lf the camera is always in motion, do the pictures stay in focus?
Simple answer: Yes.
Detailed answer: There is a lot of chatter about shoot-move-shoot versus constant motion when taking moving time lapse shots. Shoot-Move-Shoot simply means the camera only moves between exposures and stands (relatively) still during a picture. It is a very analog movement. Camera shoots, motor moves, camera shoots, motor moves, etc. In contrast, with a constant motion time lapse, the motor is slowly moving the camera the entire time. It does not stop and wait for the camera.
At first glance, it would seem that the shoot-move-shoot method would be the only way to make a time lapse work. Everyone knows you should keep a camera as still as possible when taking a picture, especially with longer exposures. This is where the confusion (mis-information) sneaks in.
In a constant motion time lapse, although the camera is always moving, the important thing to consider is how MUCH it moves during a single photo. If you have an image with a 20 second exposure but your camera only moves the width of a hair, there is not going to be visible degradation in your image. That simply isn't enough movement to have a significant effect. The movement of the shutter release, a breeze, or of footsteps nearby would have a greater effect than the subtle, constant motion of the slider during a time lapse.
In most situations, the distance your camera is moving during a photo is so infinitesimally small, it will have no considerable effect on the image. Of course you could set your slider up to move the full distance in 5 minutes with 20 second exposures and the images would be blurry. However, you would have a total of 15 photos to put together a time lapse, so it is self-defeating unless you are trying to get a 1/2 second long (at 30 fps) time lapse video.
This movement over time ratio only becomes an issue during night time lapses when you have the shutter open for long periods at a time. This balances out though as you also have to make sure that the slider move has traveled over a long enough period of time to generate enough photos to assemble a time lapse.
Because of this, the ratio is almost self-governing, and in most cases the distance the camera moves during any single photo is in the thousandths of an inch and not enough to blur. The wind or vibration of the shutter closing will move the lens more than the cart of the slider.
Many objects photographed are in motion like the stars (earth's rotation) and clouds yet they do not appear blurry unless they move too much during any one open shutter. So yes, the camera is technically moving during a constant motion time lapse, but with distances in the thousandths of an inch, there is no way it is going to effect an image.
Another way to look at this is to compare stop motion film (Wallace and Gromit, Fantastic Mr. Fox, etc.) to live action film. With stop motion, every frame of the image is in focus as nothing moves during the exposure. This creates super crisp images with no motion blur that when played back at 24fps or 30fps, have a very strobe-like effect to them. This same effect translates over to the shoot-move-shoot time lapse world as essentially you are capturing a stop motion sequence. Every frame is crisp and generally motion blur free. The resulting footage, when played back, has the same strobe-like effect of a stop motion film.
In contrast, if you were to take a single frame of a live action film, you would see that items that appear to be perfectly sharp when playing back at 24fps or 30fps actually have a bit of motion blur on them. The subtle motion blur is what gives live action film the fluid look we are used to seeing. It is a very pleasing image with no signs of significant blur when played back at full speed. Constant motion time lapse produces the same, fluid-like effect. Even if the images you are capturing have a near imperceptible amount of blur, when you play them back at 24, 30, or even 60 fps, the results will be comparable to live action footage. This a is a more "natural" look preferred by many pros in the industry.
Both styles have a unique look to them and one is not necessarily better than the other. It all depends on your personal preference and end goal. If you are looking for a more natural, video-looking time lapse, then we recommend constant motion time lapse. If you are looking for each image to be a perfectly sharp, stand - alone work of art, then shoot-move-shoot is a better option.