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Published by the author:

Harold M. MerklingerP. O. Box 494Dartmouth, Nova ScotiaCanada, B2Y 3Y8

v.1.0 1 March 19932nd Printing 29 March 19963rd Printing 27 August 19981st Internet Edition v. 1.6 29 Dec 2006Corrected for iPad v. 1.6.1 30 July 2010

ISBN 0-9695025-2-4

All rights reserved. No part of this book may be reproduced or translated without the express written permission of the author.

Printed in electronic format by the author, using Adobe Acrobat.

Dedicated to view camera users everywhere.

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PREFACE v

Merklinger: FOCUSING THE VIEW CAMERAvi

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1994 issue of Shutterbug. There is an important caveat, however. I was neverhappy with some of the technical terms I used in that article and have struggledto find new language. Specifically, in the Shutterbug article I used the termbore sight to describe an important (vector) direction for view cameras.Those words better describe a different direction. The term derives from firearms where the bore sight is simply established by by looking down the bore ofthe gun, from breech to muzzle. The camera equivalent is probably lookingthrough the center of the lens with ones eye positioned in the geometric centerof the ground view camera glass screen. To actually do this would, of courserequire a hole in the ground glass and the removal of the lens componentsleaving only the diaphragm. At the risk of confusing the readers of that earlierarticle, I have changed the meaning of bore sight to mean precisely what Ihave just described. The original direction I used that term for, I haverelabeled the principal axis of the camera. Please note that this is theprincipal axis of the camera, not the lens. This principal axis is establishedprimarily by the orientation of the film, or electronic image sensor. It is theprincipal axis that determines the apparent perspective of the image. I am toldthat, in the usual language of perspective, what I am calling the principal axis isnormally termed the line of vision.

For a normal camera, that is for a camera that has its lens axisperpendicular to the film and centered on the image, the principal axis of thecamera, the axis of the lens and the bore sight all coincide. This coincidence ofimportant axes simplifies the associated optical physics considerably. Thiscoincidence is an assumption that underlies nearly all descriptions ofphotographic optics that I have seen. For view cameras, where it cannot beassumed that these three axes coincide, the mathematics unfortunately getsrather complex. Yet the fundamental principles are still relatively simple, andare within the grasp of all of us to understand. Essentially, the Scheimpflugrule and the hinge rule explain everything; add one extra consideration anddepth-of-field is explained also.

In order to assist people visualize the Scheimpflug and hinge rules, Igenerated a few animated computer movie files. These files can be found onmy web site: http://www.trenholm.org/hmmerk/HMbook18.html.

I would also like to acknowledge that in spite of my best intent, I haverealized that I did make one or two unintended mathematical approximations(in both books) concerning depth of field and perhaps should correct some ofthe formulae and tables, but the errors introduced are so minor that thesecorrections are really of academic interest only. I worry that that to make thecorrections would be to convey the wrong message: the whole concept of depthof field is an approximation. If we really want to be super-precise there aremany more optical phenomena we should consider in addition. How preciselydo we know the actual aperture, focal length and distance to the point of focusetc? The truth is there are lots of factors we dont really know or need to knowall that precisely.

PREFACE vii

Merklinger: FOCUSING THE VIEW CAMERAviii

Harold M. Merklinger29 December, 2006.

I once had a lens instruction book that provided depth of field tables tosix-figure accuracy. Can you imagine using your cell-phone to call up yourmodel positioned a mile away from the camera and say You and thatmountain are not quite both in focus. Would you move a sixteenth of an inchfurther back, please! Thats what six-figure accuracy implies. The transitionfrom in-focus to out-of-focus is usually so gradual that we would often beunable to detect a significant change in the state of focus if the distancechanged by 25%. In this example, the model could probably move a quarter ofa mile without our being able to detect a change in effective image sharpness.

A question some people are bound to ask is, Does all this still apply fordigital cameras? The answer is an unqualified yes. Adjustable viewcameras will continue to exist in the age of the electronic camera. We may allend up looking at electronic display screens rather than ground glass screens,but the adjustable tilt and shift camera will still have its place for high qualityphotography. I expect that the most common formatssizes of film orelectronic sensorswill be smaller than the typical four by five inches, andtypical lens focal lengths will decrease as a result, but the highly adjustablecamera will endure. I expect clear advantages will arise out of improved sensorflatnessno more film sag or popand better viewing conditions: a brighter,right-way-around view even with stopped down lenses. There may even be afew built-in calculators to help us set-up the camera.

There will, nevertheless, continue to be a place for art and individualjudgement is setting up the camera. Perhaps the most common question I amasked is something like this: OK, you have shown me how to figure out thelens tilt I need if I know where to put the Plane of Sharp Focus, but how do Iknow where to put the Plane of Sharp Focus? Sometimes there is a simpleanswer, but it depends upon many aspects of the situation and the intent of thephotographer. I dont pretend to tell you where to point the camera either, orwhen to trigger the shutter. Thats all part of the art of photography. Therewill be situations where tilt and shift are of no value whatever, and there will beothers where there are multiple options for obtaining a satisfactory image.Making those decisions requires experience and judgement. Im only trying togive you tools that I hope will make it easy for you to set up the camera oncethose decisions are made.

Chapter 1: INTRODUCTION 1

Chapter 1

INTRODUCTION

What makes the view camera special is the ability to tilt, shift and swingboth the lens and the film. These adjustments permit the camera to take veryhigh quality photographs, that would not be possible any other way. The greatflexibility of the camera requires, however, that the photographer understandsomething of the optical principles that allow the camera to achieve the desiredresult. The purpose of this book is to help users of view cameras set up fortheir picturesat least so far as focus and depth of field are concerned.

The book starts with a quick overview of the method. In the GettingStarted chapter well skip over many of the details. To fully understand themethod, however, will take some careful attention. A number of definitions arenecessary to ensure that you the user, and I the author, are speaking the samelanguage. Once we understand the words, we move on to a description of thebasic optical principles of view cameras. Not all of the terms I use will befamiliar to you. A key part of the story is a rule which I have not seendescribed elsewhere. I call it the Hinge Rule. Like the Scheimpflug principle,the hinge rule states that three planes must intersect along a common line. Twoof the three planes, however, have not received much attention in the past.

The emphasis here will be on the bottom line. For the most part, I willnot attempt to prove the physics or the mathematics here; I leave that foranother book and another day.

I am not a fan of tables; I have almost never consulted depth-of-field orother tables when using ordinary cameras. (I will use the term ordinarycamera to describe a camera that lacks back and lens movements other thanfocus. I will use the term normal camera to describe one lacking movementsother than focus and shift.) The tables in this book began life as tools toillustrate the optical principles applicable to view cameras. Somewhat to mysurprise, I found that I consulted the tables more and more when actuallytaking pictures. They considerably reduced the time I spent setting up thecamera. In time, view cameras will be fitted with scales and indicators whichwill eliminate the need for these tables. For now, however, the only othersource of precise help is experience.

