Comparison of low contrast detectability between a digital amorphous silicon and a screen-film based imaging system for thoracic radiography.

Low contrast threshold detectability is investigated theoretically and experimentally for an amorphous silicon (a-Si) x-ray detector designed for digital radiography and for a standard thoracic screen-film combination. A theoretical signal-to-noise ratio is described with a human observer signal detection model. It is calculated using the detective quantum efficiency (DQE) and the modulation transfer function of the imaging system, as well as a spatial response function for the human visual system. Using a four-alternative forced choice observer perception study, the threshold contrasts of disk shaped objects ranging in size from 0.3 to 4.0 mm are determined. Significantly better contrast detectability is obtained from the digital detector, which is attributed to its higher DQE. On average, the disk shaped objects can be detected at 45% less contrast than required for screen-film. With no free parameters the experimental data agree well with those predicted by the observer model. Based upon the data, the model predicts that x-ray exposure for the a-Si detector only needs to be 30% of the exposure required to perform equally well on the contrast-detail detectability task using screen-film.     

Investigation of basic imaging properties in digital radiography. 8. Detection of simulated low-contrast objects in digital subtraction angiographic images

We investigated the effects of imaging and display conditions on the detectability of low-contrast objects in digital subtraction angiographic (DSA) images. The test images were produced by superimposition of low-contrast objects on a uniform noisy background obtained with a DSA system. We employed 18-alternative forced-choice (18-AFC) experiments and predictions based on statistical decision theory to study the dependence of the threshold contrasts of the test objects on the object size, incident x-ray exposure, display window width, and display medium. The results indicated that the threshold contrast decreased with increasing object size, and that the detectability of an object of a given size increased with increasing incident x-ray exposure and decreasing width of the display window. We found that the signal-to-noise ratio (SNR) obtained from the perceived statistical decision theory model, which includes the observer's internal noise, can accurately predict the detectability of low-contrast objects in DSA images. The threshold SNR corresponding to 50% correct detection in the 18-AFC experiments had a constant value of 3.8, in agreement with results reported previously for screen-film systems. The theoretical model will be useful for prediction of the performance of a DSA system based on its physical characteristics, and for evaluation of the tradeoff between patient exposure and diagnostic accuracy for a given DSA unit.     

Amorphous selenium flat panel detectors for digital mammography: validation of a NPWE model observer with CDMAM observer performance experiments

Model observers have been developed which incorporate a specific imaging task, system performance, and human observer characteristics and can potentially overcome some of the limitations in using detective quantum efficiency for optimization and comparison of detectors. In this paper, a modified nonprewhitening matched filter (NPWE) model observer was developed and validated to predict object detectability for an amorphous selenium (a-Se) direct flat-panel imager (FPI) where aliasing is severe. A preclinical a-Se digital mammography FPI with 85 microm pixel size was used in this investigation. Its physical imaging properties including modulation transfer function (MTF), noise power spectrum, and DQE were fully characterized. An observer performance study was conducted by imaging the CDMAM 3.4 contrast-detail phantom designed specifically for digital mammography and presenting these images to a panel of seven observers. X-ray attenuation and scatter due to the phantom were determined experimentally for use in development of the model observer. The observer study results were analyzed via threshold averaging and signal detection theory (SDT) based techniques to produce contrast-detail curves where threshold contrast is plotted as a function of disk diameter. Validity of the model was established using SDT analysis of the experimental data. The effect of aliasing on the detectability of small diameter disks was determined using the NPWE model observer. The signal spectrum was calculated using the presampling MTF of the detector with and without including the aliased terms. Our results indicate that the NPWE model based on Fourier domain parameters provides reasonable prediction of object detectability for the signal-known-exactly task in uniform image noise for a-Se direct FPI.     

Image quality assessment in digital mammography: part II. NPWE as a validated alternative for contrast detail analysis

Assessment of image quality for digital x-ray mammography systems used in European screening programs relies mainly on contrast-detail CDMAM phantom scoring and requires the acquisition and analysis of many images in order to reduce variability in threshold detectability. Part II of this study proposes an alternative method based on the detectability index (d') calculated for a non-prewhitened model observer with an eye filter (NPWE). The detectability index was calculated from the normalized noise power spectrum and image contrast, both measured from an image of a 5 cm poly(methyl methacrylate) phantom containing a 0.2 mm thick aluminium square, and the pre-sampling modulation transfer function. This was performed as a function of air kerma at the detector for 11 different digital mammography systems. These calculated d' values were compared against threshold gold thickness (T) results measured with the CDMAM test object and against derived theoretical relationships. A simple relationship was found between T and d', as a function of detector air kerma; a linear relationship was found between d' and contrast-to-noise ratio. The values of threshold thickness used to specify acceptable performance in the European Guidelines for 0.10 and 0.25 mm diameter discs were equivalent to threshold calculated detectability indices of 1.05 and 6.30, respectively. The NPWE method is a validated alternative to CDMAM scoring for use in the image quality specification, quality control and optimization of digital x-ray systems for screening mammography.     

