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Definition of "focus" Several factors determine whether the objective error in focus becomes noticeable. Subject matter, movement, the distance of the subject from the camera, and the way in which the image is displayed all have an influence. However, the most important factor is the actual degree of error in relation to the area of film exposed. Light from a point source at the correct distance will produce the image of a point on the film. A point farther away or nearer will produce an image in the form of a disk known as a "circle of confusion." The diameter of these circles increases with distance from the point of focus and so can be used as the measure of error or blurring of the image. For a 35 mm motion picture, the image area on the camera negative is roughly 0.87 by 0.63 in (22 by 16 mm). The limit of tolerable error is usually set at 0.002 in (0.05 mm) diameter. For 16 mm film, where the image area is smaller, the tolerance is stricter, .001 in (0.025 mm). Standard depth of field tables are constructed on this basis, although generally 35 mm productions set it at 0.001 in (0.025 mm). Note that the acceptable circle of confusion values for these formats are different because of the relative amount of magnification each format will need in order to be projected on a full-sized movie screen. (A table for 35 mm still photography would be somewhat different since more of the film is used for each image and the amount of enlargement is usually much less.) Another factor to be considered is that the film format's size will affect the relative depth of field. The larger the area of the film is, the longer a lens will need to be to capture the same framing as a smaller film format. In motion pictures, for example, a frame with a 12 degree horizontal field of view will require a 50 mm lens on 16 mm film, a 100 mm lens on 35 mm film, and a 250 mm lens on 65 mm film. Conversely, using the same focal length lens with each of these formats will yield a progressively wider image as the film format gets larger: a 50 mm lens has a horizontal field of view of 12 degrees on 16 mm film, 23.6 degrees on 35 mm film, and 55.6 degrees on 65 mm film. What this all means is that as the larger formats require longer lenses than the smaller ones, they will accordingly have a smaller depth of field. Therefore, compensations in exposure, framing, or subject distance need to be made in order to make one format look like it was filmed like another. Hyperfocal distance The hyperfocal distance is the nearest distance at which the far end of the depth of field stretches to infinity. Focusing the camera at the hyperfocal distance results in the largest possible depth of field. Focusing beyond the hyperfocal distance does not add depth of field to the far end (which is already at infinity), but it does subtract from the focus area in front of the hyperfocal point. Therefore there is less total depth of field. Likewise, focusing ahead of the hyperfocal distance results in a gain of focus area ahead of the focus point but loses some of the focus area beyond the focus point including the subjects near infinity. Of course, this latter approach may be appropriate for images that do not extend to infinity. The Object Field Method Traditional depth-of-field formulae and tables assume equal circles of confusion for near and far objects. Some authors, such as Merklinger (1992), have suggested that distant objects often need to be much sharper to be clearly recognizable, whereas closer objects, being larger on the film, do not need to be so sharp. The loss of detail in distant objects may be particularly noticeable with extreme enlargements. Achieving this additional sharpness in distant objects usually requires focusing beyond the hyperfocal distance, sometimes almost at infinity. For example, if photographing a cityscape with a traffic bollard in the foreground, this approach, termed the Object Field Method by Merklinger, would recommend focusing very close to infinity, and stopping down to make the bollard sharp enough. With this approach, foreground objects cannot always be made perfectly sharp, but the loss of sharpness in near objects may be acceptable if recognizability of distant objects is paramount. Hyperfocal Distance Let be the lens focal length, be the lens f-number, and be the circle of confusion for a given image format. The hyperfocal distance is given by DOF at moderate-to-large subject distances Let be the distance at which the camera is focused (the “subject distance”). When is large in comparison with the lens focal length, the distance from the camera to the near limit of DOF and the distance from the camera to the far limit of DOF are When the subject distance is the hyperfocal distance, The depth of field is mathrm approx rac mbox s < H For , the far limit of DOF is at infinity and the DOF is infinite; of course, only objects at or beyond the near limit of DOF will be recorded with acceptable sharpness. Substituting for and rearranging, DOF can be expressed as Thus, for a given image format, depth of field is determined by three factors: the focal length of the lens, the f-number of the lens opening (the aperture), and the camera-to-subject distance. Focus and f-number from DOF limits Not all images require that sharpness extend to infinity; for given near and far DOF limits and , the required f-number is smallest when focus is set to When the subject distance is large in comparison with the lens focal length, the required f-number is rac In practice, these settings usually are determined