Michael Tiemann
Well-known member
I came across some interesting maths curated by Frans van den Bergh regarding theoretical and practical MTF of digital sensors. The article that really caught my attention is here, but he's been writing and coding about the topic for about 5 years and his MFMapper toolkit has been posted to GitHub.
The long and short of it is this: if one considers a signal of repeating lines (such as a fully resolved 100 lp/mm chart), one can analyze how such a pattern will hit a sensor of a specific geometry and implementation, such as a 5 micron bayer pattern assumed for DRAGON. A 5 micron pixel pitch means 200 pixels per mm, which means that without any OLPF, the pattern might be perfectly resolved (with the white line perfectly hitting one row or column of pixels and the black line perfectly hitting an adjacent row or column). Alternatively, the pattern might be at a 45 degree angle, or it might be offset by 2.5 microns, in which case the white line half-fills one row, column, or diagonal of pixels and half-fills the adjacent row, column, or diagonal, leading to a perfect middle gray with no resolution at all. Moreover, if the pattern move relative to the pixel array, aliasing will be observed as the alternating white and black lines go from the center of one pixel pair to the next.
Just as the Nyquist limit governs the absolute limit of signal information that can be derived from a given (in this case, spatial) sampling rate, there are some other hard limits as to what can and cannot be resolved across a range of signal/sensor configurations. For example, at every multiple of the pixel pitch, the resolution drops to zero because there are an equal number of white and black lines that average out to zero. And above the 1:1 ratio, higher (spatial) frequency information "wraps around" and appears as if it is really lower (spatial) frequency information. Such ringing can make it appear that something is being resolved, when actually it's just noise.
The long and short of the analysis, however, is that even at 1/2 the spatial frequency of the array (two pixels per line or four pixels per line pair), the aliasing problem is still very severe: the sensor readings will vary between 100% MTF (1, 1, 0, 0) and 50% MTF (.5, 1, .5, 0). Applying an "optimal" gaussian point spread function to the input signal lowers the MTF from the 100%-50% range to a much smaller one, albeit below 20%, which is not very well resolved. However, at 1/3rd of the spatial frequency of the array, the post OLPF image recovers to about 50%, as shown in this chart:
Thus, the math tells us that if we want 50% MTF and decent anti-aliasing, the DRAGON sensor can only resolve a 100 lp/mm signal to 33 lp/mm, not 50, and definitely not 100. And that's before we consider the question of how the Bayer filter might further confound our equations. And obviously an incoming signal with only 50 lp/mm resolution is going to have a lower (though not terribly much lower) final resolution than a 100 lp/mm input.
I'm posting this because I think it's interesting that an 6K DRAGON sensor should properly be expected to resolve only 1024 line pairs across its width, and only a 60 mm sensor could be expected to resolve true 4K information (2000 line pairs across its width).
Comments? Criticisms?
The long and short of it is this: if one considers a signal of repeating lines (such as a fully resolved 100 lp/mm chart), one can analyze how such a pattern will hit a sensor of a specific geometry and implementation, such as a 5 micron bayer pattern assumed for DRAGON. A 5 micron pixel pitch means 200 pixels per mm, which means that without any OLPF, the pattern might be perfectly resolved (with the white line perfectly hitting one row or column of pixels and the black line perfectly hitting an adjacent row or column). Alternatively, the pattern might be at a 45 degree angle, or it might be offset by 2.5 microns, in which case the white line half-fills one row, column, or diagonal of pixels and half-fills the adjacent row, column, or diagonal, leading to a perfect middle gray with no resolution at all. Moreover, if the pattern move relative to the pixel array, aliasing will be observed as the alternating white and black lines go from the center of one pixel pair to the next.
Just as the Nyquist limit governs the absolute limit of signal information that can be derived from a given (in this case, spatial) sampling rate, there are some other hard limits as to what can and cannot be resolved across a range of signal/sensor configurations. For example, at every multiple of the pixel pitch, the resolution drops to zero because there are an equal number of white and black lines that average out to zero. And above the 1:1 ratio, higher (spatial) frequency information "wraps around" and appears as if it is really lower (spatial) frequency information. Such ringing can make it appear that something is being resolved, when actually it's just noise.
The long and short of the analysis, however, is that even at 1/2 the spatial frequency of the array (two pixels per line or four pixels per line pair), the aliasing problem is still very severe: the sensor readings will vary between 100% MTF (1, 1, 0, 0) and 50% MTF (.5, 1, .5, 0). Applying an "optimal" gaussian point spread function to the input signal lowers the MTF from the 100%-50% range to a much smaller one, albeit below 20%, which is not very well resolved. However, at 1/3rd of the spatial frequency of the array, the post OLPF image recovers to about 50%, as shown in this chart:
Thus, the math tells us that if we want 50% MTF and decent anti-aliasing, the DRAGON sensor can only resolve a 100 lp/mm signal to 33 lp/mm, not 50, and definitely not 100. And that's before we consider the question of how the Bayer filter might further confound our equations. And obviously an incoming signal with only 50 lp/mm resolution is going to have a lower (though not terribly much lower) final resolution than a 100 lp/mm input.
I'm posting this because I think it's interesting that an 6K DRAGON sensor should properly be expected to resolve only 1024 line pairs across its width, and only a 60 mm sensor could be expected to resolve true 4K information (2000 line pairs across its width).
Comments? Criticisms?