With that apology out of the way, I admit that a significant portion ofthis book is made up of various tables and graphs. These tables and graphs areintended to help you determine the amount of lens tilt required for any givensituation. They also enable you to estimate quantitatively, and in advance,where the limits of depth of field will lie.

Merklinger: FOCUSING THE VIEW CAMERA2

The tabled limits of depth of field are those based on an assumed standardof required image resolution. This is the traditional depth of field. In The INsand OUTs of FOCUS, I described another way to estimate depth of fieldbasedon object field resolution. The object field method does not require tables, butdoes take a new twist when used for view cameras. This second method iscovered only briefly.

An example is provided in Chapter 8 to help illustrate how some of thevarious tables can be used.

I will also have to admit that I have used some trigonometry: mathematicalfunctions like sine, cosine and tangent. This is a natural consequence of allowingparts of the camera to rotate relative to one-another. That is, they change theirrelative angular relationships. I had difficulty avoiding such mathematicalexpressions at first, but I found I could indeed solve most of the the relationshipsexactly without triginometry if all measurements are made either parallel to orperpendicular to the film plane. The resulting way of looking at the view cameramay seem strange, but there is a logic to it, and it does work. If you do notunderstand triginometry, dont worry. The principles are quite understandablewithout it and the whole reason for resorting to tables is to let you get away fromhaving to work with that sort of mathematics. I include the mathematical resultshere primarily to permit those who like to program their own calculators orcomputers do so.

In order to understand the tables fully, it will be necessary to understandthe optical principles described in Chapter 4. But if the math is a problem, stopreading that chapter when you get to Equation (1). Better still, read on, butignore the mathematics. There is a simple way to do just about everything,anyway.

The information and tables in this booklet have allowed me to shorten thetime necessary to set up a view camera considerablyby a factor of four or five.This probably just indicates that Im not all that skillful. I nevertheless hope youtoo will find that by understanding the hinge rule, as well as the Scheimpflugrule, and by using these tables, you will be able to work more quickly and tocapture the intended photograph more easily.

Chapter 2: GETTING STARTED 3

Chapter 2

GETTING STARTED

In what follows it will be assumed that the reader possesses some basicfamiliarity with the view camera. You know what is meant by tilting andswinging the camera back and the lens. You know that tilting the lens relativeto the backor the back relative to the lenscauses the plane of sharp focus,that surface on which the camera is accurately focused, to move out of parallelwith the film plane. You may or may not be aware that the Scheimpflug rulestates that the film plane, the lens plane and the plane of sharp focus intersectalong a common line. If you dont know this rule, thats OK. Contrary towhat some might say, I would argue that it is not absolutely necessary tounderstand the Scheimpfluh rule, anyway.

Figure 1 shows a schematic (symbolic) diagram of a normal camera: onewith the lens attached in such a way that the lens axis must stay perpendicularto the film. Figure 2 serves to indicate what happens when the lens axis (or thelens plane which is a surface perpendicular to the lens axis) is tilted. The filmplane, the lens plane and the plane of sharp focus obey the Scheimpflug rule.You need not concern yourself about it; the laws of physics will make sure thatit is obeyed. The general principle is simple: if we tilt one of the three planesrelative to any one of the others, the third plane will get tilted too.

In a normal camera, the camera is always focused on a plane that isparallel to the film. The view camera allows the photographer to focus onobjects arranged on or near a plane that is not parallel to the film. This

FIGURE 1: For a normal camera, the film plane, lens plane and plane ofsharp focus are parallel to one another.

FILM PLANELENS PLANE

PLANE OFSHARP FOCUSLENS AXIS

4 Merklinger: FOCUSING THE VIEW CAMERA

condition is achieved by tilting either the lens or the film relative to the other.That is, we can leave the lens where it is and tilt the back, or we can leave theback where it is and tilt the lens. Or, indeed, we can do a bit of both: tilt boththe back and the lens, but not by the same amount in the same direction.

The trouble comes in trying to figure out what to tilt and by how much inorder to achieve the intended position for the plane of sharp focus. A furtherchallenge arises when we want to focus on the intended plane of sharp focusand maintain correct perspective in the image.

Maintaining correct perspective is perhaps the easier task. Standardperspective usually requires that the film plane remain vertical and more-or-lesssquare to the line of sight of the camera. Sometimes we actually want falseperspective in order to make the photograph appear as though it was taken froma place other than the cameras true location. A classic example is taking apicture of a glass-covered water colour painting. If we place the camerasquarely in front of the painting, we risk seeing the camera in the final imagedue to its reflection in the glass. The solution is to move the camera to one sideand so view the painting at an angle. This eliminates the reflection. But wealso want to make the image look as though the camera had been facing thepainting squarely. We accomplish the desired perspective by having the filmface the painting squarelythat is, keep the film and the painting parallel toone anotherand let the arrangement of the back and lens effectively squintsideways at the painting. Figure 3 illustrates the resulting arrangement.

If achieving the desired perspective were the only problem, we could getby with lens and back shifts (plus rise and fall) only.

Lets look now at a somewhat more complex situation. We arephotographing a painting, but we want to include in the image, not only thepainting, but some of the room it is in. Specifically, the large painting ishanging in a church on a wall some 30 feet from the camera. We also want to

FILM PLANE

LENS PLANE

PLANE OFSHARP FOCUS

LENS AXIS

SCHEIMPFLUG LINE

FIGURE 2: For a view camera, tilting the lens causes the plane of sharp focusto tilt also. The Scheimpflug rule requires that the three planes intersect alongone line


include a plaque on the church floor indicating where the artist is buried. Wewant a sharp image of the painting, but also a sharp image of the plate on thefloor some 10 feet from the camera. To ensure both are sharp, we wish theplane of sharp focus to pass through the centers of both the painting and theplaque. Figure 4 illustrates a side view of the problem. To keep the paintingrectangular, and the other features of the building in correct perspective, the

FILM PLANE

LENS PLANE

PLANE OFSHARP FOCUSPAINTING GLASS

FIGURE 3: The view camera can squint sideways, maintaining theproportions of the painting. The final image will look as though it had beentaken straight on. Taking the picture as illustrated here avoids seeing areflection of the camera in the glass.

PLANE O

F SHARP

FOCUS

Inscription on Floor

Painting on Wall

12 ft.

30 ft.

FIGURE 4: Here the task is to adjust the plane of sharp focus so that it passesroughly through the centers of the painting and the inscription. What amountof lens tilt will accomplish this?


camera back must remain vertical and parallel to the painting. And we employthe necessary rise and/or fall to achieve the desired composition. How do wearrange for the plane of sharp focus to fall precisely where we want it to be?