on the image side of the lens, using measurements on the bed or rail with a view camera, or using lens DOF scales on manual-focus lenses for small- and medium-format cameras. Close-up DOF When the subject distance approaches the focal length, using the formulae given above can result in significant errors. For close-up work, the hyperfocal distance has little applicability, and it usually is more convenient to express DOF in terms of image magnification. Let be the magnification; when the subject distance is small in comparison with the hyperfocal distance, ight ), so that for a given magnification, DOF is independent of focal length. Stated otherwise, for the same subject magnification, all focal lengths give approximately the same DOF. This statement is true only when the subject distance is small in comparison with the hyperfocal distance, however. The discussion thus far has assumed a symmetrical lens for which the entrance and exit pupils coincide with the object and image nodal planes, and for which the pupil magnification (the ratio of exit pupil diameter to that of the entrance pupil) is unity. Although this assumption usually is reasonable for large-format lenses, it often is invalid for medium- and small-format lenses. When , the DOF for an asymmetrical lens is where is the pupil magnification. When the pupil magnification is unity, this equation reduces to that for a symmetrical lens. Except for close-up and macro photography, the effect of lens asymmetry is minimal. At unity magnification, however, the errors from neglecting the pupil magnification can be significant. Consider a telephoto lens with and a retrofocus wide-angle lens with , at . The asymmetrical-lens formula gives and , respectively. The symmetrical-lens formula gives in either case. The errors are −33% and 33%, respectively. Complications in practical application of the DOF formulae The distance scales on most medium- and small-format lenses indicate distance from the camera's image plane. Most DOF formulae, including those in this article, use the object distance from the lens's object nodal plane, which often is not easy to locate. Moreover, for many zoom lenses and internal-focusing non-zoom lenses, the location of the object nodal plane, as well as focal length, changes with subject distance. When the subject distance is large in comparison with the lens focal length, the exact location of the object nodal plane is not critical; the distance is essentially the same whether measured from the front of the lens, the image plane, or the actual nodal plane. The same is not true for close-up photography; at unity magnification, a slight error in the location of the object nodal plane can result in a DOF error greater than the errors from any approximations in the DOF equations. The asymmetrical lens formulae require knowledge of the pupil magnification, which usually is not specified for medium- and small-format lenses. The pupil magnification can be estimated by looking into the front and rear of the lens and measuring the diameters of the apparent apertures, and computing the ratio (rear diameter divided by front diameter). However, for many zoom lenses and internal-focusing non-zoom lenses, the pupil magnification changes with subject distance, and several measurements may be required. Limitations of DOF formulae
Aperture effects The aperture controls the effective diameter of the lens opening. Reducing the aperture size (by increasing the f-number) increases the depth of field; however, it also reduces the amount of light transmitted, placing a practical limit on the extent to which the aperture size may be reduced. Photography lenses almost invariably work best at medium apertures. Motion pictures make only limited use of this control. To produce a consistent image quality from shot to shot, cinematographers usually choose a single aperture setting for interiors and another for exteriors and adjust exposure through the use of camera filters or light levels. Aperture settings are adjusted more frequently in still photography, where variations in depth of field are used to produce a variety of special effects. Artistic considerations Depth of field can be anywhere from a fraction of an inch to virtually infinite. For instance a shot of a woman's face in closeup may have shallow depth of field (with someone just behind her visible but out of focus—common, for instance, in melodramas and horror films); a shot of rolling hills would be likely to have great depth of field, with the objects both in the foreground and in the background in focus. Depth of field versus format size As the equations above show, depth of field is related to the circle of confusion criterion, which is typically chosen as a fraction, such as 1/1000 or 1/1500, of the image format size. Larger imaging devices (such as 8×10 cameras) can tolerate a larger circle of confusion, while smaller imaging devices such as point-and-shoot digital cameras need a smaller circle of confusion. For the same field of view and f-number, DOF is, to a first approximation, inversely proportional to the format size. Strictly speaking, this relationship is true only when the subject distance is large in comparison with the focal length and small in comparison with the hyperfocal distance, for both formats, but it nonetheless is generally useful for comparing results obtained from different formats. At a given f-number and field of view, a smaller camera has greater DOF than a larger camera. The depth of field on an 8×10 camera using a normal lens at 22 is one half that on a 4×5 with a normal lens