NBS SPECIAL PUBLICATION 374

Method for Determining

the Resolving Power of

Photographic Lenses
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards' was established by an act of Congress March 3, 1901. The Bureau's overall goal is to strengthen and advance the Nation's science and technology

and facilitate their effective application for public benefit. To this end, the Bureau conducts

research and provides: (1) a basis for the Nation's physical measurement system, (2) scientific and technological services for industry and government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety. The Bureau consists of the Institute for Basic Standards, the Institute for Materials Research, the Institute for Applied Technology,

the Institute for Computer Sciences and Technology, and the Office for Information Programs.

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Method for Determining

the Resolving Power of

Photographic Lenses

National Bureau m Sttfj&j

MAY 6 1974 Francis E. Washer and Irvine C. Gardner

QC 100

Appendix added by C. E. Kuyatt

1113

Institute for Basic Standards

National Bureau of Standards

Washington, D.C. 20234

U.S. DEPARTMENT OF COMMERCE, Frederick B. Dent, Secretary

NATIONAL BUREAU OF STANDARDS, Richard W. Roberts, Director

Issued June 1973
Library of Congress Catalog Card Number: 72-600331

National Bureau of Standards Special Publication 374

Nat. Bur. Stand. (U.S.), Spec. Publ. 374, 32 pages (June 1973) CODEN: XNBSAV

(Supersedes NBS Circular 533, issued May 1953)

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402 (Order by SD Catalog No. C13.10:374). Price: 83, domestic postpaid; $2.75, GPO Bookstore.
Foreword

This publication is being reissued to meet the need of both amateur

and professional photographers for a simple method to determine the relative

performance of photographic lenses. It was orginally published in 1953 to provide a method of testing lens performance with equipment already on hand

or readily available and for interpreting the test results. This edition includes the information contained in the previous publication, NBS Circular 553, together with an Appendix describing the NBS

Microcopy Resolution Test Chart. Although more modern methods of lens

testing are now available, they are not easily used by the amateur photographer and therefore have not been included in this edition.

Richard W. Roberts, Director

> (Editorial Note: On page iii following the frontispiece of

>NBS-SP 374,

>there is a typographical error: Circular 533 is erroneously

>identified

>as Circular 553)

.
Contents

Page

Foreword iii

1. Introduction 1

2. Choice of criterion for judging a lens 2

3. Speed of a lens as a criterion 2

4. Quality of definition as a criterion 3

5. Significance of a resolving-power test 4

6. Charts for testing resolving power 4

7. NBS resolution test chart of 1952 5

7.1. Description 5

7.2. Metrical characteristics 6

7.3. Range of chart at the standard distance 7

7.4. Methods of extending chart range 7

(a) Change of lens to target distance 8

(b) Change of chart size by photographic means 8

7.5. Method of changing length of line patterns 10

S. Details of camera test 10

8.1. Arrangement of charts 10

8.2. Camera support 12

8.3. Use of multiple rows of charts 13

(a) Determination of focusing error 14

8.4. Illumination of charts 16

5.5. Methods of focusing 16

(a) Focusing by means of coupled range finder 16

(b) Focusing by means of focusing back 17

(c) Focusing by means of focusing scale 17

8.6. Photographic technique 17

8.7. Examination of negative 18

9. Interpretation of results , 18

9.1. Maximum resolving power of an ideal lens 18

9.2. Depth of focus for an ideal lens 19

9.3. Effect of field curvature 20

9.4. Experimental results for actual lenses 22

(a) Experimental results with high-contrast chart 22

(b) Comparative results on axis for high- and low-contrast

charts 24

10. Additional uses of test chart 25

10.1. Test for goggles and sunglasses 25

(a) Prismatic power 25

(b) Refractive power of goggles - 26

(c) Definition test 26

10.2. Resolution test for telescopes and binoculars 26

11. References 27

Appendix—NBS Microcopy Resolution Test Charts No. 1010a 28

iv
Method for Determining the Resolving Power

of Photographic Lenses 1

Francis E. Washer* and Irvine C. Gardner**

Appendix added by C. E. Kuyatt

This publication supersedes NBS Circular 533, issued May 20, 1953. It contains the

original data and a new appendix describing the NBS Microcopy Resolution Test Charts No. 1010a. It provides the photographer with two sets of charts by which the resolving

power of a photographic lens may be numericaUy measured with respect to a definite scale

of values. A detailed description is given of the jDrocedure and technique to be followed in order that comparable values may be obtained by different observers. The test provides an objective method of testing a photographic lens. The six charts of one set are printed in black ink on a white background to form a high-contrast chart. The six charts of the other

set are printed with gray ink on a gray background to form a low-contrast chart. Additional

uses of these charts are also described. These uses include the testing of goggle lenses for

definition and prismatic power and the testing of telescopes and binoculars for definition. Key words: Photographic lenses; resolution test charts; resolving power.

1. Introduction

In 1940, National Bureau of Standards Circular

| 428 [l],

2 "A test of lens resolution for the pho-

; tographer," was published. This Circular, in addition to giving detailed instructions for performing a lens resolution test, also contained 12

carefully made test charts for use in the test. These test charts were made by the Bureau of

Engraving and Printing in accordance with detailed specifications relating to width of lines and

steps between patterns. Use of the process

identical with that employed in printing postage

stamps insured exact duplications of the test patterns. This test chart has been of immense value

during the past 12 years to large numbers of people engaged in work that required an accurately made test pattern. It has been helpful

also in that it provided workers in various parts

of the country with a test chart common to all and made easier comparison of results obtained

in widely separated laboratories.

The Circular with its accompanying test chart,

together with a companion publication [2] consisting of test charts only, had been prepared

initially with the intent of being a useful tool for

the amateur photographer, in that it provided him

with a device with which he could test and rate

the lenses on his own cameras. Judging from the

extensive sales of the Circular, it has performed

its intended function. In addition, however, it has found use in the testing of a variety of optical

equipment, such as telescopes, binoculars, goggle

lenses, and sunglass lenses. During the past 12 years, there have been considerable gains in the science of applied optics,

particularly in the field of lens resolution, and it therefore seemed desirable to prepare a revision of

Circular 428 and to include in this revision some

•Retired. '•Deceased.

1 The work described in this paper was supported in part by the United

Mates Air Force and the United States Army Signal Corps.

Figures in brackets indicate the literature references at the end of this

aspects of the more recent gains in knowledge.

Some of the principal changes are in the nature of

the test chart itself. It has been found that a

multiplicity of lines in a given pattern makes it needlessly difficult to decide whether or not a

given pattern is resolved. This is especially important in visual determinations where a common

criterion of resolution is that the line count shall be the same for a given pattern in the image as in

the object. The charts, presented here, have only

three lines per pattern in all patterns, thus simplifying the process of checking line count in the

image against line count in the object. In order

to achieve greater precision in the rating of lenses,

the ratio of change of size between patterns has

been reduced from the \/2 to the \/2.

The range of the present charts is from 12 to 80 lines/mm as contrasted with 3.5 to 56 lines/mm on the old chart. While this represents an in- crease at the higher end, it eliminates the directreading range from 3.5 to 10. This, however, has

been compensated by a procedure through which

values of resolving power for the range 3.6 to 14

lines/mm can be approximated by consideration

of entire groups. While the chart is primarily

intended for use in the visual analysis of lens

performance, the length of the target lines and

their positions with respect to one another have

been so chosen that the imagery can be studied

with commercially available types of recording

microdensitometers. The charts in this new Circular are provided in two contrasts. The highcontrast charts have black lines on a white background, and the low-contrast charts have gray

lines on a gray background.

All the information on lens performance that

could be obtained by the user with the charts

contained in NBS Circular 428 can also be obtained with the charts contained in the present

Circular, so that these charts can be used in their

stead without difficulty. In addition, it is believed that the new features in these charts will make them still more useful than the earlier charts

contained in Circular 428.
2. Choice of Criterion for Judging a

Lens

The question of how to rate the performance of a lens is necessarily complex, depending as it does

upon the use of the lens. The complexity of the

problem can be somewhat reduced by confining

the scope of this article to the questions that

confront the user who is interested primarily in

pictorial quality and who is not concerned with

using the resultant negatives for precision measurements such as are required in cartography and

photolithography. It is believed that most camera users, outside the strictly professional field, are concerned with such matters as lens speed and

quality of definition, with the latter being of prime

concern.

3. Speed of a Lens as a Criterion

The speed of a lens, as determined by its maximum relative aperture, is heavily emphasized in

most discussions pertaining to lens performance.

It also receives tbe most emphasis in sales litera- ture. This emphasis arises from a variety of causes. Perhaps this s chiefly because the speed

of a lens is one of the few characteristics for which

a definite numerical system of measurement has

been fairly well established. Among seriously

minded photographers the speed of a lens is of

prime importance in that the greater light gathering power of a high-speed lens permits good pic- tures to be obtained under adverse lighting conditions.

The expression "speed" as applied to a lens is essentially a colloquialism which has been to some

extent justified by long usage. It is not a speed

in the accepted sense of expressing a rate of

change with time, but is rather a measure of the

fight gathering ability of a lens. Most photographers are at times constrained to use as short an exposure time as possible, either to stop motion

in the subject or to avoid blurring arising from camera movement, and it is obvious that a lens

having greater light gathering ability permits

the use of a shorter exposure time than that re- quired for a lens having lesser light-gathering

ability. Consequently, it is fairly natural to

refer to this property as "speed." Actually, the

light-gathering ability of a lens is determined by

the amount of light passing through the lens that

reaches a given area of the image plane. This

quantity is measured by the light flux contained

in a cone, the tip of which is in the image plane and

the base of which is the clear opening of the lens.

If, for two lenses having the same cone height, one has twice the base area, then twice the amount

of light reaches the image plane and the one lens

has twice the light-gathering ability. For a

circular lens opening, it is clear that the ratio

of the 2 diameters of the cone bases in the above

illustration is \/2, or 1.4. The maximum aperture

of a lens is customarily expressed in terms of the

focal length, the expression //4.5 signifying tl the diameter of the effective aperture is eqjl to the equivalent focal length divided by 41 (In the above, simple illustration, the cone heigJ

is the focal length, and the diameter of tbe cCt base is the effective aperture.) The aperture o|

lens, expressed in terms of focal length in t$

manner, is referred to as the relative aperMi

The number in the denominator is sometir^'i referred to as the ./-number. On changing {I

stop openings of a given lens, the light fti reaching the image plane is inversely proportion!

to the square of the /-number. Consequent^

if the stop is set at //4 and the exposure time)] Koo second, then it will be necessary to tl double this exposure time, or %0 second, wlifi the lens is set at f/5.6. It must be remembeii

that the /-numbers marked on a lens are js] termined for large object distances.

It should be noted that the maximum relatfi aperture of a lens does not completely determrt

the effective speed. For lenses of the same ml

imum relative aperture, and consequently of tj'i same nominal speed, variations of the effectrl speed may arise from differences in the numberglass-air surfaces. The Tessar type of lens hi 3 separated components and consequently 3 pa;: of glass-air surface. A modern //2 lens may ha?; 5 separated components with 5 pahs of glass-l surfaces. Each pah of surfaces entails a lossi, from 8 to 10 percent of the light incident up'' the surface. If, therefore, the Tessar lens all the //2 lens are set to the same stop opening, tj Tessar lens will transmit approximately 20 p< cent more light than the//2 lens. This differerj; is not serious when the camera is used with I emulsion having considerable latitude, althouji

by virture of multiple reflections some of tt lost light may eventually reach the emulsion f nonimage forming light and contribute to the ov^

all haze, thus reducing the contrast of the picturij

In extreme cases, these multiple reflections m^

produce ghosts.

In recent years, the use of low-reflection fill: on the glass-air surfaces has resulted in markj

reduction of the light losses. When the glas

ah surfaces have been so treated, the Id per pah of surfaces may fall as low as from 3 to; percent of the light. Consequently, the diff^ ences between treated lenses are not so pr

nounced. However, good lenses are in use th; either from choice were not coated at the time

manufacture or were made prior to the develo; ment of the low-reflection process. Most coat(

lenses have transmittances in excess of 80 percei

and may run as high as 90 percent. Transmi

tances for uncoated lenses vary from 60 to i percent, depending upon the number of pahs < glass-air surfaces. It is therefore obvious thi speed differences between lenses of same stc opening may be as high as one-third stop openii

from the above causes alone. Attempts hai

been made in recent years to alleviate this situatic

2
i by calibrating lenses in terms of the transmittance

[of an ideal lens that would transmit 100 percent

iof the light [3, 4]. Such lenses are marked in

|T-stops instead of the more familiar /-stops.

This system has the great advantage that the

]speed ratings of all types of lenses become directly

'comparable. It is unlikely that the transmitytances that have been carefuUy calibrated ac- cording to the T-stop system will show variations

p excess of ±10 percent, regardless of type of

[lens, coated or uncoated.

I. This T-stop system does have two minor disadvantages. The first is that the T-numbers are always larger than the /-numbers. A lens having

nan /-number of 2 may have a T-number of 2.2. (This may give rise to some misunderstandings if lone happens to confuse the/-numberand T-number

Isystem of marking. This will prove to be a minor

handicap, as more and more people become con- versant with the T-number system. A second

[nominal disadvantage is the fact that the familiar

tables containing depth of field data would be subject to some error as the computations of these

r tables are based on the geometric /-number. If

(the geometric /-number were to be wholly superseded by the T-number, some error would result

In estimating depth of field if the T-number were

riised without appropriate corrections. This error

|1 too small to be important.