Theres another rule that arises from the laws of optics. I call it thehinge rule. The hinge rule will tell us the precise amount of lens tilt needed.The hinge rule is another rule very much like the Scheimpflug principle, butlets skip the details for now. A consequence of the hinge rule is that therequired amount of lens tilt is related to only two things: the focal length of thelens, and the distance the lens is from the plane of sharp focus measured in avery special way. We must measure how far the lens is from the plane of sharpfocus along a plane through the lens but parallel to the film. In the example athand, the concept is quite simple. The camera back is vertical. Therefore wemeasure this special distance in a vertical direction. The special distance isquite simply the height of the lens above the plane of sharp focus, as illustratedin Figure 5. I use the symbol J to denote this distance, and the symbol todenote the amount of lens tilt needed, measured in degrees.

The required amount of lens tilt is given mathematically by thisexpression:

= arcsin (f/J).

The symbol, f, is of course the focal length of the lens. Dont be scaredoff by the math; its really quite tame. The arcsine function can be found onmany $15 scientific calculators, but we can do even better. Included in thisbook on page 96 and repeated on a card at the back of this book is a table. Thetable has columns for lenses of various standard focal lengths. In a column atthe left of the table are a number of distances. Find a distance close to that ofyour distance J, and look in that row for the angle listed under the focal length

JPLA

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ARP FOC

US


Painting on Wall

12 ft.

30 ft.

PLANEPARALLEL TO

FILM,THROUGH LENS

FIGURE 5: The amount of lens tilt required is set by the special distance Jand the focal length of the lens. J in this case is the height of the lens abovethe plane of sharp focus.


of your lens. In our example, J is equal to 8.5 ft. and the lens in use has a75mm focal length. The required tilt angle is thus about 1.75.

For small tilt angles we can even dispense with the table. For lens tiltsless than 15, we can get an approximate value of the lens tilt from either of thefollowing:

if we measure f in inches and J in feet:

= 5f/J.

If we measure f in millimeters and J in feet:

= f/5J.

Its still math, but its pretty simple math.

So we set the lens tilt to 1.75 towards the intended plane of sharp focus.Not all view cameras have tilt scales. My own does not. I use a high schoolgeometry protractor to set the tilt. I cant set it to better than about half adegree, but thats usually good enough.

(The direction of lens tilt will have a bearing on the orientation of theplane of sharp focus. The plane of sharp focus will always be parallel to thelens tilt axis. If we imagine a plane parallel to the film but passing through thelens, that plane will intersect with the plane of sharp focus. If we mark thatintersection, we will find it is a line, and it will always be parallel to the axisabout which we tilted our lens. In common view camera language, if we usevertical tilt only, the tilt axis is horizontal. If we use swing only, the tilt axis isvertical. If we use both tilt and swing, the matter gets a bit complicated.)

In essence, the hinge rule tells us that if we move the back of the camerato and fro (without changing its angle), closer to or farther from the lens, theplane of sharp focus must pivot on a line a distance J from the lens. In ourexample this pivot line is on the plane of sharp focus directly below the lens. Icall that line the hinge line. I call it that because that line is like the pin in ahinge. The plane of sharp focus hinges on that line. As we move the backaway from the lens, the plane of sharp focus will swing up in front of thecamera. If we move the camera back closer to the lens, the plane of sharpfocus will swing down, away from the lens. (Its the Scheimpflug rule workingin consort with the hinge rule that causes this rotation, by the way.) So, toachieve the desired focus in our example, we focus, using the ground glass,either on the center of the painting, or on the center of the plaque. If we havedone things right, when one is in focus, the other will be too.

Thats it; were done focusing.

But what about depth of field? Well, here the view camera really has theadvantage over normal cameras. Calculating view camera depth of field isdead simple. Plainly put, the depth of field at a distance one hyperfocaldistance, H, in front of the camera is our friend J. Like the distance J itself,this depth of field is measured in a direction parallel to the film. Either side of


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Far Limit of Depth of Field


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12 ft.

IW

IW


That line, called the hinge line, will also be parallel to the lens tilt axis.

Shortening the distance between lens and film plane causes the plane ofsharp focus to rotate (about the hinge line) away from the front of the lens.

Increasing the distance between the film plane and the lens causes theplane of sharp focus to rotate towards the front of the lens.

Depth of field, measured parallel to the film, varies directly as thedistance, J. Increasing the lens tilt decreases J and so also decreases depth offield. Depth of field measured this way is always symmetrical about the planeof sharp focus.

Now you have the basics; the rest is just details.

Well continue with a review of the definitions necessary to analyse thesituation more carefully.

Later in this book well also discuss how the object field depth-of-fieldmethod (described in The INs and OUTs of FOCUS) applies to view camerasituations.


Point Gatineau: Where the Gatineau flows into the Ottawa

In a photograph like this, there is no real necessity for tilts or swings of anykind. But I did, nevertheless, use about one-half degree of forward lens tilt inorder to ensure that the plane of sharp focus would pass below the camera.My old wooden camera could easily be half-a-degree out in almost any swingor tilt. Were the plane of sharp focus to lie on the left, right or above thecamera, the image would not be uniformly sharp. An enlarged prtion of thisimage, centered on the church, may be seen on page 84.

Chapter 3: DEFINITIONS 11

Chapter 3

DEFINITIONS

This chapter is intended to tell you exactly what I mean by variousterms, such as Parallel-to-Film Lens Plane. If you are reading this book fromstart to finish, you need not read closely and remember all these definitionsright now. But please do look for the terms you do not recognize, and givethem a quick read. The purpose of grouping the definitions here is primarily togive you one place to find all the definitions; you wont have to search throughthe whole booklet just to find a definition.

Where distances are defined, it is very important to note how thedistance is measured. For example, should we measure depth of field along aray through the lens, or in a direction perpendicular to the plane of sharp focus?There are many ways to measure some of these distances, and how they aremeasured will affect the answers one obtains. Measuring in certain directionssimplifies things, too. I have tried always to measure distances in a way that isphotographically meaningful. Theres more than one way to do it, however. Ifyou think it should be done differently, I would appreciate hearing from you.

The definitions that follow are grouped by function. First, well look atthe definitions that apply to the lens, then those for the film, and so on. Aftermost definitions is a reference to a figure which should help you understand thedefinition.

The Lens

Symbol Name Definition

lens axis The lens axis is an imaginary straightline running through the centers of allthe glass elements making up the lens.A lens is virtually always symmetricabout its axis; it is in fact a body ofrevolution about its axis. See Figure 7(overleaf).


