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director of photography, peter gray, dp, cinematography, dop, cinematographers, lighting cameraman, videographers, dv, high definition, 24p, digital films, HDW-F900, CineAlta, Varicam, AJ-HDC27F, 70mm, independent films, lighting directors, filmmakers, filmmaking, HDW-700ADEPTH OF FIELD
I will first give an overview of the subject, and then describe an accurate method for calculating Depth of Field for individual lenses. The Basics:Photographic lenses can only focus sharply in one plane in front of the lens, as observed in the resulting image formed behind the lens. That singular plane of sharpest focus is called the Principal Plane of Focus (PPF). The position of the PPF is determined by the focus or distance setting of the lens. The PPF can be moved towards the lens, or away from the lens, by the normal means of focusing (normally by adjusting the "focus ring"). In the image formed behind the lens, there is a region in front of the PPF, and a region behind the PPF, that also appears sharp. Although not technically as sharp as the image at the PPF, it appears acceptably sharp to an observer. As the distance increases from the PPF in either direction, the resulting image becomes progressively softer, eventually becoming noticeably "out of focus". Due to the effect of a progressive softening of the image as the distance from the PPF increases, the point at which a sharp image becomes noticeably soft is indistinct. The cross over point, or the "sharp/unsharp" threshold, is therefore difficult to determine. There is always a somewhat confusing area where the image is neither clearly sharp, nor clearly soft. However, we can fix the precise crossover point by defining the Circle of Confusion. Circle of Confusion:All lenses spread the image-forming light passing through them. There is minimum spreading of light for objects on the PPF, and a progressively greater spreading of light for objects located at an increasing distance from the PPF. Consider the image of an infinitely small spot of light (a theoretical point-source), positioned in front of, or behind, the PPF. Such a point source becomes a small circle of light as the image-forming light passes through the lens. The Circle of Confusion is the diameter of this "dimensionless point", that has now become a measurable circle of light in the focused image behind the lens. All point-sources of light in the field of view of a lens, will photograph as tiny circles. Point sources further away from the PPF will photograph as progressively larger circles. In practice, the point-sources of light are extremely close to each other, and will photograph as an array of overlapping circles. In a sense, the Circle of Confusion is a measure of the inherent degree of ‘out-of-focusness' of lenses away from the PPF, but it is much more than that. The Circle of Confusion not only relates to lenses; but also is integral to the system of cinema as a whole, from shooting to the projected image. Therefore, the Circle of Confusion is effected by many factors like emulsion type, film format, lens type, lens quality, filters, lighting contrast, shooting conditions, projectors, image magnification, viewing conditions, cinema screens, etc. An image shot on grainy film stock, in a smoke-filled room with soft, low-key lighting, with a diffusion filter on the lens, and projected on a small screen with a dull projector lamp; will appear to have a considerable range of acceptable focus. Compare this to an image shot on the same film format, but with a fine-gained film stock, with high-key, contrasty lighting, with an unfiltered, high-quality lens, and projected on a large, state-of-the-art screen with a very bright projector. This image will appear to have a more restricted range of acceptable focus, as any tendency towards soft focus will be much more noticeable. While a larger Circle of Confusion will be acceptable in the first example, a smaller Circle of Confusion is necessary to maintain a range of acceptable focus in the second example. If we determine that a certain numerical value for the Circle of Confusion produces acceptably sharp focus when viewed subjectively in a cinema; then larger diameters are then considered unsharp, or "out of focus", for those same shooting, and viewing, conditions. By basing the range of apparent focus on an acceptable, pre-tested value for the Circle of Confusion, we can be reasonably confident that similarly photographed images, will also appear "in focus" to most viewers, and on most screens. Ideally, working values for the Circle of Confusion should be determined through tests that mirror the actual mechanics, techniques and aesthetics of film production, and exhibition. There are generally accepted values for the Circle of Confusion that can be used as a starting point for further evaluation. Please note, the following figures are intended as a guide only. 16mm format: 35mm format: 65/70mm format: A range of useful diameters for the Circle of Confusion, expressed as fractions, and decimal values: Fraction of an Inch Decimal Inches Millimeters Depth of FieldWhen a photographed point source, no longer appears to be a sharp point to an observer of the resulting image, we then consider that image to be soft, or "out of focus" in relation to similar, sharper objects on the PPF. By measuring the diameter of this circle at the perceived crossover point where sharp is considered to become unsharp, we can thus determine the limits of sharpness on either side of the PPF, for that particular lens. Having fixed the limits in this manner, we call the range of acceptable focus, the DEPTH OF FIELD of the lens. The Depth of Field of a lens is the range of acceptably sharp focus, in front of, and behind, the Principal Plane of Focus, when viewed subjectively on a cinema screen. Depth of Field is always subjectively determined.The range of acceptable focus in front of the PPF is smaller than the range behind the PPF, in the approximate ratio of 2 : 3, or two-fifths to three-fifths. This is often simplified to a "one-third to two-thirds" ratio, which is easier for making quick mental calculations on the set. DOF Variables:There are four variables governing DOF, as far as lenses are concerned. Change the value of any variable, and the DOF will change in strict accordance with the mathematical