9-1 I and Instrumentation Design Optical OPTI-502 © Copyright 2019 John E. Greivenkamp E. John 2019 © Copyright Section 9 Stops and Pupils 9-2 I and Instrumentation Design Optical OPTI-502 Stops and Pupils Greivenkamp E. John 2019 © Copyright The aperture stop is the aperture in the system that limits the bundle of light that propagates through the system from the axial object point. The stop can be one of the lens apertures or a separate aperture (iris diaphragm) placed in the system, however, the stop is always a physical or real surface. The beam of light that propagates through an axially symmetric system from a on-axis point is shaped like a spindle. The entrance pupil (EP) is the image of the stop into object space, and the exit pupil (XP) is the image of the stop into image space. The pupils define the cones of light entering and exiting the optical system from any object point. XP EP Object Image z Stop There is a stop or pupil in each optical space. The EP is in the system object space, and the XP is in the system image space. Intermediate pupils are formed in other spaces. 9-3 I and Instrumentation Design Optical OPTI-502 Aperture Stop Greivenkamp E. John 2019 © Copyright The limiting aperture of the system may not be obvious. There are two common methods to determine which aperture in a system serves as the system stop: The first method is to image each potential stop into object space (use the optical surfaces between the potential stop and the object). The candidate pupil with the smallest angular size from the perspective of the axial object point corresponds to the stop. An analogous procedure can also be done in image space. Four apertures exist in this EP4 optical system. A EP3 EP1 1 EP2 A3 A 4 Each aperture is imaged into A2 object space to produced four potential EPs. z O EP2 has the smallest angular subtense as viewed from O. Aperture 2 is the system stop. Note: All of the potential EPs are in object space. EP4 and EP2 are virtual. Since lens A1 is the first optical element, its aperture is in object space, and A1 serves as EP1. 9-4 I and Instrumentation Design Optical OPTI-502 Aperture Stop Greivenkamp E. John 2019 © Copyright The second method to determine which aperture serves as the system stop is to trace a ray through the system from the axial object point with an arbitrary initial angle. At each aperture or potential stop, form the ratio of the aperture radius ak to the height of this ray at that surface y k . The stop is the aperture with the minimum ratio: a Aperture Stop Minimum k y k A 4 A6 A A3 1 A5 A2 a y 4 4 u0 z ak Scaled Ray: u0 is arbitrary Min yk The limiting ray is found by scaling the aa uukk yy initial ray: jjyy jj kkMIN MIN 9-5 I and Instrumentation Design Optical OPTI-502 Limiting Apertures Greivenkamp E. John 2019 © Copyright Large changes in object position may cause different apertures to serve as the limiting aperture or system stop. The EP with the smallest angular subtense can change. A different aperture would then become the system stop. However when designing a system, it is usually critical that the stop surface does not change over the range of possible object positions that the system will be used with. O1 O2 z EP1 EP2 9-6 I and Instrumentation Design Optical OPTI-502 Pupils Greivenkamp E. John 2019 © Copyright The pupil locations can be found by tracing a ray that goes through the center of the stop. The intersections of this ray with the axis in image space and object space determine the location of the exit and entrance pupils. L1 L2 z EP Stop XP The rays are extended to the axis to locate the pupil. The EP and the XP are often virtual. The EP is in the system object space, and the XP is L1 L2 in the system image space. z XP EP Stop 9-7 I and Instrumentation Design Optical OPTI-502 Intermediate Space Pupils Greivenkamp E. John 2019 © Copyright Intermediate pupils are formed in each optical space for multi-element systems. If there are N elements, there are N+1 pupils (including the stop). L2 L 1 L3 z Int. Pupil XP EP Stop 9-8 I and Instrumentation Design Optical OPTI-502 Marginal and Chief Rays Greivenkamp E. John 2019 © Copyright Rays confined to the y-z plane are called meridional rays. The marginal ray and the chief ray are two special meridional rays that together define the properties of the object, images, and pupils. The marginal ray starts at the axial object position, goes