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`ZEISS 1119
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`Sponsoring Editor: Adam Black
`Project Manager: Nancy Gee
`Manufacturing Supervisor: Vivian McDougal
`Cover Designer: Blakeley Kim
`Production Service: HRS Interactive
`Text Design: HRS Interactive
`Composition: HRS Interactive
`Illustration: HRS Interactive
`Photo Research: Carolyn Eisen Heck:
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`Library of Congress Cataloging-in—Puhlicafion Data
`
`Hecht, Eugene
`Optics / Eugene Hecht; ~ 4th ed.
`p. cm.
`Includes bibliographical references and index.
`ISBN 0-8053-8566—5
`1. Optics. 1. Title.
`QC355.3 H43
`535—dc21
`
`2002
`
`2001032540
`
`Copyright @2002 Pearson Education, Inc., publishing as Addison Wesley, 1301
`Sansome St., San Francisco, CA 94111. All rights reserved. Manufactured in the
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`5.3 Stops 171
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`Consequently, a photon takes the same time to traverse any
`one path; all the phasors (each assumed to be the same size)
`have the same phase angle. Thus, they all contribute equally to
`the likelihood of a photon arriving at P. Putting the phasors
`tip—to-tail results in a very large net amplitude, which when
`squared yields a very high probability of light reaching P via
`the lens. In the language of QED, a lens focuses light, by
`causing all the constituentprobability amplitudes to have the
`same phase angle.
`For other points in the plane containing P that are close to
`the optical axis, the phase angles will differ proportionately.
`The phasors placed tip—to—tail will gradually spiral, and the net
`probability amplitude will initially diminish quickly, but not
`discontinuously so. Notice that the probability distribution is
`not a single infinitesimally narrow spike; the light cannot be
`focused to a point. The phasors for offaaxis points cannot all at
`once add to zero; what happens, happens gradually and con—
`tinuously. The resulting circularly symmetric probability dis«
`tribution, I(r), is known as the Airy pattern (p. 469).
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`The intrinsically finite nature of all lenses demands that they
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`collect only a fraction of the energy emitted by a point source.
`The physical limitation presented by the periphery of a simple
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`lens therefore determines which rays shall enter the system to
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`form an image. In that respect, the unobstructed or clear diam-
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`eter of the lens functions as an aperture into which energy
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`flows. Any element, be it the rim of a lens or a separate
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`diaphragm, that determines the amount of light reaching the
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`image is known as the aperture stop (abbreviated AS.) The
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`' adjustable leaf diaphragm that is usually located behind the
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`first few elements of a compound camera lens is just such an
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`aperture stop, Evidently, it determines the light~gathering
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`Capability of the lens as a whole. As shown in Fig. 5.33, high-
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`ly oblique rays can still enter a system of this sort. Usually,
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`hOWever, they are deliberately restricted in order to control the
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`j quality of the image. The element limiting the size or angular
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`itreadth of the object that can be imaged by the system is
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`sailed the field stop or F.S.—it determines the field of view of
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`5.3.1 Aperture and Field Stops
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`Figure 5.33 Aperture stop and field stop.
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`the instrument. In a camera, the edge of the film itself bounds
`the image plane and serves as the field stop. Thus, while the
`aperture stop controls the number of rays from an object point
`reaching the conjugate image point (Fig. 5 .33), it is the field
`stop that will or will not obstruct those rays in into. Neither the
`region above the top nor the region below the bottom of the
`object in Fig. 5.33 passes the field stop. Opening the circular
`aperture stop would causethe system to accept a larger energy
`cone and in so doing increase the irradiauce at each image
`point. In contrast, opening the field stop would allow the
`regions beyond the extremities of the object, which were pre—
`viously blocked, to be imaged.
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`5.3.2 Entrance and Exit Pupils
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`Another concept, useful in determining whether or not a given
`ray will traverse the entire optical system, is the pupil. This is
`simply an image ofthe aperture stop. The entrance pupil of a
`system is the image ofthe aperture stop as seenfrom an axi—
`a! point on the object through those elements preceding the
`stop. If there are no lenses between the object and the A.S., the
`latter itself serves as the entrance pupil. To illustrate the point,
`examine Fig. 5.34, which is a lens with a rear aperture stop.
