Measurement and comparison of one- and two-dimensional modulation transfer function of optical imaging systems based on the random target method

Deep-learning-based image reconstruction and noise reduction methods (DLIR) have been increasingly deployed in clinical CT. Accurate image quality assessment of these methods is challenging as the performance measured using physical phantoms may not represent the true performance of DLIR in patients since DLIR is trained mostly on patient images. In this work, we aim to develop a patient-data-based virtual imaging trial framework and, as a first application, use it to measure the spatial resolution properties of a DLIR method. The patient-data-based virtual imaging trial framework consists of five steps: (1) insertion of lesions into projection domain data using the acquisition geometry of the patient exam to simulate different lesion characteristics; (2) insertion of noise into projection domain data using a realistic photon statistical model of the CT system to simulate different dose levels; (3) creation of DLIR-processed images from projection or image data; (4) creation of ensembles of DLIR-processed patient images from a large number of noise and lesion realizations; and (5) evaluation of image quality using ensemble DLIR images. This framework was applied to measure the spatial resolution of a ResNet based deep convolutional neural network (DCNN) trained on patient images. Lesions in a cylindrical shape and different contrast levels (-500, -100, -50, -20, -10 HU) were inserted to the lower right lobe of the liver in a patient case. Multiple dose levels were simulated (50%, 25%, 12.5%). Each lesion and dose condition had 600 noise realizations. Multiple reconstruction and denoising methods were used on all the noise realizations, including the original filtered-backprojection (FBP), iterative reconstruction (IR), and the DCNN method with three different strength setting (DCNN-weak, DCNN-medium, and DCNN-strong). Mean lesion signal was calculated by performing ensemble averaging of all the noise realizations for each lesion and dose condition and then subtracting the lesion-present images from the lesion absent images. Modulation transfer functions (MTFs) both in-plane and along the z-axis were calculated based on the mean lesion signals. The standard deviations of MTFs at each condition were estimated with bootstrapping: randomly sampling (with replacement) all the DLIR/FBP/IR images from the ensemble data (600 samples) at each condition. The impact of varying lesion contrast, dose levels, and denoising strengths were evaluated. Statistical analysis with paired t-test was used to compare the z-axis and in-plane spatial resolution of five algorithms for five different contrasts and three dose levels. The in-plane and z-axis spatial resolution degradation of DCNN becomes more severe as the contrast or radiation dose decreased, or DCNN denoising strength increased. In comparison with FBP, a 59.5% and 4.1% reduction of in-plane and z-axis MTF (in terms of spatial frequencies at 50% MTF), respectively, was observed at low contrast (-10 HU) for DCNN with the highest denoising strength at 25% routine dose level. When the dose level reduces from 50% to 12.5% of routine dose, the in-plane and z-axis MTFs reduces from 92.1% to 76.3%, and from 98.9% to 95.5%, respectively, at contrast of -100 HU, using FBP as the reference. For most conditions of contrasts and dose levels, significant differences were found among the five algorithms, with the following relationship in both in-plane and cross-plane spatial resolution: FBP>DCNN-Weak>IR>DCNN-Medium>DCNN-Strong. The spatial resolution difference among algorithms decreases at higher contrast or dose levels. A patient-data-based virtual imaging trial framework was developed and applied to measuring the spatial resolution properties of a DCNN noise reduction method at different contrast and dose levels using real patient data. As with other non-linear image reconstruction and post-processing techniques, the evaluated DCNN method degraded the in-plane and z-axis spatial resolution at lower contrast levels, lower radiation dose, and higher denoising strength.

컬러 LCD(liquid crystal display) 모니터의 광학적 상에 대한 성능을 평가하기 위하여 LCD 모니터를 포함한 모든 광학계의 파장별 공간주파수 반응에 가중치를 부여한 진폭전달함수(modulation transfer function ; MTF)를 이용한 다색광전달함수(polychromatic modulation transfer function ; PMTF)를 제안한다. 서로 다른 진폭들을 갖는 적색(R), 녹색(G), 청색(B)의 3개의 막대형 LCD 단위물체를 이용한 컬러 LCD의 PMTF의 시뮬레이션 결과와 실험적 결과가 잘 일치하며, 이 결과 컬러 LCD의 결상성능은 단색으로 측정하는 MTF 및 가시광의 전파장대를 사용하는 백색광 MTF와는 다른 R, G, B의 3색에 대한 PMTF로 측정하늘 것이 보다 적절하다. We propose a method for evaluating the image quality of color liquid crystal display(LCD) monitors by using the polychromatic modulation transfer function(PMTF), which is calculated from the modulation transfer function(MTF) weighted by the overall color response of the system including the test LCD monitor. We confirm that experimental results using the PMTF agree well with simulated results of the PMTF of a color LCD monitor by using three bar targets with different amplitudes and three elementary colors such as red(R), green(G), and blue(B). As a results, we should choose the PMTF instead of the white color MTF or monochromatic MTF in order to evaluate correctly the image quality of color LCD monitors.

