Given the increasing use of soft-copy in the medical field, standardization and fidelity of the display are gaining much interest. For medical imaging, it is of great importance that information in the data is accurately mapped to brightness sensation. The concept of perceptual linearization was introduced by Pizer [Computer Graphics and Image Processing, 17, 262 (1981)] to guarantee the display fidelity. It means that equal steps in the data evoke equal steps in sensation. We investigate the fidelity of achromatic displays prior to and after perceptual linearization. First, we use magnitude estimation of brightness differences between gray square patches embedded in a uniform background, to make equal-interval brightness series. Then, we extend the brightness contrast discrimination models of Whittle [Vision Research, 26, 1677 (1986)], and Kingdom and Moulden [Vision Research, 31, 851 (1991)], for gray patches in uniform background, to our supra-threshold data. A good fit is found. Finally, we apply the look-up tables that provide perceptual linearization for the gray patches to complex images. Brightness matching with a scale of reference gray patches is used to estimate gray levels at specified image locations. The experimental results indicate that the accuracy of this task is not necessarily affected by perceptual linearization.