3

NBS MONOGRAPH 93

Spot Diagrams for the

Prediction of Lens Performance

From Design Data

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
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UNITED STATES DEPARTMENT OF COMMERCE • John T. Connor, Secretary

NATIONAL BUREAU OF STANDARDS • A. V. Astin, Director

Spot Diagrams for the

Prediction of Lens Performance

From Design Data

Orestes N. Stavroudis and Loyd E. Sutton

National Bureau of Standards Monograph 93

Issued September 7, 1965

For sale by the Superintendent of Documents, U.S. Government Printing Office Washington, D.C., 20402 - Price 75 cents
Library of Congress Catalog Card Number: 65-60037
Contents

Page

1. Introduction 1

2. Methods for calculating and displaying spot diagrams 3

3. Interpreting spot diagrams 5

3.1. Direct visual inspection to obtain subjective comparisons 5

3.2. Interpreting supplementary tables and graphs obtained from

the numerical data generated by spot diagrams 6

4. References 15

5. Appendix. A compendium of analyses 15

spot Diagrams for the Prediction of Lens Performance From

Design Data

Orestes N. Stavroudis and Loyd E. Sutton

This Monograph presents an outline of the methods used at the National Bureau of Standards to predict the performance of lenses from an analysis of their designs. The

technique is based on the use of spot diagrams, which are analogs of star image tests, and

makes extensive use of high-speed digital computers. A collection of twenty-one spot

diagram analyses is included.

1. Introduction

The U.S. Air Force Reconnaissance Laboratory

at Wright Field requested the assistance of the

National Bureau of Standards in evaluating designs for aerial camera lenses. The task was to develop a procedure for the determination of the

performance of lenses from the design data alone

and to apply the procedure to specific lens design

submitted by the Air Force. An obvious solution

to this problem would be to fabricate prototypes

of each design submitted and subject them to physical tests. However the construction of prototypes is expensive and time consuming and

the need for an alternate procedure was clearly

indicated. At first rays were traced through each

system and the geometric aberrations were

calculated and plotted. The resulting graphs were forwarded to the Air Force where they were

used as aids in selecting the better designs. But

this process was slow and tedious and a great deal

of skill was required to interpret the results. With

the development of the high-speed digital computer it became possible to compute a very large

number of rays in a minimum of time, making

routine spot diagram analyses possible.

It is intended that this Monograph provide an

outline of the methods used to calculate, produce,

and interpret spot diagrams at this and other

laboratories, as well as provide a compendium of the results of our spot diagram analyses.

A spot diagram is nothing more than a plot of points representing the intersections of rays from

a given object point with a focal plane of a lens. The data for such a plot is obtained by calculating

the paths of rays through a lens to a plane in image space, using its design specifications as parameters. This procedure is illustrated in figure 1. Spot diagrams provide a representation

of the distribution of the light intensity in the

image of a luminous point object and therefore

are the geometrical optics analogs of star images.

Within the framework of geometrical optics, a

spot diagram, constructed from a numerical model

of a lens, can be interpreted in the same way as a

star image made with. a real lens. Spot diagrams

therefore provide a convenient and economical means of testing lenses prior to their fabrication.

Another experimental analog of a spot diagram

is the photogram obtained in applying the Hartmann bench test to a lens [1].' A diaphragm

consisting of a number of small holes drilled in an opaque plate is placed in front of the lens to be

tested. Light from an object point is then passed

through the diaphragm and lens and is allowed to

fall on a photographic plate displaced considerably from the Gaussian image plane. A second

exposure is made on the opposite side of the Gaussian focus. Thus, an image of the diaphragm

appears on each plate from which the direction

and position of the beams on the Gaussian image

plane can be calculated. Figure 2 illustrates the

experimental setup. Sets of such photograms

are made for a number of object points and the

results are used to calculate the aberrations of the

lens. Photograms (see fig. 3) can be thought of as spot diagrams on planes displaced considerably

from the Gaussian focus. The diaphragm plays

the role of the grid network on the entrance

pupil plane and the lens does the work of the computing machine.

The earliest published report on spot diagrams

appeared in 1946 in a paper by Hawkins and Linfoot [2J to describe the performance of several

designs of Schmidt cameras. Later, Herzberger

[3] reported on a method of calculating spot diagrams that had been in use since 1939. Increasing

interest in spot diagrams has been noted in the

technical literature since high-speed digital computers became available.

The computational procedures used to make

spot diagrams can provide a great deal of auxil1 Figures in brackets indicate the literature references on page 15.

1
Figure 1. Spot diagram construction.

Oi represents an axial object point; Oi , an off-axis object point. E is tlie entrance pupil plane. L represents the lens. P is the Image

plane. From each obj?ct point a ray is traced to a system of lattice points on the entrance pupil, thence through the lens to the image

plane P. The intersection of these rays with the imaae plane form the spot diagrams. Tlie spot diagrams associated with the object points Oi and O2 are situated in the rectangular areas Pi and P2 respectively. Only those rays actually transmitted by the lens are illustrated. Note that more rays from the axial object point are transmitted than rays from the off-axis point, resulting in the narrowing of the entrance pupil aperture.

iary information about a lens. For example, the

computer programs developed at the Bureau provide automatically the shape of the vignetted

entrance pupil. This shape is given by a plot of points on the entrance pupil plane indicating, for a giA'en object point, the intersections of those

rays which are not \'ignetted by the diaphragm

or any of the mounting edges of the lens. This

is illustrated in figures 1 and 9. Accurate in- formation of this type is virtually unobtainable

by any other means. In addition these programs

provide information on distortion and chromatic

aberration of a lens. As a representation of the image of a point

object, a spot diagram is subject to certain limitations. First, each ray is represented as contributing an equal amount to the intensity dis- tribution of the image. In reality there is a

considerable variation in the flux density asso- ciated with rays which travel along different paths

through the lens. Each surface is entered at a

different angle of incidence, resulting in different

proportions of energy transmitted according to the

Fresnel formulas [4]. Second, if a point of a spot

diagram is superimposed on another they appear

as a single point, so that the intensity distribution

in the dense portion of a spot diagram is underestimated. Third, no effort is made to take into

account the diffraction effects due to the wave

nature of light. The conditions under which these

defects became important and possible means of overcoming them will be discussed.

Figure 2. Illustrating the Hartmann bench test. A long-focal-length, wide aperture simple lens is shown clamped to the

bench. Taped to it is a mask containing a number of small circular apertures. The system is illuminated l)y coUimated light from a parabolic mirror (not shown). The light source is sliown in the lower center portion of the picture. The image of the mask is in the background.

2
2. Methods for Calculating and Displaying Spot Diagrams

Necessary in any program for the routine cal- culation of spot diagrams is a method for tracinglarge numbers of rays. At the time high-speed

digital computers were first applied to optical

problems, it was found necessary to reevaluate

the lens analytical procedures then in current use. These procedures, devised primarily for hand

computation, were inconvenient and impracticable

for machine use. One of the earliest applications

of digital computers to ray tracing was given by

Grosch in a paper read at a meeting of the Optical

Society in 1945 [5]. In 1951 more comprehensive

reports were published by Feder [6] and Allen

and Stark [7]. Later in the same year, Herzberger

[8] published a description of a process for tracing

rays by machine.

Figure 3. Hartmann photograms from the experimental

setup shown in figure 3. The three pictures on the left show photograms for an on-axis beam. The

center picture is at the focus; the upper and lower pictures are outside and

inside the position of best focus. The four pictures on the right show

photofrrams for an ofT-axis beam. The uppermost picture is outside the

plane of best focus, upper center is at the sagittal focus, lower center is at the

tangential focus, lowest is inside the tangential focus.

At the National Bureau of Standards Feder's

formulas were coded for both the IBM Card Programmed Calculator (CPC) and the Standards

Electronic Automatic Computer (SEAC) ; in fact,

this was the code used to test the SEAC on its initial run [9]. The Bureau's first lens analyses

in which total aberrations were calculated used

these codes.

The first program for the preparation of spot

diagrams was based on an interpolation process

and made use of the CPC exclusively [10]. A

relatively small number of rays were traced

through the optical system for each of several

obliquities to determine the coordinates of intersection of each ray on a focal plane. A separate

code was then used to determine the coefficients

of two interpolation polynomials, one for each

focal plane coordinate, with entrance pupil co- ordinates as arguments. Then, using a third

computer program, the coordinates of a large

number of rays on the focal plane were determined

by evaluating the interpolation polynomials. The

coordinates of the points of a grid on the entrance

pupU were used as argiiments.

This program was accurate, fairly rapid, and

utilized completely the capacity of the CPC.

However, it was subject to several drawbacks.

A large amount of preliminary hand calculation was necessary. In particular, it was necessary

to determine the shape of the entrance pupil and

restrict the coordinates to the interior of this

region. This computation could be performed

only by examining each of the rays at each surface

and at the stop to determine whether or not it was transmitted. The location of the edge of the

vignetted region was then estimated and the co- ordinates of all the points on the grid network

lying within this region were punched by hand.

In determining the coefficients of the interpolation

polynomial, tracing rays outside this region was

also necessary to avoid the inaccuracies resulting

from extrapolation. Moreover, the results applied

only to the one focal plane to which the ray

tracing referred. When SEAC became available for routine optical calculation, an overall program was devised in which the tracing of a single ray was done by a

subroutine.

Such a program was written to trace rays of a given obliquity starting from the points of a square

grid on the entrance pupil. The rays specified by

such a set of starting points were traced in a se- quence which proceeded outwards from the meridian plane along horizontal lines, each line being

ended by means of certain comparisons, described

as follows: The radii of the clear apertures for each surface and for the stop plane were part of the input data of the lens system, so that SEAC

could compare these radii with the radial displacements of the rays on each surface, and only those

rays clearing the system comprised the output.

When all the rays from one obliquity were finished,

3
Figure 4. Spot diagrams produced by oscilloscope. The dots are larger than those in a spot diagram produced by an inked

stylus and fewer spots are used. The contrast range in the reproduction

process used here does not illustrate the build-up of the intensity of over- lapping spots.

the machine would automatically proceed to the

next obliquity or, if all obliquities had been completed, halt. In this program, each ray was traced

to five separate focal planes, three of which were

usually selected for spot diagram presentation.

Both the CPC and SEAC programs were limited

to rotationally symmetric optical systems consisting of spherical surfaces. It was therefore neces- sary to trace rays only on one side of the meridian

plane, as the remainder were obtainable from the

symmetry of the system. Although for every lens

analyzed thus far the object has been at infinity,

finite object points could also be considered by

changing slightly the input data.

Experience showed the SEAC code to be more

efficient for a large computer. When the primary

computation tool of the National Bureau of Standards was changed to the IBM 704 computer in June 1957, and to the IBM 7090 in November

1961, this code was programmed for the new

machines without any basic change.

One of the inherent difficulties in routine production of spot diagrams is the reduction of the

computed results to a graphical format. Clearly an automatic method is called for. In the procedures using the CPC and in the codes for the

SEAC and the 704, provision was made for the

output, in the form of punched cards, to be used

in conjunction with an automatic plotter to produce the final spot diagram. Each punched card

contained the data for a smgle ray. The data

specified the obliquity angle and coordinates of the ray on the entrance pupil plane and on each

of five given image planes. The entrance pupil

plots and the spot diagrams could thus be plotted

from one deck of cards.

Output in the form of punched cards had an

additional advantage. By sorting the cards on one coordinate on the focal plane, a profile of the

flux distribution in the image could be obtained.

This process, reported in detail by Lucy [11], was

used in earlier analyses to predict radial and

tangential resolving power.

Although the use of card decks and plotting

machine was reasonably convenient, delays fre- quently resulted from plotting machine breakdown. In one suggested improvement in the

procedure, a cathode ray tube would be connected

directly to the output circuits of a computing

niachine. The spot diagram could be displayed

visually and recorded photographically as it was

being computed. In addition, the position of the

focal plane could be controlled directly by the

operator to find the plane of best focus by simple

visual inspection, thus eliminating both manual

calculation and the necessity for handling punched

cards.

The use of such a device would have an additional advantage over the plotting machine process

where points are printed by an inked stylus.

With the inked stylus method, a number of superimposed points appears only as a single point, and

makes a spot diagram with a dense core and a weak flare distributed over a large area appear

less favorable than it really is. However, with

the cathode ray tube display process, the intensity

of overlapping points increases materially in the

image, and a much more accurate diagram results. A simpler although less accurate procedure for the routine production of spot diagrams has been

reported by Miyamoto [12]. The coordinates of the points of a spot diagram are calculated on a

digital computer which is then programmed to print out a display of periods with these coordinates. Some experiments for displaying spot diagrams on the face of a cathode ray tube were completed

in 1959 which made use of both the IBM 7090

and SEAC [13]. Some trial results are shown in figure 4. The output of the IBM 7090 was on

magnetic tape rather than on punched cards, and

the information so recorded consisted of direction

cosines of the rays as well as their coordinates of intersections with a fixed image plane. The data was then fed into SEAC where it was converted

into analog voltages that controlled the cathode

ray tube in plotting the spot diagrams. Using the

direction cosine data, the operator was able to shift the position of the plane of the spot diagram and

thus find the location of the plane of best focus

visually. 4
Other procedures for the routine production of spot diagrams have been applied elsewhere. One

flexible approach, described by Herzberger [14], does not use higher degree polynomials where the

coefficients are determined by interpolation. In- stead lower degree polynomials are fitted by a

least squares method. In this case the number of

3. Interpreting

3.1. Direct Visual Inspection To Obtain

Subjective Comparisons

The spot diagrams presented in the appendixare, by definition, pictorial representations

(through geometrical ray tracing) of the point

imagery of the lens system analyzed. Thus,

within the scope of the validity of geometrical

optics, they would show, by visual inspection,

the crude distinction between two lenses of widely differing image quality, with the smaller

spot diagram indicating better imagery. The

directness of presenting a graphical display of numerical results and the simplicity of interpretation when the above criterion can be applied

constitute the obvious appeals of the spot diagram

approach to image evaluation. However, it should be borne in mind that some rare lenses

of very high quality are diffraction limited, and in these cases the spot diagram serves only to indi- cate this possibility by its very small size. Such

a case is shown in figure 5. An accurate evaluation of such exceptional lenses thus falls beyond

the scope of this Monograph.

