Doug Kerr
Well-known member
We are all aware of a hoary guideline regarding the choice of shutter speed to keep to an acceptable degree the "image smearing" caused by movement of the camera during the exposure.
The guideline, initially articulated in the context of full-frame 35-mm photography, suggests that:
When we take into account the effect of image size on the matter, we can say that this guideline (for better or worse) can be restated as:
We recognize that this guideline is very simplistic, and does not take into account any of the following:
• Variations in the "steadiness" of the photographer.
• The moment of inertia of the camera (which comes from its mass and its shape). [A camera with a higher moment of inertia will displace its pointing axis less in the hands of a given photographer.]
• Our criterion for acceptable smearing of the image, including what fraction of the time will we attain it (given that the phenomenon is random).
So the guideline essentially adopts assumptions for all of those (although those are probably not stated anywhere - the guideline was adopted empirically).
All that having been recognized, and accepted (since we don't really know how to take account of any of those), we need to recognize a further fundamental assumption of the guideline: that the degree of displacement of the camera's pointing axis (perhaps the standard deviation of that displacement, recognizing its random statistical nature) is proportional to the exposure time. We can recognize this in the guideline through the following train of thought:
• We have a certain situation (with regard to the photographer, moment of inertia of the camera, and so forth). With a focal length of 100 mm, the guideline recommends a shutter speed no slower than 1/100 sec.
• That means that the angular displacement of the axis that occurs during 1/100 sec shifts the image on the focal plane by an amount that we consider to be "just acceptable smearing".
• If we then consider a focal length of 200 mm, because the distance from the second principal point to the focal plane is now twice what it was before (we assume focus at a substantial distance), that same angular displacement will now cause twice the shift of the image on the focal plane (representing twice the acceptable smearing).
• To restore "just acceptable smearing", we must cut the shift of the image in half; thus we must cut the angular displacement in half.
• If in fact displacement over the duration of the exposure is proportional to exposure time, we can do that by cutting the exposure time in half.
Since that is in fact how the guideline works, then we can reasonably say that it is predicated upon the fact that displacement over the duration of the exposure is proportional to exposure time.
Doubtless the major players in today's camera industry have recently developed well-founded, sophisticated models of camera shake behavior, in connection with their work on image stabilization systems. But I suspect that little of this has been published.
A recent article, though, by three "camera phone" researchers at Stanford University, reports their development of such a model, essentially "from the ground up". They needed to do this because:
• The traditional guideline was not based on any real model at all.
• Models developed of late by the "Tokyo club" have not been revealed.
• Camera phones typically have dramatically lower moments of inertia than the cameras presumed by the traditional guideline.
The article is here:
http://scien.stanford.edu/jfsite/Papers/ImageCapture/ICIS06_CameraShake.pdf
I will be reviewing it over the next little while, and will perhaps "publish" here my detailed observations.
One result, though, seemed worthy of reporting now. The work of this study showed that, rather than the amount of displacement of the camera axis during the exposure (actually, the standard deviation of the instantaneous displacement) being essentially directly proportional to the exposure time, it is actually essentially proportional to the exposure time to the 0.56 power.
The implication of this can be grasped from this numerical example:
• If for a focal length of 100 mm, with a shutter speed of 1/100 sec (following the "guideline"), the smearing is in fact "just acceptable", then:
• For a focal length of 200 mm, the "fastest" shutter speed to attain the same smearing criterion would need to be about 1/350 sec (not 1/200 sec, as produced by the "guideline").
• For a focal length of 50 mm, the "fastest" shutter speed to attain the same smearing criterion would need to be about 1/30 sec (not 1/50 sec, as produced by the "guideline").
The article also has very interesting material on criteria for assessing image smearing, and how the pixel resolution of the camera impacts the perceptual implications of a certain degree of image shift. But that is beyond the scope of this note.
That's about it for now. Stay tuned.
The guideline, initially articulated in the context of full-frame 35-mm photography, suggests that:
With a lens of focal length f, the exposure time should be no greater than 1/f.
