Modulation Transfer Function Measurement Method Research Articles

Best Practices for Measuring the Modulation Transfer Function of Video Endoscopes

Endoscopes are crucial for assisting in surgery and disease diagnosis, including the early detection of cancer. The effective use of endoscopes relies on their optical performance, which can be characterized with a series of metrics such as resolution, vital for revealing anatomical details. The modulation transfer function (MTF) is a key metric for evaluating endoscope resolution. However, the 2020 version of the ISO 8600-5 standard, while introducing an endoscope MTF measurement method, lacks empirical validation and excludes opto-electronic video endoscopes, the largest family of endoscopes. Measuring the MTF of video endoscopes requires tailored standards that address their unique characteristics. This paper aims to expand the scope of ISO 8600-5:2020 to include video endoscopes, by optimizing the MTF test method and addressing parameters affecting measurement accuracy. We studied the effects of intensity and uniformity of image luminance, chart modulation compensation, linearity of image digital values, auto gain control, image enhancement, image compression and the region of interest dimensions on images of slanted-edge test charts, and thus the MTF based on these images. By analyzing these effects, we provided recommendations for setting and controlling these factors to obtain accurate MTF curves. Our goal is to enhance the standard’s relevance and effectiveness for measuring the MTF of a broader range of endoscopic devices, with potential applications in the MTF measurement of other digital imaging devices.

Improved On-Orbit MTF Measurement Method Based on Point Source Arrays

The modulation transfer function (MTF) is a key characteristic used to assess the performance of optical remote sensing satellite sensors. MTF detection can directly measure a sensor’s two-dimensional (2D) point spread function (PSF); therefore, it has been applied to various high-resolution remote sensing satellites (e.g., Pleiades) using point sources. However, current point source methods mainly use 2D Gaussian functions to fit the discrete digital number (DN) of the point source on the image to extract the center of the point source and fit the PSF after encrypting multiple point sources; thus, noise robustness is poor and measurement accuracy varies widely. In this study, we developed a noise-resistant on-orbit MTF detection method based on the object space constraint among point source arrays. Utilizing object space constraint relationships among points in a point source array, a homography transformation model was established, enabling accurate extraction of sub-pixel coordinates for each point source response. Subsequently, aligning the luminosity distribution of all point sources concerning a reference point source, the encrypted PSF was obtained and then fitted to obtain the MTF. To validate the method, Gaofen-2 (GF-2) satellite images were used to conduct an in-orbit imaging experiment on the point source array of the Chinese Zhongwei remote sensing satellite calibration site. Compared with the Gaussian model methods, the proposed method yielded more accurate peak positions for each point source. Standard deviations of peak position constant ratios in along- and cross-track directions improved by 2.8 and 4.8 times, respectively. The root-mean-square error (RMSE) of the collinearity test results increased by 92%, and the noise resistance of the MTF curve improved by two times. Dynamic MTF values at the Nyquist frequency for the GF-2 panchromatic band in along- and cross-track directions were 0.0476 and 0.0705, respectively, and MTF values in different directions were well distinguished.

Accuracy and precision of an edge-based modulation transfer function measurement method using a variable oversampling ratio

The edge-based method standardized in ISO 12233 approximates the modulation transfer function (MTF) as a function of horizontal or vertical spatial frequency by analyzing a supersampled edge profile obtained from the captured image of a slightly slanted bi-tonal edge. The method describes the slanted projection of pixels sampled in a square array into a linear array of subpixel-wide bins. An ad hoc correction is available to accommodate the diagonal MTF measurements. However, using a fixed oversampling ratio in the standard method degrades the accuracy and precision of the MTF estimates, owing to the periodic misalignment between the projection paths and the bin array. A new edge-based method using a variable oversampling ratio, OMNI-sine, has been proposed to remedy this misalignment. In this study, computer simulations were performed to demonstrate the accuracy and precision of the MTF estimates over a full range of finely sampled slant angles.

Edge-based modulation transfer function measurement method using a variable oversampling ratio.