Even when making only visual comparisons, one usually finds it necessary to draw a finer distinction between two lens designs than that

based on total sizes of the spot diagrams. Such

a qualitative distinction can often be based on

the relative sizes of the cores of the spot diagrams,

with the smaller core indicating better imagery.

The word "core" is merely a term used to specify

subjectively that region of the spot diagram where

the point density is highest. For most lens

designs with even reasonably good imagery,

experience has shown that such a region usually

is unique and rather easy to distinguish in each of the spot diagrams. Another convenient term

"flare", may be subjectively defined in a similar

way. The region of lowest point density occurring outside the core is called flare. It usually

consists of a relatively thin scattering of points

toward the periphery of the diagram. These

terms are found to be useful because they allow one to make comments on the general characteristics of a given spot diagram. They are applied

to star images as well. See figures 6 and 7. Core size can also be associated, at least to some extent, with the resolving power of a lens. Further qualitative considerations, based on an

experimental knowledge of the effect of the type

of emulsion used, are helpful in the use of core

size as a rough guide to resolving power. These

traced rays need not be fixed. This least squares

approach results in a small loss of accuracy that

would certainly be less than that introduced by

the plotting machine errors. Herzberger goes

further in interpreting the coefficients as aberration coefficients and has applied this concept

successfully to designing lenses. Spot Diagrams

considerations will be mentioned, largely because

they form a starting point for developing more

exact methods. For instance, when using a high

contrast emulsion, exposed and developed properly, one could reasonably expect only the core

to be recorded. In this case, the smaller core of two diagrams would be associated with a higher

resolving power. On the other hand, when using an emulsion of lower contrast, one could expect

not only the core, but also some additional points

from the region immediately surrounding the core, to contribute to the record. By examining the

size of this extended core region, one might thus

i

10 5 0 5 10 MICRONS

Figure 5. The diffraction limited case. The spot diagram was calculated for a 6 in. f/3.5 lens (006BC035 15) at 0° obliquity on the plane of best focus. The graph drawn to the same scale shows the energy distribution in an image formed by a perfect f/3.5 lens. (Data from Jen'ans and White [15]). The diffraction efiects clearly dominate the geometrical aberrations.

5
Figure 6. Illustrating core and flare. Shown is a greatly enlarged spot diagram. The departure from left-right sjTnmetry is due to plotting errors. A spot diagram with a well-defined core and a large, uniform flare. expect to obtain a relative estimate of low contrast

resolving power. The remaining points of the

diagram would be considered to constitute the

flare, which contributes nothing to the record

except that it may serve to sensitize the emulsion

in the area around the image.

Though such visual estimations might be sufficient to facilitate a choice between two lenses

in some instances, it is easy to show that, in general, better methods are needed. The chief

difficulty of such a visual method appears to be

that it might, in many cases, require an experienced and judicious observer to determine accurately just how much of the spot diagram

constitutes the extended core region, as used for low contrast resolving power predictions. The

core itself is much easier to distinguish, since it is a characteristic feature of many spot diagrams,

but, to a lesser de ree, the same difficulty sometimes arises in being sure that the proper region

of the diagram has been demarcated. It is thus

clear that purely visual estimates of resolving

power are definitely limited in accuracy, particularly in terms of obtaining absolute, rather than

relative, estimates.

The curvature of the field of a lens becomes

apparent when spot diagrams of a number of object points are observed at several focal planes, as shown in fgure 8. T'he locus of best focus of

all object points can i dicate the sur."ace on which

an extended object is best imaged. The location

of the plane of overall best definition can then be

estimated.

3.2. Interpreting Supplementary Tables and

Graphs Obtained From the Numerical

Data Generated by Spot Diagrams

The production of spot diagrams generates all the data needed for obtaining entrance pupil plots,

which represent the set of rays transmitted by the

analyzed lens system at a given obliquity.

Through comparisons of their entrance pupil plots,

the light collecting abilities of different lenses for

Figure 7. Illustrating core and flare. Shown is a greatly enlarged spot diagram. The departure from left-right symmetry is due to plotting error. The core in this spot diagram is not well

defined. The flare is weak and not uniformly distributed. corresponding object points can be estimated.

For an axial object point, the entrance pupil plots

for all lenses with the same focal length and /-

number should have the same diameter. As the

object point is moved off the axis, the typical lens exhibits a narrowing of the entrance pupil as shown

in figure 9. This narrowing is detrimental since

it reduces the amount of light reaching the edge of the field. An ideal situation would be one in which

the area of the entrance pupil projected onto a plane perpendicular to the principal ray remained

constant. Under that condition, the energy

associated with the image of a point object would

be the same over the entire field of the lens, to the

accuracy obtainable by geometrical optics.

For determining the chromatic aberrations, the

Conrady "D-d" method [16, 17] may be used. It

is a particularly convenient method to apply in conjunction with a ray-tracing code, such as that

used in computing spot diagrams, and a knowledge

of it should be more widespread. The method

makes use of the fact that the optical path length

between an object point and any point on an emanating wave front is constant, together with

Fermat's principle, which states that the optical

path length of a ray between two fixed points

possesses a stationary value with respect to arbitrary variation.

The application of the method will be described

here for the usual case in which the final medium

is air. Suppose it is required that a lens be cor- rected over the wavelength region from F(486lA)

to C (6563 A). Rays are traced only at an intermediate^ wavelength, usually that of sodium

D(5893 A). For each type of glass in the lens, the

value of AAT'is obtained, where AN=Nf—Nc, that

is, the difference between indices of refraction at the F and C wavelengths. Defining D as the

length of a given ray in a glass medium and d as the corresponding length of the principal ray, one

then calculates the quantity (D—d) AN for each

glass of the lens system. The sum of these quantities is called the Conrady Sum for that ray. By

computing the Conrady Sum for each ray in a meridian fan of rays and plotting it against the

coordinate of the ray in the entrance pupil, one

obtains the Conrady Sums curves given in the

appendix.

6
16°

10°

Figure 8. Estimated field curvature and astigmatism from spot diagrams.

In the upper panel are four sets of spot diagrams each at the focus as indicated (zero indicates the location of the Gaussian image plane). For each obliquity

angle, the location of the best tangential focus (where the spot diagram resembles most a horizontal straight line) and the location of the best radial focus (where

the spot diagram resembles most a vertical line) are estimated. These estimates are plotted in the lower panel and two curves are drawn through the points. The two curves represent a profile of the tangential and radial focal surfaces. The distance between them is a measure of the astigmatismof the lens. The

field curvature can be represented by a curve representing the average of these two curves. A detailed derivation of formulas relating such

curves to the chromatic aberrations obtained by

ray-intercept methods may be found in [16J. Here we will simply illustrate certain principles used as

a guide to interpreting the plots of Conrady Sums

directly. Figures 10 and 11 show idealized plots

of the curves produced by specified pure types of chromatic aberration. When mixtures of these

pure types are present, the overall slope of a

typical Conrady Sums curve provides a good

representation of the lateral color aberration, and

the deviations of the curve from a straight line of that indicated slope are a measure of the longitudinal color aberration.

In a quantitative analysis by means of spot

diagrams, the principal problem is to predict the

resolving power of the fabricated lens. It is not

the purpose of this Monograph to go into the

question of the meaning of resolving power and

its relevance in lens specifications. Measurement

of resolving power is essentially subjective, as it depends idtimately upon the ability of the observer

7
LENS NO. 006BB035 15 LENS NO. 006BC035 15

Figure 9. Entrance pupil plots for two 6 in. f/3.5 lenses designed for a 30° field angle.

Left is 006BB035 15; right is 006BC035 15. These plots indicate that the left lens is more efficient resulting in a more even distribution of light over the

focal plane.

to find that spacing of the lines on a test target

which renders its image barely perceptible.

Nevertheless, resolving power is used to describe

the performance of lenses and therefore it is proper

to consider means of predicting resolving power.

What is needed is a set of numbers that agree

generally with the results of some procedure for

measuring resolving power. The desired goal is that a qualitative ordering of lenses in terms of predicted resolving power should agree with the

ordering of the same lenses in terms of measured

resolving power. Once this goal is reached the

8
NO ABERRATION

PURE UNDERCORRECTION

PURE LATERAL COLOR

PURE LONGITUDINAL COLOR

ZONAL ABERRATION

Figure 10. Interpreting Conrady sums.

Axial rays.

problem is one of improving the quality of the

predictions to agree better with the measured

values.

The most straightforward approach is to prepare

profiles of the density of points in a spot diagram

in radial and tangential directions [10, 11]. From

considerations of the widths of these profiles, and

the type of emulsions to be used, an estimate of radial and tangential resolving power can be made.

This procedure is based on ,the assumption that a

straight line on an object can be considered as a sequence of colinear overlapping spot diagrams

on the image. The point density contour of the image of the line can then be approximated by

counting points in strips of equal width parallel to the ideal image of the line. Let P, represent

the number of points in the ith strip and Di the

displacement of the center of this strip from the

ideal position. Then a smooth curve drawn

through a plot of Pi against Di gives a profile of the flux density distribution in the image of the

line. Estimates of resolving power based on the measure of the half-width of the main peak in

such a profile can be easily obtained. However,

the above assumption is true only for lines of zero thickness. Because the object lines on a

resolving power chart have finite widths, their

energy profiles are not the same as those of zero width lines. The spot diagrams should also be

integrated in the proper direction to simulate a

line of a finite thickness. A typical energy

distribution profile is shown in figure 12.

Figure 11. Interpreting Conrady sums.

Ofi-axis rays.

Figure 12. Energy distribution profile.

Parallel lines are ruled on a spot diagram and the number of points in each

strip is determined. These counts are then plotted against the location of the center of the strip and a smooth curve is drawn tlrrough the points. Counts are taken with the parallel lines oriented in two directions.

9
The Bureau's method for obtaining routine re- solving power predictions from spot diagrams

uses a formula developed by Hopkins, Oxley, and

Ej^er [18]. The high contrast resolving power, R,

is given by

(which shall be referred to hereafter as the resolu- tion jormula) wliere K is an empirically determined

constant; df\s the mean grain diameter, in microns,

of the film emulsion; and ds is the diameter, in microns, of a circle centered on the vertical line of symmetry of the spot diagram and containing

30 percent of tlie diagram points. Furthermore,

the center of this circle is to be located along the

vertical line of synnnetry at that point which

minimizes d^ (i.e., in the "densest" region of the

diagram). Although the resolution formula was

originally derived for application only to rotationally symmetric spot diagrams, we have arbitrarily applied it to all with a view toward obtaining a correlation of the result with the geometric

mean of the radial and tangential resolving

powers. Further research will be necessary if a more accurate extension of the resolution formula

turns out to be desirable.

A machine program was written to locate the center and compute the radius of the smallest

circle containing 30 percent of the points in a spot

diagram, where the center is to be somewhere on

the vertical line of symmetry of the diagram.

The point representing the principal ray can be

used as a first estimate for the center. For a

specified center, a high-speed calculator can compute the squares of the distances, from this center,

of all points on the right side of the diagram, sort these values into an ascending list, and select from

the list the squared radius of the circle with that

center which just contains 30 percent of the points.

This process is done in a few seconds and may be

repeated for each of several vertical shifts of the

center, so that for each trial center a corresponding radius is calculated. Between two centers where a minimum radius is in evidence, more vertical shifts may be made with a smaller interval

between trial centers, thus locating a center for which the corresponding radius is a minimum.

Though this location program is carried out

automatically within the calculator, a detailed

graph of the function to be minimized was pre- pared for the spot diagram shown in figure 13. As illustrated in figure 14, the minimum abscissa

is sought as function of the ordinate. It should

be noted that an out-of-focus spot diagram may

have more than one minimum. However, the

minimum radius is very easily found, even though

the center of the minimum 30 percent circle, as shown in figure 14, may not be well defined.

Having located the center of concentration of the points by the process just described, the

machine program uses that center to compute

the 10 radii of a set of concentric circles containing

10, 20, and so on to 100 percent of the points of

the spot diagram. The results can then be used

in the resolution formula to obtain estimates of resolving power. The use of the resolution for- mula for estimates of high contrast resolution can be based on the diameter of either a 20 or a 30 percent circle for the value of ds. However,

Hopkins [19] recommended the 30 percent circle as preferable, and in this case K is 600 and (//is

10 M- For estimates of low contrast resolution,

the diameter of the 50 percent circle is used as the

value of ds, and here K is 871 and df is 35 m- This approach to the problem avoids the

subjectivity involved in trying to make a direct

measurement of a visually demarcated core region

and then using the result in some nonuniform

estimation procedure. An objective method which

can be applied in a routine way is naturally a

desirable goal. Such a goal is more nearly

attained by some method of the type described

here, which gives a strict percentage definition for the region of high point density and specifies use of its diameter in a definite estimation formida.

