Doug Kerr
Well-known member
An often-quoted property of, for example, an audio amplifier is its frequency response. This is a plot, by frequency, of the ratio of the amplifier output voltage (signal amplitude) to its input voltage. This ratio may be reported (and plotted) on either a voltage or a power (actually, the square of the voltage) basis.
An essentially-identical concept is used in connection with optical systems (such as photographic lenses, or the combination of a lens and a digital imaging system. The differences in the application of the concept are:
• Here the frequency is spatial (in space), for example in cycles per mm, whereas in the electrical case the frequency is temporal (in time), in cycles per second (for which there is of course the unit name hertz).
• Here the property compared between output and input is the depth of luminance/illuminance modulation, whereas in the electrical case the the property is voltage (signal amplitude).
Historically, the ratio of output luminance modulation to input luminance modulation (which we can call the "modulation transfer ratio") as a function of (spatial) frequency has been called the modulation transfer function (MTF) of the optical system.
Assuming we don't apply some different qualifying details in particular cases, then SFR and MTF are essentially synonymous.
Over the years, it became common to measure the SFR of, say, a lens by means of what is called the "slant edge" technique. The basic principle is this:
• We photograph a test target consisting of two areas of different luminance with a "sharp" edge between them.
• From the spatial variation of luminance in the "output" of the lens (the "edge spread function" for the target edge), we can determine (by a mathematical process that includes the Fourier transform, among other things) the spatial frequency response (SFR, aka MTF) of the lens.
For reasons that are beyond the scope of this note, this process is made more refined by using an edge in the test target that is not exactly vertical (thus the "slant edge" moniker).
Because of the wide use of such a target for determining SFR/MTF, and because of the general practice of, in the context of technical discussions of the measurement process, referring to the resulting test curve as SFR rather than MTF (it will of course usually be called MTF when we use it!), the slant edge test target has come to be known as the "SFR" test target (no other kind of target usually being used for measurement of SFR (MTF).
Now, as we get more sophisticated in developing metrics to assess the "sharpness" performance of a camera, we recognize that such things as noise reduction algorithms in effect degrade the MTF (that is, the SFR) as it applies to textured areas of the object/image.
To take this in account, in some cases we determine the MTF/SFR with a different technique, one that actually uses a test target with a complicated "textured" pattern (often one of overlapping circles of different diameters and different luminance, sometimes called for historical reasons a "dead leaves" pattern, but often today more aptly called a "spilled coins" pattern).
But more formally, this is spoken of as a "texture" pattern, as distinguished from a "slant edge" pattern, and the two measurement techniques are often distinguished by those two terms (which makes sense).
The analysis of the image of such a pattern proceeds quite differently from the analysis of the "edge spread function" obtained from a slant edge target, so we truly have a "different technique", not just a "different target".
But the definition of the determined MTF (SFR) is no different between the two ways of measurement, The actual measured function may be different, because the actual system response differs between the two kinds of "object".
And again, both MTF and SFR are equally-good terms for the measured function, no matter how it is measured (SFR actually being a bit better because it more directly describes what the function means).
Nevertheless, because of the strong historical association of "SFR" with the slant edge target traditionally used to measure SFR, today when speaking of response curves determined by the two techniques, it is common to call an SFR/MTF determined by the slant edge technique as an "SFR", and an SFR/MTF determined by the texture pattern technique as a "texture MTF".
Ugh.
Of course, it would be best called a "texture SFR", and the other one an "edge SFR". Or we can call one a "texture MTF" and the other one an "edge MTF".
Best regards,
Doug
An essentially-identical concept is used in connection with optical systems (such as photographic lenses, or the combination of a lens and a digital imaging system. The differences in the application of the concept are:
• Here the frequency is spatial (in space), for example in cycles per mm, whereas in the electrical case the frequency is temporal (in time), in cycles per second (for which there is of course the unit name hertz).
• Here the property compared between output and input is the depth of luminance/illuminance modulation, whereas in the electrical case the the property is voltage (signal amplitude).
Historically, the ratio of output luminance modulation to input luminance modulation (which we can call the "modulation transfer ratio") as a function of (spatial) frequency has been called the modulation transfer function (MTF) of the optical system.
We rarely hear the ratio itself, at some particular spatial frequency, called "modulation transfer ratio" but rather "modulation transfer function", one of those irritating ambiguous uses that mathematical custom encourages.
But as the matter of determining this function became more and more sophisticated, authors began to use a clearer term for this function, the spatial frequency response (SFR) function. For one thing, this made much clearer the parallel with the "audio amplifier" case.Assuming we don't apply some different qualifying details in particular cases, then SFR and MTF are essentially synonymous.
Over the years, it became common to measure the SFR of, say, a lens by means of what is called the "slant edge" technique. The basic principle is this:
• We photograph a test target consisting of two areas of different luminance with a "sharp" edge between them.
• From the spatial variation of luminance in the "output" of the lens (the "edge spread function" for the target edge), we can determine (by a mathematical process that includes the Fourier transform, among other things) the spatial frequency response (SFR, aka MTF) of the lens.
For reasons that are beyond the scope of this note, this process is made more refined by using an edge in the test target that is not exactly vertical (thus the "slant edge" moniker).
Because of the wide use of such a target for determining SFR/MTF, and because of the general practice of, in the context of technical discussions of the measurement process, referring to the resulting test curve as SFR rather than MTF (it will of course usually be called MTF when we use it!), the slant edge test target has come to be known as the "SFR" test target (no other kind of target usually being used for measurement of SFR (MTF).
Now, as we get more sophisticated in developing metrics to assess the "sharpness" performance of a camera, we recognize that such things as noise reduction algorithms in effect degrade the MTF (that is, the SFR) as it applies to textured areas of the object/image.
To take this in account, in some cases we determine the MTF/SFR with a different technique, one that actually uses a test target with a complicated "textured" pattern (often one of overlapping circles of different diameters and different luminance, sometimes called for historical reasons a "dead leaves" pattern, but often today more aptly called a "spilled coins" pattern).
But more formally, this is spoken of as a "texture" pattern, as distinguished from a "slant edge" pattern, and the two measurement techniques are often distinguished by those two terms (which makes sense).
The analysis of the image of such a pattern proceeds quite differently from the analysis of the "edge spread function" obtained from a slant edge target, so we truly have a "different technique", not just a "different target".
But the definition of the determined MTF (SFR) is no different between the two ways of measurement, The actual measured function may be different, because the actual system response differs between the two kinds of "object".
And again, both MTF and SFR are equally-good terms for the measured function, no matter how it is measured (SFR actually being a bit better because it more directly describes what the function means).
Nevertheless, because of the strong historical association of "SFR" with the slant edge target traditionally used to measure SFR, today when speaking of response curves determined by the two techniques, it is common to call an SFR/MTF determined by the slant edge technique as an "SFR", and an SFR/MTF determined by the texture pattern technique as a "texture MTF".
Ugh.
Of course, it would be best called a "texture SFR", and the other one an "edge SFR". Or we can call one a "texture MTF" and the other one an "edge MTF".
Best regards,
Doug