Doug Kerr
Well-known member
From time to time, we read of the "slant edge target" technique for determining the MTF of a lens. Just what does that mean?
The MTF (modulation transfer function) of a lens refers to its ability to carry from the scene to the image the changes in luminance that convey the detail in the scene, and how that ability varies with certain factors, notably:
• The spatial frequency (which we can think of as indicating the "fineness" of the detail)
• The distance on the image from the center
In the display of a lens MTF we are usually given by the lens manufacturer, we only get to see the MTF for two values of spatial frequency. However, for any actual technical work (including determination of the resolution of the lens), we must have the whole story: how the MTF varies over the entire range of spatial frequencies of interest (or at least its value at a substantial number of specific spatial frequencies).
Determining that in a laboratory in the obvious way requires multiple tests, using test targets with patterns of parallel lines at different spacings (thus having different spatial frequencies). This can be quite tedious.
A more efficient way is to determine the edge spread function of the lens (the variation in illuminance on the image resulting from a test object with a black and a white region with a sharp boundary between them).
We capture that variation on a digital sensor (the one in a camera, if we are really interested in the joint MTF of the lens plus the camera sensor) or a calibrated sensor in a "test camera" (whose properties we can "back out of" the resulting data).
From that single suite of data we can, by way of the Fourier transform, get the entire MTF (as a function of spatial frequency), over a wide range of spatial frequency (for the relevant location on the frame). And, if we plant these little "slant edge targets" here and there on the entire test target, we can get, in one shot, the entire MTF for a range of distances from the center of the frame.
But to be able to determine the MTF precisely through fairly high spatial frequencies, we must measure the edge spread function (the variation in illuminance on the sensor image of our "edge" target) to a very fine spatial resolution. Our need is usually well beyond the actual resolution of the sensor.
A clever ploy, involving the use of a target edge slightly rotated from alignment with the sensor grid ("slanted"), essentially constructs a "virtual sensor" with a resolution much higher than that of the sensor in reality, from which we can get description of the illuminance variation at a resolution much higher than that of the sensor itself.
This is known as the "slant edge target" technique for determining the MTF of a lens.
I have recently posted on my technical reference site, The Pumpkin, an updated version of my article on this matter, "Determining MTF with a Slant Edge Target", available here:
http://dougkerr.net/pumpkin#MTF_Slant_Edge
You may find it of interest.
Best regards,
Doug
The MTF (modulation transfer function) of a lens refers to its ability to carry from the scene to the image the changes in luminance that convey the detail in the scene, and how that ability varies with certain factors, notably:
• The spatial frequency (which we can think of as indicating the "fineness" of the detail)
• The distance on the image from the center
In the display of a lens MTF we are usually given by the lens manufacturer, we only get to see the MTF for two values of spatial frequency. However, for any actual technical work (including determination of the resolution of the lens), we must have the whole story: how the MTF varies over the entire range of spatial frequencies of interest (or at least its value at a substantial number of specific spatial frequencies).
Determining that in a laboratory in the obvious way requires multiple tests, using test targets with patterns of parallel lines at different spacings (thus having different spatial frequencies). This can be quite tedious.
A more efficient way is to determine the edge spread function of the lens (the variation in illuminance on the image resulting from a test object with a black and a white region with a sharp boundary between them).
We capture that variation on a digital sensor (the one in a camera, if we are really interested in the joint MTF of the lens plus the camera sensor) or a calibrated sensor in a "test camera" (whose properties we can "back out of" the resulting data).
From that single suite of data we can, by way of the Fourier transform, get the entire MTF (as a function of spatial frequency), over a wide range of spatial frequency (for the relevant location on the frame). And, if we plant these little "slant edge targets" here and there on the entire test target, we can get, in one shot, the entire MTF for a range of distances from the center of the frame.
But to be able to determine the MTF precisely through fairly high spatial frequencies, we must measure the edge spread function (the variation in illuminance on the sensor image of our "edge" target) to a very fine spatial resolution. Our need is usually well beyond the actual resolution of the sensor.
A clever ploy, involving the use of a target edge slightly rotated from alignment with the sensor grid ("slanted"), essentially constructs a "virtual sensor" with a resolution much higher than that of the sensor in reality, from which we can get description of the illuminance variation at a resolution much higher than that of the sensor itself.
This is known as the "slant edge target" technique for determining the MTF of a lens.
I have recently posted on my technical reference site, The Pumpkin, an updated version of my article on this matter, "Determining MTF with a Slant Edge Target", available here:
http://dougkerr.net/pumpkin#MTF_Slant_Edge
You may find it of interest.
Best regards,
Doug
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