It should be emphasized that the method cur- rently in use here, as described above, is certainly

open to improvement with respect to accuracy

of the estimates, and the need for further research

to that end is clear. Measurements of resolving power for some of the lenses of this Monograph have been provided

by the Air Force and are included in the appendix.

For nine of the lenses measured, estimates of

the high contrast resolving power had been

made by using the resolution formula. In some

cases the estimates had been based on the use

of a 20 percent circle, but information on the

size of the 30 percent circle was available to allow

calculation of estimates of the preferred 30 percent-circle type. The results are listed in table 1, where it is noted that the results for lenses A,

B, and G are subject to special conditions which

dictate their exclusion from a comparison of the

predictions and measurements. The pertinent

results for the remaining six lenses have been

carried over to table 2 for comparison purposes.

One can of course compute the linear correlation

coefficient between the compared columns of table 2, which gives the value of r as +0.625, but

it should be noted that the sample consists of only

six items. Though a high degree of accuracy can

hardly be claimed from such a result, the deviations listed in the last column of table 2 do not

appear extreme for estimations of such intrinsic

difficulty. An attempt was made to account for the source of these deviations, by reference to our

records of the computations done for these lens. In the case of lens C, it appeared very likely that

most of the deviation was due to a difference in the choice of the plane of best overall focus. It

also appeared possible, somewhat less conclusively,

that the same consideration applied to lens E.

When making predictions from the spot diagrams, as indeed again when the resolving power

is later independently measured, one must choose

a compromise plane of imagery which he judges

to be best over the entire field. In both cases

10
Figure 13. The determination of the 30-percent circle. A greatly enlarged core of that portion of a spot diagram to the right of the meridian plane. The ordinate scale shows distances from the principal ray. The abscissa is measured from the meridian plane.

Table 1. Predicted and measured resolving power in

lines/mm on axis

Eesolving power (high contrast)

Predicted Measured

Lens name From From R= T=

20% 30% radial tangen- Vrt

circle circle tial

A* (006BC035 1 5) 47* 60* 32 32 32.0 B* (BAC-2) 56 49. 7* 35.3 41.9* C (006BB035 15) 45 49 63 56 59.4 D (C03AA015 28) 45 53 56 56 56.0 E (006AA015 28) 45 52 41.0 41.0 41.0 F (024BB060 23) 44 36 36 36.0 G* {024AA060 23) 41 49 -(28)' H (006AA025 28) 34 34 35.3 31.4 33.3 K (024CC060 23) 32 34 42.0 42.0 42.0

•Notes on 3 of the above lenses- Lens A: This lens is diffraction limited on axis, so predictions are unreliable. Lens B: The measurements show too wide a spread between R and T to be

reliable. Lens G: The mean of thirty measurements labeled "Lowest resolution,

radial or tangential."

0

-10/1

-I5M

-20fi.

-25/1

•

-30/1

OO/l^—

1 1 1 1 1 1 1 1 1 0 5/1 10/1 15/1 20/1

Figure 14. The determination of the 30-percent circle.

Centers versus radii. The ordinate shows the location on the meridian

plane of the center of a circle containing 30 percent of the points in the spot diagram (shown in figure 13) measured from the principal ray. The abscissa represents the radius of that circle. The minimum radius is used in the

resolution formula. Note also that the location of the minimum, although

not well defined, could be used to provide an estimate of distortion. Table 2. Predicted and measured values for six lenses from table 1 Predicted values based on 30% circle Measured values taken as VRT

Lens name Prediction Measure- (Prediction- ment measurement)

C 49 59.4 (-10. 4) D 53 56.0 (- 3.0) E 52 41.0 (-1-11.0) F 44 36.0 (+ 8.0) H 34 33.3 (+ 0.7) K 34 42.0 (- 8.0) 2 = 266 2 = 267.7 2 = (-1.7)

such a choice is, at least to a degree, subjective,

and a more precise definition of this plane would,

for some particular lenses, be desirable. However,

future improvements toward flexibility in making

the required computations, which would facilitate the choice of this plane for the spot diagrams,

might be reasonably expected to increase the

accuracy of the predictions to some extent.

11
Any judgments as to the accuracy of the predictions are naturally limited by the fact that the

measurement of resolving power is itself subject to experimental error. We were not given nor could

we reasonably expect to obtain for these measurements, any exact bounds on the experimental error. Only the measured values were made available to

us, and, for that matter, there would always be

the possibility of human error. Another possibility is that errors of lens construction, such as decentrations, would affect the apparent accuracy

of predictions computed from blueprint data.

Nevertheless, our experience with such measure- ments indicates that they should have at least enough accuracy to make clear the need for improvement in the present accuracy of the predictions. Table 3 gives a compilation of further data on

the same nine lenses used in table 1. Here, we

give the available information, at certain off-axis obliquities, which makes possible comparisons,

as before, between the predicted and measured

values of high contrast resolving power. Whenever possible, estimates based on both 20 and 30

percent circles are listed. However, as in the case

of resolution on axis, comparisons with the meas- urements will again be made using the preferred

30-percent-circle results. Unfortunately, this

requires the omission of lens H from the tabulations carried over to table 4, since the diameter of the 30 percent circle was not included in the data

listed at the time of the report on lens H. To

keep a minimum of six other lenses in section 1 of

table 3, we have thus included results for lens G,

but with the measured value in parentheses, along

with a footnote which points out its probable

lower accuracy as a measure oi^jRT.

It should be noticed that, in section 2 of table

3, data at exactly matching obliquities for the predictions and measurements were not available

in that the entries for these tables must be compiled

from data that had been obtained in earlier in- dependent reports. When this mismatching of the available obliquities is small, it can be allowed

for, to some extent, by listing measurements in the manner shown in table 3 for lenses A and C. However, in general, a detailed study of the accuracy

of the predictions cannot be made when the

obliquities are not matched.

For section 1 of table 3 there is exact matching

of obliquities at 20°, and the numerical results are

carried over to table 4, where the deviations of

predictions from measurements are also hsted.

The entries for lenses G and F are listed below a horizontal line in table 4 as a reminder that there

are reasons for considering their measured values

less reliable than the others.

A noticeable contrast between the comparisons

in table 4 and table 2 is observed in that, for table 4, the predictions are lower than the measure- ments for each lens. Though the sample size

of compared lenses is small, this observation

indicates that predictions of this type, obtained

by the unmodified extension of the resolution

Table 3. Predicted and measured resolving 'power in lines/mm off-axis

Resolving power (high contrast)

Lens Max. Predicted Measured name halffield At From From At R = T=

obliq- 20% 30% obliq- radial tangenuity of circle circle uity of tial

Sec. 1 B 27. 5° 20° 10 8 20° 17.5 20.8 19.1 D 28° 20° 15 11 20° 25 28 26.5 E 28° 20° 8 7 20° 13.6 20. 0 16.5 F* 23° 20° 9 7 20° 38* 25* 31' G'* 23° 20° 8 7 20° --(16. 2)** H 28° 20° 15 20° 18. 7 19.

8

19.2 K 23° 20° 15 12 20° 18.5 18.5 18.5

Sec. 2 A 15° 11° 30 22 10° 31 31 31 14° 28 21 12.5° 31 31 31 15° 31 31 31 C 15° 11° 36 42 10° 43 49 45.9

14° 28 33 12. 5° 34 45 39.

1

15° 31 37 33.9

•For lens F, the spread between R and T is 13 lines, which appears questionable when compared with the spreads at 15° and 25°. The R values at

15°, 20°, and 25° were measured as, respectively, 22, 38, and 17 lines, with

corresponding T values of 24, 25, and 19 lines. **For lens G, we list 16.2 lines as the only value available, using parentheses

as a reminder that this is the mean of thirty measurements labeled "Lowest

resolution, radial or tangential." Table 4. Predicted and measured values at 20° obliquity for six lenses from table 3 P=Predicted values based on 30% circle M=Measured values talien at V-RT

Lens name P M [AP] = [P-M]

B 8 19.

1

-11.1 D 11 26.5 -15.5 E 7 16.5 -9.5 K 12 18.5 -6.6 G* 7 (16. 2) (-9. 2) F* 7 31 -24

•Footnotes of table 3 still apply to measured values. formula to an off-axis obliquity as high as 20°, are likely to err on the side of conservatism.

Judged only by the data of table 4, the 20°

predictions appear to be at least providing lower

bounds for the measured resolving powers of the

lenses. These off-axis values had been computed in the

hope that they would provide predicted values

adequate for specifying a relative ranking of lenses, at least for lenses of rather widely different

resolving power performance. Table 4, though,

provides so few contrasts in measured lens per- formance that it affords only a marginal basis for

judging this aspect of the predictions. We can

only note that, if there were valid reasons for omitting lenses F and K, the remaining lenses

could be properly ranked from the predictions in the order D, B, E, and G (E and G considered

equal) . Even then, though, the range of measured

values between lenses D and G would be only 10.3

lines. Some of the wide discrepancy exhibited by

lens F could conceivably be attributed to the

measured value, /? =38, about which we have

expressed doubts in the footnote on lens F in

table 3. The supplementary data supplied in that

12
footnote suggest that one might have expected

this value of R to be about 23, rather than 38,

hnes. If that were the case, the last measured

value in table 4 would be changed from 31 to about 24 lines. However, such a conjecture also makes it clear that all of the discrepancy of lens

F could hardh- be explained in this way.

For the comparisons made so far, it appears

that, at least in terms of absolute accuracy-, the

predictions for the higher obliquities show a greater need for improvement than the predictions

for the on-asis case. Further research effort would be needed to proA^ide a reliable basis for

effecting such an improvement, if the resulting

method of prediction were intended to be usable over a reasonably wide range of obliquities and

measured resoh"ing powers. We nmst remember

that there would be a restriction on the applicability of any method based on considerations of

geometrical optics alone, since there are some

high quality lenses in which the imagery is dominated b}- diffraction effects. Nevertheless, the

existence of such a category of lenses does not, in

itself, preclude the consideration of ways to improve the present method of predicting resolving

power for other lenses. First of all, an improved method of choosing the

plane of best overall focus would be helpful, but

this alone would probably be insufficient, since the

off-asis imagery is almost always considerably less sensitive than the on-axis unagery to small shifts

of the focal plane. Beyond this first means of obtaining a small improvement, it might be possible

to formulate some generalization of the present

method which would give a greater improvement

in accuracy, by virtue of a more efficient use of the

information content of the spot diagram.

An ob\'ious defect in the application of the

resolution formula is the presupposition that the

30 percent circle coincides with the core of a spot diagram. Certainly in the case of an off- axis spot diagram the shape of the core would

hardly be circular. A casual examination of onaxis spot diagrams would indicate that these cores very often are larger or smaller than the 30 percent

circle. Kubota and Mij'amoto [20] offer two very

simple alternate procedures. In one they simply measure the length and width of the core of the

spot diagram thus obtaining two quantities which

they relate to the radial and tangential resolving

power. In the second method a sequence of concentric circles is constructed ; the number of points

within each circle is counted and a curve of circle radius versus the number of points enclosed is plotted. Where the circle passes through the

edge of the core of a spot diagram the slope of the curve should change abruptly due to the sudden

change of the spot densitj^. The curve is therefore

inspected and the location of this inflection point

determines the radius of tlie circle which best fits the core. Kubota and Miyamoto use as estimates of the

resolving power the reciprocal of either the radius

of best fitting circle or of the measured semi-axes.

In the latter case both the radial and tangential

resolving power is estimated. This method was

tested on two lenses by comparing predicted and

measured resolving power. The results are encouraging.

Another approach taken by Miyamoto [12] and

Kubota and Miyamoto [20] has been the application of the Fourier transformation to spot diagrams

to obtain what might be described as a geometriciil

analog to the transfer function. Their results indicate that the frequency response estimates

are valid over a fairly large frequency range.

Estimates of distortion used in the routine

calculations are made in the usual way by taking

the difference between the ideal image height

and the height of the principal ray on the Gaussian

focal plane. The ideal image height is the product

of the tangent of the angle between the axis and

object point and the focal length of the lens, the

latter being determined from paraxial ray tracing.

The principal ray is defined as the central ray

of the bundle of rays from the object point that is transmitted by the lens and in practice is taken to be the ray that passes through the axial point on

the entrance pupil.

A study of figures 15 and 16 shows, however,

that the principal ray is not necessarily at the

center of a spot diagram or even at the center

of the core. This is particularly true when coma

is present in which case the principal ray is located

at the vertex of the comatic figure. The procedure

in which the principal ray is used to calculate

distortion therefore seems questionable; consequently, some estimation of the center of the

core of a spot diagram would be preferable. An

attempt has been made to use the center of the

30 percent circle determined in the resolving

power predictions as shown in figure 14 but the

uncertainty in locating this point, as mentioned

above, makes this procedure questionable.

Figures 15 and 16 suggest that it is possible for the distortion characteristics of a lens to change

with the /-number. Some preliminary studies

have been made to determine whether this phenomenon can be observed but the results have

been inconclusive.

These studies indicate that spot diagrams are useful in predicting the performance of lenses

from their design data. However the crudity of the predictions so obtained leaves much to be

desired. Means to improve their accuracy and

reliability may be found in two areas. First, the

information content of spot diagrams should be

broadened to include physical data such as measures of phase and signal strength as well as ray

coordinates, from which diffraction calculations can be made. Second, the Hopkins formula seems to be capable of a generalization based on

ellipses rather than circles, which may provide a more reliable means of predicting off-axis resolving

power.

