Modulation Transfer Function Research Articles

Design and performance evaluation of an enhanced monofocal intraocular lens

Enhanced monofocal intraocular lenses (IOLs), aimed at improving intermediate vision while maintaining distance vision comparable to traditional monofocal IOLs, are emerging as a promising option for cataract surgery. This study introduces a method for designing such enhanced monofocal IOL and conducts a thorough investigation of its optical performance. Additionally, the visual acuity (VA) of the pseudophakic eye implanted with the designed IOL is examined. The designed IOL provides image quality for distance vision comparable to that of monofocal IOLs and a depth of focus of 1.30 D, demonstrating its ability to improve intermediate vision. Moreover, the optical performance of the designed IOL based on this method can be comparable to commercial products, in terms of the modulation transfer function (MTF). The designed enhanced monofocal IOL demonstrates a potential for real application in cataract surgery.

Modulation transfer function of implantable phakic intraocular contact lens (IPCL) for myopia and presbyopia.

This study aimed to assess the optical quality of myopic and presbyopic IPCLs with different additional powers, and to investigate the effects of pupil size on the optical quality of these IPCLs using an in-vitro modulation transfer function (MTF) measurement system. Linear scatter functions (LSFs) were recorded using the OPAL Vector system and an eye phantom consisting of wet cells filled with a balanced salt solution. A myopic IPCL or a presbyopic IPCL was placed in the posterior chamber of this model. The MTF was calculated from the LSF using the fast Fourier transform techniques. The effective apertures were set at 2.0 to 5.0mm in 1.0mm steps. The in-focus MTF values of the myopic IPCL and presbyopic IPCL with additional powers of + 2.0 and + 4.0 diopters at 100 cycles/mm for an effective aperture of 3.0mm were 43%, 27%, and 24%, respectively. The in-focus MTF value of both myopic and presbyopic IPCLs was the highest when the effective aperture was set at 3.0mm, and it gradually worsened when the effective aperture became larger than 3.0mm at 20, 60, and 100 cycles/mm. Both myopic and presbyopic IPCLs provided excellent MTF values, but the additional power profile can deteriorate optical performance in presbyopic IPCL-implanted eyes, even with a low additional power. Pupil size can influence visual quality in IPCL-implanted eyes for both myopia and presbyopia.

82‐3: Optical Quality Requirements for Accurate MTF/CTF Measurements on Near‐Eye‐Displays

Modulation Transfer Function (MTF) is an important image quality metric. Traditional displays generate images on a flat display, whereas Near‐Eye‐Displays (NEDs) project virtual images with amplitude and wave‐front phase information. Poorly designed NED MTF test systems can introduce uncorrectable measurement errors, in contrast to well‐designed systems with aberration‐free optical performance.

P‐49: Angular Dependent Point Spread Function Analysis for Virtual Reality Head Mounted Displays

We demonstrate a point spread function method for measuring the angular dependence of the spatial resolution of a virtual reality head mounted display. The angular dependence of spatial resolution of the imaging detector was characterized to remove the detector's contribution at each angular location measured on the VR HMD. This method allows measuring the twodimensional spatial resolution and modulation transfer function.

58‐4: Late‐News Paper: Dynamic MTF Measurements of Gaming Monitors

Recent gaming monitors claim high refresh rates of ≥240 Hz with response times ≤1 ms. However, these temporal metrics do not clearly reveal their true spatiotemporal resolution, which depends on the velocity at which the images are displayed. This is the first study to demonstrate the line‐based dynamic modulation transfer function (MTF) measurement method for comparing the performances of different gaming monitors. A single line was scrolled on the monitors, and a small region of the screen was captured with a high‐speed camera during one display refresh period. The dynamic MTF results elucidate the dependence of spatiotemporal resolution characteristics on the scroll speed, refresh rate, and response time of the monitors.

Can processed images be used to determine the modulation transfer function and detective quantum efficiency?