The aim of this study is to propose a method for the quantitative evaluation of image quality of both monochrome and color liquid-crystal displays (LCDs) using a commercially available color digital camera. The intensities of the unprocessed red (R), green (G), and blue (B) signals of a camera vary depending on the spectral sensitivity of the image sensor used in the camera. For consistent evaluation of image quality for both monochrome and color LCDs, the unprocessed RGB signals of the camera were converted into gray scale signals that corresponded to the luminance of the LCD. Gray scale signals for the monochrome LCD were evaluated by using only the green channel signals of the camera. For the color LCD, the RGB signals of the camera were converted into gray scale signals by employing weighting factors (WFs) for each RGB channel. A line image displayed on the color LCD was simulated on the monochrome LCD by using a software application for subpixel driving in order to verify the WF-based conversion method. Furthermore, the results obtained by different types of commercially available color cameras and a photometric camera were compared to examine the consistency of the authors' method. Finally, image quality for both the monochrome and color LCDs was assessed by measuring modulation transfer functions (MTFs) and Wiener spectra (WS). The authors' results demonstrated that the proposed method for calibrating the spectral sensitivity of the camera resulted in a consistent and reliable evaluation of the luminance of monochrome and color LCDs. The MTFs and WS showed different characteristics for the two LCD types owing to difference in the subpixel structure. The MTF in the vertical direction of the color LCD was superior to that of the monochrome LCD, although the WS in the vertical direction of the color LCD was inferior to that of the monochrome LCD as a result of luminance fluctuations in RGB subpixels. The authors' method based on the use of a commercially available color camera is useful to evaluate and understand the display performances of both monochrome and color LCDs in radiology departments.

For the image quality analysis of photogrammetrical systems using the Modulation Transfer Function (MTF), the edge gradient analysis (EGA), using a Hanning function, and the grating pattern method are compared. Artificial edge and grating patterns were photographed from an airplane and were analyzed to determine the quality of the photogrammetric system. The pictures were scanned with a microdensitometer. For comparison with the artificial patterns, a natural roof edge was examined. Good agreement of all MTF measurements was found. Furthermore, the resolution found from MTF curves agreed well with the resolution obtained from three-bar targets. Generally, the MTF curves obtained from patterns in the flight direction were lower than the MTF's perpendicular to the flight direction due to airplane movement. The influence of linear image motion and its compensation was examined and is discussed. N PHOTOGRAMMETRY the image quality of photographs is of great importance. With digital image processing the image quality can be improved under certain conditions. Flight con­ ditions usually lead to reduced image quality (Holdermann, 1976). The optical transfer function (OTF) and especially the modula­ tion transfer function (MTF) are useful techniques for measuring the image quality of photographs. The MTF is the result of -the contributions of the links in the image transfer forming chain, namely, the camera, the film, image motion (in systems without forward motion compensation, FMC), vibrations, and the at­ mosphere (Tiziani, 1977). Artificial or natural edges are used for the edge gradient analysis (EGA), and varying spatial frequency patterns are used for the grating pattern technique. The aim of this paper is to compare both methods and to test their reliability. Results are shown and discussed. Furthermore, the influence of linear image mo­ tion on image quality is examined.

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

2.1 Introduction An optical system's image quality can be characterized in the domain using the impulse response (spot size) of the system, or in the spatial-frequency domain using the Fourier transform of the impulse response, the transfer function. An ideal system would form a point image of a point object. But, because of diffraction and aberrations, a real system has an impulse response of nonzero width. The impulse response of a system is the two-dimensional image formed in response to a delta-function object, and is denoted by the symbol h(x,y). The actual image, g, formed by the system is the ideal image, f (an exact replica of the object with appropriate size scaling), convolved with the impulse response, h: f(x,y)**h(x,y)=g(x,y), where the double asterisk denotes a two-dimensional convolution. A narrower impulse response gives better image quality than a wide impulse response. Alternately, we can consider the imaging process in the spatial-frequency domain. In this context, we are concerned with the imaging of sinusoids of different frequencies, rather than the imaging of point objects. The irradiance distribution of an object can be thought of as composed of spatial frequency components, in the same way as a time-domain electrical signal is composed of various temporal frequencies by means of a Fourier analysis. First, consider an irradiance distribution as a function of x and y, as seen in Fig. 2.1. This irradiance distribution can represent either an object or an image. From a one-dimensional profile of the distribution, we obtain a single-variable function that can be Fourier decomposed into its constituent frequencies (cycles/mm).