Lenses of different types or makes may show

Important differences in performance arising from

differences in the vignetting. For a given setting

I of the diaphragm the effective exposure is necessarily less at the corners of a photographic plate

,than at the center. However, in order to produce

J compact lens suitable for a hand camera of re- duced size, or in order to lessen the cost of production, the outer components of the lens, in some

[instances, are unduly reduced in diameter. When

<this is done, the speed of the lens, so far as the

center of the plate is concerned, is not reduced, but

! there is excessive vignetting, and the exposure re- ceived by the corners of the plate is much less than

i for a lens having the same normal speed but with

jthe outer components of a more generous diameter.

With black-and-white film the latitude of the emulsion in most cases, masks the effect of excessive

vignetting, and the performance of the lens is -reasonably satisfactory. With films of limited

latitude, such as color films, the effect of excessive

vignetting is more pronounced and may be suffi- cient to make the resulting pictures quite unsatisfactory. This excessive vignetting, when present,

lis effective only for the larger diaphragm openings.

As the lens is stopped down, the illumination

[Over the field becomes more uniform.

' In general, while speed of a lens is an important

'criterion in its selection, it is not one that can be

readily checked by the purchaser. However, the

tepeed markings are usually sufficiently reliable

fhat the prospective user need not be overly concerned. The principal point is to check for ex- cessive vignetting, which can be done by photographing a uniformly lighted area with the diaphragm opened wide and noting whether or not

there is marked variation in the density of the

negative from center to corner. When the change

in density from center to corner is as great as 0.6,

it is probable that the pictures will be noticeably

inferior to those where the change in density from

center to corner is less than 0.3.

4. Quality of Definition as a Criterion

For most purposes it appears that the production of a sharp, crisp image is the indispensable

attribute of a lens. The present prevalent practice of making enlargements of several diameters

from the original negative has created a general

demand for lenses giving sharper and better defined

images than were considered satisfactory some

years ago. A great variety of photographic lenses are now available, and lenses identical in focal

length and speed but of different makes and qualities sell at widely different prices. When such a

series of lenses is tested, the most marked differ- ence in performance is found to lie in the varying

sharpness of the image produced, and this one

characteristic is probably the best single criterion

for determining the quality of a lens. In advertising literature the lens makers have

not yet adopted a method of specifying the quality

of their lenses that is helpful to the purchaser.

This is not surprising, because a precise specification of lens quality is attended with many diffi- culties. It is common practice to describe a lens

as being free or sensibly free from the different

aberrations, such as chromatic and spherical aberration, coma, astigmatism, curvature, and distortion. No lens can be entirely free from these

aberrations. Furthermore, in any lens that covers an extended field of view, some of the aberrations are always present to such an extent that

they are sensible at some part of the field, either on a contact print or on an enlargement of four or

five diameters. Even if the engineering procedure

of giving graphs showing the magnitudes of the

aberrations at all points of the field were adopted,

it would still be difficult to formulate an opinion

of the relative quality of two lenses having different

aberrations.

Lenses are sometimes characterized by a state- ment that the diameter of the circle of confusion is one one-hundredth or one two-hundred-and-fiftieth

of an inch. This method of description appears

to be a quantitative one, but it does not give complete information. A measurement of the circle of confusion offers peculiar difficulties. If the

measurement is made on the photographic image

of a star, real or artificial, the diameter of the

recorded image is so largely a function of the

brightness of the star and the duration of the ex- posure that it tells little about the performance of

the lens. In fact, the astronomer customarily measures the diameter of a star image in order to determine the brightness of the star. Definite

3
statements regarding the method by which the

diameter of the circle of confusion is measured are not generally made, but it appears probable that

the values listed are commonly based upon the

results of ray tracing by mathematical computations that are required for the development of the

design of the lens. If this is the case, the diameter

of the circle of confusion is a test of the excellence

of the lens design and does not fully indicate the

performance of the finished lens. It will be readily appreciated that a good design

is a prerequisite for the construction of a good lens,

but it will also be appreciated that good workmanship and careful control during the making of the

lens are equally important. A method of specifying a lens that does not give weight to the quality

of workmanship is not a suitable criterion of the

excellence of a lens. In connection with the testing of airplane camera

lenses over a period of years, the National Bureau

of Standards has had the opportunity of studying

the suitability of a measurement of the resolving

power of a lens as a method of specifying its quality

of definition. An elaborate testing device [5, 6, 7] for measuring the resolving power has been built,

and all airplane camera lenses that are to be used on Government mapping projects must be tested

upon this instrument. Because it does not appear

practicable for the National Bureau of Standards

to undertake the general testing of hand cameras

for the public or to publish comparative ratings of the different lenses, a modified method of making a resolving-power test has been developed. This

simplified test can be made by means of apparatus

that the camera user can readily improvise, and

can be conducted by one skilled in photographic

technique to the extent that is required for the

successful operation of a miniature camera.

5. Significance of a Resolving-Pcwer

Test

The test comprises a measure of the resolving

power of the lens and camera combination, a characteristic that determines the sharpness of the

image and the degree to which it can be enlarged.

If one attempts to photograph a pattern of parallel

lines, it will be found that the lines, if too close together, will photograph as a gray patch, and the

individual lines cannot be distinguished. If, however, the lines in the object are so far apart that

the lens records them as distinct lines, the lens is said, in optical parlance, to resolve the lines. We can, therefore, give considerable information

regarding the quality of definition of a lens by a statement regarding the finest pattern of lines that it resolves. A given pattern of lines will appear finer and be more difficult to resolve as it is placed more distant from the lens. Consequently,

if the distance between just-resolvable lines on the

test chart is measured, this tells nothing of the per- formance of the lens unless the distance from lens to chart is also measured. This introduces a cer- tain amount of complication, which could be less4

ened somewhat if the separations of the lines were

given in angular instead of linear measure.

Actually, however, one is usually concerned, notj

with the fineness of detail in the object but with'

the fineness of detail upon the negative or the fin-; ished print. A large picture, or a small picture,)

when examined for quality of definition is scruti-|

nized from the distance of best seeing or perhaps,

examined with a hand lens, and it is commonly j desired that the pictures be equally sharp, regardless of size. From an artistic standpoint, there: may be much to be said against this criterion, but'

nevertheless the user of a lens commonly expects

the negative to be of approximately the same

sharpness, regardless of its size or the focal length

of the lens. In view of this, it is desirable to base

the determination of resolving power upon a> measurement of the image. In accordance with!

the established practice, the number of lines per|

millimeter, measured on the negative, of the finestl pattern resolved will be used as a measure of thei resolving power. As an illustration, if the resolving power is given as 40, lines spaced 40 to the

millimeter (the distance between the centers of the. adjacent lines in such a case, is one-thousandth of[ an inch, or 25 microns) upon the negative are^ distinguishable as separate and distinct lines. It should be mentioned that the resolution test,|

when conducted as described, is dependent not;, only upon the lens but also upon the camera con-]

struction and the characteristics of the photo-^

graphic film. A lens cannot be expected to pro-|

duce negatives of the first quality unless it isjj mounted in a camera that holds the film, free from^

curvature, in a plane normal to the axis of the lensj

and in perfect focus. Furthermore, consistently

good negatives cannot be produced unless thet camera movements are sufficiently free from lost|

motion to permit a given adjustment to be repeated!

with certainty. Even with an excellent lens and[

camera, the resolution may be limited by the type'

of film that is used. With the better lenses, thef limiting resolution in the center of the field is 1 usually determined by the film rather than by the

lens. Consequently, when testing a lens, the use

of the finest grain film that is commercially avail-f able is recommended in order that the potential'

resolution of the lens may be more closely approximated. Care should be taken to insure that the- spectral range of sensitivity of the film used fori test be approximately the same as that of the film' that is normally used in the camera. If a fine-'1 grain orthochromatic emulsion is used, the results' may be affected by the difference in spectral)1 sensitivity and consequently should not be usedi

directly as a basis for judging probable perform-! ance of the lens when used with a panchromatic*

emulsion.

6. Charts for Testing Resolving Power;

The ability of a lens to produce clear-cut images5 of an object containing fine details has long been\

accepted as a principal factor in judging lens per-l

formance. This property is closely associated;

I
with the resolving power of the lens, and throughout the years considerable thought has been

devoted to the design of various types of test charts. In general, the various types of charts

provide the user with an array of patterns arranged

in a series of diminishing size in accordance with some predetermined ratio. The chart developed

at this Bureau in the early 1930's and used as the

basis of designing the test chart that was contained

in Circular 428 was of this type.

This chart is shown in figure 1 . It consists of a

series of line patterns of such sizes that when

photographed at a 25 X reduction, the numbers

identifying the pattern give the resolving power of the lens-emulsion combination directly in lines per

millimeter. The ratio of the line spacings in the

patterns between adjacent members in the series

is approximately 1.4 (= v

/2). This chart has

proved quite successful throughout its years of

service. However, improvements have been suggested that would extend its usefulness.

Several lines of approach to the measurement of

resolving power have developed in recent years, and it is worthwhile to recount a few of the new

concepts and recommendations that have come

into being as a result. The phenomenon of false resolving power [6, 8], as it affects the study of lens

performance, has given rise to the idea that fewer

lines in a given pattern would make its detection

easier, since in one of its manifestations the line count in the image differs from that in the object

for a given pattern. This has led to the development of the three-line pattern [9] currently used by

the U. S. Air Force. Further simplification was

accomplished by the British group [10], where the

2-line, or Cobb, chart was adopted.

The belief that the interval between adjacent

members of the series of test patterns should be

smaller has led to the use of such ratios of line spacings as 1.26 {=y/2) and 1.12 (=^2). In their

resolution charts, the U. S. Air Force used the \/2

ratio initially and is now using the y/2 ratio. The

\/2 ratio is used in the Cobb chart preferred by the

British group. A completely different type of test pattern was developed in Canada [11] consisting of a series of annular rings which purports to give

greater weight to "edge effects." The effect of contrast of the object has formed

the subject of numerous investigations [9, 10, 11,

12, 13], and several of the test charts are designed

to be used at relatively low contrast. It is undeniably true that contrast plays an important part in

the evaluating of lens performance, and numerous

investigations are now in progress that deal with

this subject.

In the 3-line and 2-line targets mentioned, the

ratio of line length to line width is held constant

from pattern to pattern on the assumption that

allowing this ratio to vary introduces an element of

uncertainty into the determinations.

It is clear from the foregoing cursory discussion

that a great deal of work has been done in recent

years on the subject of resolving power, and further

= 11

NATIONAL BUREAU i OF STANDARDS

TEST CHART | 25 X

Figure 1. High-contrast resolution test chart formerly used.

This chart formed part of NBS Circular 428. The ratio of the line spacings

in successive patterns of this chart is equal to V2. When the chart is photo- graphed at the standard distance of 26/, the values of resolving power that can be measured with this chart range from 3.5 to 56 lines/mm. new developments and ideas follow so fast upon

one another that it is impossible at this time to

state unequivocally just what type of test chart is the best. Despite these circumstances, it was deemed advisable to prepare a new test chart that

incorporated at least some of the advances in

knowledge and experience gained in the past 12

years.

7. NBS Resolution Test Chart of 1952

7.1. Description

In the design of this test chart, several features

not present in the older chart are included. All

patterns have the same line count, namely, three

to each group. Two series of test patterns are

included, the spacings in the line patterns of a given group differing from those of the adjacent

group so that their ratio is approximately \/2.

However, in order to have the advantage of smaller

intervals between steps, the spacings in the initial patterns of one series differ, correspondingly by

the -\/2 from those of the other series. Consequently, considered as a whole, the range of values

provided by this chart proceed by the fourth root

of 2. Perhaps the most striking feature of the new

chart is the relatively great length of the lines

forming the patterns. This has been done for two

reasons. First, the ratio of length to width of line

is sufficiently great that the visual resolving power

as read will not be subject to variations arising

from end effects and the images will continue to look like lines down to the limit of resolution.

Second, many laboratories are now equipped with

microdensitometers, and it is desirable to have the

4S7-121—73 2 5
RESOLUTION TEST CHART 1952 Figure 2. High-contrast resolution test chart. The ratio of the lino spacings in adjacent groups is equal to V2; however,

the ratio of the line spacings of corresponding opposite patterns is Conse- quently when this chart is photographed at the standard distance of 26/, the

values of resolving power that can be measured range from 12 to 80 lines/mm im geometric series proceeding by -^2.

lines sufficiently long to permit the negative images

at 25 X reduction to be scanned in such instruments without the necessity of so far reducing the

length of the scanning slit that the loss of sensitivity of the instrument and effects of granularity

of the emulsion impair the validity of measurement. In addition, the line patterns are so ar- ranged in the chart that the negative images of

all patterns can be scanned with only two settings

of the test negative in the recording microdensitometer.

If, however, shorter lines are preferred, it is possible to obtain them by masking the lines on the

present chart. The standard Air Force chart, for

example, is of high contrast and consists of 3 lines and 2 spaces, the lines being 5 times as long as wide, thus forming a square pattern. Several

such patterns for each frequency can be formed by

blocking, or masking, out portions of the lines on

the high-contrast chart.

In general, the resolving-power test with the

black-and-white chart is adequate for determining

the probable performance of a lens. However,

it is well known that a single measure of resolving

power at any one contrast does not completely

characterize the performance of a lens. This is particularly the case if it is a general-purpose lens

that is to be used for a variety of photographic

purposes. Accordingly, the new charts accompanying this Circular are finished in two contrasts.