The modulation transfer function (MTF) and detective quantum efficiency (DQE) of x-ray detectors are key Fourier metrics of performance, valid only for linear and shift-invariant (LSI) systems and generally measured following IEC guidelines requiring the use of raw (unprocessed) image data. However, many detectors incorporate processing in the imaging chain that is difficult or impossible to disable, raising questions about the practical relevance of MTF and DQE testing. We investigate the impact of convolution-based embedded processing on MTF and DQE measurements. We use an impulse-sampled notation, consistent with a cascaded-systems analysis in spatial and spatial-frequency domains to determine the impact of discrete convolution (DC) on measured MTF and DQE following IEC guidelines. We show that digital systems remain LSI if we acknowledge both image pixel values and convolution kernels represent scaled Dirac -functions with an implied sinc convolution of image data. This enables use of the Fourier transform (FT) to determine impact on presampling MTF and DQE measurements. It is concluded that: (i)the MTF of DC is always an unbounded cosine series; (ii)the slanted-edge method yields the true presampling MTF, even when using processed images, with processing appearing as an analytic filter with cosine-series MTF applied to raw presampling image data; (iii)the DQE is unaffected by discrete-convolution-based processing with a possible exception near zero-points in the presampling MTF; and (iv)the FT of the impulse-sampled notation is equivalent to the transform of image data.

Corneal densitometry in Chinese adults with healthy corneas: associations with sex, age, ocular metrics, and optical characteristics

BackgroundStandardized corneal densitometry (CD) values in large samples of healthy Chinese individuals are scarce. Therefore, we aimed to determine the standard CD values using a Scheimpflug camera in healthy corneas, investigate the correlations of sex, age, and ocular parameters with corneal density, and explore the impact of corneal density on the forward scattering and optical quality of the eye.MethodsThis retrospective observational study involved 990 healthy Chinese individuals, including 494 males and 496 females (mean age: 23.88 ± 6.90 years). The CD values at various depths and radial areas of 0–12 mm were measured using a Scheimpflug camera. Densitometric measurements were expressed in standardized grayscale units (GSU). The optical scatter index (OSI), modulation transfer function cutoff values (MTFcutoff), and Strehl’s ratio (SR) were also determined using an optical quality analysis system.ResultsThe average CD within a 12 mm diameter area was 16.26 ± 1.35 GSU. The highest and lowest optical densities at different depths were observed in the anterior (21.41 ± 2.16 GSU) and posterior (12.00 ± 1.01 GSU) layers, respectively (P < 0.001). Similarly, the maximum and minimum optical densities at different radial areas were observed in the 10–12 mm (14.09 ± 0.93 GSU) and 2–6 mm (25.93 ± 4.77 GSU) circles, respectively (P < 0.001). There was no significant difference in the average CD within a 12 mm diameter area between males and females (P > 0.05). However, upon adjusting for age, central corneal thickness (CCT), corneal curvature, white-to-white (WTW) corneal diameter, and axial length, females exhibited a greater average CD within the 12 mm diameter and in the 6–10 mm and 10–12 mm circles than males. Age-related changes in CD were evident, except in the 2–6 mm circle. CCT, corneal curvature, WTW corneal diameter, and partial depth correlated with CD in the radial area, and CD in different areas correlated with the OSI, MTFcutoff, and SR (P < 0.05).ConclusionsThis study provides the normative CD measurement data of Chinese adults with healthy corneas, emphasizing the significance of sex, age, CCT, corneal curvature, and WTW corneal diameter in CD evaluation. Notably, elevated CD can lead to increased forward scattering within the eye, thereby affecting the optical quality.

Design for a virtual reality head-mounted display with holographic pancake optics

A design for a head-mounted display using holographic optical elements (HOEs) and pancake optics is presented. The pancake optics assembly consists of a circular polarization, quarter-wave film, and a coated 50/50 (semi-transmissive and semi-reflective) aspherical lens. The HOE and pancake optics combination was employed to reduce the volume of the system. For this design, the effective focal length was 10.901 mm, the field of view was 30 deg, and the f-number was 3.633. In terms of image quality, the modulation transfer function (MTF) values for all fields exceeded 0.3 at 65 lp/mm. The MTF values for all fields under the tolerance error also exceeded 0.3 lp/mm. The maximum optical distortion was less than 2%. The impact of the efficiency of diffracted and non-diffracted light on the visibility was analyzed to select the appropriate reflectance for the coating of the 50/50 aspherical lens and the highest hologram diffraction efficiency to achieve the best visibility.