Schemes for the optimization of chest radiography using a computer model of the patient and x-ray imaging system.

A computer program has been developed to model chest radiography. It incorporates a voxel phantom of an adult and includes antiscatter grid, radiographic screen, and film. Image quality is quantified by calculating the contrast (deltaOD) and the ideal observer signal-to-noise ratio (SNR(I)) for a number of relevant anatomical details at various positions in the anatomy. Detector noise and system unsharpness are modeled and their influence on image quality is considered. A measure of useful dynamic range is computed and defined as the fraction of the image that is reproduced at an optical density such that the film gradient exceeds a preset value. The effective dose is used as a measure of the radiation risk for the patient. A novel approach to patient dose and image quality optimization has been developed and implemented. It is based on a reference system acknowledged to yield acceptable image quality in a clinical trial. Two optimizations schemes have been studied, the first including the contrast of vessels as measure of image quality and the second scheme using also the signal-to-noise ratio of calcifications. Both schemes make use of our measure of useful dynamic range as a key quantity. A large variety of imaging conditions was simulated by varying the tube voltage, antiscatter device, screen-film system, and maximum optical density in the computed image. It was found that the optical density is crucial in screen-film chest radiography. Significant dose savings (30%-50%) can be accomplished without sacrificing image quality by using low-atomic-number grids with a low grid ratio or an air gap and more sensitive screen-film system. Dose-efficient configurations proposed by the model agree well with the example of good radiographic technique suggested by the European Commission.     

Comparison of clinical and physical measures of image quality in chest and pelvis computed radiography at different tube voltages

The aim of this work was to study the dependence of image quality in digital chest and pelvis radiography on tube voltage, and to explore correlations between clinical and physical measures of image quality. The effect on image quality of tube voltage in these two examinations was assessed using two methods. The first method relies on radiologists' observations of images of an anthropomorphic phantom, and the second method was based on computer modeling of the imaging system using an anthropomorphic voxel phantom. The tube voltage was varied within a broad range (50-150 kV), including those values typically used with screen-film radiography. The tube charge was altered so that the same effective dose was achieved for each projection. Two x-ray units were employed using a computed radiography (CR) image detector with standard tube filtration and antiscatter device. Clinical image quality was assessed by a group of radiologists using a visual grading analysis (VGA) technique based on the revised CEC image criteria. Physical image quality was derived from a Monte Carlo computer model in terms of the signal-to-noise ratio, SNR, of anatomical structures corresponding to the image criteria. Both the VGAS (visual grading analysis score) and SNR decrease with increasing tube voltage in both chest PA and pelvis AP examinations, indicating superior performance if lower tube voltages are employed. Hence, a positive correlation between clinical and physical measures of image quality was found. The pros and cons of using lower tube voltages with CR digital radiography than typically used in analog screen-film radiography are discussed, as well as the relevance of using VGAS and quantum-noise SNR as measures of image quality in pelvis and chest radiography.     

Parameters of Digital Detectors and Image Quality

The input dose for an ideal digital detector depends quadratically on the threshold contrast detail detectability (TCDD). The TCDD at the level of image quality sufficiency should be minimized for diagnosis; initial parts of detector amplitude response, as well as pulse fluoroscopy adapted to organ mobility, should be used.     

Investigation of basic imaging properties in digital radiography. 3. Effect of pixel size on SNR and threshold contrast

The effect of pixel size on the signal-to-noise ratio (SNR) and threshold detection of low-contrast radiologic patterns was investigated theoretically for digital radiographic systems. The SNR based on the perceived statistical decision theory model, together with the internal noise of the human eye-brain system, was calculated by using two-dimensional displayed digital signal spectra and noise Wiener spectra. Threshold contrasts were predicted from the calculated SNR for various combinations of object size and shape, pixel size, resolution, and noise. Predicted threshold contrasts agreed well with those determined experimentally in an observer performance study. The threshold contrast of small objects increased substantially as the pixel size increased beyond 0.2 mm. For pixel sizes of 0.1 and 0.2 mm, however, the threshold contrasts were similar. Since a digital system is not shift invariant, a range of threshold contrast results for a small object and a large pixel, depending on the alignment of the object position relative to the sampling coordinates.     

