Scheimpflug principle and tilting the lens
Theodor Scheimpflug (1865–1911) was a Captain in the Austrian Army who devised a method of correcting for perspective in aerial photography. The Scheimpflug principle is named after him and deals with the plane of focus in a view camera when the lens is tilted with respect to the film plane. The same principle apples to 35mm DSLRs when using a tilt/shift lens.
With a normal lens, the plane of focus is always perpendicular to the axis of the lens and moves towards or away from the lens as the focus ring is rotated. A tilt/shift lens focusses in an entirely different – and surprising – way; the plane of focus can be rotated and moved up and down relative to the camera / lens. For example in a landscape it is perfectly normal to rotate the plane of focus to the horizontal and lower it to just above the ground, placing everything in focus from nearby flowers to the far horizon.
The Scheimpflug principle consists of two rules, which when taken together determine the plane of focus for a tilted lens. Referring to the diagram above, imagine a camera on a tripod and levelled so that the film or digital sensor is vertical. The sensor is shown as the short green, vertical line on the image plane. Now if the lens is tilted downwards, the lens plane will cross the image plane along a line somewhere below the camera. The first rule states that the plane of sharp focus must also pass through the line of intersection of the image and lens planes.
The second rule is slightly harder to visualize. Imagine a plane through the lens, parallel with the image plane – shown in red in the diagram with the letter “J”. Also imagine a plane one focal length in front of the lens, parallel with the lens plane; this is the “front focal plane”. The second rule states that the plane of focus must also pass through the intersection of these two (red) planes. The two rules, when taken together, define the plane of sharp focus – and the green segment shows the area of the subject that will be recorded on the sensor.
On a tilt/shift lens, there are two settings that control the position of the plane of focus: the angle of tilt and the usual focussing ring. The angle of tilt setting controls the angle theta (θ) in the diagram above, while the focussing ring controls the distance between the optical centre of the lens and the camera sensor. Referring to the diagram, note that the distance J is determined only by the angle of tilt θ and the focal length of the lens f. In particular, J does not depend on the distance between the lens and the image plane. So when the focus ring is turned, the distance J remains fixed and the plane of focus rotates about the line shown as the “hinge line”. The diagram below shows the plane of focus rotating around the hinge line as the image plane moves towards the lens.
An animation of this effect is provided - click: animation
To set up the camera to take a particular shot, we will need to think about the composition and estimate two aspects: the distance that we wish to drop the plane of focus below the lens (J) and the angle to which we wish to rotate the plane of focus (ψ). This is just a matter of imagining where we wish to place the plane of focus to cut through the main points of interest in the scene.
Having estimated the distance J and the angle ψ, we need to convert these into setting on the lens: of tilt angle θ and focus distance.
The tilt angle θ is simple enough to calculate as, for any given lens, there is a direct relationship between J and θ. In the top diagram, we can see that sin θ = f / J. So to set a chosen value of J, we would need to tilt the lens by an angle θ = arcsin( f / J ). For example in a landscape with the camera on a tripod, we might wish to drop the plane of focus about 1.4 metres below the camera to a point just above ground level (to get foreground detail in focus). If we are using a 24mm lens, the angle of tilt required would be arcsin( 0.024 / 1.4 ), which is 1 degree. Rather than using a calculator in the field, it’s easier to carry a cheat-sheet – and a suitable table is provided below.
The calculation of ψ is a little more complicated as it depends on both the angle of tilt θ and the focus distance set on the focussing ring. But we are rescued by the simple condition that if the focus is set to infinity (∞), the angle ψ is 90 degrees, i.e. if the camera is mounted on a tripod in the normal way with the sensor vertical, the plane of focus will be horizontal. If we then rotate the focussing ring to shorter distances, the plane of focus rotates upwards around the hinge line; in the same example as above, if we “focus” at 1.5 metres, the plane of focus will rotate up about 45 degrees.
This is a lot easier to set up in practice than the maths might suggest. For a landscape, we just need to estimate how far we need to drop the plane of focus below the camera and use our cheat sheet to set the tilt angle, with the focus ring set at ∞. Use live view (zoomed in) to check focus on the foreground details, tweaking the tilt angle as needed to move the plane of focus vertically up / down. Then, still using live view, check the focus of the details in the distance, tweaking the focus ring as needed to rotate the plane of focus to “lay” it over the distant scene. Re-tweak if necessary to get everything in focus.
For details of the theory, see Wikipedia
Depth of field
With a normal lens, we are used to thinking of a depth of field either side of the plane of sharp focus. The depth of field depends, among other things, on the lens aperture (f/number), which can be set creatively to control how much of the scene appear to be in good focus.
When the lens is tilted, the area of good focus is wedge-shaped with the point of the wedge at the hinge line. Adjusting the lens aperture increases or decreases the angular width of the wedge either side of the plane of sharp focus. So stopping down the lens brings a wider swathe of the subject into good focus.
The figures presented below are for illustration purposes and no liability is accepted for any errors.
This cheat sheet is for a 24mm lens and the focus markings are based on the Canon TS-E 24mm f/3.5 lens. The two left-hand columns show the displacement (shown as drop) J based on the angle of tilt θ. The rest of the table shows the rotation ψ corresponding to the angle of tilt θ in the left-most column and the focus distance in the top row. Note that with the lens focussed at ∞, the rotation is 90 degrees for all angles of tilt.
|Lens focal length||Focus (meters)||0.3||0.35||0.4||0.5||0.7||1||1.5||3||∞|
|Angle of tilt θ (deg)||Drop J (meters)||Rotation from image plane ψ (deg)|