laws of optics. (1) the focal length of the lens The longer the focal length of the lens, the less DOF; and the shorter the focal length of the lens, the greater the DOF (2) the aperture setting The larger the aperture, the less DOF; and the smaller the aperture, the greater the DOF. (3) the focus-distance setting The closer a lens is focused, the less DOF; and the further away the lens is focused, the greater the DOF. (4) the circle of confusion The smaller the circle of confusion, the less DOF; and the larger the circle of confusion, the greater the DOF. In addition to these four variables, there is a lesser-known, fifth factor. I refer to the position of the Entrance Pupil of the lens. Strictly speaking, it is not another variable. Its significance as a factor in DOF calculation, is related to the way we normally measure focus distances in cinematography. Entrance Pupil:There are six principal points common to all photographic lenses. Going roughly from the front of the lens to the rear of a lens, there is the Subject Plane (the point of lens focus or the PPF), the Entrance Pupil, the Front and Rear Nodal Points, the Exit Pupil, and the Image Plane (the image plane normally corresponds with the emulsion layer of the film, i.e., the film plane). Please note that the relative positions of the principal points are not necessarily in the order suggested above, depending on individual lens design. Generally speaking, lens theory and mathematics are concerned with the relationship between these principal points. The Entrance Pupil is the first point of convergence of the light entering a lens. The Entrance Pupil position is critical to this discussion, being an integral part of Depth of Field calculation. Significantly, the Entrance Pupil is the point from which Depth of Field is both calculated, and measured. We normally measure focus distances from the camera's film-plane to the subject position. This practice is correct for setting focus on lenses. However, the correct "distance" for DOF calculation is measured from the entrance pupil to the subject position, and is not the same as the film-plane-to-subject distance. Substituting the latter is an approximation, and introduces an error in the calculation. Further more, the "distances" resulting from DOF calculation (i.e. the near and far focus extremities) are not the distances we normally measure from the film plane, but rather, should be measured from the Entrance Pupil towards the subject position. The resulting inaccuracy in (1) calculating DOF, and in (2) applying the results, may or may not be significant in practice, depending on the type of lens and the shooting parameters. DOF Anomalies:Unless tailored to a specific lens, all Depth Of Field tables and calculators (both sliding and electronic) are approximations. It is not possible to produce a single DOF table or calculator, that applies equally well to all lenses. In practice, generalized DOF tables and calculators give sufficient accuracy for a wide variety of lenses and shooting situations. However, significant errors can occur for certain types of lenses, and in some practical applications, especially when using lenses that are physically large, and in close-focus situations. The DOF for fixed-focal-length lenses (prime lenses), especially if they are physically small; correspond fairly closely to generalized DOF tables and calculators, that either do not allow for, or only approximate for the Entrance Pupil position. However, physically larger lenses, like zooms, telephoto lenses, and high-performance, prime lenses, can produce significant errors. For example, critical differences can occur with large zoom lenses when close focusing, especially at large apertures. In using some types of lenses, and in certain applications, the cinematographer may be well advised to take into account the Entrance Pupil position in determining DOF. The Elusive "E" factor:The entrance pupil is not a fixed point, but a moving one. It changes as lenses are focused; and in the case of zoom lenses, as the focal length is changed. It is therefore difficult to physically mark the Entrance Pupil position on a lens. For some lenses, the Entrance Pupil crosses the film plane, or moves entirely in an area behind the film plane. In such cases, the Entrance Pupil position can be outside the lens housing, so again, it is not easily marked for practical measuring purposes. Information about the position of the Entrance Pupil can be obtained from the lens manufacturer for each model of lens. Entrance Pupil positions are given as distances from the Front Vertex of the lens, measured rearwards towards the Film Plane. The vertex, or "highest" point, is the same as the center of the front lens-element. The front element of the lens is a reliable, physical, reference point, as the overall length of many lenses vary as you focus them. Lens manufacturers usually provide this information for more than one focus position of the lens, typically infinity, and the closest-focus position. They will also give you the overall length of the lens for that focus position. By simple subtraction, you can determine the distance from the Entrance Pupil to the Film Plane, for a particular focus position of that lens. I will call this value "E". There is another way for the cinematographer to find the Entrance Pupil position. It is the point about which a camera and lens can be panned and tilted without any "sliding" displacement of the foreground and background elements in relation to each other, as observed at the film plane (or through the viewfinder). (I suggest inserting the page number here if this procedure is described elsewhere in the manual.) This is the only practical alternative to finding Entrance Pupil positions, other than getting that information from the lens manufacturer. In the past, this point has often been incorrectly referred to as the Front Nodal Point position. So in addition to DOF considerations, knowledge of the Entrance Pupil is especially important when photographing miniatures, and for a range of other special effects work, including glass shots, front projection, etc. It is also the point from which Field of View and Lens Angles are calculated and measured. Accurate DOF:For making accurate DOF calculations, we must subtract "E" from our conventionally measured distance from the film plane to