The ISO 12233 edge-based method approximates the modulation transfer function (MTF) as a function of horizontal or vertical spatial frequency by analyzing a 1D supersampled edge gradient obtained from the captured image of a near-vertical or near-horizontal bi-tonal edge, respectively. The method involves the slanted projection of pixels in a square array into a linear array of subpixel-wide bins. It can be modified to accommodate diagonal MTF measurements; however, using a fixed integer oversampling ratio degrades the accuracy and precision of diagonal MTF estimates due to periodic misalignment between the projection paths and the bin array. In this study, an edge-based method-called OMNI-sine-is proposed to counter the misalignment and improve MTF estimates by using a variable oversampling ratio dependent on the slant angle.

52‐4: Simulation of Dynamic MTF Measurement Method for Pixelated Displays

A method for measuring the dynamic modulation transfer function (MTF) of a display is introduced. A single moving vertical line is displayed, and a high‐speed imaging light measuring device (LMD) captures a small region of the screen. The effect of smooth‐pursuit eye‐tracking of the moving line is simulated by aggregating a series of supersampled luminance profiles.

Error of the slanted edge method for measuring the modulation transfer function of imaging systems.

The slanted edge method is a basic approach for measuring the modulation transfer function (MTF) of imaging systems; however, its measurement accuracy is limited in practice. Theoretical analysis of the slanted edge MTF measurement method performed in this paper reveals that inappropriate edge angles and random noise reduce this accuracy. The error caused by edge angles is analyzed using sampling and reconstruction theory. Furthermore, an error model combining noise and edge angles is proposed. We verify the analyses and model with respect to (i)the edge angle, (ii)a statistical analysis of the measurement error, (iii)the full width at half-maximum of a point spread function, and (iv)the error model. The experimental results verify the theoretical findings. This research can be referential for applications of the slanted edge MTF measurement method.

Modified slanted-edge method to measure the modulation transfer function of camera

The slanted-edge method specified in ISO Standard 12223, which experiences large errors in the camera modulation transfer function(MTF) due to tilt angle error in the knife-edge resulting in non-uniform sampling of the edge spread function. In order to resolve this problem, a modified slanted-edge method for camera MTF measurement is proposed. By applying a simple direct calculation of the Fourier transform of the derivative for the non-uniform sampling data, the camera super-sampled MTF results are obtained. Theoretical simulations for images with and without noise under different tilt angle errors are run using the proposed method. It is demonstrated that the MTF results are insensitive to tilt angle errors. To verify the accuracy of the proposed method, an experimental setup for camera MTF measurement is established. Measurement results show that the proposed method is superior to traditional methods, and improves the universality of the slanted knife-edge method for camera MTF measurement.

A method to measure the modulation transfer function of Bayer filter color camera

With the development of optoelectronic technologies, color cameras have been widely exploited in space remote sensing, earth observations from space, environmental monitoring, urban construction, and many other fields. Currently, most commercial color cameras use a single charge coupled device (CCD) or complementary metal-oxide-semiconductor (CMOS) sensor that has a Bayer color filter array (CFA) on its pixel surface to obtain red (R), green (G), or blue (B) samples. As a way of evaluating imaging quality, modulation transfer function (MTF) can provide a comprehensive and objective metric for camera imaging performance. In the conventional knife-edge method for color camera MTF measurement, a linear uniform sampling of the edge spread function (ESF) must be completed before a fast Fourier transform (FFT) can be applied. As the sampling rate becomes large, the number of pixel points on the line which is parallel to the knife-edge become less. So taking average of the pixel points to obtain ESF can be strongly affected by the noise of sensor. Therefore it is necessary to balance the influences of sampling rate and sensor noise on the MTF measurement, and the recommended sampling rate is 4-6. When the tilt angle of knife-edge has an error, the non-uniform sampling ESF can be obtained by the slanted knife-edge method. This leads to a variation in the results of the camera MTF on a spatial frequency scale and early cut-off. The best MTF results of camera can be obtained by rotating knife-edge, calculating MTF power under different tilt angles of knife-edge, and finding the maximum MTF power. And we propose an algorithm for Bayer filter color camera MTF measurement. The algorithm processing includes extracting R, G, B colors of knife-edge images; projection; differential operation; Hanning window filtration; FFT; correction; weighting combination of R, G, B colors MTF; MTF power calculation; optimal tilt angle of knife-edge estimation. To verify the accuracy of the proposed method, the weighting response factors of R, G, B colors are calibrated and an experimental setup for color camera MTF measurement is established. The knife-edge target is rotated in angle steps of 0.02, and the MTF results are calculated under different tilt angles of knife-edge within0.1 surrounding the estimate position by the proposed algorithm. The maximum differences of MTF results between the proposed method and fringe target method are 0.061 (Nyquist frequency fc) and 0.043 (fc/2), respectively. The results show that by searching the optimal tilt angle of knife-edge, the effect of non-uniform sampling on MTF result of color camera can be eliminated. Compared with the conventional method, the proposed method is superior for the measurement of the super-sampled MTF of color camera. Meanwhile, this method can also be applied to MTF measurements of radiographic systems, such as X-ray imaging system and other systems.