Contrast, as used in this sense, is a measure of the

relative brightness of the light and dark lines on

the target. In photographic work it is convenient

to use the difference in photographic density between light and dark areas as a measure of conRES Figure 3. Low-contrast resolution test chart. The metrical characteristics of this chart are identical with those of the high

contrast cnart shown in figure 2. The contrast (see text for definition) between the gray ink of the lines and the gray background is approximately

0.20. The contrast between lines and spaces in this target is more nearly like that in natural objects than is that in the high-contrast target.

trast. The density scale is logarithmic, and a rela- tive brightness of light to dark of 1 0 to 1 is simply

a contrast of 1.00. The ordinary black-and-white

target, while frequently spoken of as a high-contrast target, actually has a contrast of less than

1.00. The test charts are shown in figures 2 and 3. Figure 2 is the high-contrast chart and consists of black lines on a white background. The contrast between the black-and-white lines on the actual

test chart is approximately 0.9. Figure 3 is the

low-contrast chart. The pattern is identical with

that of the high-contrast chart. The low contrast

is obtained by printing the lines with gray ink on

gray paper. The approximate contrast between

the lines and background is 0.20.

7.2. Metrical Characteristics

The series of numbers along the diagonals ranging from 14 to 80 and 12 to 68 give the number of

lines per millimeter on the negative when this chart, as reproduced, is photographed at a 25 X

reduction. Thus the number 14 refers to both the outer vertical 3-line group on the right and to the

horizontal 3-line group at the bottom of the figure,

whereas the number 12 refers to both the outer

vertical 3-line group on the left and to the horizontal 3-line group at the top of the figure. The

spacings of all groups are given in table 1. These

are the spacings specified in the initial design.

The actual measured values may differ in some

cases by as much as 1 percent from these design

values.

6
Table 1. Specified dimensions of -patterns on NBS test chart

Width of Width of

3-line pattern

Width of Pattern single black space be- Length of number or white tween lines

line patterns mm mm mm mm

80 0.156 0.781

0. 781 18.0

56 .223 1. 116 1.116 19.6

40 .312 1.562

1. 562 21.9

28 .446 2.232

2.232

25.1

20 625 3 125

3. 125

29 6

14 . ouo 4 464 36 0

68 0. 184 0.919

0. 582 18.0

48 .260 1.302 .825

19.6

34 .368 1.838

1. 164 21.9

24 .521 2. 604 1.649

25.1

17 . 735 3.676

2. 328

29.6

12 1.042 5. 208 36.0

For each pattern there are 2 groups of lines, 1 vertical and 1 horizontal. For most lenses it will be found that the resolving power at points not

near the center of the negative is noticeably differ- ent for lines of the same spacing when the lines are oriented differently in the field. A consideration

of the symmetry present at such a point indicates

that the greatest and least resolving powers will be

found for patterns of lines directed toward the

center of the negative and at right angles to this

direction, although one cannot say in advance

which of the directions will correspond to the

greater resolving power. If several test charts are arranged in a horizontal row for photographing at such a height that the line of images passes

through the center of the negative, the horizontal

lines will be directed toward the center of the field and are accordingly designated radial. The vertical lines are designated tangential. These terms

will be used to designate the two different resolving

powers for lines in the two characteristic direc

tions. If these two resolving powers have differ- ent values at a point, it indicates the presence of coma3 or astigmatism.

7.3. Range of Chart at the Standard Distance

The chart has been designed for use at a 25 X

reduction which is obtained by placing the target

26 focal lengths in front of the lens being tested. Under these conditions, the range of values of

the resolving power that can be directly read

3 Coma and astigmatism are optical aberrations, which do not affect the images of axial points of a well-constructed lens but may be present in the

images of points not lying on the axis of the lens. If coma is present, the image

of a point will have a blurred extension extending toward or from the center of the field. If astigmatism is present, the image of a point cannot be focused

into a sharply denned point image, but, for one setting of the lens, it will be

represented by a relatively sharp line segment lying along a radius passing through the center of the field, whereas for a second position, the image will be

a relatively well-defined line segment perpendicular to the radius.

from the images on the test negative is from 12

to SO lines/mm. In the direction of finer patterns,

the range of this test chart has been extended to 80 lines/mm as compared with the maximum of

56 lines/mm provided by the chart that accompanied Circular 428.

However, the patterns covering the range of

resolving power from 3.5 to 10 lines/mm that were present on the former test chart in Circular

428 when used at a 25 X reduction are not present on this chart in the form of 3-line patterns. These

patterns were omitted to conserve space, as it would not be possible to include these patterns

and still provide 6 charts on a single slip-in sheet. In addition, the prospective user is seldom in- terested in testing lenses with high-contrast

targets where the resolving power falls below

12 lines/mm.

However, if desired, it is possible to use this

chart to determine resolving power under 12

lines/mm. An approximate method is to treat each 3-line pattern as a single line (when the

resolving power is under 12 lines/mm, the 3-line

pattern will appear to be single lines in the image).

When this is true, the successive 3-line patterns

and intervening spaces can themselves be re- garded as a resolving-power chart, and a good

approximation of the actual value can be obtained

from the manner in which the 3-line patterns and

spaces merge. Accordingly, the resolving-power

chart when used at 25 X reduction provides a

series of values of resolving power ranging from

3.5 to 14 lines/mm, preceding in steps of \/2.

The actual values are shown in table 2. It must be remembered that the values determined

in this way are less accurate than when used for

the normal range of 12 to 80 lines/mm. In fact,

the error may be as high as 10 percent.

Table 2. Values of the resolving power at 25 Xreduction when the space between specified 3-line patterns is still defined

Pattern Resolving numbers power

Lines/mm

80 to 56 68 to 48 }

14

56 to 40

48 to 34 }

10 40 to 28

}

7 34 to 24

28 to 20

}

5 24 to 17

20 to 14

} 3.5

17 to 12

7.4. Methods of Extending Chart Range

To determine the resolving power for ranges not

present in the target at 25Xreduction, 2 courses

are open to the user. The simplest course is to change the reduction ratio by altering the distance

between the lens and the test chart. The other

course is to change the size of the target by appropriate photographic procedures.

7
(a) Change of Lens To Target Distance

The lines per millimeter marked on the chart are correct only when tests are conducted at the

standard distances of 26/. When tests are performed at other distances, the indicated values

are corrected by use of the relation

Resolving power (lines/mm) = (M/25) N, (1)

where M is the ratio of object to image size, and

Nis the number in the chart associated with each

pattern. For any value of the reduction ratio, M,

the distance, D, the test chart should be placed in front of the front nodal point of the lens is given

by the expression

D=(M+l\f, (2)

where / is the equivalent focal length of the lens under test. (This distance is sufficiently well

approximated by measuring from the front surface

of the lens to the target for values of M greater

than 10 for the usual type of camera lens.) For

convenience, the values of the resolving power

associated with ea ch pattern for a series of values

of M and D are listed. It must be remembered

that when using these test charts to determine

resolving power at finite distances, the image plane

of the lens does not coincide with the focal plane,

which is the position occupied by the image plane

when the camera is focused for parallel light. The

distance, d, separating the image plane at reduction ratio M from the focal plane is given by the

expression

d=f/M. (3

For convenience, table 3 lists the number of lines per millimeter in the image plane corresponding

to the indicated values for several values of the

reduction ratio M.

Table 3. Number of lines per millimeter in the image

-plane for several values of the reduction ratio M

M=... 1 12.5 25 50 100 D=___ 2/ 13.5/ 26/ 51/ 101/

Pattern number Resolving power in lines/mm

80

564028

20

14

3.20

2.24 1.60 1.12

0.80

.56

40

28

20

14

10

7

80

56

4028

20

14

160 112

80

5640

28

320

224

160

11280

56

68

4834

2417

12

2.72

1.92

1.36

0.96

.68

.48

3424

* 17

128.5

6

68

4834

24

1712

J 36

9668

48

3424

272

192

13696

68

48

(b) Change of chart size by photographic means

In cases where space does not permit the use of

long ranges, it is advantageous to change the size

j of the test chart itself by copying to the desired

'

size and then using the resulting negative as a

' transparency or printing it on glossy paper. If j an enlarged copy is desired, it is wise to use a i moderately long focus copying lens, because the | imagery in the center of the field is usually superior,

j It is suggested that the half-angle subtended at [ the lens by the center and corner of the test chart

,

be kept under 15°. While greater half-angles are | allowable, one is less likely to encounter noticeable . distortion and loss of definition when the half-

'

angle is kept small. The approximate focal length

j of the lens can be computed in a simple manner.

!

The distance from corner-to-corner of a single test

!

chart is approximately 100 mm. The equation

m+ 1 - v" «

v

<

j can be used to determine the value of the focal | length /, where R is the distance from center-to- i corner of the chart, m is the desired magnification, j and 0 is the half-angle subtended at the lens by

R. For R=50 mm, m=4, and /3 = 15°, the value

of / is 149 mm, or approximately 6 inches. If j charts enlarged by amount m are used in testing i lenses at a 25 X reduction, the range of the chart | is changed by 1/m. Thus for m=4, the range of! the chart will run from 3 to 20 instead of from 12

] to 80 lines/mm. In making enlargements, it is | desirable that a high-contrast emulsion be used to

j ensure clear whites and high-density black lines, i Any good process emulsion will serve for enlarging f the high-contrast target. For the low-contrast j target, it will perhaps be preferable to use an i ordinary panchromatic emulsion.

The case for m=4 is especially interesting fori this resolution chart. If the chart is enlarged

four times, it will be of such a size that the original

chart may be inserted in the central square, where | the circle charts are located. If the number on!

the negative used in the enlargement is opaqued, 1 then a new series of numbers can be lettered i on the enlarged print of the chart running from | 3 to 20. Then when the original chart is placed j in the central square on the enlarged, one will have j a new chart with the range extending from 3 to 80 i lines/mm. A chart of this type is illustrated in | figure 4. It is true that certain patterns will be i repeated on the composite chart, namely, 12, 14,

17, and 20, but this is certainly no disadvantage.

This process of expanding the range of the chart can be extended in both directions. For a reduction of the original target in the ratio 4 to 1 , the

range of the reduced target is from 48 to 320

lines/mm. If this is placed on the center of the

expanded composite target, the resulting target

has a range from 3 to 320 lines/mm when used at a distance of 26/. 8
Figure 4. resolution test chart with range extended by photographic process.

This chart is a composite formed by superimposing the high-contrast chart upon an enlarged copy of the master chart. The ratio of magnification is 4. The

range of the composite chart is from 3 to 80 lines/mm as compared to the original range of 12 to 80 lines/mm.

It may be desirable at times to produce small

replicas of the chart in the form of transparencies

for use as reticles or for studying the resolution

characteristics of microscopic systems. This can

be done quite simply by photographing the chart

to the desired size on a high-contrast fine-grain

emulsion, such as Eastman 548GH Spectroscopic

Plate or 649GH Spectroscopic Plate. With these

emulsions it is possible to photograph to a very

fine scale with minimal change in ratio of line widths. A Micro Tessar lens or a microscope

objective is best suited for this type of work. It must be borne in mind that the lens aperture must

be great enough to permit the fine lines of the

target to be resolved in the negative. Under

these conditions a sufficiently good approximation

to the ultimate resolving power of a lens is given

by the relation

Resolving power (lines/mm)

1426

/-number (5)

Thus for an//4.5 lens operating at full aperture, one cannot expect to image lines finer than 317

lines/mm. One of the authors has produced reticles with the number of lines per millimeter in the

finest pattern resolved as high as 400 lines/mm

with an//2.8 lens, and it is probable that still finer

patterns can be photographed without undue

effort. In photographing at high reductions, one must be quite meticulous in achieving the best

possible focus. The depth of focus in the image

plane for a given lens is a function of the /-number

and the number of lines to be resolved, thus

Depth of focus

4 X/-number

"resolving power (lines/mm)

With this equation the depth of focus is measured

in millimeters. The above expression is meaningful only if the resolving power does not exceed

the maximum possible for the given /-number.

For example, for the //4.5 lens with a maximum

resolving power of 317 lines/mm, this resolving

power can only be obtained for a depth of focus

of 0.056 mm. In the case of the f/2.8 lens, the

400-line pattern was resolvable for a depth of focus

of 0.028 mm. The ultimate resolving power of

this //2. 8 lens would be 509 lines/mm, which would

be obtainable for a depth of focus of 0.022 mm.

9
7.5. Method of Changing Length of Line

Patterns

The use of long lines departs from most currently

accepted practice for the formation of resolvingpower charts. However, it was, necessary in order

to obtain patterns on the negative capable of being

scanned by a recording microdensitometer. It

is reasonable to believe that the results obtained

by visual analysis of resolving-power tests made

with these long-line patterns will be essentially the same as those obtained with short-line patterns.

Before this belief is generally accepted, it is probable that some experimenters will wish to make studies of the resolving-power characteristics of lenses with both types of target under

comparable conditions. The present chart can be

readily modified to make such studies. To do this,

it is only necessary to mask the lines in an appropriate manner on the present chart.

The standard Air Force chart is a short-line

chart of high contrast and consists of 3 lines and

2 spaces. The lines are five times as long as wide,

thus forming a square pattern. Several such

patterns can be formed by blocking, or masking,

out portions of the lines on the long-line highcontrast chart described in this Circular.