Effect of dose reduction on the detection of mammographic lesions: a mathematical observer model analysis

The effect of reduction in dose levels normally used in mammographic screening procedures on the detection of breast lesions were analyzed. Four types of breast lesions were simulated and inserted into clinically-acquired digital mammograms. Dose reduction by 50% and 75% of the original clinically-relevant exposure levels were simulated by adding corresponding simulated noise into the original mammograms. The mammograms were converted into luminance values corresponding to those displayed on a clinical soft-copy display station and subsequently analyzed by Laguerre-Gauss and Gabor channelized Hotelling observer models for differences in detectability performance with reduction in radiation dose. Performance was measured under a signal known exactly but variable detection task paradigm in terms of receiver operating characteristics (ROC) curves and area under the ROC curves. The results suggested that luminance mapping of digital mammograms affects performance of model observers. Reduction in dose levels by 50% lowered the detectability of masses with borderline statistical significance. Dose reduction did not have a statistically significant effect on detection of microcalcifications. The model results indicate that there is room for optimization of dose level in mammographic screening procedures.     

Calibrating automatic exposure control devices for digital radiography

The energy responses of digital radiography detectors differ from those of screen-film systems. To provide a consistent level of image quality at different tube potentials automatic exposure control (AEC) devices must be calibrated to suit the energy response of the image receptor with which they are intended for use. AEC calibration for digital radiography systems requires an alternative parameter to optical density, ideally one related to the quality of a digital image. Energy responses of computed radiography (CR) and indirect digital radiography (IDR) image receptors have been calculated, and compared with those for screen-film systems. Practical assessments of the relative sensitivities of a CR detector made using the detector dose indicator (DDI), pixel value and signal-to-noise ratio showed similar variations with tube potential. The DDI has been used to determine the correct kV compensation curve required to calibrate the AECs for the loss in detector sensitivity with tube potential. AECs are set up relative to a predetermined air kerma incident on the detector at 80 kV for CR and IDR systems using this curve and the method used is described. Factors influencing the calibration of AECs for digital radiography including techniques, types of phantom and contributions from scatter are reviewed, and practical methods recommended for use.     

Rapid calculation of detectability in Bayesian single photon emission computed tomography

We consider the calculation of lesion detectability using a mathematical model observer, the channelized Hotelling observer (CHO), in a signal-known-exactly/background-known-exactly detection task for single photon emission computed tomography (SPECT). We focus on SPECT images reconstructed with Bayesian maximum a posteriori methods. While model observers are designed to replace time-consuming studies using human observers, the calculation of CHO detectability is usually accomplished using a large number of sample images, which is still time consuming. We develop theoretical expressions for a measure of detectability, the signal-to-noise-ratio (SNR) of a CHO observer, that can be very rapidly evaluated. Key to our expressions are approximations to the reconstructed image covariance. In these approximations, we use methods developed in the PET literature, but modify them to reflect the different nature of attenuation and distance-dependent blur in SPECT. We validate our expressions with Monte Carlo methods. We show that reasonably accurate estimates of the SNR can be obtained at a computational expense equivalent to approximately two projection operations, and that evaluating SNR for subsequent lesion locations requires negligible additional computation.     

Impact of resolution and noise characteristics of digital radiographic detectors on the detectability of lung nodules

One of the unanswered questions in digital radiography is the connection between physical image quality metrics and clinical detection performance. In this paper, we examine the impact of two physical metrics, resolution and noise, on the detectability of nodules in a pulmonary background for specific digital radiographic detectors. A detection experiment was performed on a simulated image set using anatomical backgrounds from a high-quality lung radiograph and three different simulated nodule sizes (2-3.5 mm). The resolution and noise of the resulting images were modified using existing routines to simulate a selenium-based and a cesium iodide-based flat-panel detector at comparable exposures. A location-known-exactly (LKE) observer performance experiment was performed in which four experienced chest radiologists and three physicists specializing in chest radiology scored the images. The data from the observer experiment were analyzed by receiver operating characteristic (ROC) methodology. The detectability, as measured by the parameter Az, was higher for the selenium detector than the cesium iodide detector for all nodule sizes by an average of 8.5%. For one nodule size (2.75 mm), the difference between detectors was statistically significant (p < 0.01). The findings indicate that for the particular task studied, the superior resolution performance of the selenium-based detector provided better detectability of subtle lung nodules even though the images had greater noise than images obtained with the cesium iodide detector.     