This study aimed to quantitatively assess the radiation dose using XR-QA2 and the image quality of the dual-energy subtraction mammography technique on an in-house phantom. The analysis was carried out to investigate the effect of targets/filters on dose value and image quality using an in-house phantom made of PLA + as an object representing compressed breasts. All irradiation parameters were performed in the craniocaudal position with manual mode. Mean glandular dose (MGD) was recorded, followed by the calculation of the signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), and modulation transfer function (MTF) for image quality assessment parameters. The results showed that the image quality was accepted at dose levels within the IAEA and BAPETEN tolerance limit for 60mm equivalent compressed breast using dual-energy mammography. Furthermore, the target/filter (W/Rh) reduced the dose by 1.03mGy compared to the Mo/Mo and Mo/Rh with an enhancement in image quality. This indicated that the target/filter (W/Rh) combination was optimal due to the image quality improvement obtained with lower MGD.

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.

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.

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.

Background Cornea astigmatism can be effectively corrected by implanting Toric intraocular lens (IOL) during cataract surgery and therefore improve visual acuity of patients.However, the decentration and rotation position errors were inevitable sometime.What's the difference of effect of position errors on quality of image between spherical IOL and Toric IOL needs further research. Objective This study was to evaluate the optical performance and wavefront with rotation and decentration of Toric IOL. Methods Different decentration for SN60AT IOL(spherical IOL) and Toric IOL in Hwey-Lan Lion model eyes was set with the role as follows: decentration 0.25 mm to 0.75 mm in a 5°-interval from 0° to 90°.Furthermore, Toric IOL was rotated at 5° and 10°, respectively.Then the image performances of SN60AT IOL and Toric IOL at different decentration distances and rotated degrees were evaluated with modulation transfer function (MTF) and value of wavefront aberration under all conditions. Results At the centration, the MTF curves of spherical IOL and Toric IOL were similar under 3, 4 and 5 mm pupil diameter at each spatial frequency.Under the condition of 4 mm pupil diameter, when the decentration was 0.25 mm, the MTF values of SN60AT IOL at 6 c/d and 12 c/d were 0.581 087 and 0.411 960, respectively.T3 IOL were 0.454 259 and 0.382 313, T4 IOL were 0.426 020 and 0.360 490, T5 IOL were 0.425 606 and 0.359 877.When the decentration was 0.50 mm, the MTF values of SN60AT at 6 c/d and 12 c/d were 0.573 073 and 0.412 787, respectively.T3 IOL were 0.450 943 and 0.379 481, T4 IOL were 0.423 153 and 0.356 664, T5 IOL were 0.422 881 and 0.356 230.When the decentration was 0.75 mm, the MTF values of SN60AT at 6 c/d and 12 c/d were 0.560 038 and 0.413 624, respectively.T3 IOL were 0.445 597 and 0.374 322, T4 IOL were 0.418 522 and 0.350 087, T5 IOL were 0.418 468 and 0.349 976.When the IOL decentralized along 0°, 5°, 10°, 90°meridian line, the MTF values were almostly same.The root mean square (RMS) of spherical IOL and Toric IOL was increased when the IOL decentralized from 0 mm to 0.75 mm, with the most increasing level in coma aberration and slight increase in trefoil aberration.When the T4 IOL decentralized from centre to 0.75 mm, the coma increased from 0 to C(3, -1) -0.049 79 μm, C(3, 1) -0.037 59 μm and the trefoil aberration increased from 0 to C(3, 3) 0.005 72 μm, C(3, -3) 0.004 64 μm.With the increase of rotation degrees (from 5°to 10°) of Toric IOL, the MTF was worse at high spatial frequency.Toric IOL rotation caused the increase of astigmatism and residual astigmatism and spherical error, but not high order aberration. Conclusions The tolerance of Toric IOL to decentration is very close to the spherical IOL, and optical performance is only associated with the amount of decentration but not direction.The aberration caused by Toric IOL decentration is mainly coma.The rotation of Toric IOL causes astigmatism error but not high order aberrations. Key words: Lenses, intraocular; Refraction, ocular/physiology; Astigmatism/physiopathology; Lens implantation, intraocular; Decentration; Optical performance; Visual acuity/physiology; High order aberrations