13 769-553 O—65 2
f/22 f/16 f/ll f/8

Figure 15. Spot diagrams for various f-numbers.

f/6.3

A series of spot diagrams for a 6-in. lens sliowing the effects of reducing the stop opening. Above are the entrance pupil plots. The core appears to move

downward as the diaphragm is opened indicating a change in the distortion characteristics.

f/22

DIFFERENTIAL SPOT DIAGRAMS

METROGON 15°

* 4

' 100 /I

'

f/16- f/22 f/ll-f/16 f/8-f/ll f/6.3- f/8

Figure 16. Differential spot diagrams obtained from the data used in figure 12. Rays passing through concentric zones in the entrance pupil are plotted. The contribution of the outer zones to the core is negligible indicating that image

quality may be enhanced by stopping down the lens with no loss of intensity.

The authors wish to acknowledge the important

contribution of Donald P. Feder, under whose

direction this project was conceived and under

whose supervision the difficult pioneer work was

done.

Those to whom we owe thanks are legion: the

staff, past and present, of the Computation Section, who have been most helpful even to the extent of relinquishing some of their valuable

space for our equipment; the staff, past and

present, of the Photographic Laboratory, to whom

fell the difficult task of reproducing spot diagrams

clearly and to the proper scale; Edgar Watts,

whose preparation of the illustrations has been of the highest quality; to John Whitmore of the

Editorial Section for his invaluable advice and

assistance in preparing this manuscript; the staff of the Naval Ordnance Laboratory who prepared

our earlier spot diagrams; and the many colleagues

and friends whose comments and criticisms have

contributed to the success of this work.

14
4. References

[1] Hartmann. J. Ohjectivuntersuchungen, Zeit. f. In- strumenk. U, 1-21, 33-47 (1904).

[2] Hawkins, D., and Linfoot, E. H., An improved type

of Schmidt telescope, Monthly Notices RoyAstron. Soe. 105-334 (1945).

[3] Herzberger, M., Light distribution in the optical

image, J. Opt. Soc. Am. 37, 485-93 (1947).

[4] Sommerfield, A.. Optics, Academic Press, Xew York

(1945).

[5] Grosch, H. R. J.. Ray tracing with punched card equipment (abstract), J. Opt. Soc. Am. 35, 803

(1945).

[6] Feder, D. P., Optical calculations with automatic

computing machinery, J. Opt. Soc. Am. 41, 630-

35 (1951).

[7] Allen, W. A., and Stark, R. H., Ray tracing using the IBM Card Programmed Electronic Calculator,

J. Opt. Soc. Am. 41, 636-40 (1951).

[8] Herzberger, M., Some remarks on rav tracing, J. Opt. Soc. Am. 41, 805-7 (1951).

[9] Solution of skew rav problem, XBS Tech. Xews

Bull. 34, 125 (1950).

[10] Stavroudis, 0. N., and Feder, D. P., Automatic computation of spot diagrams, J. Opt. Soc. Am. 44,

163-70 (1954).

[11] Lucy, F. A., Image quality criteria derived from

skew traces, J. Opt. Soc. Am. 46, 699 (1956).

[12] Miyamoto, K., Image evaluation by spot diagram

using a computer. Applied Optics 2, 1247-1250

(1963).

[13] Lenstar aids lens design, XBS Tech. X'ews Bull. 43, 191 (1959).

[14] Herzberger, M., Analysis of spot diagrams, J. Opt.

Soc. Am. 47, 584-94 (1957).

[15] Jenkins, Francis A., and White, Harvey E., Fundamentals of optics. Second Edition, McGraw Hill, Xew York. p. 294 (1950).

[16] Feder, D. P., Conradv's chromatic condition, J. Research XBS 52, 43-49 (1954).

[17] Conradv, A. E., Monthly notices, Roy. Astron. Soc.

64, 182, 458 (1904).

[18] Hopkins, R. E., Oxley, S., and Eyer, J., The problem

of evaluating a white Hght image, J. Opt. Soc. Am.

44, 692-98 (1954).

[19] Hopkins, R. E. (Unpublished communications)

.

[20] Kubota, H., and Miyamoto, K. On the study of the image of photographic lens by means of spot dia- gram. Report of the Institute of Industrial Science,

University of Tokyo, 13, 38-53 (1963).

5. Appendix. A Compendium

of Analyses

This section consists of a collection of spot diagram analyses of lenses completed at the National

Bureau of Standards. All but two of the designs

are the property of the U.S. Air Force. One is the

property of the Eastman Kodak Company. The

remaining one was taken from the patent litera- ture. With the exception of the latter, the lenses are identified only in terms of a code number, no

reference being made to designer or manufacturer.

Unless otherwise noted, the values of refractive

index for the glasses listed in this appendix are those specified on the lens blueprint by the designer. Thus, in some cases, these specified index

values used in the computations are for special

melts not listed in standard glass catalogs.

The spot diagrams of this appendix are all shown at a scale which is 50 times the size of the

actual images formed by the lenses. If a scale

line is included on the illustration, it merely serves

as an approximate indication of this scaling.

However, the scaling of the entrance pupil plots

will vary from lens to lens, since these are given

only to show the relative sizes of the transmitted

beams of a single lens. For each of these lenses, the object point was

at infinity, and each off-axis beam was traced

from an object point located on the meridian plane

and below the optic axis. We wish to thank the Eastman Kodak Company and the U.S. Air Force for permission to reproduce the design data contained herein.

Contents

Focal length f-number Lens Special designation

in. 2.75 f/8 275CB080 61

3 f/1.5 003AA015 28 D

6

6

6

6

6

66

6

6

6

f/1.5

f/2

f/2 f/2.5 f/2.5

f/3.5

f/3.5

f/5.6

f/6.

3

f/6.

3

OO8AAOI0 28 Lens No. 2 (006POL20 25) Lens Xo. 1 OO0AAO25 28 BAC-2

008BB035 15 008BC035 15 006XA056 45 PL-9 ME-10

E

H

B

0A

12

12

f/4 f/4.5 CO-1

012AA045 40

24

24

24

f/6

f/6

f/6

024AAOfiO 23 024BB060 23 024CC060 23G

FK

36

36

f/3.7

f/4 ALPHA

BETA

4848f/4.5

f/4.5 CO-3 BA-4

Special designation Lens f-number Focal length

A

B

CD

E

FGH

K

006BC035 15 BAC-2

006BB035 15 0C3AA015 28 OO^AAOIS 28 024BB0^0 23 024AAO iO 23 005AA025 28 024CC060 23

f/3.5

f/2.5

f/3.5 f/1.5

f/1.5

f/6

f/6 f/2.5

f/6

in.6

6

6

3

624

24

624

15
275CB080 61—The Roossinov 2.75 in. (69.88

mm) //8 122° field

Wide-angle orthoscopic anastigmat

The data for this analysis (shown in figures 17a17e) were taken from the patent hterature (U.S.

Patent No. 2,516,724) and, therefore, these results

may not represent the optimum performance that can be expected from a lens of this type. The

important feature of this lens is shown in the

increase in the size of the vignetted aperture on

the entrance pupil as the obUquity increases.

This property represents an important achievement in the development of wide-angle lensep

where there is iisually a rapid decrease of the sizt of the entrance pupil accompanied by a decrease

in the exposure at the edge of the field. This

featvire, along with what might be described as a reasonable performance in image quality, is achieved with unusual economy, as the lens consists of only six elements.

275CB080 61—M. M. Roossinov

2.75 in. (69.88 mm) //8 122° field Wide-angle orthoscopic anastigmat

Source of data: U.S. Patent No. 2,516,724 Example II

1

2

Radii Separations Outside diametersClear apertures

Glass • Index Abbe

No.

771771 35.370

22. 960

77J771

2.15 —35. 58—

771 77J

67

77! 771

66 Jl-67 1.6395 43.3

3

4

5

47. 565 -21.640

131.918

9.20

3.07

0. 493-

30

30

28

20

Jl-24

JI-28

1. 6126

1.5480

68.6

45.9

6

7

8

-129. 640

24.100

-46. 700

3. 029

9.04 —34. 94—

30

30

11

28

JI-28

JI-24

1.6480

1. 6126

45.9

58.6

9

10

-22.270

-34. 650

2.11 66 65 JI-3 1. 6242 35.9

•Described as from I^enzos Co. Catalog of 1936.

Relative entrance pupil area (275CB080 61)

X^U. Ill cUloLLUliMrU layS r^ercent of 0

deg

0 824 100.0 25 886 107.5 42 1054 127.9

54 1318 160.0

61 1582 192.0

I 10 mm I

Figure 17a.

16
LENS NO. 275CB080 61
003AA015 28—3 in.//1.5, 2V4X2V4 in. formatAerial camera lens

The spot diagrams (see figures 18a-18f) indicate

that this lens is characterized by a small amount

of astigmatism, and a fair amount of coma and

spherical aberration. Tlie field is fairly flat. The

lens was evidently designed for optimal correction

of the 0° rays. The degree of light-collecting

ability, insofar as it may be judged by the relative areas of the entrance pupil plots, is about average

for a lens having such a low /-number.

The curves for the Conrady sums and the

lateral color table show that there is considerable

chromatic aberration.

The distortion table indicates that over the

entire field distortion is well under 0.1 percent.

003AA015 28—3 in. //1.5 aerial camera lens for a 2>1X2>^

in. format

Kadii

7/1 77J +50. 016 -567.5

+131.47

+29. 908 +44.33

+43.43

+18. 194

-19. 550

-36. 76 -62.62

-27. 295 +215.6 +65.0

-83.16

Separations mm

16.0

3.8 —0. 10 -

5. 37 —1.085-

4.52

-19. 84—

3.41 — .025-

7. 57 — .10 -

3.0

15.4

Outside diameters mm

69.0

45.6

45.6

43.0

43.0

63.0

Clear apertures

67.

56.0

43.

42.

55.0

60.0

Glass

EK-210

751277

EK-210

649338

720293

EK-210

751277 EK-210

Index

1.73400

1.75100

1. 73400

1.64900

1.72000

1.73400

1.75100

1. 73400

Abbe

No.

51.2

27.7

51.2

33.8

29.3

51.2

27.7

61.2

Stop position: 10.8 mm from surface 7. Opening: 28.3 mm at //I.5.

Relative entrance pupil area (003AA015 28)

Field angle No. transmitted rays Percent of 0°

deg

0 1102 100.0

12 942 85.5

20 730 66.2

26 508 46.1

Distortion and lateral color (003AA015 28)

Field angle (nominal) Tangent Distortion Distortion Hf-Hc

/o

12 0. 21266 -20. 38X10-' -0.032 -33.3X10-5

20 .36397 -95. 26 -.087 -48.9

25 .46631 -103.58 -.074 -24.6

Resolving power (003AA015 28)

Field angle

deg

0

51012

1520

26

Predicted resolving power in lines/mm

High

contrast

15

13

Low

contrast

24

Measured resolving power in lines/mm *

5647

28

23

25

24

66

49

38

28

2820

56.0 48.0 32.6

25.4

26.5

21.9

•Courtesy of the U.S. Air Force Reconnaissance Laboratory, Wright

Field.

50 mm

Figure 18a.

18
LENS NO. 003A A0i5 28

25 °

20°

I 2

°

0°

ENTRANCE PUPILS

Figure 18b.

19
LENS NO. 003AAOI5 28
LENS NO. 003AAOI5 28
LENS NO. 003AA0I5 28
CONRflOY SUMS FOR WAVE LENGTH RANGE F-C

Figure 18f.
006AA015 28—6 in. //1. 5, 41/2X41/2 in. format

The axial bundle for this lens is very well corrected. (See figures 19a-19f.) However, the spot

diagrams for the off-axis obliquities exhibit a considerable amount of spherical aberration, together

with smaller amounts of astigmatism and coma. As a result, the table on resolving power shows

a definite decrease in resolution for the higher

field angles. The light-collecting abilitj^ is about

average out to 20° and drops off somewhat at 25°, as indicated by the plots of the entrance pupil

areas. The curves for the Conrady sums indicate that

considerable amounts of both longitudinal and

lateral chromatic aberration are present.

006 AA015 28—6 in. //1. 5 aerial camera lens for 4>^X4>^ in. format

Radii

771771 +100. 03

+2000. 00

+208. 19 +61.947

+104.12

+91. 81

+35. 905

-41.424

-87.16

-209. 71 -61.502 +354.7

+118.0

-175. 55

Separations

777771

32.

1

7.5 —0.10-

12.53 —1.215-

11. 13

-38. 86—

7.12 —.035-

19. 50 —. 10—

5.7

29.3

Outside diameters

771771139

139

95

95

90

90

119

119

Clear

apertures

771771 134

112

87.2

84.0

80.0

59.0

55.0

72.0

80.0

84.0

102

112

Glass

EK-210

751277

EK-210

649338

720293

EK-210

751277 EK-210

Index*

1.7343

1. 75226

1. 7342

1.64854

1. 7203

1. 7342

1.75226

1.7343

Abbe

No.

51.2

27.7

51.2

33.

29.3

51.2

27.7

51.2

•Melt data. Stop position: 23.368 mm from surface 7. Opening 54.7 mm at //1. 5.

