The use of imaging phantoms is a common method of evaluating image quality in the clinical setting. These evaluations rely on a subjective decision by a human observer with respect to the faintest detectable signal(s) in the image. Because of the variable and subjective nature of the human-observer scores, the evaluations manifest a lack of precision and a potential for bias. The advent of digital imaging systems with their inherent digital data provides the opportunity to use techniques that do not rely on human-observer decisions and thresholds. Using the digital data, signal-detection theory (SDT) provides the basis for more objective and quantitative evaluations which are independent of a human-observer decision threshold. In a SDT framework, the evaluation of imaging phantoms represents a "signal-known-exactly/background-known-exactly" ("SKE/ BKE") detection task. In this study, we compute the performance of prewhitening and nonprewhitening model observers in terms of the observer signal-to-noise ratio (SNR) for these "SK E/BKE" tasks. We apply the evaluation methods to a number of imaging systems. For example, we use data from a laboratory implementation of digital radiography and from a full-field digital mammography system in a clinical setting. In addition, we make a comparison of our methods to human-observer scoring of a set of digital images of the CDMAM phantom available from the internet (EUREF-European Reference Organization). In the latter case, we show a significant increase in the precision of the quantitative methods versus the variability in the scores from human observers on the same set of images. As regards bias, the performance of a model observer estimated from a finite data set is known to be biased. In this study, we minimize the bias and estimate the variance of the observer SNR using statistical resampling techniques, namely, "bootstrapping" and "shuffling" of the data sets. Our methods provide objective and quantitative evaluation of imaging systems with increased precision and reduced bias.