Can one increase the sharpness of the camera by increasing the shutter speed?
No. This will not increase the sharpness of the camera, although for moving subjects, it will decrease the amount of motion blur, and in the case of trying to capture still frames, or fast moving objects, less motion blur will lead to “sharper” object rendition. One thing to keep in mind though is that with a higher shutter speed and extremely fast moving objects, because of the lack of motion blur, rolling shutter “skew” will be more apparent than if the shutter was slower allowing the skew to be averaged out by motion blur.