Relative entrance pupil area (006 AA015 28)

Field angle No. transmitted rays Percent of 0°

deg

0 1090 100.0

12 934 85. 7 20 672 61.7

25 336 30.8

Distortion and lateral color (006 AA015 28)

Field angle Tangent Distortion Distortion Hr-Hc

(nominal)

deg 171. % 177. 12 0. 21256 -0. 007609 -0. .597 -15.1X10-'

20 . 36397 -. 043350 -1.985 -34.2

25 . 46631 -. 100580 -3. 595 -47.2

Resolving power (006 AA015 28)

Field angle

deg

0

510

121520

25

Predicted resolving power in lines/mm

High

contrast

45

Low

contrast

24

Measured resolving power*

in lines/mm

R T \/RT

41.0 41.0 41.0

36.8 32.6 34.6

24.1 22.5 23.3

14.8 19.2 16.9

13.6 20.0 16.5

10.4 10.0 10.2

*Courtesy of the U.S. Air Force Recoimaissance Laboratory, Wright Field

.

100 mm

Figure 19a.

24
LENS NO. OOeAAOIS

25°

20°

12°

0°

ENTRANCE PUPILS

Figure 19b.
26
27
LENS NO 006A A0I5 28

-.110 mm

.1 m m

Figure 19e.
CONRAOY SUMS FOR WAVE LENGTH RANGE F-C

MERIDIAN FANS LENS NO. 006AA0I5 28
Lens No. 2 (006POL20 25) 6 in. //2, 50° field

This lens was one for which onl^- the spot

diagrams and resolving power estimates were

requested. (See figures 20a-20c.) However, the

anal3^sis produced information on the number of

transmitted rays. This information is given here

as a table. The results indicate that illumination

should be maintained rather well over the field in this case. The plane of best focus is at about —0.185 mm.

Here the spot diagrams exhibit definitely better

than average image quality, and particularly so

for an //2 lens. The cores of the images remain

relatively small even in the diagrams for 18° and

25°. These higher obliquities show a moderate

amount of flare, but enough rays are retained in

the cores to keep them relatively solid, indicating

that resolving power should be maintained to a corresponding degxee over the entire field.

Lens No. 2 (006POL20 25) 6 in. f/2 aerial camera lens for a 50° field

Radii Separations Outside

diameters

Clear

apertures Index Abbe No.

1

2

mm

+131.379

+819. 36

mm

8. 832

7. 620

mm

81.2 mm78.2

1.7551 47.2

3

4

-155. 510

-1385.

5

4. 572 —13.411

79.2 76.2

1.7551 47.2

5

6

7

8

+317. 50

+152. 400

-115. 454

+146. 583

8. 382

19. 705

8. 382

9. 144

79.2 76.2

1.72

1.611

1.621

29.3

58.8

36.2

9

10

-435.43

-133. 813

9. 144

0. 457

79.2 71.4

1.611 58.8

11

12

13

+106.350

+83. 55

-338. 216

6. 096

28. 956 —73. 289

101.6 87.4

98.4

1.605

1.611

37.9

58.8

14

15

-69.210

-508. 00

3. 048 —25. 073-

124.0 104.0

121.0

1.611 58.8

Stop position: 12.289 mm from fourth surface. Opening: 73.8 mm at f/2.

Relative entrance pupil area lens No. 2 (006POL20 25)

Field angle No. transmitted rays Percent of 0°

deg

0 1094 100.0

10 950 86.8

18 784 71.7

25 024 57.0

Resolving power lens No. 2 (006POL20 25)

Field angle

Predicted resolving power

in lines/mm

High contrast Low contrast

deg

0 47 24

10 37 21 18 24 17 25 22 17

100 mm

Figure 20a.

30
LENS NO. 2 006P0L2025

250

18°

-0.38mm 0.195 mm

Figure 20b.

0.18 mm

LENS NO. 2

ENERGY DISTRIBUTION IN RADIAL AND TANGENTIAL

LINES. COORDINATES ARE

IN UNITS OF FOCAL LENGTH.

-2 0 2 XIO"

TANGENTIAL

Figure 20c. Lens No. 2—Energy distribution in radial and tangential lines. Coordinates are In units of focal length. Carves shown are for the Gaussian focal plane.

31
Lens No. 1—6 in. //2, 50° field

This lens was not studied in as complete detail as usual since only spot diagrams were requested

for the analysis. (See figures 21a-21e.) However, information on the light-gathering ability of

the lens was incidentally obtained which indicated

about average perfornuince in terms of illumination. The entrance pupil at 25° took on a typical

cat's-eye shape with an area of a little less than

half the area of the 0° entrance pupil.

The spot diagrams show a rather small core at 0° with a flare which covers only a relatively small

area. At off-axis obliquities the flare becomes

ver}' enlarged and its extreme edges were omitted

for reasons of space. At 10° and 18° the cores

are also enlarged, but only by a moderate amount

compared with the enlargement of the flares. The core is again quite small at 25°, but it is apparent that only a small percentage of the rays

are involved in forming this core. The presence

of astigmatism may be noted from the horizontal

or vertical "lines" formed in the off-axis imagery

as the focal position changes.

100 mm

Figure 21a.

Lens No. 1 —6 in. //2 aerial camera lens for a 50° field

1

2

Radii Separations Outside

diameter

Clear

aperture Glass Index Abbe

No.

+117.8

+585. 0

7mn

11.0

0. 8-

mm

80.0 mm76.3 D. B.C.6001-83 1.6203 60.3

3

4

5

+52.3

+245.0 +37.0

16.8

5.0

26. 4-

72.0 70.3

54.0

D.B.C.6001-83

L.F.8502-30

1.6203

1.5800

60.3

41.0

6

7

8

-.52.3

+117.8

-72. 75

5.0

16.

6

4.7- 66.0

62.0

63.0

63.0

L.F.8502-15 D. 0.0.6001-83

1. 6725

1. 6203

42.6

60.

3

9

10

+1767.0

-119.5

10.7

53. 7-

84.0 82.0 D.C.B.6001-83 1. 6203 60.3

11

12

13

— 585.

0

+189. 0 -1767.0

12.0

18.0

142. 0

142.0

139. 0

139.0

B.S.C.3002-35

D.B.C.6001-83

1.517

1. 6203

54.6

60.3

Stop position: 17.1 mm from fifth surface. Opening: 53.0 mm at f/2.

32
LENS NO. I

Figure 21b. -0.46 mm

eese 7 una - -1 q: z

ill Ot- C^*^ -i tru I- „ 22Z0

,9Et

9- 21-

qZ o

<i o <fl — uj ^

UJIE -I

—

^1-

r 1 1

1^o

35
006AA025 28—6 in. //2.5, 41/2X41/2 in. format

The cores of the spot diagrams for this lens

(see figures 22a-22g) exhibit more than average

symmetry, which indicates a good correction for astigmatism. Some curvature of field may be

observed from the fact that the best focus for the

12 and 20° rays is inward from the best overall

focus of —0.39 mm. Although there is a noticeable fight flare in the 25° spot diagram, the smafi

size of the core apparently compensates for this

and maintains good high-contrast resolution here. This lens appears about average in terms of

light-collecting ability and quite good with respect

to distortion. The lateral color correction looks

better than average, with the longitudinal color

not quite up to the same level.

006AA025 28—6 in. aerial camera lens for a A^iX^Vi in. format

1

2

Radii Separations Outside diameter

Clear

aperture Glass Index Abbe

No.

TUTU +79. 40

+141. 10

7. 01

771771 67.0 65.00 EK-330 1. 7551 47.2

3

4

5

+63.90

+443. 80

+43. 90

1. 52-

9. 75

5.33

62. 00 60.00

50.00

EK-210

r)F-2

1. 7340

1.6170

51.0

36.6

6

7

8

-43, 16 +571.00

-54. 45

24. 85-

3.05

9. 53 54.0

48. 00

52. 00

EDF-2

EZ-430

1.6890

1. 77670

30.9

44.7

9

10

-302. 20

-86. 66

5. 28-

5.61 59.00 57. 00 EK:-448 1. 88040 41.1

U

12

-67.10

-89. 96

-2. 42-

3.58

62.00 60.00 EK-450 1.80370 41.8

Stop position: 12.75 mm from fifth surface. Opening: 47.44 mm at f/2.5.

36

Relative entrance pupil area 006AA025 28

J. iCivi allele No. tr&nsniittGci r&ys Percent of 0°

deg

0 1012 100.0

12 822 81.2 20 614 60.7 25 438 43.3

Distortion and lateral color 006AA025 28

Field angle (nominal) Tangent Distortion Distortion Hp-Hc

deg 771771 % mm

12 0. 21256 -0. 00865 -0. 027 -0. 0048 20 . 36397 -. 04974 -.090 -. 0053

25 .46631 -. 10909 -.153 -.0021

Resolving power 006AA025 28

Predicted resolving Measured resolving power* in power in lines/mm

Field lines/mm

angle High Low R r

contrast contrast

deg

0 34 20 35.3 31.4 33.3

5 33.3 39.3 36.2

10 43.7 40.7 42.2

12 22 16

15 27.0 20.7 23.6

20 15 14 18.7 19.8 19.2

25 13 6 26.9 32.5 29.6 27!^ 9.0 7.4 8.2

•Courtesy of the U.S. Air Force Reconnaissance Laboratories, Wright

Field.

lOOmm

Figure 22a.
LENS NO. 006AA025 28

37
LENS NO 006AA025 28

3 9mm

Figure 22d, e.

38
LENS NO. 006Afl025 28

-.05mm

.1 mm

Figure 22f.
CONRADV SUMS FOR WAVE LENGTH RANGE F-C

MERIDIAN FANS LENS N0.006AA025 28

20°

•1.2" -.8" -.4" 0 ,4" -.8"

V , THE y COORDINATE OF RAY IN ENTRANCE PUPIL PLANE

FiGUEE 22g.

,001 mm

.000

-.001 mm

.001 mm

.000

- .001 mm

.001 mm

.002 mm

.001 mm

.000

— .001 m m

1.2'

40
BAC-2—6 in. //2.5, 55° field

Spot diagrams for this lens (see figures 23a-23c) were originally prepared for image planes at —0.225, 0, and +0.225 mm from the Gaussian

focus. These results were used to locate the

plane of best focus, shown at —0.150 mm, and

estimates of resolving power were made for this focal position. One could expect that the image

quality would be quite good on axis, falling off appreciably at the higher obliquities. The spot

diagrams show definite, if somewhat large, cores

at 12 and 20°, but the extensive spreading of the

points at 25° indicates that loss of resolution will be more noticeable at this obliquity. It should

be noted, of course, that this lens operates at a

relatively low /-number, which normally in- creases the difficulty of obtaining good imagery

over the entire field. Illumination appears about average through 20°

and drops off somewhat at 25°. The values of distortion remain quite low indeed out to slightly

beyond 20° and then increase rapidly closer to the

edge of the field. However, the distortion cor- rection is still adequate for ordinary purposes.

BAC-2-6 in. //2.5 aerial camera lens for a 55° field

2

Eadii

Separations Outside diameters

Clear

apertures Glass Index Abbe

No.

in. +4.900

+18.140

in.

0. 250

in. 3.175in. 3.075

3.015 EK-110 1.69680 56.15

3

4

5

+3. 855

+30. 000

+3. 740

—. 012-

.390

.180 —. 012-

2.970 2.870

2.800

2.540

EK-110

DF-375

1.69680

1.621

56.15

6

7

+2.345

+1.664

.552 —.930-

2.500 2.400

1.890 DF-375 1.621

8

9

-2.100

-3.337

.787 2.662 1.870

2.300 EDF-977 1.649

10

11

12

-6.667

+6. 000 -3. 668

—. 012-

.150

.450

2.562 2.300

2.440

2.450

EDF-977

EK-110

1.649

1.69680 56.15

13

14

-29.27

-5.882 —. 012-

.240 2.700 2.570

2.600 EK-110 1.69680 56.15

Stop position; 0.517 in. from seventh surface. Opening: 1.712 in. at //2.5.

Relative entrance pupil area (BAC-2)

Field angle No. transmitted rays Percent of 0°

deg

0 1012 100.0

12 1000 98.8 20 688 68.0

25 392 38.7

I

1

I

I

Resolving power (BAC-2)

Predicted resolving Measured resolving power* power in lines/mm

Field angle High Low R T ^ IX 1 contrast contrast

deg

0 56 25 49.7 35.3 41.9

5 33.2 29.4 31.2

10 20.6 25.5 22.9

12 10 9

15 15.2 23.2 18.8

20 8 5 17.5 20.8 19.1 25 7 4 12.0 15.3 13.5

•Courtesy of the U.S. Air Force Reconnaissance Laboratory, Wright Field.

Distortion (BAC-2)

Field angle (nominal) Tangent Distortion Distortion

deg in. %

12 0. 21256 -28.8X10-5 -0.022

20 . 36397 +86.3 +.039

25 .46631 +723.6 +. 257

100 mm

Figure 23a.

41
LENS NO. BAC-2
LENS NO. BAC-2

43
LENS NO. BAC
LENS NO. BAC - 2

25°

20°

12°

0°

+ .225 mm

Figure 23c2.

7169-553 O—65 4 45
006BB035 15—6 in. //3.54, 21/4X21/4 in. format

The most evident feature of the spot diagrams

for this lens (see figures 24a-24f) is the overall

compactness of the image points depicted. This

qualitative impression of a well-corrected design

is borne out by the table on resolving power,

which shows that some of the measured values of

resolving poAver turned out to be higher than the

predicted numerical estimates.