Serum miR-26a level is decreased in cataract patients with glaucoma and related to visual quality

ABSTRACT Clinical relevance microRNAs have been found to be involved in the progression of a variety of ocular diseases. Background Cataract and glaucoma often coexist, and combined surgery is a common treatment. The aim of this study is to analyse the correlation between miR-26a and visual quality in cataract patients with glaucoma. Methods Seventy patients with cataract and glaucoma and 70 healthy volunteers were enrolled and received phacoemulsification and trabeculectomy. The patients were divided into low and high miR-26a expression groups according to miR-26a mean expression. The objective scattering index, strehl ratio, and modulated transfer function cut-off were analysed by optical quality analysis system II. The changes of miR-26a, objective scattering index, strehl ratio, modulated transfer function cut-off, and the correlation between the indicators were analysed. The downstream genes of miR-26a were analysed by Gene Ontology and Kyoto Encyclopaedia of Genes and Genomes functional enrichment. Results There were significant differences between patients and controls in lipid biomarker levels and visual indicators. miR-26a was decreased in the patient group. Strehl ratio and modulated transfer function cut-off in the miR-26a low-expression group were lower than in high-expression group, while mean defect of the visual field and objective scattering index were higher than in high-expression group. The miR-26a expression was negatively correlated with the severity of disease and objective scattering index, and positively correlated with strehl ratio and modulated transfer function cut-off. After surgery, miR-26a, strehl ratio, and modulated transfer function cut-off were increased, and objective scattering index was decreased. The downstream genes of miR-26a were related to several biological processes and signalling pathways. Conclusion In cataract patients with glaucoma, miR-26a expression was lower than matched controls and increased following combined cataract removal and trabeculectomy.

Biometric factors associated with the postoperative visual performance of a multifocal intraocular lens

PurposeTo identify the biometric factors associated with postoperative visual performance after uneventful phacoemulsification with multifocal intraocular lens (MIOL) implantation. MethodsIn this retrospective cohort study, 72 eyes of 72 patients implanted with the HumanOptics Diff-aAY MIOL were included. Preoperative examination data including the white-to-white distance (WTW), anterior chamber depth (ACD), axial length and corneal astigmatism were gathered through the electronic medical records. One month postoperatively, the pupil parameters, corneal aberrations, corneal astigmatism, IOL tilts and IOL decentrations were measured using an OPD-Scan III aberrometer. Postoperative visual performance parameters were recorded as the visual acuity, depth of focus, modulation transfer function (MTF) and point spread function (PSF) values, area under log contrast sensitivity function (AULCSF), retinal straylight and visual function questionnaire scores. Univariate and multivariate linear regression analyses were then performed to evaluate the associations between the potential biometric factors and postoperative visual outcomes. ResultsYounger age predicted greater MTF and PSF values, better AULCSF and better retinal straylight (P < 0.05). A lower corneal trefoil predicted better MTF and PSF values (P < 0.05). Smaller IOL decentration predicted better distance-corrected near visual acuity, greater AULCSF and better retinal straylight (P < 0.05). A less negative spherical equivalent (SE) predicted better MTF values (P = 0.017), while a more negative SE predicted better Visual Function Index-14 (VF-14) questionnaire scores and satisfaction scores (P < 0.05). A higher IOL power predicted better best corrected distance visual acuity (P = 0.005). Lower preoperative corneal astigmatism predicted greater MTF values (P = 0.020). Lower postoperative corneal astigmatism, smaller corneal high-order aberrations (HOAs), smaller photopic pupil size, larger WTW and deeper ACD predicted a better AULCSF (P < 0.05). ConclusionsIOL decentration, IOL power, age, preoperative and postoperative corneal astigmatism, SE, photopic pupil size, corneal trefoil, WTW, ACD and corneal HOAs were significantly associated with postoperative visual performance. These findings might aid in patient selection prior to MIOL implantation.