An example of this type of chart modification is shown in figure 5. This chart was prepared by

making an enlarged copy of the original chart on

a glass negative. The unwanted portions of the

long-line patterns were opaqued. Copies of this negative of the desired size are then printed.

The resulting chart then contains both types of

line pattern, thus making easy a comparison of

12

I 7

III

28

20

Figure 5. Short-line target derived from long-line target.

This chart is formed by appropriate masking out portions of the long line pattern on two sides of the target. This modification may be used in comparison studies of short-line and long-line targets.

results obtained with long-line and short-line

patterns. Use of a chart of this type is especially

advantageous in comparison studies, as there can be no question of the prevalence of comparable

conditions.

If one does not wish to use the direct copy as a

reticle or test chart, the reverse pattern can easily

be obtained by contact printing. This may be

done fairly readily with the aid of a small distant

light source, which minimizes the lack of sharpness

resulting from imperfect contact between the

negative and the emulsion surface. A high-pres- sure mercury arc serves very well for this purpose

as it is small, and its high intensity helps to avoid

long exposure times.

In making copies of this kind it is difficult to maintain the same contrast for all patterns. When

the fine lines are exposed sufficiently to be well

defined, the coarse patterns are likely to be over- exposed. This effect can be minimized by appropriate dodging. It is also helpful to place the

emulsion surface in the image plane of maximum

contrast instead of in the image plane of maximum

resolving power, provided the image plane of

maximum contrast will resolve the finest pattern.

8. Details of Camera Test

8.1. Arrangement of Charts

The resolving power is not the same across the

entire negative but is usually greatest at the center and decreases along any radius. It is commonly

considered that a lens is perfectly symmetrical

about its axis, and that the performance of the

lens will accordingly be identical throughout a

given zone concentric to the center of the field.

Figure 6. Arrangement of camera and charts for test. The charts are conveniently mounted on a 1- by 4-inch board. The spacings of the individual charts aresuch that the angle between successive charts, measured at the camera lens, is 5 degrees.

10
A perfectly symmetrical lens is probably never

realized because of the unavoidable errors in

workmanship, but, except for the most exacting

purposes, it is satisfactory to treat the field as symmetrical. Accordingly, if the resolving power

is measured at selected points along a given diameter, the values obtained may be considered representative for the entire picture area. It is convenient to measure the resolving power at 5-degree

intervals with the charts arranged in a horizontal row, as shown in figure 6. Figure 7 is a schematic

drawing showing the spacing of the charts^and the

position of the camera with respect to the row of

charts. The distances are given in terms of/, so each coefficient must be multiplied by the focal

length of the lens under test to determine the

required spacing for 5-degree intervals. For convenience, table 4 lists the value of the spacings

reckoned from the zero position for values of 0

up to 45 degrees by 5-degree steps for 4 values of

the focal length. The distance separating lens and

zero chart is also given for the same 4 values of

focal length.

&l Figure 7. Plan view of arrangement of camera and charts for test.

This is a plan view of the arrangement of charts and camera shown in fig. 5. The distances are given in terms of /, the focal length of the camera lens

If, the distances A C and AD are made equal, the camera is located on the perpendicular bisector of length CD and is, therefore, directly opposit the central chart: 11
300

cr

LUQ

O

croo

<

cr

LUCO

cr

<i_i

r>toz

<

50 100 FOCAL LENGTH IN MILLIMETERS

150

Figure 8. Length of negative diagonal as a function of the half-angle of view, /§, for several values of the focal length.

This graph can be used to evaluate the half-angle of view for a given camera when the focal length of the lens and the length of the negative diagonal is known.

Table 4. Distance (/ tan /3) normal to lens axis, to chart I located at angle /3 from central target and distance along 1 lens axis from front of lens to central target for several j values of the focal length, f

f (in mm) 25 50 75 100

2Bf (in mm) 650 1, 300 1,950 2,600

tan p 26 / tan 0

Degrees mm mm 771771 mm

0 0. 0000 0 0 0 0

5 .0875 57 114 171 227

10 .176 115 e 229 344 458

15 .268 174 348 522 696

20 .364 237 473 710 946

25 .466 303 606 909 1,212

30 .577 375 751 1,126 1,501

35 .700 455 910 1,365 1,820

40 .839 545 1,091 1,636 2, 182 45 1.000 650 1,300 1,950 2,600

The larger values of the angles are given to provide complete data for the testing of lenses of extremely wide angle. The field of a lens of 50-mm

focal length used with a 35-mm film (24 X 36 mm

negative) extends only 23.4 degrees when measured

from the center to the extreme corner. The magnitude of the angle separating center and corner

of the negative can be determined approximately

with the aid of figure 8. The length of the diagonal

of the negative is measured and the nominal focal length of the lens is noted. With these values as ordinate and abscissa, respectively, a point is located on the graph. If the point falls on one of the sloping lines, the value of the angle is given

directly. If the point falls between two lines, the

value of the angle can be determined sufficiently

closely by interpolation. The angle so determined

is one-half the total angle of view of the camera.

8.2. Camera Support

The camera support should be sufficiently rigid

that no vibration effects will be likely to impair the

quality of definition. If the camera is attached

to the tripod in the usual manner and leveled, the row of images will extend across the photograph,

as indicated in figure 9, and the resolving power
I near the corners will not be determined. If a

tilting-head tripod is used with the camera so mounted that the camera may be rotated about an

S axis parallel to the lens axis, the camera can then

be adjusted so that the recorded images on the

photograph will fall along a diagonal, as indicated

in figure 10. In this manner, the resolving power

: can be determined in the corner of the field. This same result can be obtained by keeping the camera

leveled on the tripod and rotating the board, upon

which the charts are mounted, through the proper

angle. This latter course is usually, however, less convenient.

8.3 Use of Multiple Rows of Chart

It will be readily understood that the correct resolving power for a lens will not be obtained

unless it is correctly focused. If many lenses

are to be tested, it is advantageous to have the

arrangement of charts shown in figure 11, as it largely eliminates the making of several exposures

in order to make sure that good focus is obtained.

There are five rows of charts, placed one above the

other, all at different distances from the lens, but

not far from the horizontal plane containing

the camera axis. The lens to be tested is placed

at a perpendicular distance, 26/, from the center

of the middle row, and the camera is focused

upon the central chart of this row. If the focus

is correct, the central row of charts will be the

sharpest on the resulting negative. If an error has been made in the setting, one of the nearer or farther rows of images will be sharper than the

central one, and if the error in focusing is not too

great, one row will be in good focus, and the

resolving powers can be read from it without

making an additional exposure. If the five rows

of charts are used as shown, they can be spaced

in the direction of the line of sight, so that the

planes of best imagery of the different rows, measured in a direction perpendicular to the

film, will be spaced 0.1 mm. The proper spacing

of the rows measured from the central row is given in table 5 for Sd= +0.2, +0.1, 0-0.1, and

-0.2.

In setting up the charts and camera, care must

be taken that the distances are exact and that the

axis of the camera is perpendicular to the row of charts, with the lens opposite the central target.

For a camera of short focal length, it is convenient

to do the work indoors. The charts and the camera can then be adjusted to the same height

by measuring upward from the floor. The dis- tance from the camera to the central chart should
Table 5. Values of the distances dD, measured from a plane distant 26f from the lens, necessary to displace the image plane by amounts Sd.

6d

/ in mm

25 50 75 100

SD mm mm mm mm mm

+0.

5

-208.

8

-250.

0

-267. 9 -277.

8

.4 -178.6 -20S. 3 -220. 6 -227.3

. 3 -144.2 -163.0 -170.4 -174.4

. 2 -104.2 -113.6 -117.2 -119.0

.1 -56.8 -59.5 -60.5 -61.0

0 0 0 0 0 -.1 69.4 65.8 64.7 64.

1

-.2 156.2 138.9 133.9 131.6 -.3 267.9 220.6 208.3 202.7 -.4 416.7 312.5 240.4 277. S -.5 625.0 416.7 375.0 357.

1

be measured from the first principal point 5 of the lens. In general, the location of this point

will not be known, but it will be sufficiently ac- curate to measure from the front surface of the

lens. It will be found most convenient to measure

all horizontal distances on the floor and to use plumb bobs to properly locate the parts above the

measured points. If plumb bobs are not conveniently available, large screw eyes hung with

the pointed ends downward are a satisfactory

substitute. Four plumb bobs are desirable, one

to locate the front surface of the lens, one to locate

the center of the central chart, and one each at the corners of two outermost charts. The projections of these points are located at A, B, C, and

D on figure 7. The distance AB should be 26/.

In order to be sure that the camera is directly

opposite the central target, AC and AD must bejl equal. This condition locates the camera on the

| perpendicular bisector of CD. With the camera!

over A, it must be so oriented by means of the; view finder, or ground glass, that the central chart I appears in the center of the photograph. If I these adjustments are all accomplished as de-

;

scribed, the camera will be directed squarely at the central chart.

If many cameras are to be tested, it is convenient

to lay off the distances on the floor and indicate

the significant points by tacks. If plumb bobs

are permanently attached to the strip that carries the charts and to the tripod, it is a simple matter

to restore the correct adjustment by adjusting the

plumb bobs over the tacks. A rack, such as is shown in figure 11, equipped with plumb bobs and

used in this manner with a system of tacks indicating the positions for the commoner focal lengths

will be found to be an especially convenient piece

of testing equipment for photographic clubs, as it will enable each member to acquire for himself

valuable and useful information about the per- formance of his lenses.

(a) Determination of Focusing Error

It sometimes happens that the unsatisfactory

performance of a lens is a result arising from errors

in the focusing scale or in the adjustment of the

coupled rangefinder. Errors of this nature can be

detected by photographing the test chart at various distances in front of the lens without

Figure 11. Test rack with multiple rows of charts.

This is a very convenient arrangement for mounting the charts if many lenses are to be tested. This arrangement also enables one to test the adjustment

of a coupled range finder. The method of determining the proper separation of the rows of charts is given in section 8.3.

5 The principal points are two points, designated as first and second, on the axis of the lens. In order to simplify the mathematical equations defining

object and image positions, it is convenient to measure object and image distances, respectfully, from these points. Their properties are discussed in most

books on optics! See chapter 4 of "The Principles of Optics", by Hardy and Perrin (McGraw-Hill Book Co., Inc., New York, N. Y.).

14
changing the position of the lens with respect to the film plane during successive exposures or by

a single exposure with several targets spaced at varying distances from the lens. By a proper

selection of distances and proper interpretation of the results, the direction and the approximate

magnitude of the focusing error can be determined.

Let one target be set at (M0 +i)/ distance from

the lens, where M0 is the ratio of object to image

size (in the usual case, M0 =25), and /is the focal

length of the lens in millimeters. Then

D0 =(M0 +i)y

d0 =

(7)

(8)

where D0 is the object distance, and d0 is the

image distance. Now let another target be

placed at distance D from the lens, then

D=(M+l)f (9)

(10)

The difference in position of the image planes is then given by the relation

M S J _ AM0 -M)

M Mo J (M„M)

whence

M= MpJ

f+M0 dd'

(11)

(12)

and the distance 5D of the second target from the

first is given by the relation

SD=D-D0

- Mljbd

f+MoSd

For M0 =25, the relations become

V25-M\ U=3\-25MT)-

and

M5D25/

'~f+255d'

625/ 8d

f+258d

(13)

(14)

(15)

(16)

It is convenient to so set the target distances

that 8d ranges from +0.5 to —0.5 mm. For convenience, table 5 lists values of 8D for this range

of values of 8d for 4 values of /. It must be re- membered that these are distances measured from

the plane distant D0 =26f from the lens. The

varying values of D will produce a variation in M,

so that the image of the targets will not be identical in size.

Table 6 gives the values of M corresponding to the various values of 8D and / for which the values

of 8D are shown in table 5. These values of M

are necessarily approximate because the true position of the plane of best imagery is not known.

The values of M are therefore computed on the

assumption that the failure to compensate for

change in image size by resetting the image plane

is negligible for the small range involved. In the

worst case, for the 25-mm lens this effect can

change M by only 4 percent, and it is safe to as- sume that this error will usually be less than

1 percent.