For this lens, illumination and curvature of

field should present no problems, and the cor- rection of distortion appears reasonable for ordinary applications. The flatness of the curves

for the Conrady sums indicates good correction

of longitudinal chromatic aberration, although

there is a definite residual of lateral color. 006BB035 15—6 in f/3.54 aerial camera lens for a 2}iX2],i

in. format

1

2

Radii Separations Clear apertures Glass Index Abbe

No. mm

+72. 87 +135.3

mm

9. 60

0.62-

mm

62. 00

58. 68 EK-320 1. 74450 45.8

3

4

5

+43. 71

+83. 14

+31. 21

10. 58

5. 29

52. 07-

54. 22

49. 30

40. 34

EK-110 EDF-21. 69680

1. 68900

56.2

30.9

6

7

8

-36.42

-2327.

0

-45. 90

3.09

9. 52

0. 19-

39. 07

46. 91

49. 18

EDF-15

EK-415

1. 67252

1. 74450

32.2

43.9

9

10

-1570.0 -114.6

7. 52

53.42

55. 00 EK-310 1. 74500 46.4

Stop position: 26.14 mm from fifth surface. Opening: 28.76 mm at//3.54. Relative entrance pupil area 006BB035 15

Field angle No. transmitted rays Percent of 0°

deg

0 816 100.0

7 806 98.8

11 770 94.4

14 662 81.1

Distortion and lateral color 006BB035 15

Field angle (nominal) Tangent Distortion Distortion Hp-He

deg in. % in. 7 0. 12278 -85.3X10-5 -0. 117 -12.9X10-5

11 . 19438 -353.6X10-5 -.306 -24.1X10-6

14 .24933 -779.2X10-5 -.526 -36.3X10-5

46

Resolving power—High contrast target—Supper XX

006BB035 15

Field angle Predicted re- solving power in lines/ mm

Measured resolving power* R T

: \RT

deg

0 45^9 63 56 59.4

2.5 53 66 54.5

5 63 57 59.9

7 40-44

71. 0 56 49 52.4

10 43 49 45.9

11 36-42

12.5 34 45 39.1

14 28-33

15 31 37 33.9

'Courtesy of the U.S. Air Force Reconnaissance Laboratory, Wright Field. Resolving power—Low contrast target—Pan X—006BB035 15

Field angle Predicted re- solving power in lines/ mm

Measured resolving power* R T ^fRT

deg

0 23 56 44 49.6

2.5 42 47 44.4

5 47 47 47.0

7 23

7.5 40 39 39.5

10 24 36 29.4

11 23 12.5 24 34 28.6

14 22

15 24 31 27.3

*Courtesy of the U.S. Air Force Reconnaissance Laboratory, Wright Field.

100 mm

Figure 24a.
LENS NO. 006BB035 15

14°

7 o

0 o

ENTRANCE PUPILS

0.1 mm

-0.i23mm -0.049mm +o.025mm

Figure 24b, c, d, e.

769-553 O—65- 47
CONRADY SUMS FOR WAVE LENGTH RANGE F-C

MERIDIAN FANS LENS NO. 006BB035 15

-5

0° +5 —^ 0

t -5

-0.4" -O.Z" 0 0.2" 0.4" 0.6" 0.8" THE y COORDINATE OF RAY IN ENTRANCE PUPIL PLANE

Figure 24f.
006BC035 15—6 in. //3.5, 21/4X21/4 in. format

The off-axis spot diagrams here show dense

cores, each with a surroimdiBg flare, but with all the rays converging into quite small areas. (See

figures 25a-25f.) In the report on this lens it was noted that the 0° bundle, which shows

excellent correction according to geometrical

optics, produces a spot diagram which, at best

focus (—0.042 mm), is slightly smaller than the

corresponding Airy disk of physical optics. (See

figure 5.) The resolving power actually obtainable under such a condition will be limited by the

effects of diffraction.

This lens appears to have about average lightcollecting ability and to be somewhat better than

average in the correction of distortion. Both

longitudinal and lateral chromatic aberration may

be observed in the ciu-ves for the Conrady sums.

006BC03o 15—6 in. f/3.5 aerial camera lens for a 2>^X2Ji in. format

Radii

mm

+58.89

+159.

9

+51. 10 -106.0

+28. 10

-33.20

-50. 61

+4186.

4

-56. 26

Separations mm

9.9

18.9

2.55

-23.2—

7.8

—6.1—

12.15

Outride

diameters mm

57.0

50.0

50.0

38.0

44.0

Clear apertures mm

54.0

54.0

46.0

32.0

32.0

28.7

40.8

40.8

Glass

670472

611588

621362

617366

573568

Index

1.611

1.621

1.617

1. 5725

Abbe

No.

58.8

36.2

36.6

56.8

Stop position: 13.2 mm from fifth surface. Opening: 26.58 mm at//3.5. Relative entrance pupil area—006BC035 15

Field angle No. transmitted rays Percent of 0°

deg

0 824 100.0

7 726 88.1

11 576 69.9

14 436 52.9

Distortion and lateral color—006BC035 15

Field angle (nominal) Tangent Distortion Distortion Hf-Hc

deg in. %

7 0. 12278 + 59. 7X10-5 +0. 081 +55.2X10-5

11 0. 19438 +206. 7 +0. 178 +67.9

14 0. 24933 +364.6 +0. 245 +56.8

Resolving Power—006BC035 15

Field angle

Predicted resolving power in lines/mm

High contrast Low contrast R T

deg

0 47-60 25 32 32 32.0

2.5 32 35 33.5

5 31 31 31.0

7 35-39 17 7.5 28 28 28.0

10 31 31 31.0

11 22-30 12 12.5 31 31 31.0

14 21-28 11 15 31 31 31.0

Measured resolving power in lines/mm*

•Courtesy of the U.S. Air Force Reconnaissance Laboratory, Wright Field.

:oo mm

Figure 25a.

49
50
CONRADY SUMS FOR WAVE LENGTH RANGE F-C

MERIDIAN FANS LENS NO. 006BC035 15

INCHES + 5X 10"^
006XA056 45—//5.6, 90° field Relative entrance pupil area—006XA056 45

The plane of best focus for this lens (see figures

26a-26f) was judged to be at the —0.342 mm

position although the overall imagery at —0.477

mm is almost equally good. These spot diagrams

exhibit dense cores of a small size from 0 through

35°, becoming moderately enlarged for the 40 and

45° obliquities. The light-collecting ability and

control of distortion for this lens are superior.

The numbers computed for the table on lateral color are approximately equal to the slopes of the

Conrady sum graphs at the origin. Inspection of

these graphs shows that due to a displacement of

the bundle of rays, the correction of lateral color

is actually somewhat better at 40 and 45° than

the last two values in the lateral color table would

indicate. The Conrady sum graphs also show

the presence of longitudinal color, except near the

middle of the field at about 27°. The curves range gradually from downward bending at 0° to approximately equal upward bending at 45°.

006XA056 45—6 in.//5.6 aerial camera lens for a 90° field

1

2

Radii Separation Outside

diameter

Clear

aperture Index AbbeNo.

in. +3. 1551

+4. 2068

in.

0. 4922

. 2650-

in.

4. 100

in.4.004

3. 638

1.617 36.6

3

4

+11.146

+1.8354

.0947

.7004-

3.765 3.635

2. 804 1.700 41.0

5

6

+2. 1942

+6. 5220

.3407

. 2991-

2. 595 2. 468

2.396

1.8004 41.1

7

8

9

+8. 5632

+0. 8605

aspheric

.1514

.5245

. 3029-

2. 079

1.514

1.954

1.452

1.331

1.670

1.607

47.4

59.5

10

11

12

aspheric

-0. 8605

-8. 5632

.5245

.1514

. 2991-

1.471

1.984

1.266

1.409

1.859

1.607

1.670

59.5

47.4

13

14

-5. 2825

-2. 0337

.3407

1. 1752

2.465 2. 245

2.338

1.8004 41.1

15

16

-1.8354

-11.146

.0947

. 2650-

4.131 2. 987

4. 004 1.700 41.0

17

18

-10. 443 -5. 6355

.5096

2. 9119-

5. 089 4.633

4.962

1.575 41.4

stop position: 0.15145 in. from ninth surface. Opening: 1.072 in. at ;/5.6.

Field angle No. transmitted rays Percent of 0°

deg

0 1052 100.0 10 1052 100.0

18 1048 99.6 27 1068 101.5 35 1080 102.7 40 1078 102.5 45 1008 95.8

Distortion and lateral color—006XA056 45

Field angle (nominal) Tangent Distortion Distortion Hp-He

deg in. % tn. 10 0. 17633 +4.2X10-S +0. 0039 -42.6X10-'

18 .32492 +22.4 .0114 -69. fi 27 . 50953 +58.5 .0191 -88.1

35 . 70021 +64.2 .0152 -109.4

40 .83910 +23.9 .0047 -164.8

45 1.00000 +27.9 .0046 -353.

8

Predicted resolving power—006XA056 45

Field angle

Predicted resolving power

in lines/mm

High contrast Low contrast

deg0 48 23

10 48 24

18 60 23 27 30 20 36 16 14 40 10 9 46 10 8

Figure 26a.

52
LENS NO. 006XA056 45
LENS NO. 006XA056 45
CONRADY SUMS FOR WAVE LENGTH RANGE F-C
PL-9—6 in. //6.3, 90° field

The spot diagrams indicate very little curvature

of field for this lens. (See figures 27a-27d.)

The imagery for the plane at —0.30 mm appears

quite favorable for a lens of so few elements

which covers a 90° field. It is noteworthy that

the pattern of points that produces the central core

of the diagram at 20° is, in a general way, re- tained at the higher obliquities, with a definite core still present in the spot diagram at 45°. Such cores are needed to keep the high-contrast

resolution near the edge of the field up to a level comparable with that at low obliquities.

Illumination appears to be reasonably well

maintained over the field, in terms of the number

of rays transmitted at the various obliquities.

This lens shows very good correction for dis- tortion, which remains within 0.02 percent over

the entire field.

PL-9—6 in. //6.3 aerial camera lens for a 9X9 in. format

1

2

Radius Separation Outside diameter

Clear

aperature Glass Index AbbeNo.

30. 18

44.69

mm

13.32

. 023

mm

58.7 mm

58.1 620603 1. 6203 60.3

3

4

22.59

18.65 1.42 —33.32—

41.0 40.06 720293 1. 7200 29.3

5

6

-18.65

-22.59

1.42

. 019-

41.0 40. 06

720293 1. 7200 29.3

7

8

-44. 69

-30. 18 12.53

3.1

58.0 57.40 623569 1. 6227 56.9

9

10

CO

at 41.70

107.7

152.7 517645 1.517 64.5

Stop position: 16.66 mm from fourth surface. Opening: 17.5 mm at //6.3.

Distortion—PL-9

Field angle (nominal) Tangent Distortion Distortion

in. % 10 0. 17633 -4.3X10-5 -0.0041

20 .36397 — 11.4 —. 0052

35 . 70021 56.

1

+'. 0133

40 . 83910 97.7 +.0194

42.5 .91633 81.8 +.0149

45 1.00000 -4.1 -.0007

Figure 27a.

56
LENS NO. PL 9

Figure 27b, c.

0.0 mm
LENS NO. PL 9

58

•+0.30 mm

Figure 27d.
ME-10—6 in.//6.3, 90° field

The spot diagrams of this four-element lens

(see figures 28a-28d) are interesting because they

illustrate some of the difficulties of obtaining

good imagerv^ over such a wide field. The central

cores of these diagrams are quite small at 0 and

10° and stiU fairly small at 35°—the most important part of the field. Beyond 35°, however, it is clear that the density of the points begins to drop off, and the general pattern of the points at

40, 42.5, and 45° is quite different from the pattern at low obHquities. In some designs the basic

pattern of the points does not undergo so much

change and, perhaps because of this, there is a somewhat denser core of points in the spot diagrams at 40 to 45°. Illumination is fairly weU maintained over the

field, in terms of the relative number of rays

transmitted at each obliquity. Distortion reaches

a maximum of about 0.1 percent at 35°. ME-IO—6 in. //6.3 aerial camera lens for a 90° field

1

2

Radii Separations Outside diameterClear

aperture

Glass Index Abbe

No. mm

25.01

35.00

771771

9.71

1. 95-

777771 47.0

777 77i

46.0 DBC-3 1. 611 57.2

3

4

19.90

16.53

1.05

25. 28-

33.5

30.5 EDF-3 1.720 29.3

5

6

-16.53

-20.00

.99 3.2-

33.5

30.5 EDF-3 1.720 29.3

7

8

-40. 07

-27. 30

11.0

50.0

48.0 DBC-3 1. 611 57.2

Stop position: 11.25 mm from fourth surface. Opening: 18.0 mm at//6.3.

Distortion—ME-10

Field angle Tangent Distortion Distortion (nominal)

deg 777. %

10 0. 17633 20.8X10-5 +0. 0195 20 .36397 150.7 +.0684

35 . 70021 425.8 +. 1005 40 .83910 243.0 +. 0479 42.5 .91633 -25.6 -.0046

45 1.00000 -493.

2

-.0815

100 mm

Figure 28a.

59
10°

0°

I mm -.30 mm

Figure 28b.