LENS

FILM

FILM PLANE

LENS AXIS

LENS PLANE

THICK LENSFILM

FILM PLANE

LENS AXIS

FRONT NODAL POINT

REAR LENS PLANE

FRONT LENS PLANE

REAR NODAL POINT

INTER-NODALDISTANCE

FIGURE 7

FIGURE 8


lens plane The lens plane is an imaginary planepassing through the optical center of thelens, and oriented perpendicular to thelens axis. If a lens is optically thick,there are actually two lens planes: afront lens plane through the front nodalpoint of the lens, and a rear lens planethrough the rear nodal point. SeeFigures 7 and 8.

front nodal point The front nodal point is the effectiveoptical center of the lens as seen fromthe front of the lens, that is, the sideaway from the film. See Figure 8.

front lens plane The front lens plane is an imaginaryplane through the front nodal point, andperpendicular to the lens axis. SeeFigure 8.

rear nodal point The rear nodal point of a lens is theoptical center of the lens as seen fromthe back side (film side) of the lens. SeeFigure 8.

rear lens plane The rear lens plane is an imaginaryplane through the rear nodal point, andperpendicular to the lens axis. SeeFigure 8.

inter-nodal distance The inter-nodal distance is the distancebetween the front nodal point and therear nodal point, measured along thelens axis. It can occur that for some lensdesigns, the front nodal point is actuallycloser to the film than the rear nodalpoint. When this happens theinter-nodal distance has a negativevalue. See Figure 8.



FIGURE 9

LENS

FILM

FILM PLANE

LENS PLANE

OBJECT AT INFINITY

FOCAL LENGTH, f

f

LENS

FILM PLANE

PLANE OF SHARP FOCUS(at infinity)

LENS AXIS

LENS PLANE

f

OFF-AXIS RAY

f '

EFFECTIVE FOCAL LENGTH, f'

FOCAL LENGTH, f

IMAGE PLANE

OBJECTS ARRANGEDON A PLANE

LENS AXIS

LENS PLANE

FRONT FOCAL PLANE

f

f

FOCAL PLANE

IMAGESOF

OBJECTS

FIGURE 11

FIGURE 10


thin lens A thin lens is one where the inter-nodaldistance is very small in relation to itsfocal length. Many lenses for viewcameras, especially those ofsymmetrical or near-symmetricaldesign, are optically thin even thoughthe actual thickness of the glass is large.For the sake of simplicity, it will beassumed that lenses are thin, unlessotherwise stated.

f focal length The focal length of a lens is the distancefrom the rear nodal point of a lens to thesharp image of a very distant objectlocated in front of the lens but on thelens axis. See Figure 9.

off-axis angle If an object in front of the lens does notlie on the lens axis, we can describe itsposition in part through the off-axisangle, . is the angle between the lensaxis and a line from the front nodalpoint to the object. See Figure 10. ( isthe Greek letter Delta.)

f' effective For a distant object not located on thefocal length lens axis, the effective focal length, f',

of a lens is greater than its nominal focallength, f. That is, the distance from therear nodal point of the lens to the sharpimage of that object is f', and f' isgreater than f. See Figure 10.

focal plane The focal plane of a lens is an imaginaryplane parallel to the lens plane (that is,perpendicular to the lens axis) and onefocal length behind the rear nodal pointof the lens (measured along the lensaxis). See Figure 11.



FIGURE 12

f

d = f/8

DIAPHRAGM

If d = f/8,

N = 8.

FIGURE 13

LENS

FILM

FILM PLANE

LENS AXIS

LENS PLANE

PERPENDICULARTO FILM PLANE


front focal plane The front focal plane is an imaginaryplane perpendicular to the lens axis andone focal length in front of (away fromthe film) the front nodal point of thelens. A small object located anywhereon the front focal plane will be focusedan infinite distance behind the lens. SeeFigure 11.

image plane Objects arranged on an imaginary planein front of the lens will be imaged on animaginary plane, the image plane,behind the lens. The image plane is notnecessarily perpendicular to the lensaxis. See Figure 11. When the imageplane and the film plane coincide, allobjects are in focus.

d lens diameter A lens normally contains a diaphragm orother stop which blocks some of thelight that would otherwise pass throughthe lens. This stop is usuallyapproximately round, and its diameter,as seen from the front of the lens, iscalled the lens diameter, or working lensdiameter. The effective lens diametersas seen from the front, the rear and asmeasured at the diaphragm may all bedifferent. But what usually matters isthe diameter as seen from the front. SeeFigure 12.

N f-number The lens diameter is often described byits size in relation to the focal length ofthe lens. A lens whose diameter isone-eighth of its focal length is said tobe an f-8, often written f/8, lens. In thiscase the f-number or numerical aperture,N, is equal to 8. See Figure 12.

lens tilt The total effective lens tilt, , is theangle between the lens axis and a lineperpendicular to the film plane. SeeFigure 13. ( is the Greek letterAlpha.)



FIGURE 14

LENS

FILM

FILM PLANE

LENS AXIS

LENS PLANE

A

PARALLEL-TO-FILMLENS PLANE(PTF PLANE)


H hyperfocal distance For an ordinary or normal camera,that is one having no lens tilt, thehyperfocal distance is the distance,measured parallel to the lens axis, fromthe lens to the inner limit of depth offield, when the lens is focused atinfinity. The hyperfocal distance is notstrictly a property of the lens or its focallength and numerical aperture. Thehyperfocal distance also depends uponthe assumed maximum permissible sizeof the circle of confusion at the film.When a lens is focused at its hyperfocaldistance, the depth of field extends fromone-half the hyperfocal distance toinfinity.

Q image quality factor If the maximum permitted diameter ofthe circle of confusion (a) is equal to thelens focal length, f, divided by Q, thehyperfocal distance is Q times the lensworking diameter, d.

PTF plane parallel-to-film The parallel-to-film lens plane, or PTFlens plane plane, for short, is an imaginary plane

through the front nodal point of the lens,and parallel to the film plane. SeeFigure 14.

The Film and the Image Space

film plane It is assumed in this book that the film islocated on an imaginary plane, calledthe film plane. The film plane may haveany orientation and may lie any distancebehind the lens. The film plane is theprimary reference plane for the viewcamera. In general, all other angles aremeasured with respect to the film planeor with respect to a line perpendicular tothe film plane. See Figure 14.



FIGURE 15

LENSFILM PLANE

LENS PLANE

OBJECT AT INFINITY

f

a

cg


A lens-to-film distance Also called the back focus distance, thelens-to-film distance is the distance fromthe film plane to the rear nodal point ofthe lens, measured in a directionperpendicular to the film plane. In TheINs and OUTs of FOCUS, I used thesymbol B to denote the lens-to-imagedistance. For most purposes in thepresent book, the symbols A and B maybe used interchangeably, since theimage is assumed to be sharply focusedat the film. It is frequently useful tomeasure A in focal lengths. Thedistance A measured in focal lengths isdenoted as A/f. See Figure 14.