Performance comparison of an active matrix flat panel imager, computed radiography system, and a screen-film system at four standard radiation qualities

Four standard radiation qualities (from RQA 3 to RQA 9) were used to compare the imaging performance of a computed radiography (CR) system (general purpose and high resolution phosphor plates of a Kodak CR 9000 system), a selenium-based direct flat panel detector (Kodak Direct View DR 9000), and a conventional screen-film system (Kodak T-MAT L/RA film with a 3M Trimax Regular screen of speed 400) in conventional radiography. Reference exposure levels were chosen according to the manufacturer's recommendations to be representative of clinical practice (exposure index of 1700 for digital systems and a film optical density of 1.4). With the exception of the RQA 3 beam quality, the exposure levels needed to produce a mean digital signal of 1700 were higher than those needed to obtain a mean film optical density of 1.4. In spite of intense developments in the field of digital detectors, screen-film systems are still very efficient detectors for most of the beam qualities used in radiology. An important outcome of this study is the behavior of the detective quantum efficiency of the digital radiography (DR) system as a function of beam energy. The practice of users to increase beam energy when switching from a screen-film system to a CR system, in order to improve the compromise between patient dose and image quality, might not be appropriate when switching from screen-film to selenium-based DR systems.     

Simulation study of a quasi-monochromatic beam for x-ray computed mammotomography

The purpose of this simulation study was to evaluate the feasibility, benefits, and potential operating parameters of a quasi-monochromatic beam from a tungsten-target x-ray source yielding projection images. The application is intended for newly developed cone beam computed mammotomography (CmT) of an uncompressed breast. The value of a near monochromatic x-ray source for a fully 3D CmT application is the expected improved ability to separate tissues with very small differences in attenuation coefficients. The quasi-monochromatic beam is expected to yield enhanced tomographic image quality along with a low dose, equal to or less than that of dual view x-ray mammography. X-ray spectra were generated with a validated projection x-ray simulation tool (XSpect) for a range of tungsten tube potentials (40-100 kVp), filter materials (Z=51-65), and filter thicknesses (10th to 1000th value layer determined at 60 kVp). The breast was modeled from ICRU-44 breast tissue specifications, and a breast lesion was modeled as a 0.5 cm thick mass. The detector was modeled as a digital flat-panel detector with a 0.06 cm thick CsI x-ray absorption layer. Computed figures of merit (FOMs) included the ratio of mean beam energy post-breast to pre-breast and the ratio of lesion contrasts for edge-located and center-located lesions as indices of breast beam hardening, and SNR2/exposure and SNR2/dose as indices of exposure and dose efficiencies. The impact of optimization of these FOMs on lesion contrast is also examined. For all simulated filter materials at each given attenuation thickness [10th, 100th, 500th, 1000th value layers (VLs)], the mean and standard deviation of the pre-breast spectral full-width at tenth-maximum (FWTM) were 16.1 +/- 2.4, 10.3 +/- 2.2, 7.3 +/- 1.4, and 6.5 +/- 1.5 keV, respectively. The change in beam width at the tenth maximum from pre-breast to post-breast spectra ranged from 4.7 to 1.1 keV, for the thinnest and thickest filters, respectively. The higher Z filters (Z=57-63) produced a quasi-monochromatic beam that allowed the widest tube potential operating range (50-70 kVp) while maintaining minimal beam hardening and maximal SNR2/exposure and SNR2/dose, and providing a contrast greater than that obtained in the unfiltered case. Figures of merit improved with increasing filter thickness, with diminishing returns beyond the 500th value layer attenuation level. Operating parameters required to produce optimal spectra, while keeping exposures equal to that of dual view mammography, are within the capability of the commercial x-ray tube proposed for our experimental study, indicating that use of these highly attenuating filters is viable. Additional simulations comparing Mo/Mo, Mo/Rh, and W/Rh target/filter combinations indicate that they exhibit significantly lower SNR2/exposure than the present approach, precluding them from being used for computed mammotomography, while maintaining dose limitations and obtaining sufficient SNR. Beam hardening was also much higher in the existing techniques (17%-42%) than for our technique (2%). Simulations demonstrate that this quasi-monochromatic x-ray technique may enhance tissue separation for a newly developed cone beam computed mammotomography application for an uncompressed breast.     