These changes in Mare quite important because

failure to appreciate this factor may result in erroneous conclusions regarding the condition of

focus of the lens under test. The change in M

changes the scale in the chart, which is designed

to be direct reading for M=25. Consequently,

when used for a different value of M, the values of

resolving power inscribed on the chart must be

multiplied by M/25, as listed in table 7, to get the

true values. The change in size between successive

patterns on the chart is 1.1892 or 0.8409. Therefore, if one were testing an //4 lens and had an

indicated reading of 48 lines/mm for 8d=-\-.l,

5 =0, and 5= —.1, he might assume that the focus was satisfactory. However, on making the cor- Table 6. Values of the reduction ratio M for targets set at such distances from the lens that their proper focus would

differ by amounts 8d from the image plane for M0 = 25

Sd

/ in mm

25 50 75 100 M

mm

+0.5 16.7 20.0 21.4 22.2

.4 17.8 20.8 22.1 22.7

.3 19.2 21.7 22.7 23.3

.2 20.8 22.7 23.4 23.8

.1 22.7 23.8 24.2 24.4

0 25.0 24.0 25.0 25.0 -.1 27.8 26.3 25.9 25.6 -.2 31.2 27.8 26.8 26.3 -.3 35.7 29.4 27.8 27.0 -.4 41.7 31.2 28.8 27.8 —. 5 50.0 33.3 30.0 28.6

Table 7. Values of the factor M/25 by which the indicated

resolving power must be multiplied to obtain the true

resolving power

f in mm 25 50 75 100

Sd M/25 mm

+0.5 0.67 0.80 0. 86 0.89

.4 .71 .83 .88 .91

.3 .77 .87 .91 .93

t 2 .83 .91 .94 .95

!i .91 .95 .97 .98

0 1.00 1. 00 1.00 1.00 -.1 1.11 1.05 1.03 1.02 -.2 1. 25 1. 11 1.07 1.05 -.3 1.43 1. 18 1.11 1.08

1.67 1. 25 1. 15 1. 11

2. 00 1.33 1.20 1.14

15
rections, the true resolving power would be 44, 48,

and 53 lines/mm, which shows that the lens is out

of focus by —.1 mm, and that the lens should be

moved 0.1 nearer to the image plane to yield optimum results. Errors of this type are not likely to occur at the small /-numbers because of the

small depth of focus. They are quite likely to oc- cur at large /-numbers. For example, at //ll,

where the depth of focus is appreciable, failure to make the necessary corrections can result in

marked errors. This is shown in table 8. Here

casual inspection of the indicated readings would

lead to the belief that the position of best focus

lies between the values of 5g£= + .2 and +.1,

whereas when corrections are made the position

of best focus is clearly at 8d= — .2 mm.

Table 8. Indicated and corrected values of the resolving power for a 25-mm lens capable of resolving 60 lines per

millimeter tested at fill for several values of Sd

id

Resolving power

(lines/mm)

Indicated Corrected mm

0.4 48 34

.3 56 43

.2 56 46

.1 56 51 0 56 56 -.1 48 53 -.2 48 60 -.3 40 57 -.4 34 57 -.5 28 56

Fortunately, errors of this sort decrease with

increased focal length and become almost nonexistent for values of / greater than 100 mm. It must be considered for the short-focal-length

lenses when the test is made at /-numbers above

//5.6. It also must be guarded against when the

emulsion used places an upper limit on the resolving power. For example, if the practical upper

limit of the emulsion is 40 lines/mm, the depth of focus may be great enough to occasion difficulty. All of these difficulties can be avoided however by

making the proper correction for the change in re- duction ratio. An estimate of the probable depth

of focus for a lens of a given /-number is given by

the formula

Depth of focus in mm=

4X/-number . Resolving power in lines/mm

8.4. Illumination of Charts

Satisfactory negatives cannot be obtained unless the charts are uniformly illuminated. If lenses of the shorter focal lengths, such as are used in miniature cameras, are to be tested, it is convenient to make the exposures indoors. Windows directly behind the camera are certain to produce unsatisfactory illumination because of

16

specular reflection from the charts. In the usual

home, a room is seldom found with the windows [ ^

so arranged that none of the charts will reflect j

!e

l light directly into the lens with consequent over- )

1°' exposure of such charts. It is advisable to make j the test at night or with shades drawn and to ! depend upon photoflood lights for the illumination. I Two photoflood lights placed, one at either side,

[

«j 3 or 4 feet in front of the plane of the charts (that st is, toward the camera) and 4 or 5 feet beyond jr either end of the group of charts, will give satis- j, factory illumination. For lenses of longer focal

j i

f length, the distance 26/ becomes so great that it ,

|e is usually more convenient to make the exposure t | outdoors. i |[ Frequently, one or more of the images are found \ j| to be overexposed as a result of light from the j light sources being specularly reflected into the is lens from the glossy surface of some of the charts. » This can usually be prevented by careful adjust- oi ment of the light sources until all charts appear J equally bright when viewed from the position j occupied by the camera lens. Examination of ; the image in the view finder will frequently enable i a the experimenter to locate trouble of this kind | f before making the test exposures. This difficulty I can be eliminated altogether if polarizing filters

j are placed over the light sources that illuminate i the charts. A similar filter is used over the lens, j

, and by proper adjustment the excessive light from

the areas of specular reflection can be reduced to I a point where it is no longer troublesome. Unless 1 the polarizing filter is of excellent quality, howj

1 ever, the resolving power of the lens and filter may be less than that of the lens alone.

i 8.5. Methods of Focusing i

(a) Focusing by Means of Coupled Range Finder

If the camera is equipped with a range finder i

' coupled to the lens, it may be advisable in order I

1 to attain greater precision, to focus with the help

of a low-power telescope, focused to view distant

objects. A 3- or 4-power telescope can be held

directly behind the range finder so that the light

passes from the object through the range finder,

then through the telescope, and then to the eye. With this arrangement, the images are magnified

and their coincidence can be more exactly determined. If a suitable telescope is not available, one barrel of an opera glass may be alined with ' the eye aperture of the range finder and satisfac- I tory results obtained. A prism field glass is not

recommended, as the higher magnification and

the loss of light by the extra reflections at the

j prism surfaces make it less desirable for this pur- 1 pose. If the multiple rows of charts shown in figure 11 are available, the range-finder setting is made on the middle row. If one of the other rows is sharpest on the negative, it indicates that

the reading through the range finder has not been

accurately made or that the range finder is out of

adjustment. The truth of this latter conclusion
should not be assumed unless the experiment is repeated several times and a consistent failure to focus on the central row is established.

(b) Focusing by Means of Focusing Back

If the camera has no range finder but is equipped

with a focusing back, it is advisable to use it for

securing the correct focus. The grain of the

ground glass is apt to introduce some uncertainty

in deciding upon the best focus. Focusing maybe done more precisely if the ground glass is temporarily replaced by a piece of clear glass of

the same thickness. Marks should be made near

the center of the surface of the glass that corre- sponds to the ground surface. A wax pencil or a wax crayon, such as comes in children's color sets,

is convenient for this purpose. When looking

squarely at the clear glass, the image can be seen only in the center of the field. Focusing must be

done with a magnifying lens. The highest power

available in a simple magnifier is recommended,

and focusing is correct when the wax-pencil marks

and the image are simultaneously in focus in the

field of the magnifying lens.

(c) Focusing by Means of Focusing Scale

If the camera has no range finder or ground glass

but is provided with a focusing scale, it is probable

that no indicated value on the scale will correspond

exactly to the required distance of 26/. In such

a case the distance from the chart to the lens may

be altered to correspond exactly to the nearest

indicated value. If this is done the nominal re- solving power read directly from the negative will not be correct, because it will not give the actual

number of lines per millimeter. The true resolving

power can be found by the following proportion:

The actual number of lines per millimeter is to the

value read from the chart as the distance from the

chart as the distance from the camera to the chart

is to 26 focal lengths. When the test is conducted

in this manner, results unfavorable to the lens will be obtained if the focusing scale is not accurate,

because the lens will have been incorrectly focused

for the indicated distance.

Another and perhaps better method of testing a

lens on a camera equipped with a focusing scale is available. The camera is set up 26 focal lengths

from the chart in the usual manner, and the corre- sponding setting on the focusing scale is estimated

from the nearest indicated values. With this setting, if the resulting negative is not satisfactorily sharp, the setting on the scale is left fixed

and the distance from the camera to the chart is altered by small steps until an exposure is obtained

of satisfactory quality. If the alteration of the

distance from 26 focal lengths is not greater than

10 percent, the readings of resolving power will be

satisfactorily accurate. If the alteration of the

distance has been more than 10 percent, the setting on the focusing scale should be appropriately

altered and another series of exposures made,

starting again at the distance of 26/

8.6. Photographic Technique

The fast or moderately fast film that is com- monly used for pictorial photography will resolve

from 40 to 50 lines/mm. A high-grade photographic lens, with a fine-grain high-resolution film, will afford a resolving power much better than

this, at least at the center of the field. The

resolution that one obtains with a given lens- emulsion combination is a function of a large

number of parameters, such as resolution of lens,

resolution of film, gamma, spectral sensitivity of

film, and contrast rendition of film. Values of resolving power comparable with those that will be attained in use are obtained by using the films

and emulsions that are regularly used. On the

other hand, the fine-grain high-resolution film

gives results more completely dominated by the

lens and therefore is likely to show greater differ- ences between different lenses. Inasmuch as fine- grain resolution films and those made for general use differ in other parameters than resolution

(spectral sensitivity, contrast rendition, etc.), the

correlation of results obtained with fine-grain film

and with the more usual low-resolving-power film,

although high, is not perfect.

Various methods have been proposed for combining resolving power of films and lenses. If, for example, A and B are the resolving powers, re- spectively, of lens and film, it has been suggested

that C, the resolving power of the combination, is given by the formula

Q2 A}~^~ B2

' (19)

These can, however, be regarded only as approximate formulas to be used for "rule-of-thumb"

purposes as the problem is much more complex

than is suggested by the formulas.

If one is desirous of choosing a lens-film combination that will give the maximum sharpness,

and which, if other things were equal, would give

results more characteristic of the lens and less characteristic of the film, then Eastman Panchromatic Micro-file, or Agfa Minipan are suggested. With these films more than 100 lines/mm

can be clearly resolved if the photographic lens

produces an image of the requisite sharpness.

For cameras not using motion-picture film, a fine- grain film, such as Panatomic X or Finopan,

should be employed. The films giving the highest

resolution are of the photomechanical type, such

as Reprolith or Kodalith.

It is self-evident that there must be no vibration

of the camera or charts when the exposures are made. The camera should be on a very rigid tri- pod or clamped to a table of the proper height, and

the charts should be rigidly supported. When

there is any doubt about the rigidity of the camera

17
support, the following corrective procedure has

been found advantageous. The general illumination is reduced to such an extent that the exposure

with the largest diaphram opening is not less than

3 or 4 seconds. When making an exposure the

shutter is set at "time," a black card is held immediately in front of the lens but not touching it, and the shutter is opened either by the cable or

finger release. After all tremor from opening the

shutter has subsided, the card is taken from in front of the lens for the duration of the exposure,

then replaced, and the shutter closed. By this procedure there is very little likelihood that making the exposure will cause harmful vibrations to the camera.

If one is already familiar with the use of one of the fine-grain developers, it is probably advisable

that it should be used, although a fine-grain developer will not increase the resolving power of the

emulsion. Most tests of lens resolution at this Bureau have been conducted with buffered D76

[14] and DK20 [15]. The film should be exposed

and developed to yield a film of medium density.

Exposures should be repeated until a negative,

well-focused and of good technical quality, is obtained.

8.7. Examination of Negative

On a satisfactory test negative the images should

lie on a diagonal of the negative, with the central

chart very close to the exact center of the negative.

Furthermore, the negative should be of medium

density and of first quality, photographically. No

attempt should be made to read the value of the

resolving power until such a negative is obtained.

To properly interpret such a negative, it should

preferably be examined with a compound microscope magnifying 30 or 40 diameters, although a good magnifying glass, magnifying 10 or 15 diameters, can be used on the coarser patterns. One

may also examine the negative indirectly by making a 10 or 15 diameter bromide enlargement from

the negative and then using the magnifying glass on the enlargement. When this method is used

there is danger that the lens will not be judged

fairly, because faults originating in the enlarging

may be attributed to the lens under test. As has been mentioned, the resolving powers for the vertical and horizontal lines are referred to as the tangential and radial resolving powers, respectively. On each chart (of the row in best focus, if multiple rows are used) the finest patterns of verti- cal and horizontal lines that are resolved are read

and counted. A pattern of lines is resolved if the

individual lines can be clearly distinguished and if the number of lines is the same as the number of

lines in the test chart. This checking of the number of lines is important because diffraction effects sometimes produce a spurious resolution in which

the lines are apparently clearly distinguishable on

the negative but the total number of lines does not

check with the number in the original pattern.

The number of lines per millimeter in each pattern '

is given in figure 2 and table 3. Typical results of j the tests on lenses of miniature cameras are given j in the following section.

9. Interpretation of Results

A brief discussion of the resolving-power char- i acteristics as predicted from theoretical considera1

tions [16] is perhaps desirable before proceeding to the problem of interpreting results obtained with

the resolution charts. This theory has long been

established, and predictions from it will be used in

this circular only for the purpose of providing a yardstick against which to compare the perform- ance of lenses. Since the predicted characteristics are for an ideal lens and without limitations imposed by the film, it should not be surprising if experimental results for actual lenses deviate to some extent from those predicted. These deviations result from aberrations inherent in any

actual lens. These departures do not however

signify that the theory is without value in the

prediction of lens performance. In general, the

theoretical values are the ultimate that can be

expected under a given set of conditions. Except

for very small apertures, observed values are always lower because of the limitation of the film and also because photographic lenses, except when

of very narrow field, are not sufficiently well cor- rected to give the Airy diffraction disk as the

image of a point.

9.1. Maximum Resolving Power of an Ideal

Lens

The smallest separation of two star images

theoretically distinguishable on the basis of

diffraction of light is, according to the usual

criterion,

where X is the separation in the image plane, F

the focal length of the lens, d the diameter of the

lens aperture, and X the wavelength of the incident

light. For present purposes, it will be assumed

that the same equation is valid when the images

are composed of parallel lines instead of points.

