Editing Scheimpflug principle (section)

==Depth of field==
[[File:ScheimpflugDoF.png|thumb|Figure 5. Depth of field when the PoF is rotated]]

When the lens and image planes are parallel, the [[depth of field]] (DoF) extends between parallel planes on either side of the plane of focus. When the Scheimpflug principle is employed, the DoF becomes [[Wedge (geometry)|wedge]] shaped (Merklinger 1996, 32; Tillmanns 1997, 71),{{Efn|When the lens plane is not parallel to the image plane, the blur spots are [[ellipse]]s rather than circles, and the limits of DoF are not exactly planar. There is little data on human perception of elliptical rather than circular blurs, but taking the [[major axis]] of the ellipse as the governing dimension is arguably the worst-case condition. Using this assumption, Robert Wheeler examines the effect of elliptical blur spots on DoF limits for a tilted lens in his Notes on View Camera Geometry; he concludes that in typical applications, the effect is negligible, and that the assumption of planar DoF limits is reasonable. His analysis considers only points on a vertical plane through the center of the lens, however. Leonard Evens examines the effect of elliptical blur at any arbitrary point in the image plane, and concludes that, in most cases, the error from assuming planar DoF limits is minor.}} with the apex of the wedge at the PoF rotation axis,{{Efn|Tillmanns indicates that this behavior was discovered during the development of the Sinar e camera (released in 1988), and that prior to that, the DoF wedge was thought to extend to the line of intersection of the object, lens, and image planes. He does not discuss the rotation of the PoF about the apex of the DoF wedge.}} as shown in Figure 5. The DoF is zero at the apex, remains shallow at the edge of the lens's field of view, and increases with distance from the camera. The shallow DoF near the camera requires the PoF to be positioned carefully if near objects are to be rendered sharply.

On a plane parallel to the image plane, the DoF is equally distributed above and below the PoF; in Figure 5, the distances <var>y</var><sub>n</sub> and <var>y</var><sub>f</sub> on the plane VP are equal. This distribution can be helpful in determining the best position for the PoF; if a scene includes a distant tall feature, the best fit of the DoF to the scene often results from having the PoF pass through the vertical midpoint of that feature. The angular DoF, however, is ''not'' equally distributed about the PoF.

The distances <var>y</var><sub>n</sub> and <var>y</var><sub>f</sub> are given by (Merklinger 1996, 126)

: <math>y_x = \frac f {v'} \frac {u'} u_\mathrm{h} J \,,</math>

where <var>f</var> is the lens focal length, <var>v′</var> and <var>u′</var> are the image and object distances parallel to the line of sight, <var>u</var><sub>h</sub> is the [[hyperfocal distance]], and <var>J</var> is the distance from the center of the lens to the PoF rotation axis. By solving the [[#PoF_ImageSide|image-side equation for {{nowrap|tan <var>ψ</var>}}]] for <var>v′</var> and substituting for <var>v′</var> and <var>u</var><sub>h</sub> in the equation above,{{Efn|Merklinger uses the approximation {{nowrap|<var>u</var><sub>h</sub> ≈ <var>f</var>&thinsp;<sup>2</sup>/<var>N</var><var>c</var>}} to derive his formula, so the substitution here is exact.}} the values may be given equivalently by

: <math>y_x = \frac {Nc} {f} \left ( \frac {1} {\tan \theta} - \frac {1} {\tan \psi} \right ) u' \,,</math>

where <var>N</var> is the lens [[F-number|<var>f</var>-number]] and <var>c</var> is the [[circle of confusion]]. At a large focus distance (equivalent to a large angle between the PoF and the image plane), {{nowrap|<var>v′</var> ≈ <var>f</var>}}, and (Merklinger 1996, 48){{Efn|Strictly, as the focus distance approaches infinity, {{nowrap|<var>v′</var> cos <var>θ</var> → <var>f</var>}}; hence, the approximate formulas differ by a factor of {{nowrap|cos <var>θ</var>}}. At small values of <var>θ</var>, {{nowrap|cos <var>θ</var> ≈ 1}}, so the difference is negligible. With large values of tilt, as occasionally might be needed with a large-format camera, the error becomes greater, and either the exact formula or the approximate formula in terms of {{nowrap|tan <var>θ</var>}} should be used.}}

: <math>y_x \approx \frac {u'} u_\mathrm{h} J \,,</math>

or

: <math>y_x \approx \frac {Nc} {f} \frac {u'} {\tan \theta} \,.</math>

Thus at the hyperfocal distance, the DoF on a plane parallel to the image plane extends a distance of <var>J</var> 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 <var>f</var>-number (larger [[aperture]]) than would be required if the PoF were parallel to the image plane.

===Selective focus===
[[File:Jcouples17.jpg|thumb|James McArdle (1991) ''Accomplices'']]

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&nbsp;mm lens for a small-format camera, the total vertical DoF at the [[hyperfocal distance]] is approximately{{Efn|The example here uses Merklinger's approximation. For small values of tilt, {{nowrap|sin&thinsp;''θ'' ≈ tan&thinsp;''θ''}}, so the error is minimal; for large values of tilt, the denominator should be {{nowrap|tan&thinsp;''θ''}}.}}

: <math>2J = 2 \frac {f} {\sin \theta} = 2 \times \frac {90 \text{ mm}} {\sin 8^\circ} = 1293 \text { mm} \,.</math>

At an aperture of ''f''/2.8, with a circle of confusion of 0.03&nbsp;mm, this occurs at a distance ''u′'' of approximately

: <math>\frac {f^2} {Nc} = \frac {90^2} {2.8 \times 0.03} = 96.4 \text { m} \,.</math>

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.