subject position, perform the calculation, and then add "E" again to the end result. This will allow us to measure all focus distances in the normal way (film plane to subject), while maintaining complete accuracy in DOF calculation by effectively using entrance-pupil-to-subject distances throughout the equation. We need to keep this issue in its proper perspective, and not strive for a degree of accuracy that is beyond its practical application. In generating a DOF table in a spreadsheet program, or programmable calculator, a single value for "E" may be sufficiently accurate for each lens. I'd recommend using the value of "E" for the closest focus position of the lens, assuming it does not deviate too much from the value at other focus positions. This is because close-focus situations are usually the area of greatest inaccuracy in generalized DOF tables/calculators, and especially for physically large lenses. Advantages:Some advantages of calculating DOF by this method are: 1. It puts precise DOF information at the cinematographer's fingertips, rather than relying on, or trying to estimate from, an approximate value. This allows the cinematographer and focus puller to concentrate on the things that really matter on a film set. 2. You can use exact values for the aperture (i.e. half stops, third stops, etc.), the precise focal length (i.e. intermediate zoom settings like 77mm), and the precise distance (in either imperial or metric units). This saves time, and improves accuracy, especially when trying to extrapolate the "in-between" values in a table, or to "guesstimate" them on a sliding calculator. 3. Very importantly, you can avoid focus problems in those situations where generalized DOF information is misleading, or inaccurate. DOF tables can be particularly useful for quickly cross referencing information; for example, in deciding how to change the focal length, and/or aperture, in order to maintain a certain focus split. The following formulas, can be incorporated in a spreadsheet program in a personal computer, to generate precise DOF tables tailored to specific lenses. These tables can be used in conjunction with an extremely useful tool on the set, namely, a hand-held, programmable calculator, for quick and easy DOF computation of unprecedented accuracy. The Mathematics:DOF is calculated from the Hyperfocal distance of the lens. The Hyperfocal distance is a unique focus position of a lens, where the far limit of DOF precisely reaches infinity, no more and no less. When a lens is set to the Hyperfocal distance, the near limit of DOF is always half the Hyperfocal distance. Mathematically, the Hyperfocal distance "H" is a straight forward relationship between Focal length ("L"), Aperture ("A"), and the Circle of Confusion ("C"), as follows: Having calculated the Hyperfocal distance, the Near "N" and Far "F" limits of DOF are calculated separately, as follows: "D" is the Distance measured from the film plane to the subject position, and "E" is the distance from the Entrance Pupil to the film plane. By subtracting "E" from "D", and also from "N" and "F", all distances will now correspond to the Entrance Pupil to Subject distance: The equations can be expressed in a single line as follows. This form of the equation will be required for programming a spreadsheet or calculator: (1) If the Focal Length and Circle of Confusion are expressed in millimeters, the following formula will express the Hyperfocal distance in feet and decimal feet. (One millimeter = 0.0032808 feet) Alternative to formula (1) expressed in feet: Likewise, if the Focal Length and Circle of Confusion are expressed in millimeters, the following formula will express the Hyperfocal distance in meters. (One meter = 1000 millimeters) Alternative to formula (1) expressed in meters: Similarly, you need to keep the unit values consistent by incorporating conversion factors to feet or meters for "L" and "E" in the remaining two equations. Choose the appropriate set of formulas according to how you want to express the final result, i.e. in "feet" or in "meters". Then simply input your measured distance-variables in either whole feet or meters. Unfortunately, I can't take you through the steps to program a calculator or spreadsheet program, due to differences between the various types available. Rest assured however, that it is relatively straight forward once you master the basics of the device, or the software. In the case of a programmable calculator, I'd recommend limiting the input of data to the necessary "changing" variables, namely ("L", "A" & "D") for zoom lenses, ("A" & "D") for prime lenses. It is a somewhat laborious task to enter information otherwise held constant for each and every computation. I'm referring specifically to the value for "E" and the Circle of Confusion, because once determined for a particular lens, they will normally remain constant. I recommend using different formulas (in the same, or in separate calculators) for different combinations of "E" and "C", and likewise, a different formula for each prime lens depending on its focal length. This will speed up the process, lessen the chance for human error, and help keep your mind clear to concentrate on the job at hand. "E constant" Approach:A variation of this method is to substitute an approximate, or average, value for the Entrance Pupil position. In this way, a single DOF table or a calculator can perhaps be used to represent a number of lenses with reasonable accuracy. It is best to choose an average value for the Entrance Pupil positions based on the actual lenses in your camera package. Beware of any lenses deviating significantly from the chosen average. The degree of accuracy is governed by how much the approximate, or average, value of "E" deviates from the real values. If the range of "E" values is not very wide ranging, this method should be of sufficient accuracy for some families, or other collections, of individual lenses. This method tends to work best with lenses that are physically small in size. Acknowledgments:I would like to thank David W. Samuelson, Jonathan Maxwell of Imoerial College, London, and Iain A. Neil who is the Senior Vice-president of Optics at Panavision, for current information about the Entrance Pupil. Copyright © Peter Gray (30th June, 1998)
Peter Gray
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