Some thoughts on tripod vibration and shutter speed:
Having seen the Charlie Kim studies on the Markins site my interest was piqued...after a bit of arithmetic, I realised the oscillations shown for the tripods mean that the resolution of the system is limited to 25lp/mm, ie contrast at 40lp/mm is 0%, so all my concerns about lens performance, enlargement limits etc are severely capped. Simply, 1/(2.amplitude)=resolution limit, for the scenario where the length of the lens is the same as the focal length (its worse for teles). Without mirror lock up, the oscillations are 0.02mm -> 1/0.02/2=25 (the factor of 2 is there because line pairs only need to overlap by half their width to achieve zero contrast, full overlap produces spurious resolution)
http://www.markins.com/charlie/report.html
If you want a tripod to reveal the capacity of a lens, it strikes me that the movement on the film should be less than the diffraction limited resolution/2. This means that the MTF curve for the lens will sit beneath the limits imposed by tripod vibrations. This can be achieved by one of two means a) reduce the amplitude of oscillation b) reduce the time the shutter is open, so that only a portion of the vibration cycle is recorded on the film. As a) is shown to be very difficult unless “bolted to a rock”, b) seems the viable alternative. Using simple harmonic motion, I came up with the following formula for obtaining the shutter speed t required for diffraction limit resolution to be seen:
Arcsin(fstop/1500.1/2.1/A)/w=t
In the Markins report, the amplitude of the vibration, A was 0.02mm without mirror lockup, and the frequency w was 10Hz. This is using a decent tripod and ball head and a 250mm focal length. This gives a shutter speed, t of 1/500s at f8, WHEN TRIPOD MOUNTED! This produces a vibration creating zero contrast at a frequency of ~200lp/mm which is the same as the diffraction limit at f8. If the vibration is allowed to go full cycle, ie shutter speed is 1/10s, then the resolution drops to A which produces 1/0.02/2=25lp/mm. [note: if you are going to put numbers through this, w needs multiplying up by 2.pi so its in rads.s-1 instead of Hz, also note that this is for a 250mm lens, so it works out as a "1/(2.focal length)|tripod mounted" rule, iff the relationship with focal length is linear]
You could substitute A for f_length/10000, where focal length is /mm. Handheld, w=3 and A =0.15 which produces t of 1/1000s "1/(4.focal length)|not tripod mounted" rule.
Once the shutter speed is so slow that the period of oscillation of the tripod is less than the time the shutter is open, then the full swing of the front element is recorded on the film and the absolute amplitude of the vibrations dictates the resolution limit of the system.
Unfortunately, the frequency of oscillations actually increases with a stiffer tripod set up. This is why there is only a factor of 2 difference between the speed required for handheld vs tripod mounted. The increase in frequency needs to be outpaced by the decrease in the amplitude of the oscillation. This makes me wonder whether instead of increasing the rigidity of my ball head, I’d be better off trying to reduce the frequency of oscillation by increasing the mass of the lens and camera, and by damping the connection between the camera and ball head. Indeed, I read in an old Zeiss camera review that for ultimate resolution, a hydro damped head which is not locked off outperforms a rigid setup. Indeed, maybe this report is what has sparked this thought-experiment.
One major caveat to all of this is that the test was done with a Hasselblad...where I guess the shutter is heavier than my ME Super’s, yet the mass of the two is not very dissimilar. From these numbers, I can see why people would complain about shutter vibration and look to heavy tripods.
Having seen the Charlie Kim studies on the Markins site my interest was piqued...after a bit of arithmetic, I realised the oscillations shown for the tripods mean that the resolution of the system is limited to 25lp/mm, ie contrast at 40lp/mm is 0%, so all my concerns about lens performance, enlargement limits etc are severely capped. Simply, 1/(2.amplitude)=resolution limit, for the scenario where the length of the lens is the same as the focal length (its worse for teles). Without mirror lock up, the oscillations are 0.02mm -> 1/0.02/2=25 (the factor of 2 is there because line pairs only need to overlap by half their width to achieve zero contrast, full overlap produces spurious resolution)
http://www.markins.com/charlie/report.html
If you want a tripod to reveal the capacity of a lens, it strikes me that the movement on the film should be less than the diffraction limited resolution/2. This means that the MTF curve for the lens will sit beneath the limits imposed by tripod vibrations. This can be achieved by one of two means a) reduce the amplitude of oscillation b) reduce the time the shutter is open, so that only a portion of the vibration cycle is recorded on the film. As a) is shown to be very difficult unless “bolted to a rock”, b) seems the viable alternative. Using simple harmonic motion, I came up with the following formula for obtaining the shutter speed t required for diffraction limit resolution to be seen:
Arcsin(fstop/1500.1/2.1/A)/w=t
In the Markins report, the amplitude of the vibration, A was 0.02mm without mirror lockup, and the frequency w was 10Hz. This is using a decent tripod and ball head and a 250mm focal length. This gives a shutter speed, t of 1/500s at f8, WHEN TRIPOD MOUNTED! This produces a vibration creating zero contrast at a frequency of ~200lp/mm which is the same as the diffraction limit at f8. If the vibration is allowed to go full cycle, ie shutter speed is 1/10s, then the resolution drops to A which produces 1/0.02/2=25lp/mm. [note: if you are going to put numbers through this, w needs multiplying up by 2.pi so its in rads.s-1 instead of Hz, also note that this is for a 250mm lens, so it works out as a "1/(2.focal length)|tripod mounted" rule, iff the relationship with focal length is linear]
You could substitute A for f_length/10000, where focal length is /mm. Handheld, w=3 and A =0.15 which produces t of 1/1000s "1/(4.focal length)|not tripod mounted" rule.
Once the shutter speed is so slow that the period of oscillation of the tripod is less than the time the shutter is open, then the full swing of the front element is recorded on the film and the absolute amplitude of the vibrations dictates the resolution limit of the system.
Unfortunately, the frequency of oscillations actually increases with a stiffer tripod set up. This is why there is only a factor of 2 difference between the speed required for handheld vs tripod mounted. The increase in frequency needs to be outpaced by the decrease in the amplitude of the oscillation. This makes me wonder whether instead of increasing the rigidity of my ball head, I’d be better off trying to reduce the frequency of oscillation by increasing the mass of the lens and camera, and by damping the connection between the camera and ball head. Indeed, I read in an old Zeiss camera review that for ultimate resolution, a hydro damped head which is not locked off outperforms a rigid setup. Indeed, maybe this report is what has sparked this thought-experiment.
One major caveat to all of this is that the test was done with a Hasselblad...where I guess the shutter is heavier than my ME Super’s, yet the mass of the two is not very dissimilar. From these numbers, I can see why people would complain about shutter vibration and look to heavy tripods.
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