Secondary Quantum Noise Research Articles

Image simulation and a model of noise power spectra across a range of mammographic beam qualities

The aim of this work is to create a model to predict the noise power spectra (NPS) for a range of mammographic radiographic factors. The noise model was necessary to degrade images acquired on one system to match the image quality of different systems for a range of beam qualities. Five detectors and x-ray systems [Hologic Selenia (ASEh), Carestream computed radiography CR900 (CRc), GE Essential (CSI), Carestream NIP (NIPc), and Siemens Inspiration (ASEs)] were characterized for this study. The signal transfer property was measured as the pixel value against absorbed energy per unit area (E) at a reference beam quality of 28 kV, Mo/Mo or 29 kV, W/Rh with 45 mm polymethyl methacrylate (PMMA) at the tube head. The contributions of the three noise sources (electronic, quantum, and structure) to the NPS were calculated by fitting a quadratic at each spatial frequency of the NPS against E. A quantum noise correction factor which was dependent on beam quality was quantified using a set of images acquired over a range of radiographic factors with different thicknesses of PMMA. The noise model was tested for images acquired at 26 kV, Mo/Mo with 20 mm PMMA and 34 kV, Mo/Rh with 70 mm PMMA for three detectors (ASEh, CRc, and CSI) over a range of exposures. The NPS were modeled with and without the noise correction factor and compared with the measured NPS. A previous method for adapting an image to appear as if acquired on a different system was modified to allow the reference beam quality to be different from the beam quality of the image. The method was validated by adapting the ASEh flat field images with two thicknesses of PMMA (20 and 70 mm) to appear with the imaging characteristics of the CSI and CRc systems. The quantum noise correction factor rises with higher beam qualities, except for CR systems at high spatial frequencies, where a flat response was found against mean photon energy. This is due to the dominance of secondary quantum noise in CR. The use of the quantum noise correction factor reduced the difference from the model to the real NPS to generally within 4%. The use of the quantum noise correction improved the conversion of ASEh image to CRc image but had no difference for the conversion to CSI images. A practical method for estimating the NPS at any dose and over a range of beam qualities for mammography has been demonstrated. The noise model was incorporated into a methodology for converting an image to appear as if acquired on a different detector. The method can now be extended to work for a wide range of beam qualities and can be applied to the conversion of mammograms.

Spectral analysis of fundamental signal and noise performances in photoconductors for mammography

This study investigates the fundamental signal and noise performance limitations imposed by the stochastic nature of x-ray interactions in selected photoconductor materials, such as Si, a-Se, CdZnTe, HgI(2), PbI(2), PbO, and TlBr, for x-ray spectra typically used in mammography. It is shown how Monte Carlo simulations can be combined with a cascaded model to determine the absorbed energy distribution for each combination of photoconductor and x-ray spectrum. The model is used to determine the quantum efficiency, mean energy absorption per interaction, Swank noise factor, secondary quantum noise, and zero-frequency detective quantum efficiency (DQE). The quantum efficiency of materials with higher atomic number and density demonstrates a larger dependence on convertor thickness than those with lower atomic number and density with the exception of a-Se. The mean deposited energy increases with increasing average energy of the incident x-ray spectrum. HgI(2), PbI(2), and CdZnTe demonstrate the largest increase in deposited energy with increasing mass loading and a-Se and Si the smallest. The best DQE performances are achieved with PbO and TlBr. For mass loading greater than 100 mg cm(-2), a-Se, HgI(2), and PbI(2) provide similar DQE values to PbO and TlBr. The quantum absorption efficiency, average deposited energy per interacting x-ray, Swank noise factor, and detective quantum efficiency are tabulated by means of graphs which may help with the design and selection of materials for photoconductor-based mammography detectors. Neglecting the electrical characteristics of photoconductor materials and taking into account only x-ray interactions, it is concluded that PbO shows the strongest signal-to-noise ratio performance of the materials investigated in this study.

A comparative analysis of OTF, NPS, and DQE in energy integrating and photon counting digital x‐ray detectors

One of the benefits of photon counting (PC) detectors over energy integrating (EI) detectors is the absence of many additive noise sources, such as electronic noise and secondary quantum noise. The purpose of this work is to demonstrate that thresholding voltage gains to detect individual x rays actually generates an unexpected source of white noise in photon counters. To distinguish the two detector types, their point spread function (PSF) is interpreted differently. The PSF of the energy integrating detector is treated as a weighting function for counting x rays, while the PSF of the photon counting detector is interpreted as a probability. Although this model ignores some subtleties of real imaging systems, such as scatter and the energy-dependent amplification of secondary quanta in indirect-converting detectors, it is useful for demonstrating fundamental differences between the two detector types. From first principles, the optical transfer function (OTF) is calculated as the continuous Fourier transform of the PSF, the noise power spectra (NPS) is determined by the discrete space Fourier transform (DSFT) of the autocovariance of signal intensity, and the detective quantum efficiency (DQE) is found from combined knowledge of the OTF and NPS. To illustrate the calculation of the transfer functions, the PSF is modeled as the convolution of a Gaussian with the product of rect functions. The Gaussian reflects the blurring of the x-ray converter, while the rect functions model the sampling of the detector. The transfer functions are first calculated assuming outside noise sources such as electronic noise and secondary quantum noise are negligible. It is demonstrated that while OTF is the same for two detector types possessing an equivalent PSF, a frequency-independent (i.e., "white") difference in their NPS exists such that NPS(PC) > or = NPS(EI) and hence DQE(PC) < or = DQE(EI). The necessary and sufficient condition for equality is that the PSF is a binary function given as zero or unity everywhere. In analyzing the model detector with Gaussian blurring, the difference in NPS and DQE between the two detector types is found to increase with the blurring of the x-ray converter. Ultimately, the expression for the additive white noise of the photon counter is compared against the expression for electronic noise and secondary quantum noise in an energy integrator. Thus, a method is provided to determine the average secondary quanta that the energy integrator must produce for each x ray to have superior DQE to a photon counter with the same PSF. This article develops analytical models of OTF, NPS, and DQE for energy integrating and photon counting digital x-ray detectors. While many subtleties of real imaging systems have not been modeled, this work is illustrative in demonstrating an additive source of white noise in photon counting detectors which has not yet been described in the literature. One benefit of this analysis is a framework for determining the average secondary quanta that an energy integrating detector must produce for each x ray to have superior DQE to competing photon counting technology.