Wave retrieval for Sentinel-1 synthetic aperture radar under complex sea state

ABSTRACT In this paper, sea surface waves during complex sea state (i.e. tropical cyclones (TCs) and Kuroshio current) are inverted from dual-polarized (vertical – vertical (VV) and vertical – horizontal (VH)) synthetic aperture radar (SAR) images using an existing algorithm, namely, the parameterized first-guess spectrum method (PFSM). In particular, the wind term is included in two modulation transfer functions (MTFs), i.e. tilt modulation and velocity bunching. More than 3000 Sentinel (S-1) images acquired in interferometric wide (IW) mode and extra wide (EW) mode are collected, and the operational CyclObs wind product provided by the French Research Institute for Exploitation of the Oceans (IFREMER) is collected corresponding to the TC images. Note that these images are located within 500 km away from TC eyes. The wave spectra during the TCs are then inverted using the PFSM algorithm and the SAR-derived wind product. Simultaneously, the 0.05° gridded wave spectra collocated with these images are simulated using a third-generation numeric wave model, called WAVEWATCH-III (WW3), in which the reconstructed wind based on the European Centre for Medium-Range Weather Forecasts (ECMWF), the Copernicus Marine Environment Monitoring Service (CMEMS) current, and the CMEMS sea level are treated as the forcing field. Comparison of the SAR wave retrievals and simulations reveals that the root mean square errors (RMSEs) of the significant wave height (SWH) and mean wave period (MWP) are 0.55 m and 0.43 s, their correlation coefficients (COR) are 0.94 and 0.92, and their scatter index (SI) values are 0.17 and 0.07. These results demonstrate the better performance of the PFSM algorithm using theoretical MTFs, i.e. an RMSE of 0.68 m and COR of 0.90 for the SWH and an RMSE of 0.60 s and a COR of 0.87 for the MWP. Although the accuracy of the wave retrieval from the SAR image under complex sea state is improved when implementing the tilt and velocity bunching MTFs with the strong wind term, SWH retrievals by algorithm PFSM suffer saturation problem at SWH > 8 m.

Framework for evaluating photon-counting detectors under pile-up conditions.

While X-ray photon-counting detectors (PCDs) promise to revolutionize medical imaging, theoretical frameworks to evaluate them are commonly limited to incident fluence rates sufficiently low that the detector response can be considered linear. However, typical clinical operating conditions lead to a significant level of pile-up, invalidating this assumption of a linear response. Here, we present a framework that aims to evaluate PCDs, taking into account their non-linear behavior. We employ small-signal analysis to study the behavior of PCDs under pile-up conditions. The response is approximated as linear around a given operating point, determined by the incident spectrum and fluence rate. The detector response is subsequently described by the proposed perturbation point spread function (pPSF). We demonstrate this approach using Monte-Carlo simulations of idealized direct- and indirect-conversion PCDs. The pPSFs of two PCDs are calculated. It is then shown how the pPSF allows to determine the sensitivity of the detector signal to an arbitrary lesion. This example illustrates the detrimental influence of pile-up, which may cause non-intuitive effects such as contrast/contrast-to-noise ratio inversion or cancellation between/within energy bins. The proposed framework permits quantifying the spectral and spatial performance of PCDs under clinically realistic conditions at a given operating point. The presented example illustrates why PCDs should not be analyzed assuming that they are linear systems. The framework can, for example, be used to guide the development of PCDs and PCD-based systems. Furthermore, it can be applied to adapt commonly used measures, such as the modulation transfer function, to non-linear PCDs.

Developing a novel phantom for image quality evaluation in digital radiography

Evaluation of image quality in digital radiography is important to ensure accurate diagnosis. However, to perform image quality tests accurately and effectively, complex techniques and numerous phantoms are required. The aim of the study was to develop a novel phantom to allow a comprehensive evaluation of image quality in digital radiography. High-Density Polyethylene (HDPE) was used as the main material for the phantom. Physical image quality parameters such as effective Modulation Transfer Function (eMTF), effective Normalized Noise Power Spectra (eNNPS), effective Detective Quantum Efficiency (eDQE), as well as contrast and signal-to-noise ratio (SNR) evaluations can be conducted using the phantom. Preliminary preparation work was carried out through Monte Carlo simulations. The validation of the phantom was performed by comparing with standard phantom results. Physical image quality measurements were performed using an indirect digital radiography system. It was observed that there was a good agreement between the image quality measurement results performed with the standard phantom and the developed phantom. A strong correlation was determined between integrated effective DQE (IeDQE) results (R ≥ 0.97) obtained with HDPE and PMMA phantom. Simulation results regarding the transmission factor showed that HDPE could be an alternative to Polymethyl Methacrylate (PMMA) as a phantom material.