PTF plane Parallel-to-film The parallel-to-film lens plane, or PTFlens plane plane, for short, is an imaginary plane

through the front nodal point of the lens,and parallel to the film plane. SeeFigure 14.

c diameter of the When the image of a very tiny spot doescircle-of-confusion not lie precisely at the film plane, the

image on the film will be a small circleof diameter, c. This circle is called thecircle of confusion. See Figure 15.

a largest permissible For the traditional method fordiameter for c calculating depth of field, it is assumed

that there is a largest diameter whichmay be tolerated for thecircle-of-confusion. This largestpermissible diameter is denoted as a.See Figure 15.

g depth of focus For a stated value of the largestpermissible diameter of the circle ofconfusion, a, and for a lens of numericalaperture, N, the depth of focus is simplyequal to the product of N and a: g =Na. In order to be rendered withacceptable resolution, the sharp imagemust lie within a distance, g, either sideof the film plane. See Figure 15.



FIGURE 16

LENS

FILM PLANE

PLANE OF SHARP FOCUS(PSF)

LENS AXIS

LENS PLANE

D

FIGURE 17

FILM PLANE

PLANE OF SHARP FOCUSLENS PLANE

OBJECT

R

Z

PTF PLANE

RAY

FIGURE 18

FILM PLANEPLANE OF SHARP FOCUS

(PSF)

LENS PLANE

PARALLEL-TO-PSFPLANE(PTPSF)


The Plane of Sharp Focus and the Object Space

PSF plane of sharp focus The plane of sharp focus is that plane infront of the camera, every point ofwhich is focused precisely on the filmplane. Any small object located on theplane of sharp focus is in perfect focus.See Figure 16.

D lens-to-PSF distance Distance D is that from the front nodalpoint to the plane of sharp focus,measured in a direction perpendicular tothe plane of sharp focus. D is theshortest distance between the plane ofsharp focus and the lens. For somepurposes it is useful to measure D inunits of one focal length. D/f will beused to denote the distance D measuredin this way. See Figure 16.

R lens-to-object The distance from the lens to somedistance object lying on the plane of sharp focus

is denoted as R when the distance ismeasured simply as the shortest directline from the object to the front nodalpoint of the lens. See Figure 17.

Z lens-to-object The distance from the lens to some distance object lying on the plane of sharp focus

is denoted by Z when the direction ofmeasurement is perpendicular to thefilm plane. See Figure 17.

PTPSF parallel-to-PSF The parallel-to-plane of sharp focus lenslens plane plane is an imaginary plane through the

rear nodal point of the lens, parallel tothe plane of sharp focus. We will usethis term rarely. See Figure 18.



FIGURE 19


LENS PLANE

L1

L2

NEAR LIMIT OFDEPTH OF FIELD

FAR LIMIT OFDEPTH OF FIELD

FIGURE 20


LENS PLANE

K1

K2

NEAR LIMIT OFDEPTH OF FIELD

FAR LIMIT OFDEPTH OF FIELD

FIGURE 21


LENS PLANE

L1

L2

FILM PLANE

PTF PLANE

Z

m = L1/Z

l = L2/Z

Lpf


L depth of field Objects within some distance, L, of theplane of sharp focus will be imagedsharply enough to be considered infocus. The depth of field, L, ismeasured in a direction perpendicular tothe plane of sharp focus. Since thedepth of field is not necessarily equal onboth sides of the plane of sharp focus,we may use L1 to denote the depth offield on the lens side of the plane ofsharp focus, and L2 to denote depth offield on the far side. See Figure 19.

Lpf depth of field A variation on ways to describe depth offield is to measure its extent in adirection parallel to the film plane.Such a measure of depth of field isdenoted as Lpf. See Figure 21.

K depth of field Objects within some distance, K, of theplane of sharp focus will be imagedsharply enough to be considered infocus. The depth of field denoted by Kis measured along a ray from the lens tosome specified point on the plane ofsharp focus. As for the depth of field, L,we may use K1 and K2 to denote thedepth of field on the lens side and the farside of the plane of sharp focusrespectively. Note that the onlydifference between L and K is thedirection in which the distance inmeasured. See Figure 20.

m depth of field The depth of field, L, may be expressedfraction as a fraction of the distance Z. m is that

fraction (or coefficient) applying on thelens side of the plane of sharp focus: L1= mZ. See Figure 21.

l depth of field The depth of field, L, may be expressedfraction as a fraction of the distance Z. l is that

fraction (or coefficient) applying on thefar side of the plane of sharp focus: L2= lZ. See Figure 21.



FIGURE 22


LENS PLANE

S

FILM PLANE

FIGURE 23

LENS

FILM

FILM PLANE

LENS AXIS

LENS PLANE

PLANE OF SHARP FOCUS

SCHEIMPFLUGLINE

FIGURE 24

FILMPLANE

PTF PLANE

LENS PLANE

PLANE OFSHARP FOCUS

SCHEIMPFLUGLINE

HINGE LINE

f

J

FRONTFOCAL PLANE


S spot size, or The spot size, S, is the diameter andisk of confusion object must be in order to be registered

at full contrast on the film. If an objectis smaller in size than S, it may stillshow up in the image, larger than itshould be, and at reduced contrast. SeeFigure 22. The spot size, or disk-of-confusion was discussed at length inThe INs and OUTs of FOCUS.

plane of sharp focus The angle is the angle of the plane ofangle sharp focus, relative to the film plane.

See Figure 23. ( is the Greek letterPhi.)

hinge line tilt The angle is the tilt of the hinge linecompared to the horizontal plane. ismeasured in the PTF plane. ( is theGreek letter Theta.)

Other Terms and Distances

Scheimpflug line In order for a view camera image to besharp, the rules of optics state that thefilm plane, the lens plane and the planeof sharp focus must intersect along acommon line in space. That line is theScheimpflug line. See Figure 23. Sincethe Scheimpflug line is seen on end, it isrepresented in the figure as a dot.

hinge line The rules of optics state that forrectilinear, flat-field lenses, the PTFplane, the front focal plane and the planeof sharp focus must intersect along acommon line. That line is the hingeline. The hinge line is always parallel tothe Scheimpflug line. See Figure 24.