WE-C-304A-08: The Instrumentation Noise Equivalent Exposure (INEE): Including Conversion, Secondary Quantum, Structure and Electronic Noise

Purpose: To provide a quantitative and clinically relevant measure of the instrumentation noise of digital x‐ray imagers, using the Instrumentation Noise Equivalent Exposure (INEE). Method and Materials: The NPS was “decomposed” into constituent elements of primary quantum noise,Poisson excess noise (Swank noise), secondary quantum noise, structure noise and additive electronic noise using a plot of the total measured NPS versus exposure and using known relationships based on a generalized parallel cascade model analysis. The INEE was determined by measuring the exposure at which the total instrumentation noise and primary quantum noise were equivalent. Exposures at the INEE correspond to a drop in DQE of one‐half. To demonstrate the usefulness of this new metric, the spatial‐frequency‐dependent INEE was measured on a clinical (indirect) dynamic flat panel detector(FPD) with a pixel pitch of 194 μm and a 600 μm thick CsI:Tl phosphor.Results: The INEE was measured to be 2.0, 7.1 and 75 μR at 0, 1 and 1.2 cycles/mm, respectively. Above 1.2 cycles/mm the detector was instrumentation‐noise‐limited at all exposures, resulting in a degradation in image quality beyond that dictated by the noise in the incident x‐ray quanta alone. Hence, above 1.2 cycles/mm the DQE was always less than half the maximum value. Conclusions: In this work, all sources of instrumentation noise were incorporated into the INEE formalism, consisting not only of the additive electronic noise, but also including the Poisson excess noise (i.e. noise resulting from the phosphor), secondary quantum noise (i.e. noise resulting from the conversion and transmission of quanta) and structure noise (i.e. noise resulting from variations in the detector sensitivity). The INEE can be used to assess quantum‐noise‐limited operation at all spatial frequencies of interest by characterizing the total instrumentation noise in terms of equivalent detector entrance exposure. (Partial support: NIH grants R01EB008425, R01EB002873, R01NS43924)

Challenges of pixelated scintillators in medical X-ray imaging

In current X-ray detectors, spatial resolution is limited by optical photon diffusion in the scintillator layer. A method to prevent photons from reaching neighboring pixels is the embedding of opaque walls within the scintillator. The realization of a pixelated scintillator faces, several challenges to obtain a good imaging performance, especially a high detective quantum efficiency (DQE). To maintain a high X-ray absorption, a high volume fill-factor is required. Losses of secondary light quanta have to be kept to a minimum to maintain an acceptable gain. Moreover, the signal per primary X-ray quanta should have a low variation with the depth of interaction to avoid a high secondary quantum noise (Swank-noise). Light scatter inside the scintillator causes both enhanced light loss and Swank-noise. For this work, a pixelated scintillator has been built from electrochemically etched silicon pore arrays, which are filled with cesium iodide (CsI:Tl). With a pixel pitch of 50 μm, wall thicknesses of 6.5 μm and pore depths of nearly 400 μm are achieved. The modulation transfer function is 40% at 4 lp/mm and 10–20% at 8 lp/mm. The ability of the pores to transport light quanta from their origin to the photodiode is expressed in a light guiding efficiency, which is determined as 6.5% in the better cases. The maximal DQE(0) is 0.28, while the X-ray absorption with the given thickness and fill-factor is 0.57. The difference is explained by high Swank-noise due to optical scatter inside the CsI-filled pores, in agreement to Monte-Carlo simulations of the photon transport inside the pore array structure.

Analysis of the spatial-frequency-dependent DQE of optically coupled digital mammography detectors.

The effect of optical coupling efficiency on the spatial-frequency-dependent propagation of signal and noise is considered for x-ray image detectors for digital mammography in which a phosphor screen is optically coupled to a charge-coupled device (CCD) image array. For experimental purposes, optical coupling between a Gd2O2S:Tb phosphor screen and a CCD image array was provided by relay lenses. Neutral density filters were inserted between the lenses to vary the optical coupling efficiency without altering the inherent spatial resolution. The total coupling efficiency, defined as the number of electrons (e-) recorded in the CCD per x-ray interaction in the phosphor, was calculated in each case. The modulation transfer function, and the contributions to the total noise power spectrum (NPS) of x-ray quantum noise, secondary quantum noise, and inherent detector noise were measured as a function of coupling efficiency. These data were used to calculate the spatial-frequency-dependent detective quantum efficiency [DQE(f)]. The NPS due to x-ray quantum noise had a significant spatial-frequency dependence for coupling efficiencies of more than 9 e- per x-ray interaction, but little spatial-frequency dependence for coupling efficiencies of less than 2 e- per x-ray interaction. These results indicate that to preserve high spatial-frequency values of DQE(f), and to ensure that images are x-ray quantum-noise limited at high spatial frequencies, a coupling efficiency on the order of 10 e- per x-ray interaction is required.(ABSTRACT TRUNCATED AT 250 WORDS)