When we take into account the effect of image size on the matter, we can say that this guideline (for better or worse) can be restated as:
With a lens whose full-frame 35-mm equivalent focal length is f', the exposure time should be no greater than 1/f'.
We recognize that this guideline is very simplistic, and does not take into account any of the following:
• Variations in the "steadiness" of the photographer.
• The moment of inertia of the camera (which comes from its mass and its shape). [A camera with a higher moment of inertia will displace its pointing axis less in the hands of a given photographer.]
• Our criterion for acceptable smearing of the image, including what fraction of the time will we attain it (given that the phenomenon is random).
So the guideline essentially adopts assumptions for all of those (although those are probably not stated anywhere - the guideline was adopted empirically).
[Before I proceed, let me note that here I will only deal with shake due to "angular" displacement of the camera axis; I do not deal with "translational" displacement, in which the camera shifts its position. This is in fact of practical consequence in the case of objects at a short distance. But here I exclude that situation.]
All that having been recognized, and accepted (since we don't really know how to take account of any of those), we need to recognize a further fundamental assumption of the guideline: that the degree of displacement of the camera's pointing axis (perhaps the standard deviation of that displacement, recognizing its random statistical nature) is proportional to the exposure time. We can recognize this in the guideline through the following train of thought:
• We have a certain situation (with regard to the photographer, moment of inertia of the camera, and so forth). With a focal length of 100 mm, the guideline recommends a shutter speed no slower than 1/100 sec.
• That means that the angular displacement of the axis that occurs during 1/100 sec shifts the image on the focal plane by an amount that we consider to be "just acceptable smearing".
• If we then consider a focal length of 200 mm, because the distance from the second principal point to the focal plane is now twice what it was before (we assume focus at a substantial distance), that same angular displacement will now cause twice the shift of the image on the focal plane (representing twice the acceptable smearing).
• To restore "just acceptable smearing", we must cut the shift of the image in half; thus we must cut the angular displacement in half.
• If in fact displacement over the duration of the exposure is proportional to exposure time, we can do that by cutting the exposure time in half.
Since that is in fact how the guideline works, then we can reasonably say that it is predicated upon the fact that displacement over the duration of the exposure is proportional to exposure time.
[In fact, that relationship is intuitively a little hard to swallow. It essentially assumes movement of the camera axis in the same direction at a fixed rate for the entire duration of the exposure. It might apply if the camera was on a tripod which was falling over.]
Doubtless the major players in today's camera industry have recently developed well-founded, sophisticated models of camera shake behavior, in connection with their work on image stabilization systems. But I suspect that little of this has been published.
A recent article, though, by three "camera phone" researchers at Stanford University, reports their development of such a model, essentially "from the ground up". They needed to do this because:
• The traditional guideline was not based on any real model at all.
• Models developed of late by the "Tokyo club" have not been revealed.
• Camera phones typically have dramatically lower moments of inertia than the cameras presumed by the traditional guideline.
The article is here:
http://scien.stanford.edu/jfsite/Papers/ImageCapture/ICIS06_CameraShake.pdf
I will be reviewing it over the next little while, and will perhaps "publish" here my detailed observations.
One result, though, seemed worthy of reporting now. The work of this study showed that, rather than the amount of displacement of the camera axis during the exposure (actually, the standard deviation of the instantaneous displacement) being essentially directly proportional to the exposure time, it is actually essentially proportional to the exposure time to the 0.56 power.
The implication of this can be grasped from this numerical example:
• If for a focal length of 100 mm, with a shutter speed of 1/100 sec (following the "guideline"), the smearing is in fact "just acceptable", then:
• For a focal length of 200 mm, the "fastest" shutter speed to attain the same smearing criterion would need to be about 1/350 sec (not 1/200 sec, as produced by the "guideline").
• For a focal length of 50 mm, the "fastest" shutter speed to attain the same smearing criterion would need to be about 1/30 sec (not 1/50 sec, as produced by the "guideline").
The article also has very interesting material on criteria for assessing image smearing, and how the pixel resolution of the camera impacts the perceptual implications of a certain degree of image shift. But that is beyond the scope of this note.
That's about it for now. Stay tuned.
