by Harold M. Merklinger Depth of Field For View Cameras—Part I as published in Shutterbug, November 1993. Having established the basic op- where g=Aa/d. (There is a slight ap- March ‘93) we find the near and far tical principles of view cameras (in proximation used here, but the error is limits of depth of field as shown in “The Scheimpflug Principle”, Shut- usually less than 1%.) Figure 1 will Figure 2. First we use the Scheimp- terbug, Nov. ’92 through March. ’93), help to understand the geometry. For flug rule and the hinge rule to de- we can now tackle the job of cal- ordinary cameras we then use the lens termine where the film plane must be culating depth of field in the tradi- equation to determine what object to achieve the desired plane of precise tional manner. Following the standard distances correspond to those limits. sharp focus. A distance, g, either side method, we will assume a suitable Within those object distance limits of the film plane we draw two lim- standard of image resolution and then lies the zone of acceptable focus. It is iting planes parallel to the film plane. determine where an object must lie to often more convenient to express the For images focused at either of these be imaged in accord with that stan- lens diameter in terms of the f- limiting planes, the circle of confu- dard. Since we are dealing with the number of the lens, N. We make the sion on the film will be the maximum view camera, however, the story is further assumption that the lens-to- allowable. We then determine where more complicated than is the case for image distance and lens-to-film dis- the planes of sharp focus would be for ordinary cameras. tance are approximately equal to the these limiting planes. The results de- We begin in the time-honored focal length of the lens, f. We then fine the boundaries of the region way. A lens of aperture diameter, d, find that the distance, g, is ap- where objects will be acceptably well intercepts the light from a distant proximately equal to the product of defined. This region is wedge-shaped, point source and focuses it at dis- the f-number, N, and the allowable di- with the sharp edge of the wedge is at tance, A, behind the lens. If we are ameter of the circle of confusion, a. the hinge line. The algebra involved prepared to accept a circle of confu- That is, g is equal to N times a. in calculating the exact limits is a bit sion of diameter, a, then any other ob- Utilizing view camera principles tedious, but the result itself is quite ject will be “in focus” if its image lies discussed in Part IV of “The easy to understand. anywhere in the range A+g to A-g, Scheimpflug Principle” (Shutterbug, In relating the size of the circle of FAR LIMIT OF DEPTH OF FIELD LENS d Figure 1: This figure shows how depth of field is estimated for ordinary FILM LENS AXIS a cameras. A maximum permissible diameter, a, for the circle of confusion is set. Then one uses the lens g equation to calculate the near and far g LENS PLANE limits of depth of field where a small object would be imaged on the film A as a circle of diameter, a. Between NEAR LIMIT OF DEPTH OF FIELD these limiting planes, any object will be rendered with “acceptable FILM PLANE definition”. The distance, g, is equal to the f-number times the diameter of PLANE OF SHARP FOCUS ZONE OF the allowable circle of confusion, a. ACCEPTABLE g = Na, N = f/d DEFINITION Figure 2: Depth of field for view LENS PLANE FRONT FOCAL cameras is calculated in much the PLANE same way as for ordinary cameras. In f this case the limiting planes define a wedge-shaped zone of acceptable A LENS definition. The size and placement of g AXIS ZONE OF this zone depends in a complicated ACCEPTABLE DEFINITION way upon the lens tilt, a, and the tilt of the plane of sharp focus, F. The optical principles involved were J described in “The Scheimpflug FILM PLANE HINGE LINE Principle, Part IV” previously published in Shutterbug. The PTF PLANE Scheimpflug Line and Hinge Line are shown as dots because the lines are SCHEIMPFLUG LINE actually perpendicular to the paper. www.mr-alvandi.com LENS PLANE Figure 3: A practical way to describe NEAR LIMIT depth of field for view cameras is illustrated here. Depth of field is PLANE OF expressed as a distance, m or l, A SHARP measured perpendicular to the plane FOCUS of sharp focus. The place where Z m depth of field is estimated is understood to be a position along the plane of sharp focus, a distance Z l from the lens. Z is measured in a direction perpendicular to the Film FILM PLANE Plane. Since the depth of field, m or HINGE LINE FAR LIMIT l, is directly proportional to Z, it is PTF PLANE possible to express m and l as a fraction of the distance Z. SCHEIMPFLUG LINE confusion to lens aperture size, the tilt angles of the plane of sharp focus. ness when the camera back is swung analysis implicitly assumed that the I don’t really suggest using this table more than a few degrees. lens axis was perpendicular to the in normal photography. It would help I have constructed a second set of film. We know that is probably not to be a surveyor and to have a transit tables that tells us the depth of field, the case for the view camera. I will handy if you were to attempt to use m and l, as a fraction of the distance argue that for the purpose of cal- Table 1. We will use it in an example Z. Table 2 is one of these. Again, I culating the size of the ‘splotch’ of later in this article, however. have chosen the f-number, N, to be 22 confusion, it does not matter whether A description of depth of field and the maximum allowable diameter the lens is tilted or not. If the lens is which is less complete, but perhaps of the circle of confusion to be one- tilted, the circle of confusion may be- more useful, is given in Figure 3. In fifteen-hundredth of the lens focal come an ellipse of confusion, but the this description we describe the depth length. maximum dimension of that ellipse of field in terms of distance measured Let’s apply this table to a real will probably be about equal to the perpendicular to the plane of sharp fo- photographic problem. Remember the diameter of the circle of confusion cus. I will use the symbol “m” to de- cement plant from the last article? derived for an untilted lens. We could note this distance on the lens side of Figure 4 gives an approximate get picky here, but it just isn’t worth the plane of sharp focus, and the sym- cross-section through the scene being the trouble. We have bigger issues to bol “l” for the equivalent distance on photographed. The camera is sitting deal with. the far side of the plane of sharp fo- on a small rise, about even in level Our biggest problem is how to de- cus. with the base of the cement plant tow- scribe the wedge-shaped region with- The next problem is how to de- er. Between the camera and the tower in which objects are acceptably well scribe where along the plane of sharp is a marshy field, perhaps 10 feet low- imaged. The most complete and ac- focus we wish to know the depth of er than the camera lens. In the fore- curate description is to calculate the field. One answer would be to meas- ground are some daisies. The ob- tilt angles for the near and far limits ure distance from the hinge line, jective is to get the daisies, the grass of depth of field. To illustrate, Table along the plane of sharp focus. That is in the marsh and the tower all in ac- 1 (on the last page of this article) useful in some cases, but just about ceptable focus. We know from the ex- shows a sample table of results for impossible in others. The solution pected wedge shape of the zone of ac- lenses at f/22 and for an allowable proposed is that we measure distance ceptable focus, that the depth of field circle-of-confusion of one-fifteen- from the camera lens to a spot on the near the daisies will be small. At the hundredth of the lens focal length. plane of sharp focus, in a direction tower, that zone must include all of The table shows the angles for the perpendicular to the film plane. I will the tower. But the grass must be in- near and far limits of depth of field call this distance “Z”. In my some- cluded too. A rough first guess would for various values of the lens-to- what limited experience, it is usually be that the plane of sharp focus hinge line distance, J (expressed in easy to estimate this distance, though should pass within inches the daisies focal lengths), combined with various it will seem a strange way to do busi- and through the mid-height of the Figure 4: Here’s a cross-section of the location where I took a photograph of a cement plant.