DoF, however, is not equally distributed about the PoF. The distances yn and yf are given by (Merklinger 1996, 126) where f is the lens focal length, v′ and u′ are the image and object distances parallel to the line of sight, uh is the hyperfocal distance, and J is the distance from the center of the lens to the PoF rotation axis. By solving the image-side equation for for v′ and substituting for v′ and uh in the equation above, the values may be given equivalently by where N is the lens f-number and c is the circle of confusion. At a large focus distance (equivalent to a large angle between the PoF and the image plane), , and (Merklinger 1996, 48) or Thus at the hyperfocal distance, the DoF on a plane parallel to the image plane extends a distance of J on either side of the PoF. With some subjects, such as landscapes, the wedge-shaped DoF is a good fit to the scene, and satisfactory sharpness can often be achieved with a smaller lens f-number (larger aperture) than would be required if the PoF were parallel to the image plane. Selective focus The region of sharpness can also be made very small by using large tilt and a small f-number. For example, with 8° tilt on a 90 mm lens for a small-format camera, the total vertical DoF at the hyperfocal distance is approximately At an aperture of f/2.8, with a circle of confusion of 0.03 mm, this occurs at a distance u′ of approximately Of course, the tilt also affects the position of the PoF, so if the tilt is chosen to minimize the region of sharpness, the PoF cannot be set to pass through more than one arbitrarily chosen point. If the PoF is to pass through more than one arbitrary point, the tilt and focus are fixed, and the lens f-number is the only available control for adjusting sharpness. Derivation of the formulas Proof of the Scheimpflug principle In a two-dimensional representation, an object plane inclined to the lens plane is a line described by . By optical convention, both object and image distances are positive for real images, so that in Figure 6, the object distance u increases to the left of the lens plane LP; the vertical axis uses the normal Cartesian convention, with values above the optical axis positive and those