Noise and threshold contrast characteristics of a digital fluorographic system

The noise and threshold contrast characteristics of a Picker DAS 211 digital fluorography system are described. Leeds test objects were used to measure contrast-detail-dose relationships for digital fluorography and the results compared with similar measurements using screen-film radiography and 100 mm photofluorography. Noise and spread function measurements were made and from them threshold contrast (CT) values were calculated using the theory of signal detection developed by Hay and Chesters. Comparison with the results of visual assessment of images indicated generally good agreement between theory and practice depending upon the value taken for the threshold signal-to-noise ratio. It is concluded that calculations of CT can provide a means of summarising system performance based only upon objective measurements. This would be of value in quality assurance and performance assessment but should be used in addition to, not instead of, the traditional visual methods since these are important in maintaining a link with clinical practice.     

Signal detectability in digital radiography: spatial domain figures of merit

The usefulness of Fourier-based measures of imaging performance has come into question for the evaluation of digital imaging systems. Figures of merit such as detective quantum efficiency (DQE) based on Fourier domain parameters are relevant for linear, shift-invariant systems with stationary noise. However, no digital imaging system is shift invariant, and realistic images do not satisfy the stationarity condition. Our methods for the task-based evaluation of imaging systems, based on signal detectability in the spatial domain, do not require such assumptions. We have computed the performance of ideal and quasi-ideal observers for the task of signal detection in digital radiography. Signal detectability in terms of an observer signal-to-noise-ratio (SNR) has been compared to results obtained from a Monte Carlo simulation of the digital image-acquisition process. The simulation incorporates the effects of random amplification and secondary quantum blur, integration over pixel area, and electronic noise. The observer figures of merit that have been previously shown to bracket human performance directly specify the usefulness of the images for the stated diagnostic task. In addition, the observer figures of merit give a task-dependent measure of imaging system efficiency in terms of the ratio of an output SNR2 to an input SNR2. Thus, the concept of "detective quantum efficiency" reappears in a natural way but based in the spatial domain and not dependent on shift invariance and stationarity assumptions. With respect to the optimum amount of system blur, our simulations indicate that under certain task-dependent conditions, large signals are fairly insensitive to blur in the x-ray transducer, while an optimum blur is found for small signals.     

Evaluating the impact of X-ray spectral shape on image quality in flat-panel CT breast imaging

In recent years, there has been an increasing interest in exploring the feasibility of dedicated computed tomography (CT) breast imaging using a flat-panel digital detector in a truncated cone-beam imaging geometry. Preliminary results are promising and it appears as if three-dimensional tomographic imaging of the breast has great potential for reducing the masking effect of superimposed parenchymal structure typically observed with conventional mammography. In this study, a mathematical framework used for determining optimal design and acquisition parameters for such a CT breast imaging system is described. The ideal observer signal-to-noise ratio (SNR) is used as a figure of merit, under the assumptions that the imaging system is linear and shift invariant. Computation of the ideal observer SNR used a parallel-cascade model to predict signal and noise propagation through the detector, as well as a realistic model of the lesion detection task in breast imaging. For all evaluations, the total mean glandular dose for a CT breast imaging study was constrained to be approximately equivalent to that of a two-view conventional mammography study. The framework presented was used to explore the effect of x-ray spectral shape across an extensive range of kVp settings, filter material types, and filter thicknesses. The results give an indication of how spectral shape can affect image quality in flat-panel CT breast imaging.     

Automated assessment of low contrast sensitivity for CT systems using a model observer