It is also more convenient to express the maximum

resolving power, Nm in lines per millimeter. It can be shown that the equation

Nm =^~ lines per millimeter, (21)

where b is the /-number, is equivalent to eq 20,

for A =575 millimicrons. This relation is valid

for axial imagery. For extra axial points,_ it is necessary to use the two additional approximate

relations, one for maximum resolving power for tangential lines,

18
Nt p=—^— cos

3

/3 lines per millimeter (22)

and another for maximum resolving power for radial lines, 142fi NTp=^ cos p, (23)

where 0 is the angular separation from the axis

for the point considered. Table 9 gives the values

computed for the resolving power in both orientations at 5-degree intervals from 0° to 45° for a

series of/-numbers, ranging from 4 to 64, in a form

convenient for use. The foregoing discussion and

computations are based on the assumption of the

object being a great distance from the lens, so that the image plane and focal plane coincide.

For finite distances the /-number must be multiplied by (m Jrl)/m., where m is the ratio of object

distance to image distance. Thus for the value

m=25, which is suggested for use in testing camera

lenses, the values listed in table 9 must be reduced

by multiplying by 0.96. When a lens is used in

copying at 1 to 1, the values listed in the table

must be halved.

Table 9. Maximum attainable resolving -power in lines per millimeter for an ideal lens as a function of stop- opening

Resolving power for tangential lines at angular

Relative separation from axis of- aperture (/-number)

0° 5° 10° 15° 20° 25° 30° 35° 40° 45°

4 356 362 340 321 295 265 231 196 160 126

5.6 255 252 244 230 212 190 166 140 115 90

8 178 176 170 160 148 132 116 98 80 63

11 130 128 124 117 108 97 84 71 58 46

16 89 88 85 80 74 66 58 49 40 31 22 65 64 62 58 54 48 42 36 29 23 32 45 44 43 40 37 33 29 25 20 16

45 32 32 31 29 26 24 21 18 14 11 64 22 22 21 20 18 16 14 12 10 8

Resolving power for radial lines and angular separation from the axis of—

0° 5° 10° 15° 20° 25° 30° 35° 40° 45°

4 356 355 351 344 334 323 308 292 273 252

5.6 255 254 251 246 240 231 221 209 195 180

8 178 177 175 172 167 161 154 146 136 126

11 130 130 128 126 122 118 113 106 100 92

16 89 89 88 86 84 81 77 73 68 63 22 65 65 64 63 61 59 56 53 50 46

; 32 45 45 44 43 42 41 39 37 34 32 45 32 32 32 31 30 29 28 26 25 23

64 22 22 22 21 21 20 19 18 17 16

It must be remembered that these values of

resolving power are predicted for the case of an

ideal lens. It is unlikely that any actual lens will

yield full theoretical resolving power, although

values very close to the maximum can be obtained

near the center of the field for moderate apertures

by using fine-grain slow emulsions, such as Eastman Spectroscopic Plates, 548 GH or 649 GH.

However, at the large /-numbers, it can happen

that ordinary emulsions will be able to resolve

finer detail than the lens is theoretically capable

of resolving. For example, the maximum resolving

power of a lens at//32 is 45 lines/mm on the axis,

and there are many emulsions in common use that

will resolve 60 lines/mm or better.

9.2. Depth of Focus For an Ideal Lens

When a lens forms an image of an object located

at an infinite distance in front of the lens, there

exists a small finite range in the image space for which a recognizable image of the object is formed.

This range is called "depth of focus" and refers to the distance measured along the axis in the image

space that may be traversed without the resolving

power, measured in the image plane, falling below an arbitrarily selected value. It is not to be confused with "depth of field", which refers to the

range in the object space for which all point objects

are imaged with a radius of the circle of confusion

remaining less than or equal to some arbitrarily

selected value.

It can be shown that the depth of focus, df, in millimeters can be computed from the relation

46

df =^ (24)

where b is the /-number, and A7" is the resolving

power in lines per millimeter for which the depth

of focus is sought eq 24 is based on geometric

optics and is restricted to values of N lying

between zero and Nm , where Nm is the maximum

resolving power computed by eq 21, which is based on physical optics. The value of df

is independent of angular separation from the axis

for a given /-number, and consequently no

additional equations for the off-axis conditions

are necessary.

With the aid of eq 24 supplemented by eq 21,

it is possible to compute the probable depth of focus for a given resolving power at a specified

/-number. The results of such computations are given in table 10. It may be noted that depth

of focus increases with /-number for any selected

value of the resolving power, and that for a given

/-number depth of focus increases with decreasing

resolving power. It is clear on consideration of Table 10. Maximum depth of focus for an ideal lens as a function of f-number for a series of values of the resolving power in the focal plane

Relative aper- ture (/-number)Maximum depth of focus for resolving power, in lines/mm, of—

320 160 80 40 20 10

22.8 4

5.6

8

1116

22

mm

0. 025

.035

.050

mm

0. 05

.07 .10

.14 .20

mm

0. 10 .14 .20

.28

.40 .55

.80

mm

0. 20 .28 .40

. 56 .80

1. 10 1.60

2. 20

mm

0. 40

.56

.80

1.12 1.60

2. 20

3. 20

4. 40

mm

0. 80

1.12

1.60

2.24

3. 20

4. 40

6. 40

8. 80

19
the values listed in the table that focusing becomes more critical both for smaller /-numbers and. for

finer detail in the image.

It must be mentioned that the values of depth

of focus computed from eq 24 for an ideal lens are

likely to be larger than the values observed for an

actual lens. However, for the actual lens, the

depth of focus will usually be at least 62 percent

of that computed for the ideal lens, so that the

table nonetheless serves as a useful guide. It sometimes happens that a given pattern appears

to be resolved over a greater range than that

indicated in the table. This is more likely to occur when photographing high-contrast targets.

When this does occur, it is frequently a spurious

resolution, and consequently some care is required

in interpreting the results.

9.3. Effect of Field Curvature

It usually happens that a lens does not give

uniformly good definition throughout the entire

image plane. One may have a condition where

the central and edge definition are good but therej

is an annular zone between the center and edge)

where the definition is less good. This is usually a consequence of curvature of the image or fieldj curvature. All lenses exhibit this characteristic

in varying degree, but when an excessive amount!

of field curvature is present, it may impair the use-* fulness of the lens. In order to present a clearer!' picture of this phenomena, the results of resolving)

power measurements on a lens are shown in

figure 12. Each frame of the figure shows how;

the resolving power in an image plane of the lensj1 for a target pattern of lines in a given orientation

and located at an infinite distance from the lens

varies as the image plane moves from a position

inside to a position outside best axial focus. Forj

a given frame, the zero of abscissas marks the! position of best visual focus on the axis at //5.6, 1 and positive values indicate positions farther from

the lens. The region of useful imagery for tangential, T, and radial, R, lines are shown for the

aperture ratios, //5.6 and //ll for each 5-degree

interval of angular separation from the axis.

T-0°

- f

LENS 8

f =i95mm.

f /5J5

1I

T-5°

1

T-IO

: i

T-I5° }T-20°

-

: J

-

- J

T-30"

-

-

J—

R-rf

J

LENS 8 f=i95mmf/5.6 I

:

R-5°

- J

R-IO°

^ }

R-I5° }

-

R-20°

: J

R-25°

R-30* J

R-tf LENS 8 f=l95mm

1 f/n

R-5°

\V. -

RIO"JR-20°JR-25°

R-30°

-2 2 4 -4 -2 0 2 4 -4 -2 0 2 J4

POSITION OF THE IMAGE PLANE , MILLIMETERS Figure 12. Resolving power versus position of the image plane for an actual lens at apertures f15.6 and fill. The resolving power throughout the region of usable imagery is shown for tangential (T) and radial (R) lines at 5° intervals from 0° to 30°. The

abscissae marks the position of best visual focus on the axis at //5.6, and positive values of abscissae indicate positions farther from the lens. The effect curvature and change of depth of focus with aperture are clearly illustrated by these curves.

zero of

of field

20
Examination of these curves shows that the

resolving power in the image plane rises to a max- imum and falls in very similar fashion for both

tangential and radial line patterns as the image

plane moves through the image forming region

throughout the entire angular field of the lens.

If one considers a single vertical array of curves,

for example, those marked T~0° to T-30°, inclusive, it is evident that the maxima of these curves do not all occupy the same position with respect

to the zero of abscissa, which marks the position

of the plane of best visual focus on the axis. This

results from the fact that the surface of best fo- cus for a lens is not a true plane but is instead a curved surface. This phenomenon is referred to

as field curvature. In addition, there is a differ- ence between the surfaces of optimum definition for tangential lines (i.e., lines drawn tangent to circles with a point on the optical axis as center) and

radial lines (i.e., lines parallel to radii drawn from

a point on the optical axis). Curves drawn showing the position of these maxima are called curves

of primary (for tangential lines) and seconclaiy

(for radial lines) curvature. Such curves are illus- trated in figure 13. It may also be noted that the tangential and

radial maxima of resolving power do not always

occur at the same position. This is particularly

noticeable in figure 12 for T-25° and R~25°, where

the separation along the axis amounts to approximately 2 mm. Consequently, when the tangential lines are clearly resolved by this lens, the radial are _poorby resolved. This effect is called astigmatism, and the measured difference between the

two maxima is called the astigmatic difference.

It is clear from the above considerations that

optimum imagery throughout the image plane is seldom possible for any actual lens at its maximum

stop opening. Fortunately, however, most users do not have occasion to strain the capabilities of their equipment, since the resolving powers of emulsion in common usage are considerably below

that of the lens. Because of this, it is usually

possible to select a compromise focus where a

small reduction in resolution on the axis is accepted

in order to obtain tolerable resolution throughout

the extra-axial regions. This is the idea underlying the concept of the image plane of best average

definition as opposed to the image plane of best

axial focus. The effect of curvature of field is masked in a very large degree when the lens is stopped down.

This effect is clearly shown in figure 12 when the curves of resolving power versus position of the

image plane for relative aperture //5.6 are compared with those for relative aperture //ll. The

increase in depth of focus with increasing /-number,

as predicted in eq 24, is clearly shown in these

illustrations. Because of the increased depth of focus with decreased stop opening, a general improvement in definition throughout the image

plane is frequently encountered when the imagery

obtained with a lens set at a small stop opening is compared with that obtained with the same lens

set at a larger stop opening. At first thought,

this behavior seems to be at variance with theory,

which predicts that the resolving power for any

given part of the image plane is a maximum at the

largest stop opening. However, the image curvature usually precludes the positioning of the image

plane so that all resolving power maxima for

angular separations from the axis are present

therein. On the contra^, any given image plane can contain only a few of the maxima, and. the

small depth of focus existing at the larger stop

openings for maximum resolving power at various

angular separations from the axis further serves

to limit the number of maxima obtainable in the

image plane.

When an image plane has been selected which

contains several resolving power maxima and is held fixed while the stop opening is reduced, it is clear that the depth of focus increases for all maxima. Consequently, there is greater likeli- hood of the given image plane including more maxima than it did at the full stop opening, and,

as a result, the definition considered throughout

the entire image plane will show improvement.

In fact, some improvement is likely, even if more maxima are not included because the increased

0 I 1 1 I 1 -2 0 2 -2 0 : POSITION OF THE IMAGE PLANE, mm

Figure 13. Field curvature for four types of lens.

Curve P shows the primary curvature and is the focus of the positions of maximum resolving power for tangential lines at the indicated angular separations from the axis. Curve S shows the secondary curvature and is the

focus of the positions of maximum radial resolving power for radial lines at the indicated angular separations from the axis. The zero abscissae marks

the position of best axial focus and positive values of abscissae indicate posi- tions farther from the axis. 21
depth of focus for any selected value of the

resolving power makes it probable that some

regions will be benefited by an increase in resolving

power, even if additional maxima are not reached.

This type of improvement of definition does not

continue indefinitely with diminishing stop opening. Ultimately the limitations set by diffraction

theory become significantly effective, and the

maximum resolving power of the lens falls below

the resolving power of the emulsion, and the overall definition then begins to worsen with diminishing stop opening.

9.4. Experimental Results of Actual Lenses

The primary purpose of this Circular is the

description of these test charts and the methods of

use. However, it may be of interest to list some

results obtained in using these charts for the test- ing of a representative group of lenses. The

results of tests will be discussed under the categories (a) experimental results with the highcontrast chart and (b) comparative results on axis

for high- and low-contrast cbart. The greater

emphasis will be placed on the high-contrast

targets, as this type of chart has been widely used

for a long period of time. It is probable that the

low-contrast chart will be used more extensively if the results of current research indicate that lens

ratings obtained therewith prove as useful as those

obtained with the high-contrast chart.

(a) Experimental Results with High-Contrast Chart

The resolving powers of five lenses of the type

used on small hand-held cameras were determined,

using the procedures described in section 8. In

addition, the resolution of a pinhole camera was

determined. The values of the resolving power of

these lenses for several apertures are listed in table

11. The lenses were chosen at random, and the

values listed should not be generalized as characteristic of any particular make or type of lens. The lenses tested include both foreign and domestic

products.

Eastman Panchromatic Microfile film was used

in making the test negatives for lenses A and B.

