right|thumb|Computer-generated representation of a dolly zoom
thumb|Frame from an animation showing a dolly zoom being performed. At the top of the image is the camera's view; the cubes stay the same size as the teapots in the background grow bigger. At the bottom of the image is a plan view showing the camera moving back while zooming in, illustrating how the effect is achieved.
thumb|In the video inset, the object moves with the camera and it does not zoom, so the FOV does not change; thus there is no dolly effect.
A dolly zoom (also known as a Hitchcock shot, Vertigo shot, is an in-camera effect that appears to undermine normal visual perception.
The effect is achieved by zooming a zoom lens to adjust the angle of view (often referred to as field of view, or FOV) while the camera dollies (moves) toward or away from the subject in such a way as to keep the subject the same size in the frame throughout. The zoom shifts from a wide-angle view into a more tightly packed angle. In its classic form, the camera angle is pulled away from a subject while the lens zooms in, or vice versa. The dolly zoom's switch in lenses can help audiences identify the visual difference between wide-angle lenses and telephoto lenses. Thus, during the zoom, there is a continuous perspective distortion, the most directly noticeable feature being that the background appears to change size relative to the subject. Hence, the dolly zoom effect can be broken down into three main components: the moving direction of the camera, the dolly speed, and the camera lens' focal length.
History
The effect was first created by Irmin Roberts, a Paramount second-unit cameraman, who devised the method for Alfred Hitchcock's film Vertigo. At the time, Roberts had already designed a special camera capable of fast focal lens changes that allowed short-range projections. His expertise in focal lenses most likely prompted his innovation of the dolly zoom, which was more popularly recognized as the "trombone shot" or "contra zoom". Despite this step forward for cinematography, Roberts was not properly credited at the end of Vertigo. This shot has since been used in many other films, including Goodfellas, Jaws, and the Lord of the Rings films. Rainer Werner Fassbinder uses the effect twice in one shot in Chinese Roulette (1976).
Uses
Among the many creative uses the dolly zoom can provide to cinematographers, the shot can be divided into two types: the dolly-in/zoom-out and the dolly-out/zoom-in. The dolly-in/zoom-out shot is usually centered on a subject, where the background is pushed away from the character to create a profuse amount of uneasiness. For example, Poltergeists famous dolly zoom stretches the background to make it seem as if the door is much farther away from the character than it actually is. In contrast, the dolly-out/zoom-in shot shrinks the background to seem much closer than it really is.
The shot follows Mikey's short walk between the two settings, and the camera
pans to the side and tracks backwards away from Junior's car,
causing the background to "grow" in size as the cinematographer zooms the lens
in and the camera moves backwards. Here, the effect is used to avoid a
compromise that would otherwise be necessary: a longer focal length throughout the shot would show less of the surrounding streetscape, and a wider one would introduce distortion that would make Mikey appear smaller than Junior. The
technique allows the cinematographers to achieve the framing and perspective
they want at both ends of an extended take without needing to introduce an additional
cut into the scene or disturbing the viewer's immersion by making the movements of the camera more apparent.
Notable examples
Jaws (1975) uses a dolly zoom to focus on Martin Brody's realization that there is a shark on the beach.
In Raging Bull (1980), Martin Scorsese uses dolly zoom shot to disorient the audience and put them in Jake LaMotta's shoes, and thus creating a vertigo effect.
In Goodfellas (1990), Scorsese uses dolly zooms to convey tensions between characters. This shot is most famously employed in Henry's dive into paranoia, where he eats at a diner with Jimmy while tracking a window to see if anybody has been following him.
In The Lord of the Rings: The Fellowship of the Ring (2001), Frodo stands by as a dolly zoom signifies an entrance of an enemy from the woods.
In Shaun of the Dead (2004), a dolly zoom places comedic emphasis on Shaun's bravery, which ultimately fails when his shotgun jams.
Optics
For most purposes, it can be assumed that the image space and the object space are in the same medium. Thus, for an object in focus, the distance between the lens and image plane <math>s_\text{i}</math>, the distance between lens and the object <math>s_\text{o}</math>, and the focal length <math>f</math> are related by
:<math>{1 \over s_i} + {1 \over s_o} = {1 \over f}.</math>
Then the transverse magnification is
:<math>M = {s_\text{i} \over s_\text{o = {f \over (s_\text{o} - f)}.</math>
The axial magnification <math>M_\text{ax}</math> of an object at <math>s_\text{o}</math> is the rate of change of the lens–image distance <math>s_\text{i}</math> as the lens–object distance <math>s_\text{o}</math> changes. For an object of finite depth, one can conceive of the average axial magnification as the ratio of the depth of the image and the depth of the object:
:<math>M_\text{ax} = \left| {d \over d(s_\text{o})} {s_\text{i} \over s_\text{o \right| = \left| {d \over d(s_\text{o})} {f \over (s_\text{o} - f)} \right| = \left| {-f \over (s_\text{o} - f)^2} \right| = {M^2 \over f}.</math>
One can see that if magnification remains constant, a longer focal length results in a smaller axial magnification, and a smaller focal length in a larger axial magnification. That is, when using a longer focal length while moving the camera/lens away from the object to maintain the same magnification M, objects seem shallower, and the axial distances between objects seem shorter. The opposite—increased axial magnification—happens with shorter focal lengths while moving the camera/lens towards the object.
Calculating distances
To achieve the effect, the camera needs to be positioned at a certain distance from the object that is supposed to remain still during the dolly zoom. The distance depends on how wide the scene is to be filmed and on the field of view (FOV) of the camera lens. Before calculating the distances needed at the different fields of view, the constant width of the scene has to be calculated:
:<math> \text{distance} = \frac{\text{width{2\tan\left(\frac{1}{2}\text{FOV}\right)}.</math>
For example, a FOV of 90° and a distance of 2 meters yield a constant width of 4 meters, allowing a 4-meter-wide object to remain still inside the frame during the effect.