Super resolution deep learning reconstruction for coronary CT angiography: A structured phantom study

PurposeSuper-resolution deep-learning-based reconstruction: SR-DLR is a newly developed and clinically available deep-learning-based image reconstruction method that can improve the spatial resolution of CT images. The image quality of the output from non-linear image reconstructions, such as DLR, is known to vary depending on the structure of the object being scanned, and a simple phantom cannot explicitly evaluate the clinical performance of SR-DLR. This study aims to accurately investigate the quality of the images reconstructed by SR-DLR by utilizing a structured phantom that simulates the human anatomy in coronary CT angiography. MethodsThe structural phantom had ribs and vertebrae made of plaster, a left ventricle filled with dilute contrast medium, a coronary artery with simulated stenosis, and an implanted stent graft. By scanning the structured phantom, we evaluated noise and spatial resolution on the images reconstructed with SR-DLR and conventional reconstructions. ResultsThe spatial resolution of SR-DLR was higher than conventional reconstructions; the 10 % modulation transfer function of hybrid IR (HIR), DLR, and SR-DLR were 0.792-, 0.976-, and 1.379 cycle/mm, respectively. At the same time, image noise was lowest (HIR: 21.1-, DLR: 19.0-, and SR-DLR: 13.1 HU). SR-DLR could accurately assess coronary artery stenosis and the lumen of the implanted stent graft. ConclusionsSR-DLR can obtain CT images with high spatial resolution and lower noise without special CT equipments, and will help diagnose coronary artery disease in CCTA and other CT examinations that require high spatial resolution.

Modulation transfer function of digital breast tomosynthesis: a comparison of various edge devices.

The modulation transfer function (MTF) is a fundamental tool for assessing the sharpness of digital breast tomosynthesis (DBT) systems and is primarily measured using edge devices. We compared the MTF of a Senographe Pristina DBT system using four-edge devices. These devices were composed of stainless steel with a thickness of 0.6, 0.8, and 1.0mm, and 1.0mm tungsten, based on different international guidelines. We evaluated spatial frequencies at MTFs of 0.5 (MTF50%) and 0.1 (MTF10%). The collimator-equipped and non-collimator configurations of the DBT were compared. We found no appreciable differences between scan and chest wall-nipple directions. Both MTF50% (2.90-2.99 cycles/mm) and MTF10% (6.69-6.94 cycles/mm) demonstrated minimal variation across the different edge devices. The collimator-equipped system exhibited an MTF50% that was approximately 5% higher than that of the non-collimator configuration. The choice of the edge device did not appreciably impact the MTF.

Parallel compressive super-resolution imaging with wide field-of-view based on physics enhanced network

Parallel compressive super-resolution imaging has attracted increasing attention in recent years. However, the super-resolution quality depends on modulation masks and reconstruction algorithms. A deep-learning method provides an efficient solution, but in wide field-of-view (FOV) scenarios, the differences between optical transfer functions (OTFs) of each pixel increase the system complexity and limit its practical application. This study proposed a wide FOV parallel compressive super-resolution imaging approach based on a physics-enhanced network. First, the network and modulation masks of an arbitrary 128 × 128-pixel region were trained; then, the trained network was fine-tuned for the rest of the 128 × 128-pixel regions in the entire wide FOV, which effectively eliminated the OTF variability. Numerical simulations and practical experiments demonstrated that through the proposed approach, super-resolution images of 1020 × 1500 pixels can be reconstructed from 272 × 400-pixel low-resolution measurements using only three designed masks, with the resolution enhanced 3.75×3.75 times and the peak signal-to-noise ratio improved by 89.4% compared to the results of the previous compressed sensing algorithm. Besides, the training time was dramatically reduced by 95.5-fold compared with the traditional training strategy for each region alone. This approach decreases the imaging complexity of wide FOV and achieves the high-quality super-resolution reconstruction under few trained masks, thus we believe it can promote rapid imaging for super-resolution and a wide FOV ranging from infrared to terahertz.