Eastman Spectroscopic plate, type V-B was used

for lens C. Eastman Plus-X film was used for lenses D and E. Eastman Panchromatic plate was

used for the pinhole camera F. The negatives

for A, B, D, and E, from which some of the

measurements were made, have been enlarged

and are reproduced in figure 14. It is unlikely

that any of the finer patterns will be resolved in the reproduction, as they were in the original

negatives. However, an examination of the

coarser patterns will show differences in the quality

of definition and some of the effects of astigmatism

at the larger angles. In table 11, it is clear that the values of resolution for axial imagery are usually higher than for other portions of the field. This is to be expected

Table 11. Resolving power at various apertures of severat lenses of the type used on small hand-held cameras ]

EquivRelative

Resolving power in lines per millimeter

(angular separation from axis)

Lens alent

focal length

aper- ture (/-numTangential Radial

ber)

0° 5° 10° 15° 20° 0° 5° 10° 15" 20°

A

mm

SO

1 22.8

45.6

68

6880

80

5668

6880

5668

5668

48

68

56

68

28

565680

68

6848

48

68

68

80

80

80

80

56

56

56

68

6880

56

68

68

8068

8048

48

48

68

6880

68

8048

48

40

56

68

80

5680

48

40

8

1116

( 22

8080

56

56

68

80

56

56

6880

5648

68

8056

48

68

80

56

56

B 50

f 4.5

5.6

1 8

I 16

56

5656

56

56

34

28

28

3456

20

1724

34

56

142034

3448

2434

48

5648

56

56

5656

56

40

40

56

56

56

4040

48

56

56

48

56

80

8068

48

5680

80

68

C 85 f 2

\ 5.6

I 11

68

68

68

68

68

68

34

48

48

1720

24

68

68

68

68

68

68

48

68

68

34

5680

D 101

f 4. 5 5.6

1 16

3440

40

40

34

34

3440

48

48

28

2840

48

48

28

28

3440

40

28

28

3440

40

34

40

4040

34

34

40

48

4848

28

28

48

4848

20

1424

3440

28

28

28

3440

E 101. _.

4.5

5. 6

8

| 111622

{ 32

28

28

34

28

34

34

34

28

28

28

28

3428

28

24

20

2428

28

28

24

1212

1720

1717

17

7

714

12

12

512

28

28

3428

3434

34

34

28

3440

40

40

34

34

34

3440

40

40

34

28

28

28

28

28

34

34

20

20

28

28

20

2428 F 5.6 5.6 5.6 5.6 4.8 5.6 5.6 5.6 4.8 4.8

in consequence of field curvature. Astigmatic j differences are also noticeable. Lens A demon1

strates the improvement in over-all definition that

results when the lens is stopped down; at //ll,

j this lens is resolving 80 lines/mm for all regions | except at 20°, where the resolution for tangential ! lines falls to 68 lines/mm.

The emulsions of both Microfile film and | Spectroscopic plates have resolution in excess of | 100 lines/mm. Consequently, the limit of resolu- - tion is chiefly determined by the lens or chart

and not the emulsion. Lens B has the same focal length as A but yields 56 lines/mm on the axis. Consequently, it cannot be used to resolve as fine 1 detail as A. Lens G resolves 68 lines/mm on the j axis, but it has a greater focal length than A. i Therefore, to compare results of A and C for resolution of object detail, the values obtained for C should be multiplied by the ratio of focal j lengths, which is in this case 1.7. The product of j 68 and 1.7 is 115, hence C will show finer object I detail than A on the axis, but is lower in perform- ! ance in the extra-axial region at 15 degrees.

While the resolution of Plus-X emulsion is not ! as high as Microfile, nonetheless, it is sufficiently

high that it can be used satisfactorily, particularly ! for the longer focal length lenses, such as D and E. \ The performance of lenses D and E cannot fairly I be compared with lenses A and B because of the i difference in emulsion used.

22
Figure 14. Results of tests of resolving power.

Halftone reproductions of enlargements made from negatives for four of the lenses whose test results are listed irj table 11. The upper row is a black and

white reproduction of a Kodachrome negative made with lens A. Microfile film was used in obtaining the negatives for the second and third rows for lenses A and B. Plus-X film was used for lenses D and E.

It is interesting to note, however, that when the

values of resolving power obtained for lenses D

and E are multiplied by 2 (i. e., ratio of the focal

lengths) the adjusted values compare favorably

with those obtained for lenses A and B.

The subject of rating lenses is a somewhat

controversial one because of the natural tendency

of each worker in the field to develop a method that

is sufficient for his own particular purpose. Such

rating methods are quite satisfactory so long as one remembers that each method has its limitations and ought not to be considered as applicable

to all types of lenses. For example, a rating

method for copying cameras where high speed

is not required cannot be applied to airplane- camera lenses, where high speed is important.

The requirements for a lens whose negatives are always contact printed should be different from

those for lenses whose negatives are to be enlarged.

For the use of small hand-held cameras, perhaps

the simplest method of rating lenses is to compute

the degree of enlargement possible before it becomes evident that further enlargement does

not add to the detail observable to the eye at normal viewing distance. Viewing distance varies

for different people but usually lies within the

range from 10 to 14 inches. The average eye

cannot distinguish detail finer than 7 lines/mm

at 10 inches or 5 lines/mm at 14 inches. Taking

the 14-inch distance as the more usual, then a negative may be enlarged until the coarsest detail

is 5 lines/mm. For most pictorial subjects, even

greater coarseness of detail will be satisfactory,

particularly at the corners or edge of the field. On the basis of a 14-inch viewing distance and a

5 lines/mm minimum in the enlargement, it is evident that so far as axial imagery is concerned,

all 5 lenses, A through E, are satisfactory for all indicated apertures. At aperture //5.6, considering imagery throughout the field, lenses A and C

will yield satisfactory enlargements. At aperture

//ll, lenses A, B, C, and D will yield satisfactory

enlargements.

The resolution of the pinhole camera, listed as

lens F in table 11, is of course very low because

of the very small relative aperture. However,

23
it is interesting to note that this low resolution is of the same order of magnitude as the resolving

power of the eye at a viewing distance of 14 inches.

Consequently, contact prints of the negative

made with this camera will contain all the detail

that can be readily seen with the unaided eye.

It is probable that a lens that }delds high values

of the resolving power with a fine-grain panchromatic film when tested with the aid of the high- contrast charts will have a high degree of color

correction. Some support for this belief was

obtained by photographing the high-contrast

charts with Kodachrome film with lens A. The

values of the resolving power observed on the

color negative were essentially the same as those

shown in table 11 for lens A. A reproduction of

this negative is shown in figure 14. The fact that values of 80 lines/mm were obtained throughout most of the image field suggests that this t}"pe of film might well be used in testing cameras for which other tj7pes of fine-grain film may not be

readily obtainable.

The black and white lines of the image on the

color film for lens A, as viewed through a microscope, were reproduced accurately, with no trace

of color at the edges of the tangential lines. If appreciable amounts of chromatic aberration were

present in the lens, the patterns for the different colors would not be exactly the same size, color

fringes would appear, and the white spaces sepa100%

Figure 15. Comparative results on axis for a lens tested with high- and low-contrast charts. These curve? are microdensitometer traces made by scannirjg the negative images of the high- and low-contrast charts. The light area of the reproduction of the chart at the bottom of the figure shows the portion of the image

actually 'scanned.

rating the black lines would have colored edges.|,

This effect would be most pronounced for thei tangential lines near the edge of the image area.[

Although the number of tests made with the colorl film were few in number, the results indicate that,

the charts may be used to determine the suitability! of a lens for use in taking photographs in color. [

(b) Comparative Results on Axis for High- and LowContrast Charts

The same arrangement of charts and posi-J

tioning of the camera, described in section 8.1 for testing with the high-contrast chart can be

used with the low-contrast chart. In some cases,

it may be desirable to use both simultaneously.

In this event, the two types of chart can be placed

side by side or above one another, as preferred, i The values of the resolving power determined for the low-contrast chart wall usually be lower than , those obtained with the high-contrast chart.

The interpretation can be done visually in a | satisfactory manner. However, if one has access - to a recording microdensitometer, the interpreta-

) tion can be done with its aid. The difference ; in performance of a lens for the 2 types of chart,

as determined with the aid of a recording microdensitometer, is shown in figure 15. \ In making this test, the 2 charts were placed

side by side and photographed at the standard j distance of 26/. The charts were located at apj proximately 2.5° from the axis and on opposite

sides thereof. Consequently, the imagery for

j both can be regarded as near axial. In addition,

the symmetrical location of the charts insures that

the imagery is being compared under the same

experimental conditions. The images were registered on Eastman V-G emulsion. The exposed

plate was processed in Eastman D-19 developer

at 68° F for 3 minutes. The microdensitometer

traces of the two images were made with the inLINE FREQUENCY, LINES/mm

Figure 16. Variation of contrast in the image as a function

of line frequency

These curves show the measured values of image contrast taken from the

traces shown in figure 14. Curve 1 shows the results for the high contrast

target and curve 2 shows the results for the low-contrast target. 24
strument operating at the same sensitivity. The

area of each negative actually scanned is indicated

by the light area of the reproduction of the chart

shown at the bottom of figure 15. The transverse scale of the reproduction of the chart and

the microdensitometer traces are the same in the figure. The microdensitometer traces and

the reproduction of the chart are so placed in the figure that ready comparison of the performance of the lens for any pattern of both high- and

low-contrast chart is facilitated. For either

trace, the distance between the peaks and the

valleys is a measure of the contrast in the image.

On the original traces, it is clearly evident that the

68-line pattern is resolved for the high-contrast

chart, whereas the 48-line pattern is the finest one

definitely resolved for the low-contrast chart.

The curves in figure 16 show the manner in which contrast in the image decreases as the

indicated resolving power or line frequency in

lines per millimeter increases [12]. Curve 1 shows the results for a high-contrast target

(target contrast approximately 1.4), and curve 2 shows the results for a low-contrast target (target contrast approximately 0.17, which is somewhat

lower than that of the low-contrast charts provided with this Circular). The emulsion used in

this test has a fairly high contrast. When similar

tests are performed with low-contrast emulsions,

the image contrasts obtained will be lower, and

the observable resolving power will be lower than

those shown for the V-G emulsion.

10. Additional Uses of Test Chart

Because the test chart in NBS Circular 428 was

found useful for so many optical tests performed

in the testing of goggles, sunglasses, and telescopes,

it was thought advisable to include a discussion of

such uses. It has been used mainly in connection

with definition tests and for this purpose the chart

is specified for use in testing for compliance with

the following specifications.

10.1. Test for Goggles and Sunglasses

(a) Prismatic Power

Federal specifications usually require that goggle

lenses should, among other requirements, be free from prism effect caused by nonparallelism of the

lens surfaces, be free from refractive power, and

not lower the visual acuity of the user. Because

it is impracticable to eliminate these defects in

their entirety, tolerances for each have been

established. In the case of nonparallelism of

surfaces, the prism effect must not exceed 1/16

prism diopter (4 minutes angle between surfaces).

Lenses shall not be negative in refractive power

in any meridian and shall not have in any meridian

a positive refractive power exceeding -f- 1/16

diopter. A line pattern with lines separated not more than 24 seconds should be clearly distinguishable when viewed through the lens placed

in front of an 8-power telescope.

In order that the charts, accompanying this Circular, will enable the user to test for prismatic

power of goggle lenses, a prism target has been

included to permit the detection of prism effect in excess of 1/16 diopter. The 2 concentric circles in the center of the chart are of such size that

their radii subtend angles of 1 and 2 minutes when

viewed at a distance of 35 feet. A simple 1/16

diopter prism having a refractive index of 1.5 will deviate a beam of light by 2 minutes of arc. Consequently, when properly used, this chart can

be used as a go-not-go test for prismatic effect on goggle lenses. The arrangement for testing a goggle lens is shown in figure 17. The exact statement of the test from Federal

Specification GGG-G-501b is as follows: "Prismatic power.—The lenses are to be tested for

prismatic power with an 8-power telescope which

has an effective aperture of 0.75 inch and is equipped with cross hairs in the focal plane of

the ocular. The telescope is to be focused on an

illuminated target, placed at a distance of 35 feet from the telescope objective, comprising a central

dot and a concentric circle 0.5 inch in diameter.

The telescope is to be so alined that the image of the central dot falls on the intersection of the

cross hairs in the focal plane of the ocular. The

lens is to be held in front of the objective lens of the telescope and if the intersection point of the

cross hairs falls without the image of the circle,

the prismatic power of the goggle lens exceeds

1/16 prism diopter."

It is worthy of mention that the use of tele- scopes having more than 8-power or with an

effective aperture other than 0.75 inch will not

necessarily lead to erroneous values. The advantage of the low power is that the imagery is less likely to be blurred if appreciable refractive

power is also present in the lens under test. Use

of telescopes having less than 8-power leads to considerable uncertainty in the determination

because the limit of resolution of the eye is usually

not less than 1 minute. Use of telescopes having

Federal Specification: GGG-G-501b__

GGG-G-511a.

GG-T-621...

U. S. Army Specification: 5 1-70-2 C

Commercial Standard: CS159-49

Goggles, eyecup, protective, impact-resisting (chippers',

grinders', etc.). Goggles, eyecup, protective

(welders)

.

Transits, 1-minute; and transit

tripods.

Optical components for fire control instruments; general

specification governing the manufacture, assembly, and

inspection of.

Sun glass lenses made of ground

and polished plate glass thereafter thermally curved.

25
35 FT 3=^

Figure 17. Arrangement of chart and telescope for testing goggle lenses. The upper portion of the figure shows the relative positions of chart A,

telescope T, and goggle lens 0. When no goggle is in front of telescope T, the

cross-hairs in the occular of the telescope are superimposed upon the image of the chart as shown at B. if a goggle, whose surfaces are out of parallel by

4 minutes of arc, is placed in front of T, the cross-hairs are displaced as shown

in C.

as much as 20-power or higher is satisfactory, but

in such cases it may be necessary to reduce the

effective aperture of the telescope to achieve

sufficient depth of focus to minimize the blurring

that may arise from refractive power in tbe goggle

lens. Caution should be exercised in the reduction of effective aperture that it not fall below the

pupil diameter of the average eye.

