by Harold M. Merklinger The Scheimpflug Principle—Part IV as published in Shutterbug, March 1993. In Part I we reviewed the ject side of—the front nodal point of tance! We’ll give this three-plane in- Scheimpflug rule which applies for the lens. I’ll call this plane the Front tersection line a name too: the “hinge thin, rectilinear, flat-field lenses. This Focal Plane. The significance of the line”. We don’t know at what angle rule states that the film plane, lens front focal plane is that an object any- the plane of sharp focus passes plane and plane of sharp focus inter- where on this plane is focused an in- through the hinge line, but it must sect along a common line. This rule is finite distance behind the lens. pass through it. So long as we keep certainly a help, but it is not com- The significance of the PTF plane the film orientation fixed, we know at plete. There are an infinite number of takes a little more description, but it’s least one line on the plane of sharp fo- ways to meet the requirements of the related. With the help of Figure 1 you cus that remains fixed in space— Scheimpflug rule and still not have will understand that the light rays unless we change the lens tilt (or the camera in focus. We need some- from an object anywhere on the PTF swing) or the back tilt (or swing). thing else to help us set up. That plane are also aimed at the film an in- The Hinge Rule, simply stated, is something else is the subject for this finite distance behind the lens, no that the plane of sharp focus, the front month. matter how close (or far) the film focal plane and the PTF plane inter- I’m going to call this month’s rule plane is to the lens. The rays are not sect along a common line: the hinge the “hinge rule”—for reasons which I necessarily in focus, however. If the line. I know of no book on photog- hope will become clear. Pay close at- lens were aligned with its axis per- raphy that describes this principle. If tention; this could be a little con- pendicular to the film, the lens would you have seen it, please let me know; fusing. There are two more planes we need to have 180° of coverage to I’d like to see another reference. have to deal with—five in all! The ‘see’ any object on the PTF plane. Scheimpflug rule addresses three of But remember: we’re talking about In practice the hinge rule tells us the planes, and the hinge rule address- view cameras, so by tilting the lens that if we know the film orientation es three. Fortunately one plane—the we can actually place an object on the (often vertical) and we know the lens plane of sharp focus—is common to PTF plane where the lens can ‘see’ it. tilt or swing, we know how far from both rules. Placing the film where it can image the lens the plane of sharp focus will The first new plane I will call the that object sharply is not possible, but pass, measured along the PTF plane. I “Parallel-to-Film, Lens Plane”—or that doesn’t matter. It’s the principle will use the symbol J for this dis- PTF plane, for short. This plane is of the thing that counts. tance. Figure 2 shows J and all the placed through the center of the lens OK, here it comes. An object on other symbols and relationships I will but oriented parallel to the film plane, the PTF plane can only be focused be using. We can even attach a dis- as shown in Figure 1. If the lens is a sharply at infinity when it is si- tance scale to the tilt (or swing) scales ‘thick’ lens, this PTF plane passes multaneously on the PTF plane and using the formula for J indicated in through the front nodal point of the the front focal plane. That is, it must Figure 2. We need a new scale for lens. Fortunately, for the hinge rule, it lie at the intersection of the front fo- each focal length and unit of distance does not matter whether the lens is cal plane and the PTF plane. This ac- (feet, meters etc.), or we can use just thick or not, so long as we remember tually tells us a lot we need to know. one scale that measures in focal that the PTF plane passes through the If we know the orientation of the film lengths. The distance J/f (the distance front nodal point. plane, and if we know where the lens J divided by the focal length, f) is al- The second new plane is associat- is, and how it is tilted, we know ways related in a relatively simple ed exclusively with the lens. This something else very important. We way to the lens tilt angle α. Table 1 plane is parallel to the lens plane, but now know that the plane of sharp fo- shows some examples of that re- one focal length in front of it. It is cus must pass through the intersection lationship. perpendicular to the lens axis, but one of the PTF plane and the front focal Now, put this hinge rule together focal length in front of—on the sub- plane—no matter the lens-to-film dis- with the Scheimpflug rule and you LENS PLANE FRONT FOCAL f PLANE LENS AXIS Figure 1: Two new planes are introduced. The Front Focal Plane is parallel to the Lens Plane, but lies one focal length in front of it. The Parallel-to-Film Lens Plane (or PTF plane, for short) is parallel to the film FILM PLANE PLANE OF SHARP FOCUS plane but passes through the center HINGE LINE of the ‘thin’ lens. The Front Focal Plane, the PTF plane and the plane PARALLEL-TO-FILM LENS PLANE of sharp focus intersect at the “hinge (PTF Plane) line”. SCHEIMPFLUG LINE www.mr-alvandi.com f J = LENS PLANE FRONT FOCAL PLANE sin f 1 Figure 2: The Scheimpflug rule and = 90° + tan-1{ - } f A sin tan the hinge rule combine to provide a A complete solution to the view camera LENS optical configuration. The lens-to AXIS hinge line distance, J, together with the lens focal length, f, determine the required lens tilt, a. The lens-to-film distance, A, and the lens tilt PLANE OF SHARP FOCUS J determine the orientation F of the FILM PLANE HINGE LINE plane of sharp focus relative to the film plane. PARALLEL-TO-FILM LENS PLANE (PTF PLANE) SCHEIMPFLUG LINE have the complete solution. And moved towards and away from the ground as possible and still see the when we do this, you’ll understand lens, the Scheimpflug line travels up uprights. We then measure the lens- why I called the line the hinge line. and down the lens plane. The hinge to-ground distance—vertically, par- With the help of Figure 3, you’ll see line stays fixed. The only way we can allel to the film plane. The next step that as the camera back is racked to solve both rules is to have the plane is to tilt the lens forward so that the and fro, the plane of sharp focus ro- of sharp focus hinge up and down, ro- front focal plane intersects the PTF tates on the hinge line. I call it ‘hing- tating on the hinge line. plane at the ground right beneath the ing’ on the hinge line because, behind Let’s consider an example. We set lens. Table 1 shows the lens-to-hinge for objects behind the hinge line, no up our camera on a football field. The line distances (J) for various com- image is possible. An object behind uprights are visible in the scene, so binations of lens focal length and tilt the hinge line, even if seen by the we keep the back vertical in order to angles. We are using a 90 mm lens 41 lens, cannot (even in principle) be im- achieve the correct perspective. We inches above the ground, so we tilt it aged on the film. The ‘visible’ part of want every blade of grass between the 5°. The plane of sharp focus now the plane of sharp focus ends at the camera and the goal posts to be in passes through the grass immediately hinge line. We use its extension, of sharp focus. We mount the camera on below the lens. Watching the ground course, in applying the Scheimpflug the tripod, set its back vertical, and glass now, we move the back for- rule. Notice how, as the back is raise the back to see as much of the wards, closer to the lens. The plane of LENS PLANE PTF PLANE (Doesn’t move) FRONT FOCAL PLANE 1 FILM PLANE 1 PLANE OF SHARP FOCUS Figure 3: If the film plane is moved 1 closer to the lens, the plane of sharp focus swings away from the lens, SCHEIMPFLUG LINE rotating on the hinge line. As the film HINGE LINE (Must remain stationary) is moved away from the lens, the plane of sharp focus swings up in LENS PLANE front of the lens. So long as the FRONT FOCAL PTF PLANE PLANE angular orientation of the lens plane (Doesn’t move) and the film plane remain unchanged, the hinge line must remain fixed in space.