at 22. Similarly, a 35 mm camera with a normal lens at 8 has the same depth of field as a 6×7 cm camera with a normal lens at 16. This can be an advantage or disadvantage, depending on the desired effect. For the same amount of foreground and background blur, a small-format camera requires a smaller f-number than a large-format camera. Many point-and-shoot digital cameras cannot provide a very shallow DOF. For example, a point-and-shoot digital camera with a 1/1.8″ sensor (7.18 mm × 5.32 mm) at a normal focal length and 2.8 has the same DOF as a 35 mm camera with a normal lens at 13. In many cases, the DOF is fixed by the requirements of the desired image. For a given DOF and field of view, the required f-number is proportional to the format size. For example, if a 35 mm camera required 11, a 4×5 camera would require 45 to give the same DOF. For the same ISO speed, the exposure time on the 4×5 would be sixteen times as long; if the 35 camera required 1/250 second, the 4×5 camera would require 1/15 second. In windy conditions, the exposure time with the larger camera might allow motion blur. For cameras of different formats to achieve the same depth of field when shooting from the same position, with focal lengths that capture the same field of view, it is necessary to use the same absolute aperture diameter with each, not the same f-number. Consider formats that differ approximately by factors of two: 35 mm, 6×7 cm, 4×5 inch, 8×10 inch. For a chosen camera position and field of view, to keep the same depth of field, double the f-number each time you step up to the next film size. For example: 5.6 on 35 mm, 11 on 6×7, 22 on 4×5, 45 on 8×10. This doubling is not exact but is a very good rule of thumb. Also adjust exposure, ISO speed, or both by two stops (factor of four) each time: 1/60, 1/15, 1/4, 1 sec. In some cases, movements (tilt or swing) can be used with view cameras to better fit the DOF to the scene, and achieve the required sharpness at a smaller f-number. A few small-format cameras can employ the same principle by using tilt/shift lenses. Depth of field in photolithography In semiconductor photolithography applications, depth of field is extremely important as integrated circuit layout features must be printed with high accuracy at extremely small size. The difficulty is that the wafer surface is not perfectly flat, but may vary by several micrometres. Even this small variation causes some distortion in the projected image, and results in unwanted variations in the resulting pattern. Thus photolithography engineers take extreme measures to maximize the optical depth of field of the photolithography equipment. To minimize this distortion further, chip makers like IBM are forced to use chemical mechanical polishing machines to make the wafer surface even flatter before lithographic patterning. In ophthalmology and optometry A person may sometimes experience better vision in daylight than at night because of an increased depth of field due to constriction of the pupil (i.e. miosis). Digital editing of depth of field Digital image processing can increase the depth of field of a photograph by combining images from multiple shots at different focus depths, or by using techniques such as Wavefront coding. Available programs for multi-shot DOF enhancement include Helicon Focus and CombineZ5. See the linked online article by Rik Littlefield. DOF limits and hyperfocal distance Let be the distance at which the camera is focused (the “subject distance”), be the lens focal length, be the lens f-number, and be the circle of confusion for a given image format. The distance from the camera to the near limit of depth of field and the distance from the camera to the far limit of depth of field then are given by Setting the far limit of DOF to infinity and solving for the focus distance gives where is the hyperfocal distance. Setting the subject distance to the hyperfocal distance and solving for the near limit of DOF gives For any practical value of , the focal length is negligible in comparison, so that Substituting the approximate expression for hyperfocal distance into the formulae for the near and far limits of DOF gives Combining, the depth of field is mathrm = rac mbox s < H DOF at moderate-to-large subject distances When the subject distance is large in comparison with the lens focal length, mathrm approx rac mbox s < H For , the far limit of DOF is at infinity and the DOF is infinite; of course, only objects at or beyond the near limit of DOF will be recorded with acceptable sharpness. Focus and f-number from DOF limits Not all images require that sharpness extend to infinity; the equations for the DOF limits can be combined to eliminate and solve for the subject distance. For given near and far DOF limits and , the subject distance is The equations for DOF limits also can be combined to eliminate and solve for the required f-number, giving rac When the subject distance is large in comparison with the lens focal length, this simplifies to rac Most discussions of DOF concentrate on the object side of the lens, but the formulae are simpler and the measurements usually easier to make on the image side. If and are the image distances that correspond to the near and far limits of DOF, the optimum image distance is The required f-number is rac The image distances are measured from the camera's image plane to the lens's image nodal plane, which is not always easy to locate. In most cases, focus and f-number can be determined with sufficient accuracy using the approximate formulae
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