`The image of the aperture stop in L is virtual (see Table 5.3)
`and magnified. It can be located by sending a few rays out
`from the edges of the AS. in the usual way. In contrast, the
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`as
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`172 Chapter5 Geometrical Optics
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`Entrance
`pupfl
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`Exit
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`Figure 5.34 Entrance pupil and exit pupil.
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`exit pupil is the image ofthe A. S. as seen fi-om an axialpoint
`on the image plane through the interposed lenses, if there
`are any. In Fig. 5.34 there are no such lenses, so the aperture
`stop itself serves as the exit pupil. Notice that all of this just
`means that the cone of light actually entering the optical sys-
`tem is. determined by the entrance pupil, whereas the cone
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`pu il
`13
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`\x.‘\‘
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`Entrance
`u il
`l3 P
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`Figure 5.35 A front aperture stop.
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`leaving it is controlled by the exit pupil. N0 rays from the
`source point proceeding outside of either cone will make it to
`the image plane.
`To use a telescope or a monocular as a camera lens, you
`might attach an external front aperture stop to control the
`amount of incoming light for exposure purposes. Figure 5.35
`represents a similar arrangement in which the entrance and
`exit pupil locations should be self—evident. The last two dia-
`grams include a ray labeled the chief ray. It is defined to be
`any rayfrom an ofi—axis object point that passes through the
`center of the aperture stop. The chief ray enters the optical
`system along a line directed toward the midpoint of the
`entrance pupil, En , and leaves the system along a line passing
`through the center ofthe exit pupil, Exp. The chief ray. associ-
`ated with a conical bundle of rays from a point on the object,
`effectively behaves as the central ray of the bundle and is rep-
`resentative of it. Chief rays are of particular importance when
`the aberrations of a lens design are being corrected.
`Figure 5.36 depicts a somewhat more involved arrange-
`ment. The two rays shown are those that are usually traced
`through an optical system. One is the chief ray from a point on
`the periphery of the object that is to be accommodated by the
`system. The other is called a marginal ray, since it goes from
`the axial object point to the rim or margin of the entrance pupil
`(or aperture stop).
`In a situation where it is not clear which element is the
`actual aperture stop, each component of the system must be
`imaged by the remaining elements to its left. The image that
`subtends the smallest angle at the axial object point is the
`entrance pupil. The element whose image is the entrance pupil
`is then the aperture stop of the system for that object point.
`Problem 5.44 deals with just this kind of calculation.
`Notice how the cone of rays, in Fig. 5.37, that can reach the
`image plane becomes narrower as the object point moves off-
`axis. The effective aperture stop, which for the axial bundle of
`rays was the rim of L1, has been markedly reduced for the off—
`axis bundle. The result is a gradual fading out of the image at
`points near its periphery, a process known as vignetting.
`The locations and sizes of the pupils of an optical system
`are of considerable practical importance. In visual instru—
`ments, the observer’s eye is positioned at the center of the exit
`pupil. The pupil of the eye itself will vary from 2 mm to about
`8 mm, depending on the general illumination level, Thus a
`telescope or binocular designed primarily for evening use
`might have an exit pupil of at least 8 mm. (You may have
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`5.3 Stops 173
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`Exit
`pupil
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`Entrance
`pupil
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`Figure 5.36 Pupils and stops for
`a three-lens system.
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`heard the term night glasses—they were quite popular on
`roofs during the Second World War.) In contrast, a daylight
`version will suffice with an exit pupil of 3 or 4 mm. The larg—
`er the exit pupil, the easier it is to align your eye properly with
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`the instrument. Obviously, a telescopic sight for a high-pow-
`ered rifle should have a large exit pupil located far enough
`behind the scope so as to avoid injury from recoil.
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`Figure 5.37 Vignetting.
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` L1
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`Efl'eclivei
`aperture I
`stop
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