How do aperture and the tilt portion of a tilt shift lens relate?

Question

I have found that you can use the tilt feature of a tilt shift lens to do some pretty neat things with depth of field. I can throw it 8° to the right and everything on the left side of the image drops out of focus, along with a narrow band on the far right side. I also understand that a large aperture will narrow the range of areas in an image that are in focus. So do the two relate? If I have a larger aperture tilt shift lens, will that multiple the effect of a 8° tilt?

I am sorry for noting this, but I am not a math person and would prefer any simplified version of the science portion if at all possible, but feel free to include any equations if that will help others.

Answer 1

Changing aperture has the same overall effect on depth-of-field with a tilted lens that it has on an untilted lens.

Tilting a lens changes the visible consequences of any change in aperture because it (when viewed sideways) changes the shape of the in-focus area from a rectangle to a wedge (with the point towards and above or below the camera, depending on tilt direction). The diagrams on this page include some good visualisations of the effect.

decreasing/increasing the aperture (increasing/decreasing f-number) effectively causes the width of the base of the wedge to increase/decrease accordingly. This results in the effect of the change in aperture becoming progressively smaller close to the point.