|
The assumed underlying probability of detection distribution is important when trying to estimate the mean of the population from a limited sample such as that obtained from minimum resolvable temperature (MRT) tests. If the underlying population is normally distributed, then the best estimate of the population mean is the arithmetic average of the observers' individual MRT values. On the other hand, nearly all visual psychophysical data is plotted on a logarithmic scale with log intensity increments. Thus it is reasonable to assume that MRT responses should also be treated as a logarithmic response. With a log-normal distribution, the population mean is estimated from the geometric average of the observers' responses. Choosing a log-normal underlying distribution over a linear distribution does not affect existing forward-looking infrared (FUR) detection theory, since the threshold value is identical for both distributions and the distributions are essentially the same from 20 to 80 percent cumulative probability. The linear normal distribution is not bounded and therefore, mathematically, can provide a finite probability of detection for unrealizable negative signal-to-noise ratios. Since the log-normal distribution is bounded to positive values it appears to adequately represent the real world. To determine the underlying distribution for the standard MRT four-bar target, 2700 detection responses were obtained for various signal-to-noise ratios and spatial frequencies. Although any individual observer may have a linear distribution, the resultant composite data easily fits a log-normal distribution. Furthermore, limited laboratory data on actual FLIRs also indicate that a log-normal distribution provides a better mathematical approximation. As a result, the geometric average of observer responses is recommended for determining the composite MRT value.
|