The holographic method and experimental results for recording two-dimensional modulation transfer functions (MTF) of lenses are described. The conditions for hologram-filter recording are determined. The existence of optimum ratio between reference and object beam intensities, at which the results of measuring MTF match with those expected, will be demontrated. The cause of formation of parasite intensity modulation in correlation distribution will be revealed and the way to eliminate it will be suggested. The requirements for granularity of the recording medium for hologram-filters are determined. It will be shown that the results of measuring the two-dimensional MTFs of lenses with symmetrical and nonsymmetrical point spread functions by the holographic method are satisfactorily matching with the expected results and the evidence obtained through harmonic analysis.

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.

Digital breast tomosynthesis (DBT) is becoming an important part of breast cancer screening and diagnosis. Compared to two-dimensional mammography, tomosynthesis introduces limited three-dimensional (3D) resolution, but maintains high in-plane resolution, low dose, and allows for similar clinical protocols. The scanning motion and oblique projections of tomosynthesis acquisitions introduce shift-variance to the image quality, in addition to effects such as source blurring and geometric magnification. Shift-variant detector response caused by oblique incidence has been extensively studied previously and is most easily mitigated by letting the source and detector move in sync. In addition, conical reconstruction grids, that is, a grid aligned with the central tomosynthesis projection, have been proposed to compensate for magnification effects. This paper introduces a shift-variant cascaded systems model for tomosynthesis and validates it against measurements. As an example, the model was used to investigate the shift-variance of a tomosynthesis system. The shift-variant cascaded systems model was validated on a slit-scanning photon-counting DBT system, with synchronous source-detector movement, using simple back-projection in a conical reconstruction volume. The modulation transfer function (MTF), normalized noise-power spectrum (NNPS), and detective quantum efficiency (DQE) were used as figures of merit. Simulations were performed for single points while measurements were done over a finite volume, assuming local shift invariance. To investigate the full extent of shift-variance, 80 locations across the volume were simulated, and the MTF and DQE at 2.5lp/mm were calculated as a function of position. The simulated metrics generally agreed well with their corresponding measurements. The frequency at 50% MTF along the scan direction showed a relatively small variation, ranging from 2.1 to 2.4lp/mm for the different locations. The frequency at 50% MTF along the chest-mammilla direction showed a larger variation, ranging from 2.9 to 3.8lp/mm. All points exhibited a similarly shaped NNPS but the noise magnitude varied with slice height. The zero-frequency DQE in reconstructed slices was lower than that of the projections, an effect likely caused by noise-aliasing increasing the zero-frequency noise. A shift-variant cascaded systems model has been developed for slit-scanning tomosynthesis using simple back-projection. The model was successfully validated against measurements. Even though the study was performed on a slit-scanning system, several parts of the framework can be applied and extended to other tomosynthesis geometries. The conical reconstruction grid has low variation in image quality in the scan direction where the 3D information is acquired, but source and geometric magnification still dominate in the slit direction, causing a larger variation in image quality. We conclude that image quality is close to shift-invariant in the scan direction, but not in the height and chest-mammilla directions, and we recommend that small measurement volumes are used when measuring image quality in these directions to minimize the effects of shift variance.

In direct volume rendering, the use of transfer functions allows the visualization of specific parts of the volume, revealing significant structures such as boundaries between different materials. To interactively specify an adequate transfer function is a very challenging and time-consuming task. Besides, a user can settle with a transfer function that does not reveal the overall structure inside the volume. Hence, the importance of generating adequate transfer functions automatically. Since Kindlmann and Durkin's seminal work on the semi-automatic generation of transfer functions, many research works have been conducted attempting to improve their proposal. Despite some fine resulting visualizations, many of these works aimed to diminish the problem of boundary overlaps, in the data domain, by using two-dimensional transfer functions, thus decreasing the focus on the automatic generation and leaving to the user, again, the task to manually isolate isosurfaces. Moreover, fine-tuning two-dimensional transfer functions is less intuitive than adjusting one-dimensional ones. This paper redirects Kindlmann and Durkin's concepts of boundary characterization and proposes a new method to automatically generate one-dimensional transfer functions, more robust to boundary overlaps. This work also suggests a rendering filter to isolate detected isosurfaces in the visualization.