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FIGURE 25

LENS

FILM PLANE


LENS AXIS

SCHEIMPFLUG LINE

LENS PLANE

PRINCIPAL AXIS

BORE SIGHT

FILM(or imagesensor)

6\PERO 1DPH 'HILQLWLRQ

Chapter 4: OPTICAL PRINCIPLES 29

Chapter 4

VIEW CAMERA OPTICAL PRINCIPLES

The fundamental optics of normal cameras are described by just onerule: the lens equation. Normal cameras are those having the lens axis fixedin a direction perpendicular to the film plane. The lens equation relates thelens-to-film distance, A, the lens-to-plane of sharp focus distance, D, and thefocal length, f, to one-another. Although the standard lens equation does notapply for off-axis rays, the matter is circumvented by measuring all thedistances in a direction perpendicular to the film plane, or parallel to the lensaxiswhich is the same thing for normal cameras. View camera designcomplicates things by allowing the photographer to tilt or swing the lens andthe film plane independently. Distances measured parallel to the lens axis areno longer equivalent to those measured perpendicular to the film plane. Tomake matters even more complicated, swinging the lens and/or the film, alsorotates the plane of sharp focus so that distance measured perpendicular to theplane of sharp focus now presents yet a third way to measure things.Fortunately, we can explain view camera optical principles with just two orthree basic rules. Using these rules it is possible to focus the view camerasystematically, and to understand depth of field for tilted planes.

Well discuss the details of the view camera lens equation itself a littlelater. Happily, the view camera lens equation can be interpreted in the form oftwo relatively simple rules that require no understanding of the mathematics.These rules are the Scheimpflug Rule and what I call the Hinge Rule. Togetherthey tell us everything that the view camera lens equation does.

The Scheimpflug rule is well known to many view camera users. Thisprinciple states that for thin, flat-field, rectilinear lenses, the film plane, the lensplane and the plane of sharp focus must intersect along a common line. Figure26 illustrates. The line where all three planes intersect, well call theScheimpflug line. Since the figure depicts a cross-section through the scene ina direction perpendicular to all three planes, the planes are drawn as straightlines. In three dimensions, the planes would extend out of the paper, at rightangles to the page. The Scheimpflug line, which also extends out of the paper,is shown as a simple dot. No matter how the lens and film are tilted and/orswung, it will always be possible to find some direction from which to look atthe camera so that it looks something like Figure 26. In this book we use thesymbol to denote the lens tilt relative to the film plane, and to denote theresulting tilt of the plane of sharp focus relative to the film.

For thick lenses, the Scheimpflug rule must be adjusted to account forthe inter-nodal distance of the lens. As illustrated in Figure 27, any ray is


FIGURE 26: The Scheimpflug Principle states that the Film Plane, theLens Plane and the Plane of Sharp Focus must intersect along acommon line.

LENSFILM

FILM PLANE PLANE OF SHARP FOCUS

LENS AXIS

LINE OF INTERSECTION(SCHEIMPFLUG LINE)

LENS PLANE

FRONT LENS PLANE

PLANE O

F SHARP

FOCUS

BACK LENS PLANE

INTER-NODAL DISTANCE

LENS AXIS

FILM PLANE

LINE PARALLEL TOLENS AXIS CONNECTS

TWO SCHEIMPFLUG LINES

OFF-AXIS RAY

FIGURE 27: For thick lenses, the Scheimpflug Principle must beadjusted. Any ray or plane which passes through the lens planes,moves from one lens plane to the other in a direction parallel to thelens axis.

assumed to pass from one nodal plane to the other in a direction parallel to thelens axis. The same is true for the extensions of the plane of sharp focus andfor the film plane.


The Scheimpflug principle is a necessary condition for the lens equationto be satisfied, but it is not enough. With reference to Figure 26, suppose thatthe lens and lens plane are swung about the Scheimpflug line, keeping thedistance from the lens to the Scheimpflug line constant. Well also keep thefilm plane and the plane of sharp focus fixed. If the Scheimpflug rule wereenough, the image would stay in focus as we swing the lens. We know fromexperience that the image does not stay in focus. As the lens moves throughthe full range, we will find one, two or no places where the image is in focus.

The needed additional information is contained in the hinge rule. Thisrule states that the parallel-to-film lens plane (PTF plane), the plane of sharpfocus (PSF) and the front focal plane must intersect along a common line. Thissecond important line, well call the hinge line. This rule is depicted in Figure28. The hinge rule and the Scheimpflug rule together solve the view cameralens equation for usno matter where the object and the image lie.

The hinge rule alone can help a lot if we know where we wish the planeof sharp focus to be, relative to the lens and film. If we know the desiredorientation of the film plane, and how far the lens is from the plane of sharpfocus (measured along the PTF plane), we know something else. We know therequired lens tilt. Well call the lens-to-plane of sharp focus distance,measured along the PTF plane, J. When the film plane is oriented vertically,and the lens tilt axis is horizontal, J will represent the height of the lens abovethe plane of sharp focus.

(Table III on pages 96 and 97 shows several examples the relationshipbetween J and for a number of common focal lengths. This table gives us

FILM PLANE PLANE OF SHARP FOCUS

LENS AXIS

SCHEIMPFLUG LINE

LENS PLANE

HINGE LINE

FRONT FOCALPLANE

PARALLEL-TO-FILM LENS PLANE(PTF Plane)

f

J

FIGURE 28: The Hinge Rule states that the Front Focal Plane, theParallel-to-Film Lens Plane and the Plane of Sharp Focus must alsointersect along a common line. J is measured parallel to the PTFPlane.


the angle, , needed for a variety of J distances for each focal length. Table IVon pages 98 and 99 show similar information in a slightly different form. InTable IV, the distance J is given for a range of tilt angles.)

If J is measured in focal lengths, there is just one simple relationshipbetween J and :

(1a)

This may, alternatively, be written as:

(1b)

This expression may be further abbreviated, as shown on page 6 in the GettingStarted chapter.

If the film is racked to and fro, the Scheimpflug rule and the hinge rule,working together, cause the plane of sharp focus to rotate or pivot about thehinge line (see Figure 29). (For convenience in calculating J/f, Table V givesthe value of J/f for the same range of J distances and focal lengths used inTable III.)

In practice, it is generally easiest to first use Table III to determine therequired lens tilt or swing, then focus using the camera back to put the plane of

Jf

=1

sin .

FILM PLANEPLANE OF SHARP FOCUS

SCHEIMPFLUG LINE

LENS PLANE

HINGE LINE

FRONT FOCALPLANE

PTF PLANE

FIGURE 29: The Hinge Rule, together with the Scheimpflug Rule,requires that if the film is moved closer to the lens, the Plane of SharpFocus must move away from the lens, rotating about the Hinge Line.

= arcsin (fJ

).


Af

= (sin )1

tan ()+

1

tan .

sharp focus in the desired orientation. Should this not be possible, we can usethe following equation to determine the required lens-to-film distance, A:

(2a)

Again, if the lens-to-film distance is expressed in focal lengths, the same graphor table can be used for lenses of all focal lengths. (Table VI shows values ofA/f for various combinations of normalized distances, J/f, and desired plane ofsharp focus angles, .) We can also rewrite Equation (2a) to solve for :

(2b)

The relationships between , , and A/f are shown graphically inFigures 62 and 63 on pages 104 and 105.

