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Message: <blockquote data-quote="elkcub" data-source="post: 1280537" data-attributes="member: 14473">The problem, I think, is that it's easy to confuse several very different conceptual frameworks.  The concept of a modulation transfer function is mathematical, and relies on the method of Fourier analysis.  This was developed to decompose time series into component frequencies.  For example, the vibrations of a guitar string, or the frequencies that constitute light.When this method is applied to the space dimension (i.e., not time) we talk about "spatial frequency."  In this framework, an image is conceptualized as a collection of dark-light alternations (frequencies), where contrast plays the role of amplitude.  In temporal analysis, a frequency is the number of cycles per unit time, e.g., a guitar string vibrates so many times a second, so we have cycles/sec or Hz.  In the case of spatial analysis the unit is a mm, so the spatial frequency is the number of cycles per unit space, e.g., cycles/mm.  Since each pair of dark and light lines on a uniform grid represents one cycle, the metric is referred to as lp/mm.  However, the number of "line pairs," or cycles, is the same as the number of dark lines, so this is often abbreviated as "lines" per mm.  In the field of optics they mean the same thing — namely, the number of cycles per mm.  I might add that phase can be altered by offsetting the spatial grid left or right, but that's not often of interest.  A cycle can begin anywhere one wishes, but unless phase angle is a consideration its easiest to think of a cycle beginning with the edge of a dark line, i.e., zero phase angle.  Again, it's a matter of convention.   There are many allied fields such as television, digital displays, analog/digital photography, surveying, vision science, optometry, etc. which use similar spatial grids for measurements but have adopted different naming conventions.  These, as we see, often come into conflict.  Arguing about which is right or wrong, however, is largely a waste of time.  It's a matter of the context in which the terms are used.  Trying to shape an optician to talk like a psychologist, for example, is futile — and since there are more of them on BF than there are of me, I adapt.  Still it does grate on one's nerves to realize that an "optical illusion" is infrequently understood to be what it is, — namely, a mis-perception!  But, ... I wander.  :-OEd</blockquote>

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