60


CO-1—12 in. //4, 9X9 in. format Resolving power—CO-1

This lens (see figures 29a-29d) is similar to a Biotar and the general pattern of the image-points

is representative of that type of lens. The spot

diagrams show a large weak flare of light around

each of the central cores, particularly for the 12,

20, and 25° obliquities. For these angles, 9, 25,

and 20 percent, respectively, of the points computed were too widely spaced to be included in the spot diagrams, and the thinnest part of the

flares had to be omitted. These flares cause a

loss of contrast, especially for low-contrast objects,

but this loss will not be reflected in the resolution

figures since the cores are fairly small. Thus this

lens furnishes an example of a case in which resolution figures are an incomplete criterion of overall

quality of imagery.

Distortion is held to within 0.1 percent over the

entire field. It was noted in the report on this

lens that the chromatic aberration was checked

and found to be within tolerance. The depth of focus appears to be fairly large.

CO-1—12 in. //4 aerial camera lens for a 9X9 in. format

1

2

Radius Separations Outside

diameters

Clear

apertures Glass Index AbbeNo.

in. +3. 0457

+7.0008

in.

0. 7228

-—. 3736-

in.

3. 800

in.

3. 720

3.538 DBC-9 1. 651 55.8

3

4

+6. 6272 +2. 1264 .4819

. 2772-

3. 550

2. 500

3.300

2. 500 DF-1 1.605 38.0

5

6

+3. 6732

+6. 0539

.3252

.7228-

2.800

2. 500

2.620 DBC-9 1.651 55.8

7

8

-8. 5874 -4. 4405

.2650

. 3854-

2.800

2.620

2. 500 DBC-9 1.651 55.8

9

10

-2. 3961

-10. 0319

.3614

.3614-

2. 500

3. 250

2.600

3.150 DF-1 1.605 38.0

11

12

-11. 6256 -3. 0457

.7228 3.700

3.370

3.580 DBC-9 1.651 65.8

Stop position: 0.463 in. from sixth surface. Opening: 2.265 In. at//4.

Field angle

Predicted resolving power

in llnes/mmt Measured resolving pov/er

in lines/mm* R T R T

deg

0 35 35 35.8 35.8

5 27.9 31.6

10 23.4 24.2

12 33 25

15 15.2 22.1

~ 20 31 23 13.2 18.8

25 25 15 14. 2 15.4

fPredicted by measuring dimensions of spot diagram. •Courtesy of the U.S. Air Force Reconnaissance Laboratory, Wright

Field.

Distortion—CO-1

Field angle Tangent Distortion Distortion (nominal)

deg in. %

12 0. 21256 -15.7X10-5 -0.0062

20 .36397 -171.1 -.0392

25 .46631 -557.9 -. 0997

10 mm

Figure 29a.

7&9-553 O—65 6

63
Figure 29b - . 15 mm

+ .15 mm

Figure 29d,
012AA045 40—12 in. //4.5, 80° field

This design is unusual in that it covers a wide

field and at the same time operates at a relatively

low /-number. (See figures 30a-30g.) The position at —0.67 mm was chosen as the plane of best

focus because of the dense cores produced here at both the 0 and 38° obhquities. Curvature of field will be noted from the fact that at 28° the best

focus would definitely be farther from the lens. However, the general appearance of these spot

diagrams is favorable because both the cores and

the total areas of the image points depicted remain

relatively small. The latter consideration is important for the resolution of low-contrast

objects. The tables show that the number of rays transmitted drops off only slightly at the edge

of the field and that distortion is held to within

0.4 percent.

The Conrady sum graphs show the presence of considerable chromatic aberration. However,

most of the lateral color occurs quite near the

edge of the field.

012AA045 40—12 in. //4.5 aerial camera lens for an 80°

field

Radius

mm

+339. 01

+182. 72

+568. 59

+214. 32

+183. 58

+149. 09

+123. 19

+80. 36

-80. 36

-123. 19

-220. 66

-183. 58

-180.48

-518. 14

-154. 91

-297. 35

Separation

mm

10 —48. 5—

10

—141.44-

12

48. 39

42. 83

60.6 —20

60.6

42. 83

12

48. 39 —97. 42-

10 —45. 21-

10

Clear aperture mm

324

277

276

247

168

157

124

96

71.8

71.

92

116

129

158

206

230

235

277

Glass

BK-7

BK-7

EK-110

SF-15 EK^48

EK-110

EK-110

EK-448

SF-15 EK-110

BK-7

BK-7

Index

1. 51625

1. 51625

1.

1. 69874

1. 88040

1.

1.

1.88040

1. 69874

1.

1. 51625

1. 51625

Abbe

No.

64.0

64.0

56.15

30.1

56. 15

56. 15

30.1

56. 15

64.0

64.0

Stop position: 10 mm from ninth surlace. Opening; 70.8 mm at //4.5.

Relative entrance pupil area (012AA045 40)

Field angle No. transmitted rays 07 r,f no

/o 01 u

deg

0 996 100.0

16 996 100.0 28 1008 101.2

34 946 95.0

38 828 83.1

Distortion and lateral color (012AA045 40)

Field angle (nominal) Tangent Distortion Distortion Hf-Hc

deg

1628

34

38

0. 28675

. 53171

. 67451

. 78129

+59."xi0-5

+703. 2 +1926.7 +3608.

8

%

0. 017

. Ill .240 .388

in. -91.9X10-5 +32.6

+266. 5 +547. 5

Predicted resolving power (012AA045 40)

Field angle

Predicted resolving power

in lines/mm

High contrast Low contrast

deg

0 36 22 16 14 13

28 8 7 34 12 9

38 24 17

Figure 30a.

67
LENS NO. 0I2AA045 40
LENS NO. 0I2AA045 40
CONRADY SUMS FOR WAVE LENGTH RANGE F-C
024.\A060 23—24 in.//6, 46° field

The desigzi drawing of this lens shows that it features great economy of means in its design.

(See figures 31a-31f.) From the spot diagrams

and the figures on resolving power given here,

it appears that the quality of imagery depicted

compares favorably at 0° with somewhat more

elaborate lenses designed for similar uses. However, the oflf-axis image quality at the plane of best focus (—1.19 mm) falls off noticeably,

particularly at 16°. The inward curvature of the

field at the 10° and 16° obliquities does not indicate

that a different choice of focal plane would produce

a significant improvement of imager}-. The 0°

bundle would be upset by any sizable shift from

the plane at —1.19 mm in this case. The correction of distortion is impressive in

this lens, remaining under 0.05 percent out to

20°. The Conrady sum graphs show the presence

of both types of chromatic aberration, consisting,

at 20°, largely of overcorrected lateral color. The

positive slope of the 20° curve indicates that the

blue image height is greater than that of the red.

024AA060 23—24 in. aerial camera lens for 46° field

Radius

+6.028

-69. 14 -n.37

+5.442

Separation

-21.05

+5.333

-7.581

0.8

- .9 •

.23

-1.5 -

.23

1. 07

Glass

611572

Index

1.611

580410 i 1.580

Abbe No.

41.0

529516

611572

1.529

1.611

51.6

57.2

stop position: 0.836 in. from fourth surface. Opening: 3.44 in. at //6.

Relative entrance pupil area (024AA060 23)

Field angle No. transmitted rays Percent of 0°

deg

0 698 100.0 10 672 96.1 16 586 84.0 20 504 72.2

Resolving power (024AA060 23)

Field angle

deg

0

510

151620

22.0

Predicted resolving power in lines/mm

High contrast Low contrast

20

10

Measured resolving power in hnes/mm*

lowest resolution

radial or tangential

28. 0±2. 5 18.5±1.3

17.9±1.8

16.4±1.3

16. 2±1.6

12. 4±2.

1

•Courtesy of the U.S. Air Force Reconnaissance Laboratory. Wright Field. The mean of 30 measurement's labeled "Lowest Resolution, radial or tangential." ztProbable error.

Distortion and lateral color (024AA060 23)

Field angle (nominal) Tangent Distortion Hp-He

deg in. % in. 10 0.17633 +25.8X10-5 0. 006 +31.3X10-5

16 .28675 +136.

3

.020 +100.0

20 .36397 +400.1 .045 +213. 6

I in.

I 1 10 mm

Figure 31a.

71
LENS NO, 024AA060 23
LENS NO. 024AA060 23
CONRADY SUMS FOR WAVE LENGTH RANGE F-C
024BB060 23—24 in. //6, 9X18 in. format

For this lens (see figures 32a-32g), the best of the image planes shown in the spot diagrams

appears to be that at —0.68 mm. and the resolving

power estimates for 10, 16, and 20° are for that

focal position. However, at 0°, the best plane is definitely between the two planes at —0.68 mm

and —0.17 mm, and the size of the image at this

obliquity is particularly dependent on the image

plane position. Thus, the required adjustment was computed for each ray of the 0° spot diagram,

and the resolving power estimates at 0° are given

for a plane at —0.425 mm. The off-axis imagerydid not appear sufficiently sensitive to small

focal shifts to require such a special computation,

since estimates were needed only for the geometric mean of radial and tangential resolving

powers. For the oflF-axis obliquities, the spot

diagrams indicate a small amount of astigmatism,

which may be observed in the small dark fines forming the cores of the images. These lines are roughly vertical at the inward focal planes and

graduaUy change to become horizontal with in- creasing back focal distance. Judging from the

appearance of the spot diagrams at the —0.68 mm

plane, the image quafity appears reasonably good

out to about 16°, and then the points begin to spread out somewhat more in the 20° diagram,

although the greater symmetrv* which is apparent

in the 20° diagram might well tend to compensate

for this spreading of the points.

Illumination holds up rather well over the field in this lens. Distortion appears weU corrected

for ordinary appfications. The Conrady sum

graphs indicate an excellent correction of chromatic aberration.

024BB060 23- -24 in. //6 aerial camera lens for a 9X 18 in. format

Radius

+6.000

+32.000

Separa- Outside I Clear Hons 'diameters! aperture

3

' +24.000

4 i +4.283

5 1 +7.000

I 6 i +10.235

-10.800 -7.000

-4.603 +200.0

11 +200.0

12 -6. 156

in.

1.20 —.30-

.80 —.40-

.80 -1.40-

.80 —.30-

.80 —.20-

1.25

m.

5. 375

4.875

4. 320

4.661

3.660

5.000

4.04

3.46

Glass

DBC-9

LF-2

DBC-2

3.340

3.781

4.200

4. 681

5. 219

3. 10 DBC-2

3. 650

5. 018

5. 018

LF-1

DBC-9

Index

1. 651

1. 580

1.617

1.617

1.573

1.651

Abbe

Xo.

55.8

54.9

54.9

55.8

Stop position 0.6 in. from sixth surface. Opening: 3.094 in. at //6.

Relative entrance pupil area (024BB060 23)

Field angle N^o. transmitted rays

=

X ercent of 0

deg

0 678 100.0

10 650 95.9

16 570 84.1 20 468 69.0

Distortion and lateral color (024BB060 23)

Field angle (nominal) Tangent Distortion Distortion Hf-Hc

deg 10

16

20

0.17633

.28675 .36397

in. +164. 8X10-5

+722.

9

+1498.8

%

0.039

.105

.171

in. -20.1X10-S

—15. 0 +1.2

Resohing power (024BB060 23)

Field angle

Predicted resolving power in lines.'mm Measured resolving

in lines.imn power*

High

contrast Low

contrast R T

deg

0

5 44 24 36

36

2522

36

36

3124

36

36

28

23

10

15 24 13

16 20 7

20

25 g 5 38

17

25

19

3118

•Courtesy of the U.S. Air Force Recoimaissance Laboratory, Wright Field.

10 mm

FicrRE 32a.

75
LENS NO. 024BB060 23
LENS NO. 024BB060 23

—.68 mm .imm -.17mm

Figure 32d, e, f.
CONRADY SUMS FOR Wfl VE LENGTH RANGE F-C

MERIDIAN FANS

LENS NO. 024BB060 23

20° .00005

-.00005

16° .00005

10°

0°

5" -I.O" -0.5" 0 0.5" I.O" 1.5" V.THE y COORDINATE OF RAY IN ENTRANCE PUPIL PLANE Figure 32g.

2.0

-.00005

.00005

-.00005

.00005

.00005
024CC060 23—24 in. //6, 46° field

These spot diagrams indicate a slight inward

curvature of field at 10 and 16°. (See figures

33a-33g.) The best focus was taken to be at —0.68 mm and the resolution estimates given here were computed at that plane. (Estimates were

also made for the plane at —1.19 mm as a check,

but the small increase in resolution obtained at 10

and 16° was far outweighed by a larger loss of

resolution at 0°.) The imagery depicted at —0.68

mm looks particularly favorable out to about 16°.

It is clear that the image quality will not be quite

up to the same level closer to the edge of the field at obliquities of 20° or more.

Illumination appears a little better than average

in this case, and distortion seems well corrected

for ordinary applications. The longitudinal color

correction is good, while the lateral color is undercorrected, as shown by the Conrady sum graphs.

This indicates that the blue image height is less than that of the red at the higher obliquities.

024CC060 23—24 in. //6 aerial camera lens for a 46° field

Kadlus

Separation Outside diameterClear

aper- ture Glass Index AbbeNo.

1

2

in. +5. 099

-27. 173

in.

1.166

.059

.413

.291

.486

1.263

.923

.400

.413

.077

1. 226

20. 666

in.

5.000

in.

