Suppose an object is photographed using 2 different cameras. (Assume the photographs are gray scale to simplify discussion.) Even when conditions such as lighting, camera angle, and magnification are identical, the 2 resulting images will differ. Which one is better?

Because an image never perfectly duplicates its object, the image that comes closest to resembling its object could be considered the better image. Is it possible to say that one image contains 88% of the details in the object and that another image has 92%? Not quite, but it is possible to come close.

Just as sound is a mixture of frequencies, so are images. Whereas sound is a mixture of temporal frequencies, images are a mixture of spatial frequencies (Fig 8-23). An image of a single spatial frequency always has the same spatial frequency as the original but with lower contrast. In other words, the spatial frequency does not change from the original to the image, but the contrast does. A photograph will always have less contrast than the original. One lens might image a single spatial frequency at 92% contrast, whereas another lens might image the same frequency at 88% contrast. The ratio of image contrast divided by object contrast (eg, the 88% and the 92% cited in the earlier example) is called the transfer factor because it measures how well the contrast of a single spatial frequency is transferred from the object to the image.

Figure 8-23 Spatial frequencies. The left and middle panels have identical frequencies, but the left has higher contrast. The left and right panels have the same contrast, but the right has a lower frequency. (Illustration b y Edmond H. Thall, MD.)

The transfer factor changes as the spatial frequency changes. As a general rule, the transfer factor decreases as spatial frequency increases. A graph plotting transfer factors on the vertical axis versus spatial frequency on the horizontal axis is called the modulation transfer function (MTF). Modulation is another word for contrast. Every lens has a unique MTF, and by comparing the MTF of lenses, it is possible to determine which lens is better for an intended purpose.

Like the PSF, the MTF completely describes the imaging properties of a lens—in fact, the MTF and PSF are closely related. The MTF can be calculated from the PSF by employing Fourier transform mathematics. Further details of this process are beyond the scope of this discussion.

Chapter Exercises

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