through the edge of the entrance pupil, and defines image locations and pupil sizes. It propagates to the edge of the stop and to the edge of the exit pupil. The chief ray starts at the edge of the object, goes through the center of the entrance pupil, and defines image heights and pupil locations. It goes through the center of the stop and the center of the exit pupil. y marginal ray height y chief ray height u marginal ray angle u chief ray angle Marginal Ray Object EP y y u u z Chief Ray 9-9 I and Instrumentation Design Optical OPTI-502 Images and Pupils Greivenkamp E. John 2019 © Copyright The heights of the marginal ray and the chief ray can be evaluated at any z in any optical space. Image When the marginal ray crosses the axis, an image is located, and the size of the image is yh given by the chief ray height in that plane. y0 z Whenever the chief ray crosses the axis, a Pupil pupil or the stop is located, and the pupil radius is given by the marginal ray height in yh that plane. PUPIL y0 z Intermediate images and pupils are often virtual. The chief ray is the axis of the unvignetted beam from a point at the edge of the field, and the radius of that beam at any cross section is equal to the marginal ray height in that plane. 9-10 I and Instrumentation Design Optical OPTI-502 On-Axis Ray Bundle Greivenkamp E. John 2019 © Copyright The stop limits the ray bundle from the axial object point. The marginal ray is at the edge of the on-axis ray bundle. The EP defines the ray bundle in object space from the axial object point. The ray bundle that will propagate through the system fills the EP. The XP defines the ray bundle converging to the axial image point in image space. The ray bundle emerging from the system appears to come from a filled XP. XP EP Object z Image Stop The stop and the intermediate image (not shown) define the ray bundle in the intermediate optical space. In any additional optical spaces, the intermediate pupils and images will define the ray bundles. 9-11 I and Instrumentation Design Optical OPTI-502 Ray Bundles Greivenkamp E. John 2019 © Copyright The pupils are the image of the stop and do not change position or size with an off-axis object. The EP and the XP also define the skewed ray bundles that enter and exit the optical system for an off-axis object point. The off-axis ray bundle that will propagate through the system fills the EP. The off-axis ray bundle emerging from the system appears to come from a filled XP. The skewed ray bundles are centered on the chief ray for that object point. XP EP Object z Image Stop 9-12 I and Instrumentation Design Optical OPTI-502 Vignetting Greivenkamp E. John 2019 © Copyright For an off-axis object point, the beam of light through the system is shaped like a spindle of skew cone-shaped sections as long as no aperture other than the stop limits the beam. If the beam is intercepted by one or more additional apertures, vignetting occurs. The top and or bottom of the ray bundle is clipped, and the beam of light propagating through the system no longer has a circular profile. For example, reducing the lens diameters in the previous example produces vignetting at the top of the first lens and the bottom of the second lens. Vignetting Object z Image XP Appearance: Stop Vignetting XP Vignetting Apertures Vignetted XP 9-13 I and Instrumentation Design Optical OPTI-502 Field of View Greivenkamp E. John 2019 © Copyright The Field of View FOV of an optical system is determined by the object size or the image size depending on the situation: - the maximum angular size of the object as seen from the entrance pupil - the maximum object height - the maximum image height - the maximum angular size of the image as seen from the exit pupil Field of View FOV: the diameter of the object/image Half Field of View HFOV: the radius of the object/image Full Field of View FFOV is sometimes used instead of FOV to emphasize that this is a diameter measure. 9-14 I and Instrumentation Design Optical OPTI-502 Field of View – Object Measures Greivenkamp E. John 2019 © Copyright EP HFOV 1/2 L h tan1/2 z L 1/2 h h u tan 1/ 2 L Since the EP is the reference position for the FOV, this defining ray becomes the chief ray of the system in object space. For distant objects, the apparent angular size of the object as viewed from the EP or from the front principal plane P or the nodal point N are approximately the same.