(b) Refractive Power of Goggles

The same arrangement shown in figure 17 can also be used to measure refractive power,

provided the focusing movement of the telescope

is suitably calibrated. It is usually convenient

to use an externally focusing telescope with a rack and pinion movement. The instrument is calibrated for zero power by focusing on the

test chart and then scratching a suitable index

line on the draw tube to show the position of zero power. A standard lens of +1/16 diopter

power is then placed in front of the objective

and the position of best focus found. This position is also marked. Thereafter when testing

goggle lenses, if the position of best focus falls within the range between these two marks, the

lens satisfies the refractive power tolerance

ranging from 0 to +1/16 diopter. If a standard!

+ 1/16 diopter lens is not readily available, aj standard +1/8 diopter lens may be used. In!

this case, it is necessary to accurately halvei

the distance between the zero and 1/8 marks

I

and mark this halfway point as +1/16 diopter. |

(c) Definition Test The same arrangement shown in figure 17 can also be used in conducting a definition

test. In Federal Specification GGG-G-501b,

the definition requirement is that pattern No.

20 shall be clearly resolved at a target distance

of 35 feet. The line spacing for pattern No.

20 in the present chart is the same as that for pattern No. 20 in NBS Circular 428. Con-H

sequently, the new chart can be satisfactorily

used to test the definition requirements.

10.2. Resolution Test for Telescopes and

Binoculars

It is frequently desirable to determine the

limit of resolution for telescopes and binoculars.

The limit of resolution is defined as the smallest

angle separating 2 points for which the 2 points

are still distinguishable as separate points. The

theoretical limit of resolution for a telescope can be approximately determined from the

formula

Limit of resolution in seconds

5.0

ii

diameter of objective in inches (25)

However, it sometimes happens that a telescope

is diaphragmed in a manner not clearly noticeable, so that the effective aperture is reduced.

The above relation is then no longer true. In

addition, various lens aberrations tend to in- crease the limit of resolution, so that the only

satisfactory way to determine the limit of reso- lution is by measurement. It has been shown

at various times that the limiting angle of reso- lution for lines is substantially the same as that for points. Consequently, the line patterns in the new chart can be readily used to determine limit of resolution. To do this, it is only necessary to view the chart through

the telescope under test, with the chart placed

at some convenient distance in front of the

objective.

For the convenience of the user, the angular

separations of the line elements of the various

patterns have been computed for a series of distances and are listed in table 12. Similarly,

table 13 gives the angles subtended by the

circle targets. To make a determination of the

limit of resolution, it is only necessary to view

the target through the telescope at a given

distance and note the last pattern that is dis- tinctly resolved. The limit of resolution can

26
then be found in table 12. It must be remembered that the magnification used must be high

enough to make the readings significant. If the limit of resolution of the eye is assumed

to be 1 minute, then the product of the limit

of resolution and magnification of the telescope

must exceed 60 seconds before one can assume

that the eye is not the limiting factor in the

determination. It is frequently desirable to place an auxiliary telescope behind the telescope

being tested in order to make certain that the

overall magnification is sufficiently great.

Table 12. Angular separation of lines in the various

patterns at different viewing distances

Pattern numberLine width

Angular separation for a target distance of—

25 ft 35 ft 50 ft 100 ft mm Seconds Seconds Seconds Secon ds 80 0. 31 8. 5 6.0 4.2 2.1

56 .45 12.1 8.6 6.0 3.0

40 .62 16.9 12.1 8.5 4.2

28 .89 24.2 17.3 12.1 6.0

20 1.25 33.8 24.2 16.9 8.5

14 1.79 48.3 34.5 24.2 12.1

68 0.37 10.0 7.1 5.0 2.5 48 .52 14.1 10.1 7.0 3.5

34 .74 19.9 14.2 10.0 5.0

24 1.04 28.2 20.1 14.1 7.1 17 1.47 39.8 28.4 19.9 10.0

12 2. 08 56.4 40.3 28.2 14.1

Table 13. Dimensions of circle targets and angular

subtenses at a series of viewing distances

Circle numberRadius

Angle separating center and periphery for target distance of—

25 ft 35 ft 50 ft 100 ft

1 mm3.09

6.19

min

1.4 2.8

min

1.0

2.0

min

0.70

1.4

min

0. 35

2 .70

Width of lines forming circles and cross

Angle subtended by width of line for target distance of—

25 ft 35 ft 50 ft 100 ft mm

0.155 Seconds

4.2 Seconds3.0 Seconds2.1 Seconds

1.0

The authors express their appreciation to other

members of the staff of the National Bureau of

Standards for assistance rendered during the vari- ous phases of the preparation of this paper.

Edgar D. Watts assisted in the design of the test chart and made the drawings used to illustrate

this paper. Walter R. Darling and William P. Tayman made measurements on the engraved

chart to insure its accuracy. Fred W. Rosberry,

Roland V. Shack, and William P. Tayman assisted

in assembling the photographic equipment, made

the necessary charts and chart holders, made and

read the test negatives that are used in describing

the test methods and results.

11. References

[1] A test of lens resolution for the photographer. I. C. Gardner, NBS Circular 428 (1941).

[2] Charts for testing lens resolution, NBS Miscellaneous

Publication Ml66 (1940).

[3] Compensation of the aperture ratio markings of a photographic lens for absorption, reflection, and

vignetting losses. I. C. Gardner. J. Research

NBS 38, 643 (1947) RP1803, 10 cents; J. Soc. Mot.

Pict. Eng. 49, 96 (August 1947).

[4] Sources of error in and calibration of the F-number of photographic lenses. F. E. Washer. J. Research

NBS 41, 301 (1948) RP1927; Soc. Mot. Pict. Eng.

51, 242 (1948).

[5] Precision camera for testing lenses. I. C. Gardner

and F. A. Case. J. Research NBS 18, 449 (1937)

RP984.

[6] Resolving power and distortion of typical airplane- camera lenses. F. E. Washer. J. Research NBS

22, 729 (1939) RP1216.

[7] Characteristics of wide-angle airplane-camera lenses. F. E. Washer. J. Research NBS 29, 233 (1942)

RP498.

[8] Spurious resolution of photographic lenses. R. N.

Hotchkiss, F. E. Washer, and F. W. Rosberry, J. Opt. Soc. Am. 41, 600 (1951).

[9] C. W. Kendall and B. A. Schumacher, Photo Technique 3, No. 4, 51 (1941).

[10] E. W. H. Selwyn and J. L. Tearle, Proc. Phys. Soc.

LV1~II, 493 (1946).

[11] L. E. Howlett, Can. J. Research 24, Sec. A, No. 4, 15 (1946).

[12] New resolving power test chart. F. E. Washer and

F. W. Rosberry. J. Opt. Soc. Am. 41, 597 (1951).

[13] Research and development in applied optics and

optical glass at the National Bureau of Standards. A review and bibliography. I. C. Gardner and

C. H. Hahner. NBS Miscellaneous Publication 194

(1949).

[14] J. I. Crabtree, Trans. Soc. Motion Picture Engrs. 11,

77-87 (1927).

[15] J. I. Crabtree and B. W. Henn, Am. Phot. 33, 78

(1939).

[16] Region of usable imagery in airplane-camera lenses. F. E. Washer. J. Research NBS 34, 175 (1945)

RP1636.

Washington, August 14, 1952.

27
Appendix. NBS Microcopy Resolution Test Charts No. 1010a

Starting December 1, 1967, the microcopy

resolution test charts previously issued by NBS

as Standard Reference Material No. 1010 were

replaced with a new chart having higher spatial

frequencies [1] and designated as Standard Refer- ence Material 1010a.

The previous type was designed in 1963 and

had 21 patterns of black bars on a white background ranging from 1 to 10 cycles/mm. These

patterns were arranged to permit the extension of the chart to include higher spatial frequencies [2]. The new type has five additional patterns with

spatial frequencies of 11, 12.5, 14, 16, and 18 cycles/

mm. In every other respect both charts are

identical and may be used for the same purposes

[3]-American industry and Government spend

about a third of a billion dollars annually to microfilm records and preserve films. To assure that the

microfilmed images are of adequate quality to store the required information, microfilm contracts

generally stipulate that the resolving power of the

complete microfilming system be evaluated by

means of NBS microcopy resolution test charts. The charts are placed in several locations on the camera copy board and are photographed, in the same manner as a document to be recorded. The

resulting image is then examined with a microscope. The number of cycles/mm in the smallest

pattern in which the bars can be counted with

reasonable assurance is the resolving power of the

system.

For many years the charts containing these patterns were produced and issued by NBS as part of the Bureau's standard reference materials program. At present the charts are procured from commercial sources and subjected to quality control

by the Electron and Optical Physics Section. The

current volume is about 25,000 charts per year. Because of the limitations imposed by the

methods and materials used in the production of the charts, the 18 cj^cles/mm pattern does not

meet the high quality standards maintained for the 10 cycles/mm pattern. Despite these limitations, the additional spatial frequencies should

prove to be of great value to many users, although

most systems in use today will probably not re- solve them.

The new chart bears the designation 1963-A

because it is a minor modification of the 1963

design. All NBS microcopy resolution test charts,

regardless of date of issue, satisfy the requirements

of all Government specifications for microfilming

services. If future specifications should require

charts having spatial frequencies above 10 cycles/

mm, the new charts will, of course, be required.

The new charts, NBS Standard No. 1010a,

Microcopy Resolution Test Chart, are sold in

sets of five [4]. Instructions for the use of the

charts are supplied with each order.

References

[1] Standardization and research at the National Bureau

of Standards, by C. S. McCamy, Appl. Opt. 6, 28

(Jan. 1967).

[2] The NBS microcopy resolution test charts, by B. H.

Fouquet, Proceedings of the Twelfth Annual Meeting

of the National Microfilm Association, pp. 67-76

(1963).

[3] Standard Reference Materials issued by NBS are described in the Catalog of Standard Reference

Materials, NBS Special Publication 260. The

current edition of NBS Special Publication 260 may

be purchased from the Superintendent of Documents,

U.S. Government Printing Office, Washington, D.C.

20402. In addition, Supplements which up-date the Catalog are available from the Office of Standard

Reference Materials, National Bureau of Standards,

Washington, D.C. 20234.

[4] These standards may be purchased from the Office of Standard Reference Materials, National Bureau of Standards, Washington, D.C. 20234. As of January

1, 1973, the 'price was $14 per set of five.

28

1.0

I.I

111 —

Jfr 1

3.

6

!ff 'Li

1.25

I 2.5

1 2.2

2.0

1.8

1.4 I 1.6

MICROCOPY RESOLUTION TEST CHART

NATIONAL BUREAU OF STAN0AR05 — 1963

1.0

1 2.8 2.5

13.2

3.6 1

2.2 m 1

2.0

1-25 III 1.4 i 1.6

MICROCOPY RESOLUTION TEST CHART

NATIONAL BUREAU OF STANDARDS- 1963-A Figure Al. The microcopy resolution test chart designed 'and announced\ in 1963 {left) went on sale December 1, 1964. The chart designed and announced in 1967 {right) went on sale December 1, 1967. These

charts are for illustration only and should not be used for test purposes.

U.S. GOVERNMENT PRINTING OFFICE: 1973
FORM NBS-114A (1-71) U.S. DEPT. of comm. 1. PUBLICATION OR REPORT NO. 2. Gov't Accession

RIRI IfifiRAPHIC DATA „ _ , No. SHEET NBS SP-374

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

Method for Determining the Resolving Power of Photographic

Lenses

5. Publication Date T„„ Q 1Q77 June Vj (

$

6. Performing Organization Code

7. AUTHOR(S)

Francis E. Washer, Irvine C. flardner and Chris E. Kuvatt

8. Performing Organization

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Ptoject/Task/Work Unit No. 2320157

11. Contract/Grant No.

12. Sponsoring Organization Name and Address Same as no. 9

13. Type of Report & Period Covered

Final

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

Supersedes NBS Circular 533

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.) This publication supersedes NBS Circular 533, issued May 20, 1953 „ It

contains the original data and a new appendix describing the NBS Microcopy

Resolution Test Charts No. 1010a. It provides the photographer with two

sets of charts by which the resolving power of a photographic lens may be

numerically measured with respect to a definite scale of values. A detailed

description is given of the procedure and technique to be followed in order

that comparable values may be obtained by different observers. The test provides an objective method of testing a photographic lens. The six charts of

one set are printed in black ink on a white background to form a high-contrast

chart. The six charts of the other set are printed with gray ink on a gray

background to form a low=contrast chart. Additional uses of these charts are also described. These uses include the testing of goggle lenses for definition

and prismatic power and the testing of telescopes and binoculars for definition.

17. KEY WORDS (Alphabetical order, separated by semicolons)

Photographic lenses; resolution test charts; resolving power.

18. AVAILABILITY STATEMENT

|~xl UNLIMITED.

I I FOR OFFICIAL DISTRIBUTION. DO NOT RELEASE

TO NTIS.

19. SECURITY CLASS

(THIS REPORT)

UNCLASSIFIED

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

21. NO. OF PAGES

32

22. Price

$3.00

USCOMM-DC 66244-P71
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