Purpose: Low contrast sensitivity of CT scanners is regularly assessed by subjective scoring of low contrast detectability within phantom CT images. Since in these phantoms low contrast objects are arranged in known fixed patterns, subjective rating of low contrast visibility might be biased. The purpose of this study was to develop and validate a software for automated objective low contrast detectability based on a model observer.Methods: Images of the low contrast module of the Catphan 600 phantom were used for the evaluation of the software. This module contains two subregions: the supraslice region with three groups of low contrast objects (each consisting of nine circular objects with diameter 2-15 mm and contrast 0.3, 0.5, and 1.0%, respectively) and the subslice region with three groups of four circular objects each (diameter 3-9 mm; contrast 1.0%). The software method offered automated determination of low contrast detectability using a NPWE (nonprewhitening matched filter with an eye filter) model observer for the supraslice region. The model observer correlated templates of the low contrast objects with the acquired images of the Catphan phantom and a discrimination index d' was calculated. This index was transformed into a proportion correct (PC) value. In the two-alternative forced choice (2-AFC) experiments used in this study, a PC ≥ 75% was proposed as a threshold to decide whether objects were visible. As a proof of concept, influence of kVp (between 80 and 135 kV), mAs (25-200 mAs range) and reconstruction filter (four filters, two soft and two sharp) on low contrast detectability was investigated. To validate the outcome of the software in a qualitative way, a human observer study was performed.Results: The expected influence of kV, mAs and reconstruction filter on image quality are consistent with the results of the proposed automated model. Higher values for d' (or PC) are found with increasing mAs or kV values and for the soft reconstruction filters. For the highest contrast group (1%), PC values were fairly above 75% for all object diameters >2 mm, for all conditions. For the 0.5% contrast group, the same behavior was observed for object diameters >3 mm for all conditions. For the 0.3% contrast group, PC values were higher than 75% for object diameters >6 mm except for the series acquired at the lowest dose (25 mAs), which gave lower PC values. In the human observer study similar trends were found.Conclusions: We have developed an automated method to objectively investigate image quality using the NPWE model in combination with images of the Catphan phantom low contrast module. As a first step, low contrast detectability as a function of both acquisition and reconstruction parameter settings was successfully investigated with the software. In future work, this method could play a role in image reconstruction algorithms evaluation, dose reduction strategies or novel CT technologies, and other model observers may be implemented as well.     

Image quality assessment in digital mammography: part I. Technical characterization of the systems

In many European countries, image quality for digital x-ray systems used in screening mammography is currently specified using a threshold-detail detectability method. This is a two-part study that proposes an alternative method based on calculated detectability for a model observer: the first part of the work presents a characterization of the systems. Eleven digital mammography systems were included in the study; four computed radiography (CR) systems, and a group of seven digital radiography (DR) detectors, composed of three amorphous selenium-based detectors, three caesium iodide scintillator systems and a silicon wafer-based photon counting system. The technical parameters assessed included the system response curve, detector uniformity error, pre-sampling modulation transfer function (MTF), normalized noise power spectrum (NNPS) and detective quantum efficiency (DQE). Approximate quantum noise limited exposure range was examined using a separation of noise sources based upon standard deviation. Noise separation showed that electronic noise was the dominant noise at low detector air kerma for three systems; the remaining systems showed quantum noise limited behaviour between 12.5 and 380 μGy. Greater variation in detector MTF was found for the DR group compared to the CR systems; MTF at 5 mm(-1) varied from 0.08 to 0.23 for the CR detectors against a range of 0.16-0.64 for the DR units. The needle CR detector had a higher MTF, lower NNPS and higher DQE at 5 mm(-1) than the powder CR phosphors. DQE at 5 mm(-1) ranged from 0.02 to 0.20 for the CR systems, while DQE at 5 mm(-1) for the DR group ranged from 0.04 to 0.41, indicating higher DQE for the DR detectors and needle CR system than for the powder CR phosphor systems. The technical evaluation section of the study showed that the digital mammography systems were well set up and exhibiting typical performance for the detector technology employed in the respective systems.     

Linear response theory for detectors consisting of discrete arrays

The optical transfer function (OTF) and the noise power or Wiener spectrum are defined for detectors consisting of a lattice of discrete elements with the assumptions of linear response, Gaussian statistics, and stationarity under the discrete group of translations which leave the lattice fixed. For the idealized classification task of determining the presence or absence of a signal under signal known exactly/background known exactly (SKE/BKE) conditions, the Wiener spectrum, the OTF, along with an analog of the gray-scale transfer characteristic, determine the signal-to-noise ratio (SNR), which quantifies the ability of an ideal observer to perform this task. While this result is similar to the established result for continuous detectors, such as screen-film systems, the theory of discrete lattices of detectors must take into account the fact that the lattice only supports a bounded but (in the limit of a detector of arbitrarily great extent) continuous range of frequencies. Incident signals with higher spatial frequencies appear in the data at lower aliased frequencies, and there are pairs of signals which are not distinguishable by the detector (the SNR vanishes for the task of distinguishing such signals). Further, the SNR will in general change if the signal is spatially displaced by a fraction of the lattice spacing, although this change will be small for objects larger than a single pixel. Some of the trade-offs involved in detectors of this sort, particularly in dealing with signal frequencies above those supported by the lattice, are studied in a simple model.