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In this chapter, we develop the mathematical relationships between the data and the MTF for the point-spread function (PSF), line-spread function (LSF), and edge-spread function (ESF). One item of notation in this section is that we use * to denote a one-dimensional convolution and ** to denote a two-dimensional convolution. We also consider the relationship between measurement data and MTF for random-noise targets and bar targets. We can use this simple approach as a handy reality check, comparing a measured spot size to calculated MTF values. Often when computers are part of the data-acquisition and data-processing procedures, we cannot check and verify each step of the MTF calculation. In these situations, we can manually verify the computation. First, we visually assess the size of the impulse response to determine the full width of the blur spot by using a measuring microscope -€” a single-tube combination of objective and eyepiece mounted on a micropositioner stage with appropriate vernier readout.
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