Modulation Transfer Function Model Research Articles

Computer simulation of mammographic imaging for applications in CAD

A method is described for the computer simulation of mammograms. Software has been developed to model the conversion of input X-ray quanta to visible light photons inside a phosphor screen. In this method, we separated the physics processes that convert X-ray quanta to visible light photons inside a fluorescent screen into five mathematical transformations. Standard FFT techniques were used. We extended Swank's one-dimensional fluorescent screen MTF model into a two-dimensional photon diffusion model by solving the 2D Boltzman diffusion equation. The simulation software divides the fluorescent screen into multiple thinner sub-layers and integrates the visible light output of every sub-layer over the whole screen into the final image. The simulation software was tested by two comparisons: modulation transfer function (MTF) and noise power spectrum. Both test results show that the method and the simulation software work correctly. For the modulation transfer function and the shape of the noise power spectra, the difference between the simulation and the experimental values of an actual fluorescent screen was within 8%. Qualitatively, the simulated and actual images of test objects looked similar. Using the developed method, we will be able to produce simulated mammograms that can be used to evaluate computer-aided diagnosis (CAD) methods and techniques.

Modulation transfer function of photoconductive x-ray image detectors: effects of charge carrier trapping

An analytical expression for calculating the modulation transfer function (MTF) due to distributed carrier trapping in the bulk of the photoconductor of a direct conversion pixellated x-ray image detector is derived using the trapped charge distribution across the photoconductor. The analytical expressions of trapped charge distributions are also derived by solving the continuity equation for both types of carriers (electrons and holes). The MTF of photoconductive x-ray detectors is analysed in terms of normalized parameters, namely (a) the normalized x-ray absorption depth (absorption depth/photoconductor thickness) and (b) normalized carrier schubwegs (schubweg/thickness). Trapping of the carriers that move towards the pixel electrodes degrades the MTF performance, whereas trapping of the carriers that move away from the pixels improves the sharpness of the x-ray image. The MTF model is applied to polycrystalline CdZnTe detectors and is fitted to recently published experimental results. The theoretical model shows very good agreement with reported experimental data.

A mechanistic inter-species comparison of flicker sensitivity

The general validity of both the Rovamo [Vision Res. 39 (1999) 533] and Barten (Contrast sensitivity of the human eye, SPIE Optical Engineering Press, 1999), modulation transfer function models for describing flicker sensitivity in vertebrates was examined using published data for goldfish, chickens, tree shrews, ground squirrels, cats, pigeons and humans. Both models adequately described the flicker response in each species at frequencies greater than approximately 1 Hz. At lower frequencies, response predictions differed between the two models and this was due, in part, to dissimilar definitions of the role played by lateral inhibition in the retina. Modelled flicker sensitivity for a matched retinal illuminance condition enabled a direct inter-species comparison of signal processing response times at the photoreceptor level. The modelled results also quantified differences between species in post-retinal signal processing capability. Finally, the relationship between flicker frequency response curves and the perception of temporal signals in real visual scenes was examined for each species. It is proposed that the area under the flicker sensitivity function may offer a single “figure of merit” for specifying overall sensitivity to time signals in a species’ environment.

Early results on the characterization of the Terra MODIS spatial response

A project to characterize the Moderate Resolution-Imaging Spectroradiometer (MODIS) spatial response (SR) using preflight Modulation Transfer Function (MTF) validation data and on-orbit imagery is described, and the results from the analyses are presented. The preflight validation data are used to estimate the optical blurring parameters to complete a system MTF model for MODIS bands 1 and 2. The model and data indicate that the prelaunch MTF is higher for band 2 than for band 1. The on-orbit imagery is used in a two-image MTF estimation technique to characterize the on-orbit MTF for MODIS bands 1 and 2. Three data sets coincident with MODIS collects are used, Landsat-7 ETM+ imagery of Maricopa Agricultural Center, Arizona, on September 26, 2000 and May 24, 2001 and ASTER imagery of Mono Lake, CA, on September 29, 2000. The on-orbit MTFs obtained to date are consistent with prelaunch validation MTF measurements in the cross-track direction, but are less than prelaunch MTFs in the in-track direction. Further analysis is in progress to confirm these results.

Analytical charge collection and MTF model for photodiode-based CMOS imagers

An analytical charge collection model is derived to assess the impact of the photodiode size, doping profile and surface recombination velocity on the modulation transfer function (MTF) and the charge collection efficiency of CMOS imagers. The effects of the microlens and optical isolation are also quantitatively analyzed. The calculated MTF results agree well with measured data of fabricated imagers based on three different pixel designs.

A model for the modulation transfer function of cardiovascular x-ray systems.

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.