The Impact of Back Optic Zone Design in Orthokeratology on Visual Performance.

To evaluate the visual performance in adolescents undergoing orthokeratology (OrthoK) treatment with two different optical zone diameters (OZDs). This randomized, double-masked, self-controlled prospective study was conducted at Tianjin Eye Hospital (Tianjin, China) in June 2022. Thirty-six eligible schoolchildren were enrolled and fitted with corneal refractive therapy lenses with two sizes of OZDs (5 mm [5OZ] and 6 mm [6OZ]). Each participant was randomized to wear the 5OZ in one eye and the 6OZ in the contralateral eye. Subjective visual quality was assessed using visual acuity, refraction, contrast sensitivity function, and visual symptoms, and the objective optical quality was assessed using ocular higher order aberrations (HOAs) and modulation transfer function (MTF). Thirty-five myopic children completed a 1-month follow-up visit. The 5OZ lens induced significantly smaller treatment zone diameters than the 6OZ lens (P < 0.001). Subjective visual quality did not differ significantly between the two groups. Compared to baseline, aberrations of Z40, coma-like, spherical-like, and total HOAs in both groups increased significantly (P < 0.05). For the 3-mm pupils, spherical aberration in the 5OZ group was significantly higher than that in the 6OZ group (P < 0.05). The MTF value of the 6OZ group was significantly higher than that of 5OZ group for 0.3 and 1.5 cycles per degree for the 3-mm pupils (P = 0.006 and P = 0.026, respectively). However, HOAs or MTF did not differ significantly between the two groups for the 5-mm pupils. The difference induced by varying OZD was significant only in the smaller pupil condition. The selection of OZD in OrthoK designs in real-world patient management should be done while considering individual pupil size. This study revealed that the objective visual quality of small OZD lenses was only slightly affected for the small pupil size.

Analytical Model of Point Spread Function under Defocused Degradation in Diffraction-Limited Systems: Confluent Hypergeometric Function

Analytical Model of Point Spread Function under Defocused Degradation in Diffraction-Limited Systems: Confluent Hypergeometric Function

Characterizing Modulation Transform Functions for varying Zeff materials

Compton Backscatter Imaging (CBI) is a decades old approach to imaging surfaces where positioning of a detector and x-ray source for transmission imaging is either not possible or convenient. For that reason, it has been explored and utilized in areas of explosive detection and security applications, railway infrastructure integrity, and aerospace safety. Within these applications, much of the focus is on resolution for specific signatures within the target medium, particularly voids that indicate decreased structural integrity. The purpose of this research is to characterize the Modulation Transfer Function (MTF) signature of plastic, lead, steel, aluminum, and copper. MTF contrast analysis yields greater results in image clarity and post processing when compared to altering the image capture alone. Doing so would allow researchers to configure scanning equipment to detect key elements specific to CBI imaging of potential explosive devices. While past research has focused on an explosive penalty or contraband, the goal for this research is to target components of a device like the wiring or power source.

Foveated pancake lens design for improved optical performance and eye rotation support.

We propose a novel, to our knowledge, approach to address the limitations of traditional pancake lenses for virtual reality headsets, such as low image contrast and poor performance when eyes rotate. The design leverages the foveated nature of human vision, achieving a superior modulation transfer function in the foveal area to enhance optical performance significantly. Furthermore, the pancake lens design is presented that considers the rotation of the user's pupil position, maintaining optimal image quality even when the user's eye rotates. The proposed method presents the parameters and optimization of a novel pancake lens that utilizes the characteristics of the human visual system and accounts for the rotation of the pupil position of the user, leading to improvements in image quality and user experience. The lens design and image simulation results are presented to demonstrate the effectiveness of the approach.