Effective modulation transfer function measurement method for an off-axis optical system.

The most common modulation transfer function (MTF) measurement equipment operates along a coaxial testing light path. It can be used to test several fields along one radial direction and is suitable for an optical system with rotational symmetry. However, off-axis optical systems need multidimensional adjustment and complex mechanical structures to measure the MTF of fields. In this paper, we propose a MTF testing module to address this issue by adding a rotatable mirror to redirect the light. The testing module greatly simplifies MTF measurement of off-axis imaging systems in both the process and mechanism. The figure error of the rotatable mirror is analyzed to ensure testing accuracy. MTF testing of a free-form surface prism using this novel method was successfully implemented and the results are presented. The method can be extended to the measurement of other parameters, such as the effective focal length.

Towards task-based assessment of CT performance: System and object MTF across different reconstruction algorithms

To investigate a measurement method for evaluating the resolution properties of CT imaging systems across reconstruction algorithms, dose, and contrast. An algorithm was developed to extract the task-based modulation transfer function (MTF) from disk images generated from the rod inserts in the ACR phantom (model 464 Gammex, WI). These inserts are conventionally employed for HU accuracy assessment. The edge of the disk objects was analyzed to determine the edge-spread function, which was differentiated to yield the line-spread function and Fourier-transformed to generate the object-specific MTF for task-based assessment, denoted MTF(Task). The proposed MTF measurement method was validated against the conventional wire technique and further applied to measure the MTF of CT images reconstructed with an adaptive statistical iterative algorithm (ASIR) and a model-based iterative (MBIR) algorithm. Results were further compared to the standard filtered back projection (FBP) algorithm. Measurements were performed and compared across different doses and contrast levels to ascertain the MTF(Task) dependencies on those factors. For the FBP reconstructed images, the MTF(Task) measured with the inserts were the same as the MTF measured from the wire-based method. For the ASIR and MBIR data, the MTF(Task) using the high contrast insert was similar to the wire-based MTF and equal or superior to that of FBP. However, results for the MTF(Task) measured using the low-contrast inserts, the MTF(Task) for ASIR and MBIR data was lower than for the FBP, which was constant throughout all measurements. Similarly, as a function of mA, the MTF(Task) for ASIR and MBIR varied as a function of noise--with MTF(Task) being proportional to mA. Overall greater variability of MTF(Task) across dose and contrast was observed for MBIR than for ASIR. This approach provides a method for assessing the task-based MTF of a CT system using conventional and iterative reconstructions. Results demonstrated that the object-specific MTF can vary as a function of dose and contrast. The analysis highlighted the paradigm shift for iterative reconstructions when compared to FBP, where iterative reconstructions generally offer superior noise performance but with varying resolution as a function of dose and contrast. The MTF(Task) generated by this method is expected to provide a more comprehensive assessment of image resolution across different reconstruction algorithms and imaging tasks.

Improvement of the edge method for on-orbit MTF measurement

The edge method is a widely used way to assess the on-orbit Modulation Transfer Function (MTF). Since good quality is required for the edge, the higher the spatial resolution, the better the results are. In this case, an artificial target can be built and used to ensure a good edge quality. For moderate spatial resolutions, only natural targets are available. Hence the edge quality is unknown and generally rather poor. Improvements of the method have been researched in order to compensate for the poor quality of natural edges. This has been done through the use of symmetry and/or a transfer function model, which enables the elimination of noise. This has also been used for artificial target. In this case, the use of the model overcomes the incomplete sampling when the target is too small or gives the opportunity to assess the defocus of the sensor. This paper begins with a recall of the method followed by a presentation of the changes relying on transfer function parametric model. The transfer function model and the process corresponding to the changes are described. Applications of these changes for several satellites of the French spatial agency are presented: for SPOT 1, it enables to assess XS MTF with natural edges, for SPOT 5, it enables to use the Salon-de-Provence artificial target for MTF assessment in the HM mode, and for the foreseen Pleiades, it enables to estimate the defocus.