Hydrodynamic modulation of short wind‐wave spectra by long waves and its measurement using microwave backscatter

In this paper we use results of microwave backscattering experiments over the past decade to attempt to present a coherent picture of the ocean wave‐radar modulation transfer function (MTF) based on composite surface theory, short‐wave modulation, and modulated wind stress. A simplified relaxation model is proposed for the modulation of the gravity‐capillary wavenumber spectrum by long waves. The model is based on the relaxation rate and the equilibrium gravity‐capillary wavenumber spectrum. It differs from previous models by including all airflow modulation effects in the response of the equilibrium spectrum to changes in the airflow. Thus the explicit modulation of individual source functions such as wind input, short‐wave dissipation, and nonlinear interactions need not be known in order to calculate the hydrodynainic MTF. By combining this new model of the hydrodynamic MTF with microwave measurements, we attempt to determine wind shear stress modulation caused by the long waves. In order to extract the hydrodynamic MTF from the microwave data, we remove tilt and range change effects from the measured MTFs using the published analytical forms for these effects. Our results show that the inferred hydrodynamic MTF is higher for II polarization scattering than for V polarization. Since this is impossible if we have obtained the true hydrodynamic MTF, these results strongly indicate a problem with composite scattering theory as it has been traditionally applied. One explanation for this result may be the effects of intermediate‐scale waves suggested by Romeiser et al. (1993). Since these effects are much stronger for H polarization than for V polarization, they may explain our observed discrepancy and, if so, imply that V polarization return should yield an acceptable upper limit for the true hydrodynamic MTF. Thus we incorporate our V polarization results into the proposed model to estimate an upper limit for the wind shear stress modulation along the long‐wave profile. We infer that the primary source of modulation of Bragg resonant waves depends strongly on Bragg wavenumber and windspeed. For low values of these quantities, straining by long‐wave orbital velocities dominates the modulation process, while for higher values modulated wind stress becomes increasingly important. Our calculations indicate that wind stress modulation dominates the process for 3 cm Bragg waves at moderate to high wind speeds.

An analytical, aperture, and two-layer carrier diffusion MTF and quantum efficiency model for solid-state image sensors

A two-dimensional analytical model is formulated for calculating the pixel response, modulation transfer function (MTF), and quantum efficiency of front-side illuminated, solid-state image sensors. Included in this unified model are the effects of lateral diffusion of charge carriers within a two-layer substrate and less than full pixel sampling apertures. The results of this model are compared to those of a numerical, three-dimensional Monte Carlo algorithm and to the analytical results reported by Blouke and Robinson. We find good agreement between the quantum efficiency and MTF calculated by the present model and by the three-dimensional Monte Carlo method. However, we find higher quantum efficiency and lower MTF than the previously reported analytical two-layer model. The unified aspect of the present model correctly combines the effects of sampling aperture and lateral diffusion.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Modulation transfer function and quantum efficiency correlation at long wavelengths (greater than 800 nm) in linear charge coupled imagers

The spectral modulation transfer function (MTF) of several architecturally identical commercial linear silicon charge coupled imagers (CCIs) was measured and compared to an MTF theory that included the effects of detector aperture and lateral diffusion in one dimension. A successful match between experimental data and theory was possible for proper choices of the detector aperture function and minority carrier lifetime. Long-wave (> 800-nm) MTF and spectral quantum efficiency (QE) data were very well correlated over the set of CCIs that were measured, indicating the key role of carrier lifetime (or equivalently carrier diffusion length) in determining both characteristics. This correlation was verified by exercising the MTF and QE models, tailored for the CCIs devices, with carrier lifetime as one of the free parameters.

MTF Simulation Including Transmittance Effects and Experimental Results of Charge-Coupled Imagers

A modulation transfer function (MTF) model for front-illuminated charge-coupled imagers (CCI's) which takes into account the periodically varying light transmittance of the photoelement array surface is derived. An inexpensive direct MTF measurement technique for CCI's was developed and is described. Experimental MTF measurements confirm the complete MTF model. Spatial resolution measurements and MTF simulation results of practical CCI photoelement array structures show that the periodically varying surface-light transmittance of the photoelement array contributes significantly to the behavior of the overall MTF and aliasing of the imager.

MTF simulation including transmittance effects and experimental results of charge-coupled imagers

A modulation transfer function (MTF) model for front-illuminated charge-coupled imagers (CCI's) which takes into account the periodically varying light transmittance of the photoelement array surface is derived. An inexpensive direct MTF measurement technique for CCI's was developed and is described. Experimental MTF measurements confirm the complete MTF model. Spatial resolution measurements and MTF simulation results of practical CCI photoelement array structures show that the periodically varying surface-light transmittance of the photoelement array contributes significantly to the behavior of the overall MTF and aliasing of the imager.