4. 790

4. 390 DBF671-520 1. 66770 52.0

3

4

-23. 747 +3. 818

4. 750 4.320

3. 570 BF605-434 1. 60390 43.4

5

6

+5. 364 +7. 595

3. 750 3.480

3.370 DBC589-610 1. 59020 61.0

7

8

-10.120 -6.482

3.750

3.270

3.540 DBC589-610 1. 59020 61.0

9

10

-4. 608

+27. 586

4. 750

3. 660

4.200 BF605^34 1.60390 43.4

11

12

+27. 586 -6. 144 5.0004. 260

4. 650 DBF671-520 1.66770 52.0

Stop position: 0.560 in. from sixth surface. Opening: 3.305 in. at //6.

Relative entrance pupil area (024CC060 23)

Field angle No. transmitted rays Percent of 0°

deg

0 698 100.0

10 654 93.7

16 594 85.1

20 522 74.8

Distortion and lateral color (024CC060 23)

Field angle (nominal) Tangent Distortion Distortion Hp-He

deg

1016

20

0. 17633

. 28675 .36397

in. -172.2X10-5

-787.3

-1708.9

%

-0.041 -.114 -.196

in. -62. 7X10-5

-107.

8

-145. 7

Resolving power (024CC060 23)

Predicted resolving Measured resolving power* in Field angle power in lines/mm lines/mm

High Low R T

contrast contrast

deg

0 32 21 42.0 42.0 42.0

5 41.7 37.2 39.4

10 26 16 26.2 26.2 26.2

15 25.2 22.4 23.8

16 21 13 20 15 8 18.5 18.5 18.5

•Courtesy of the U.S. Air Force Reconnaissance Laboratory, Wright Field.

I in.

100 mm

Figure 33a.

79
LENS NO. 024CC060 23 LENS NO. 024CC060 23
LENS NO. 024CC060 23 LENS NO. 024CC060 23
LENS NO 024CC060 23

.1 mm

Figure 33f.

.17 mm

82
CONRADY SUMS FOR WAVE LENGTH RANGE F-C

0°

MERIDIAN FANS LENS NO. 024CC060-23

.00010

.00005

— .00005

.00010

.00005"

-.00005

.00005

.00005

.00005

•2.0' -1.5' -I.O' -0.5 0 0.5 1.0 1.5 V.THE y COORDINATE OF RAY IN ENTRANCE PUPIL PLANE

Figure 33g.

2.0

83
ALPHA—36 in. //3.7, 9X18 in. format

This lens is characterized by a remarkably flat

field. (See figures 34a-34c.) Both the appear- ance of the spot diagrams and the figures on re- solving power indicate that the small and solid

image core observed at 0° is to a large extent

retained over very nearly the entire field. The

increased flare observable toward the edge of the

field scarcely affects the resolution, but may be

expected to reduce the performance somewhat in

terms of contrast. The figures on predicted

resolving power are given for the best of the three

focal planes depicted here, that is, at —0.23 mm.

The position of best overall focus can be estimated

a little more accurately from the results depicted.

Thus, the imagery may be judged to be slightly

better for all angles except 15° at about —0.18 mm.

Illumination, as judged by estimates of the rela- tive number of rays transmitted, was found to be

at a satisfactory level over the entire field. Distortion rose slowly with increasing field angle to a maximum value of 0.18 percent at 15°. ALPHA 36 in. //3.7 aerial camera lens for a 9X18 in. format

Radius Separation Outside diameterGlass Index Abbe No.

1

2

in. +13. 646

+32. 889

in.

1.529

. 146

in.

12.5 SK-4 1. 61272 68.6

3

4

+9.395

+6. 742 1.274

.437

11.5 r-4 1. 61659 36.6

5

6

+6. 609

+6. 483 2.507 —3. 277

10.125 SK-4 1. 61272 58.6

7

8

9

+291. 26 +6.354

.437

1.529 —5. 643

7.75

7.25

F-4 SK-41. 61659

1. 61272

36.6

58.6

10

11

-6. 742

-10. 104

3. 732

.146

10. 75 F-4 1.61659 36.6

12

13

-91. 02

-15. 830

1.384 —20. 711.5 sk:-4 1.61272 58.6

stop position; 0.729 in. from nintli surface. Opening: 6.136 in. at //3.7.

Resolving power—ALPHA

Field

angle

deg

0

5

710

1112.6

15

Predicted resolving power*

34

41

41

41

34

19

19

21

Lowest

measured

resolving power**

3030

25

25

20

lOOmm

Figure 34a.

ALPHA

— 0.23mnn O.omm

Figure 34b.

+ o.23mm

•Predicted by measuring dimensions of spot diagrams. •Courtesy of ttie U.S. Air Force Reconnaissance Laboratory, Wright Field.

84
ALPHA

2 JXIQ-** 0 I

Figure 34c. Alpha—Energy distribution in radial and tangential lines.

Coordinates are in units of focal length. Curves shown are for the Gaussian focal plane.
BETA—36 in.//4, 9X18 in. format Resolving power—BETA

The spot diagrams for this lens (see figures

35a-35c) indicate that the image quahty of the

15° bundle definitely will be less favorable than

those obtained at 0, 7, and 11°. The chief reason

for this effect is a pronounced curvature of field that places the best focus for only the 15° bundle

on the plane located at +0.46 mm. Of the three

focal planes depicted here, the one at —0.46 mm

shows the best overall imagery and was used to obtain the figures on predicted resolving power.

The imagery at this plane appears good at the

lower obliquities, despite the loss in resolving

power toward the edge of the field. By inspecting

the complete set of spot diagrams, it is possible

to judge, a little more accurately than it was known prior to these results, where the best focal

plane is located. In this case, it appears that for a plane at about —0.37 mm the resolving power

at 0° would be somewhat higher than the estimate

given for the plane at —0.46 mm. At the same

time, it appears that the off-axis imagery would be

only slightly affected by such a shift of focal

position.

Illumination appears to be adequate in this lens, as judged by estimates of the relative number of rays transmitted at the different obliquities. Distortion was negative at all field angles and rose slowly in magnitude to a value of —0.42 percent

at 15°. This correction is considered good for all purposes except precision mapping. Both lateral and longitudinal color were found to be quite well

corrected in this lens, which was designed for a wavelength range from 6563 to 9000 A. However,

this evaluation of the chromatic aberration is subject to a small uncertainty. The refractive index

of SK-4 at 9000 k had to be estimated, and the exact value is not known.

BETA—36 in. //4 aerial camera lens for a 9X18 inch format

Radii Separations Outside

diameter

Clear

apertures Glass Index*

1

2

in. 20.00

720.00

in.

1. 152

.036

in.

9.2

in. 9.0

8. 87 SK4 1.60694

3

4

11.901 -360.0

2. 160

. 036

8.8

8. 65

8. 05 SK4 1. 60694

5

6

00

13. 433

.676

1.969

8.5

8. 05

7.45 LLF-1 1.54064

7

8

-43. 552

11. 327

.684

2.700

7, 05

6. 85

6. 65 SF12 1. 63728

9

10

-11.753

36.00

.576

. 072

7.37

6. 75

7.1 LLF-1 1.54064

11

12

36.00

-12. 945

2. 160

.540

7.7

7.1

7,5 SK^ 1.60694

13

14

33. 256

-27. 744

1.080 8.5

8.3

8.3 BK-7 1. 51098

Field angle Predicted resolving power* Measured resolving power** R T R T

deg

0 25 25 39 35

5 28

7 14 10

8 24 24

11 19 6

11.5 21 21 13.5 26 25

15 3 11 15.5 6 12

* Predicted by measuring dimensions of spot diagrams. •*Courtesy U.S. Air Force Reconnaissance Laboratory. n

\1 [1

I in.

100 mm

Figure 35a. BETA

15°

7°

0°

- 0.46mm O.omm

FiGUBE 35b.

+ 0.46mm

86
BETA

ENERGY DISTRIBUTION IN RADIAL AND TANGENTIAL

LINES. COORDINATES ARE

IN UNITS OF FOCAL LENGTH

0 I 2X10-" 0 2

Figure 35c. Beta—Energy distribution in radial and tangential lines.

Coordinates are in units of focal length. Curves shown are for the Gaussian focal plane.
CO-3—48 in.//4.5, 9X18 in. format

This lens (see figures 36a-36d) was designed to have a maximum half-field coverage of 11.9°. The analysis was extended out to 15° to include

the same angles that were used in analyzing

another similar 48 in. lens. For this particular

lens, however, the imagery at the edge of the field will be much closer to that depicted at 11° than

at 15°. At the best focal plane, near —0.55 mm,

the spot diagrams show dense cores at 0 and 11°

with the core tending to spread over a larger area

for intermediate angles near 7°. The core at 0°

appears dense because only a small percentage of

the total rays traced are involved in forming the

thin flare observed here. Illumination over the field for this lens was

found to be sufficient. Distortion is positive over

the entire field and rises to a value of 1.75 percent

at 11.9°. This lens was corrected for color over

the wavelength range from 6563 to 9000 A. The

correction obtained was found to be very good,

particularly with respect to lateral color. This

evaluation of the chromatic correction is subject

to a small imcertainty, however. The refractive

index of SK-4 at 9000 A had to be estimated, and

the exact value is not known.

CO-3—-48 in. //4.5 I. R. night lens for a 9X 18 in. format

Resolving power—CO-3

1

2

Radius Separation Outside

diameter

Clear aperture

Glass Index' Abbe

No.

in. +17.910

+842. 11

in.

1.440

. 048—

in.

10. 95

in. 10.70

10.60 BK-7 1. 51098 64.0

3

4

+12. 655

-32. 086

2. 160

. 048—

10. 40

10. 20

9.80 SK-4 1. 60594 58.6

5

6

-32. 330

+21. 838

.672 —2. 784—

10. 00

9. 80

9. 00 SF-12 1. 63728 33.8

7

8

+41. 631 +8. 4498

.672 —2. 784—7.70

7.60

7.10 LF-5 1. 57260 40.8

9

10

-16. 128 -51.447

.672 —1. 968—7.20

6. 85

7. 00 SF-12 1. 63728 33.8

11

12

+82.759

-20.961

1.440 —31. 108.60

8.00

8.40 SF-12 1. 63728 33.8

Stop position: 5.6 mm (0.220 in.) behind seventh surface. Opening: 187.2 mm (7.370 in.) at //4.5. *Index=iV^'.

Field angle

Predicted resolving power in lines/mm R T

deg

0 18 18

7 10 10

11 18 16

15 6 4

n

H

1 in.

' 100 mm'

Figure 36a.

88


.1 mm

Figure 36d.

91
BA-4—48 in.//4.5, 18X18 in. format

For this lens (see figures 37a-37e), the plane of

best focus is farther from the lens than the Gaussian focus and is close to the plane depicted at +0.36 mm. The central cores of the spot diagrams appear to have a stronger than average

concentration of points, with the exception of the

diagram at 15°, where a larger percentage of the

light is spread out to form flare. However, the

total areas covered by these diagrams remain

quite small, which should help in maintaining the

resolution of low-contrast objects. The lightgathering ability of this lens was indicated at the

time it was analyzed by arrows marking the

vignetting on graphs of meridian and sagittal fans

of rays. These arrows indicated that the entrance

pupil at 15° is of about the same width and roughly

half the height of that at 0°. This gradual nar- rowing to a cat's-eye shape is quite typical, and

the implied loss of illumination at the edge of the

field does not appear to be excessive.

Distortion is held to within 0.07 percent over

the entire field and is negative at 15°. This lens was designed to operate over an unusual wavelength range: 6563 to 9000 A. At the latter wavelength, the refractive index of SK-4 had to be estimated and the exact value is not known.

Assuming that this estimate is substantially correct, the analysis indicated good correction of

lateral color and a definite residual of undercorrected longitudinal color. This residual, if actually present, appears to be correctable through

a minor modification, however.

BA-4r—48 in. //4.5 I.R. night lens for a 18X18 in. format

Radius

in. +17. 385

+40. 442

+11. 737 +5. 799

+8. 464

-9. 301 -6.345

-13. 827

+410. 78

-30. 095

Separation

m.

1. 679

-- . 148-

1. 232

3. 204

-10. 845—

2. 958

1.371 —.148—

1.725

-30. 395—

Outside

diameter

in.

12. 400

11. 500

9. 900

9. 650

11. 400

12. 400

Clear

aperture

in.

12. 000

11. 675

11.200

9. 801

8. 732

8. 405

9. 552

11. 043

Glass

SK-4

F-15 SK-16

SK-16

F-15

11. 692

12. 000 F-15

Index*

1. 61272

1. 60565

1. 62041

1. 62041

1. 60565

1. 60565

Abbe

No.

58.6

37.9

60.3

60.3

37.9

37.9

Stop position: 6.774 in. from fifth surface. Opening 7.100 in. at //4.5. 'Nd given In table. Spot diagram calculations used Na'

Resolving power—BA-4

Field angle

(leg0

.5710

11

12.5 15

Predicted resolving power

in lines/mm*

25

25

25

17

25

20

25

25

Measured resolving power

in lines/mm"

3137

22

21

3533

•Using dimensions of spot diagrams. **Courtesy of U.S. Air Force Reconnaissanse Laboratory, Wright Field.

HI in.

I lOOmm I

Figure 37a.

92
BA-4 f/4.5 f'=48

— .72 mm

.1 mm

Figure 37b.
m

.1 mm

Figure 37c.

— .36 mm

94
BA - 4 f /4.5 f

' = 48"

95
BA-4 f/4.5 f'- 48 "

15°

7°

0°

+ .36 mm

.1 mm

Figure 37e.

96

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