Moiré fringes as two-dimensional autocorrelation of transmission function of linear gratings and its application for modulation transfer function measurement

In this work, we show that the transmission moiré pattern is two-dimensional autocorrelation of transmission function (2D-ACTF) of two superimposed linear gratings that make a small angle with each other. In this approach, the properties of moiré fringes vs. the relative displacement of the gratings are formulated. By measuring 2D-ACTF of two similar gratings, we evaluate the modulation transfer function (MTF) of the gratings’ generating system. This work is the generalized form of our previous works. The implied MTF measurement method is easier and faster than our previous methods.

Modulation transfer function measurement method for fiber optic imaging bundles

In this study a method is presented for measuring the modulation transfer function of line-array fiber optic image bundles. The measurements are performed using a designed experimental setup containing a tunable V-shape spatial filter, using three frequencies at one third of Nyquist frequency, two thirds of Nyquist frequency, and Nyquist frequency, respectively. Comparing the measured MTF curve of the fiber optic image bundles with the theoretically computed MTF curve, we have obtained good agreement.

MTF measurement method for medical displays by using a bar-pattern image

— A modulation-transfer-function (MTF) measurement method that uses a bar-pattern image for medical displays such as liquid-crystal displays (LCDs) and cathode-ray tubes (CRTs) has been investigated. A specific bar-pattern image on the display was acquired with a high-resolution single-lens reflex-type digital camera equipped with a close-up lens. The MTF was calculated from the amplitudes of the fundamental-frequency components, which were extracted from the profile data across the bar patterns by using Fourier analysis. Actual comparisons with the conventional line technique were performed for a medical CRT. The adequate accuracy and excellent reproducibility of the method were confirmed. Furthermore, unlike the line method, an advantageous feature which can use an input signal with sufficient amplitude was theoretically proved. Horizontal and vertical MTFs at the central position of the display area were measured up to the Nyquist frequency for several medical displays. From these measurements, this method has the capability to detect slight differences between the displays measured. This proposed method is useful in understanding and quantifying the medical display's performance due to excellent reproducibility and accuracy.

Modulation transfer function estimation from nonspecific images

Measurement of the modulation transfer function (MTF) to quantify the quality of an imaging system proves to be very important in the context of Earth observation satellites. In particular, this measurement is essential to carry out the focusing of the telescope, or to implement a deconvolution filter whose goal is to enhance the image contrast or to reduce the noise. Its knowledge also allows us to compare the characteristics of different known and unknown satellites. We suggest an univariate MTF measurement method using nonspecific views. First of all, the landscape has to be characterized to discriminate ground structure information from MTF information. Once this separation is carried out, landscape structure information can be extracted, allowing a classification between very uniform scenes and more structured ones. Then the MTF, which is described by a bidimensional analytical physical model, can be assessed using an artificial neural network. The principle is to use the artificial neural network to learn the MTF of simulated or perfectly known images, and then use it to assess the MTF of totally unknown images. We show that this method is robust even if noise is taken into account. As a result, maximum MTF assessment errors are less than 10%. This enables us to suggest further developments, including a general scheme for assessment of image quality.

Modulation transfer function measurement method for electrically addressed spatial light modulators

The modulation transfer function (MTF), when used with amplitude modulation (m(A)) data, is a vital coherent optical performance measure for a spatial light modulator (SLM). A new image plane amplitude MTF (MTF(A)) measurement method is presented for electrically addressed SLMs. It involves digital analysis of the output image of a square-wave pattern written onto the SLM. Modulation-level effects are also addressed. Optical laboratory results are presented for two liquid-crystal SLMs. The need to consider amplitude rather than intensity modulation (when coherent optical processing applications are considered) is noted in terms of SLM biasing.

ディスプレイのＭＴＦ測定方法

Modulation transfer function (MTF) quantitatively describes a display' s resolution characteristics. It involves two measurement methods : the impulse method and the sinusoidal method. The authors compared the two methods and showed that the sinusoidal method is the best of the two because the video circuit characteristics are involved in the results. The MTF measurement method for moving images is also investigated.