solid-state x-ray-sensitive detectors. The method is based on the use of edge techniques and allows us to obtain the MTF of a linear detector from its edge-spread function (ESF). ESF measurement techniques are discussed in detail, and calculation of the corresponding MTF's are shown.

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.