Returning to the matter of the lens equation, the basic lens equationtheone we usually read aboutmay be written as:

(3)

where A is the lens-to-film distance, D is the lens-to-plane of sharp focusdistance, and f is the focal length of the lens. Note that, for normal cameras,distances A and D are usually assumed to be measured in a direction parallel to

1A

+ 1D

= 1f

LENS

FILM PLANE


LENS AXIS

LENS PLANE

f

OFF-AXIS RAY

FOCAL PLANE (for focus)

D '

A 'f '

FIGURE 30: The object distance, D', and image distance A'are illustrated here for an oblique ray, making angle with thelens axis.

= 90 + arctan fA sin ()

-1

tan .


1A'

+ 1D '

= 1f'

, f ' = f

cos

the lens axis, or perpendicular to the film plane, or perpendicular to the planeof sharp focus.

The lens equation for oblique raysthose not parallel to the lensaxisis given by the following equation:

(4)

where is the off-axis angle, A' is the lens-to-film distance measured along theray, D' is the lens-to-plane of sharp focus distance measured along the ray, andf' is the effective focal length of the lens. Figure 30 (on the previous page)illustrates.

A consequence of the lens equation for oblique rays is that the effectivefocal length of a lens is not a fixed quantity. As a lens is tilted or swung inview camera use, its effective focal length changes. The focal length usuallyappears to increase as the lens is tilted. The change is negligible for smallangles of tilt, but can be quite significant for angles of 25 and more. Table Ion page 90 in the Tables section shows the results. The major consequence ofthis effect is that when a lens is tilted, the cameras angle of view changes.One may discover that when lens tilt or swing is used, a focal length shorterthan anticipated is needed to cover the intended angle of view. If the mainsubject is closer to the lens axis after the lens is tilted or swung than it was withno tilt or swing, however, the effect may seem to go in the opposite direction.The effective focal length may appear to shorten. Moving the lens axis awayfrom the main subject increases effective focal length; moving the lens axiscloser to the main subject shortens the effective focal length. The point to be

FILM

FILM PLANE


LENS AXIS

SCHEIMPFLUG LINE

LENS PLANE

D

f

FRONT FOCAL PLANE

HINGE LINE

A

PTF PLANE

FIGURE 31: The distances and angles important for the view cameralens equation, Equation (5), are illustrated here. D is measuredperpendicular to the Plane of Sharp Focus.


1A

+1D

=sin + sin (-)

f sin

FILM PLANE

FILM PLANE


LENS AXIS

SCHEIMPFLUG LINE

LENS PLANE

D

f

FOCAL PLANE

RECIPROCALHINGE LINE

APLANE PARALLEL TO


FIGURE 32: The reciprocal hinge rule states that if the film isrotated about the reciprocal hinge line in the direction shown, theScheimpflug line moves downward along the lens plane. ThePlane of Sharp Focus must then move farther from the lens, butwithout changing its angle relative to the lens plane. The angles and change, but does not.

made here is that the expected angle of view may be different from thatexpected, based upon the marked focal length of the lens. Tilting or swinging alens changes its effective focal length.

The lens equation for view cameras can be written as:

(5)

where A is the lens-to-film distance, and D is the lens-to-plane of sharp focusdistance. Both these distances are measured in a direction perpendicular to therespective planes of interest, as shown in Figure 31. The expression after the= sign is very nearly equal to 1/f for a surprising range of angles. If and are both less than 25, for example, the error will be less than 10%. If is lessthan 5, can be as large as 95 for a similar error.

It may also be observed that we can interchange A and D, or and, with no net change to Equation (5). This implies that there is areciprocal hinge line and a reciprocal hinge rule. The reciprocal hinge linelies at the common intersection of the film plane, the (rear) focal plane, and aplane through the rear nodal point of the lens, parallel to the plane of sharpfocus. The reciprocal hinge rule then states that if the film plane is rotatedabout the reciprocal hinge line, the plane of sharp focus moves closer to or


farther from the lens without changing its orientation. Figure 32 illustrates. Ioriginally thought this might not be of much use. While reading a 1904photography text by the British author Chapman Jones, however, I realized thatit is essentially the reciprocal hinge rule that has allowed view camera users touse back tilt as a substitute for lens tilt. According to Chapman Jones, oneshould never attempt to adjust the camera using lens tilt. He claims that willjust result in trouble. If one must set the lens axis out of perpendicular with thefilm, only back tilt should be consideredeven though this may lead tounnatural perspective.

If one keeps the lens-to-film distance constant as one tilts a lens, theplane of sharp focus moves in a complicated way that is not easy to understand.The plane of sharp focus changes both its range from the camera and itsangular orientation as the lens tilt is adjusted. Furthermore, the apparentmovement of the plane of sharp focus depends upon the lens-to-film distancethat is set. Thus the effect of tilting the lens is difficult to anticipate. It is verydifficult to learn how to judge the right amount of lens tilt by adjusting the lenstilt directly. I refer in Chapter 10 to it being like driving a car on ice.

Adjusting the back tilt is a much friendliermorepredictableoperation. According to the reciprocal hinge rule, rotating theback about some fixed axis (on the film plane) merely regulates the distance ofthe plane of sharp focus from the camera without changing its angularorientation. The angular orientation is fixed by the relative positions of thelens and the axis about which the back is being tilted. The plane of sharp focusmust remain parallel to the plane defined by the lens and the back tilt axis.

The reciprocal hinge rule makes it easier to understand some of thearguments over whether base tilts or axis tilts are preferable for the cameraback. The ideal, I guess, is to be able to position the back tilt axis so as todetermine the desired orientation of the plane of sharp focus.

The difficulty I see with using back tilts is how to maintain correctperspective. One solution Ive heard proposed is to determine the requiredamount of tilt by tilting the back, but then transfer that amount of tilt to the lens(in the opposite direction) and straighten the back. This method is not rigorous.It often works well enough, but not always.

The lens equation for view cameras, Equation (5), implies that theeffective focal length is always less than the nominal focal length of the lens.This may seem to be at variance with the statement made earlier to the effectthat the effective focal length is often longer than the marked focal length.What really matters is where the main subject is relative to the lens axis. If themain subject initially lies near the lens axis, but the lens is tilted or swung tosharpen some other object, the focal length will seem to increase. If, on theother hand, the main subject is initially well off the lens axis, and one tilts thelens axis towards the main subject, the focal length will seem to decrease.


Tilt and Swing

So far, and for that matter almost throughout this book, it is assumed thatwe are looking at the camera in such a way that only lens tilt need be ofconcern. Now, real view cameras have tilt and swing movements for the lens.Having to accommodate both swing and tilt complicates the mathematicsconsiderably, and so in this book Ill avoid that issue as much as possible. Twotables are included, however, to help out a bit. Tables IIa and IIb willeventually help us to deal with depth of field under circumstances where bothtilt and swing are used. For small angles (less than 10 degrees) swing and tiltcan be considered as independent of one another.

For the most part, in this book, I use the word tilt very generally tomean whatever angle the lens axis makes to a normal to the film plane. Instandard view camera language, swing refers to the rotation of the lens carrierabout a vertical axis. Tilt refers to the rotation of the lens about a horizontalaxis. For most cameras, the tilt axis moves with the swinging of the lenscarrier. Thus the swing and tilt motions interact to some extent.

If we use both tilt and swing, the total effective tiltfor the purposes ofdetermining effective focal length and depth of field, for examplecan befound from Table IIa. We simply read off the resultant value from theappropriate row and column. In this case, it does not matter whether the rowsrepresent tilt and the columns represent swing, or vice versa. We just need toknow the two numbers.

The swing and tilt do interact to affect the orientation of the plane ofsharp focus. And here it does matter which is which. A useful way to describethe result is to examine the tilt of the hinge line in the PTF plane. Imagine, forexample, that we have a camera with its film vertical. We tilt the lens forwardand adjust the back focus so that the Plane of Sharp Focus lies horizontal. Thehinge line is also horizontal. But, if we also swing the lens to the left, the planeof sharp focus rotates such that it rises on the left of the camera (if we arelooking forward) and falls on the right. The hinge line must also rise on the leftand sink on the right. The angle by which the hinge line rotates is given inTable IIb. I have used the symbol, , to represent this angle. I dont want todwell on this matter, Tables IIa and IIb are included just to help out a bit inthose frequent circumstances where the film plane is vertical.

Discussion

The view camera provides us with two focus controls: the lens tilt, andthe back extensionthat is, adjustment of the film-to-lens distance. Most userswould consider the back extension to be the main focusing tool. As we haveseen, however, the main thing that adjusting the back does is to change theorientation of the plane of sharp focus. Adjusting the back focus causes the


plane of sharp focus to rotate about the hinge line. Lens tilt, on the other hand,changes the distance (J) between the lens and the plane of sharp focus. Thuslens tilt is, in a sense, the true distance-regulating tool. The distance that lenstilt regulates is a bit strange in that it is measured in a direction parallel to thefilm. We usually think of focusing distance as measured perpendicular to thefilm.

I have not found it difficult to adapt to this different frame of reference.In fact, the advantages far outweigh the disadvantages. Instead of fiddling withseemingly endless cycles of adjust the tilt, focus, adjust the tilt again, refocusetc., I find I can now usually set the tilteven before the camera is on thetripodthen set the back, and thats it, done, so far as focus is concerned! Nomore iterations.

It would be handy to do away with Tables III and IV by having adistance scale (instead of an angle scale) on the tilt adjustment mechanism. Atrue distance scale would require a different scale for each focal length. A J/fscale would be slightly less convenient, but one scale would serve for alllenses.

These are the basic principles. The topics of perspective and distortionwill be covered in the next chapter. And after that well use the principlesdescribed here to analyze the depth of field situation.

Chapter 5: PERSPECTIVE and DISTORTION 39

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Chapter 6: DEPTH of FIELD 49

Chapter 6

DEPTH OF FIELD

There are at least two ways to think about depth of field. In thetraditional treatment of the depth of field, one uses the following logic. Firstestablish an image resolution criterionexpressed by the maximumpermissible size of the circle of confusion. Then determine the depth of focusneeded to achieve that circle of confusion for the lens aperture being used.Finally, calculate where objects may lie in order that their images are at theextreme limits of the permissible depth of focus.

Another possible philosophy is that described in The INs and OUTs ofFOCUS. In this object field method, one first asks what resolution isrequired at the object. Then one calculates what is necessary to achieve it interms of the physical lens aperture diameter and the distance to the plane ofsharp focus. The object field method has the advantages that we can adjust therequired resolution to suit the requirements of the individual picture, and thatprecisely the same calculations work for all formats and all focal lengths.

Both of these methods can be applied to view cameras. And they are, ofcourse, completely consistent with one another. First, well look at thetraditional method. This method is probably more familiar to you. Thisscheme is, however, the more complex of the two, especially where viewcameras are concerned. As well later see in the Chapter 7, the simplest routeto the image-based solution is via the object-based methodbut well look atthe traditional methods first.

Image-Based Depth of Field

Following the steps outlined for the traditional method above, we set themaximum diameter of the circle of confusion as a. The permissible focus erroris then (approximately) g = Na, either side of the film plane, where N is thef-number. Imagining that the film plane were moved to one extreme limit ofthe depth of focus and then the other, the plane of sharp focus moves through awedge-shaped region of space in front of the camera. This wedge describes theregion within which objects will be imaged at the film with a circle ofconfusion smaller than diameter a.

We need, then, to decide what diameter to use for the maximumdiameter of the circle of confusion, and then how to describe that wedge. Firstwell consider the size of the circle of confusion. One of the often-used


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21

FIGURE 41: For an allowable depth of focus g, the depth of fieldextends from 1 to 2: the shaded area above.

numbers is one fifteen-hundredth of the focal length of the lens. Thiscorresponds to the 1/30 mm number often used for 35 mm cameras, forexample. It is indeed convenient to use some fraction of the lens focal length,because it will turn out that we can make one set of tables serve for all lensesthat way. I offer the caution, however, that it may actually make more sense touse some fraction of the format diagonal rather than focal length. It will beeasy to change criteria anyway, because the determining factor is the depth offocus which is simply the product of the f-number and the diameter of thecircle of confusion. Thus one table can serve for many combinations of a andN, so long as the product of a and N remains unchanged.

I propose two ways to describe the depth-of-field wedge. The straightforward way is to state the angles between the film plane and the depth of fieldlimits. The angle for the near limit of depth of fieldon the lens side of theplane of sharp focuswill be called 1. The angle to the limit of depth offield on the far side of the plane of sharp focus will be called 2. See Figure41.

Angles are not always easy to estimate in the photographic environment,and so I propose a second alternative. Suppose we wish to determine the depthof field, about the plane of sharp focus, some specified distance in front of thecamera. We can express the depth of field measured in a directionperpendicular to the plane of sharp focus as a fraction of the lens-to-plane ofsharp focus distance. To keep things consistent, well measure thelens-to-plane of sharp focus distance in a direction perpendicular to the filmplane. The way of measuring things just described will not always seem

Chapter 6: DEPTH of FIELD 51

natural, but we have to be consistent. This scheme of things is showngraphically in Figure 42.

Expressing depth of field as a fraction of the lens-to-plane of sharp focusdistance has its limitations. It is possible for the depth of field to become toolarge to be described accurately this way. If the angle between 1 or 2 and becomes equal to or greater than 90, the depth of field, expressed as a fractionof the lens-to-plane of sharp focus distance, becomes infinite. In p

focusing the view camera

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