CLARICE L. NORTON*Ogden ALC

Hill Air Force Base, Utah 84401

Optical and ModulationTransfer FunctionsInterim Report of ISP Commission I Working Group

IntroductionHISTORY OF ISP ACTIVITY IN OPTICAL AND

MODULATION TRANSFER FUNCTIONS (MTF)

T HE FIRST significant work of Commission I(Primary Data Acquisition, the Interna­

tional Society of Photogrammetry (ISP) onOptical Transfer Functions OTF coveringmany years of study was reported by Brock,1

presented the theory of transfer functions,methods of measuri ng photogrammetriclenses, and general applications in aerialphotography. The results of an interlabora­tory testlofa 12-inch,f/4Iens) in which eightlaboratories in four nations (West Germany,England, Sweden and the United States) par­ticipated showed a spread in MTF values both

ABSTRACT, The Working Group on Optical and Modulation TransferFunctions is concerned with OTF and MTF standards, with compara­tive lens testing using OTF techniques, with OTF test equipment andits control, and with evaluation of the quality of aerial and spacephotography. The status of work within these fields is reported withemphasis on applications.

Simple and informative control tests using OTF techniques are nowroutine in lens manufacture. The standards of several nations pointou t differen t concepts and different controls. As a result, the WorkingGroup will propose revision of Section 6 of Commission I document"Procedures for Calibrating Photogrammetric Cameras and RelatedOptical Tests."

The application of MTF techniques to analysis of remote sensingimagery are becoming increasingly impo·rtant. MTFs derived fromaerial and satellite photographs ofperiodic targets, and artificial andnatural edges have been successfully employed to analyze sensarperformance and image quality. Comparing these MTFs withlaboratory 'resolution and MTF data for the same camera system, thephotogrammetrist can establish 'resolution values for the operationalimages. Other photogrammetric and cartographic applications ofMTFs 01' related functions include: analysis of pointing precision andaccuracy; quality control studies; and the determination of the fidel­ity with which image detail can be transferred through the mapreproduction process.

A project to assure optimum image quality ofaerial photography isbeing conducted by the US Air Force. All phases of the photographicprocess are being examined and new standards are being writtenand/or old ones modified. An Image-Quality Manual is being writtenwhich at certain stages requires MTF analyses.

Chairman of the Working Group on ImageQuality at the 1968 ISP Congress. That report

* Presented at ISP Symposium, Comm. I, Stock­holm, August 1974. Mrs. orton served as Secre­tary of Comm. 1 1968-1972.

on-axis and at 15° off-axis, the later as high as30 percent. Although the study could not in­clude an analysis of the cause of the differ­ences, it greatly emphasized the need for astudy of measuring errors and a means forcontrolling them.

203

204 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING 1975

A section on transfer-function measure­ment was written for inclusion in the ISPdocument "Recommended Procedures forCalibrating Photogrammetric Cameras andRelated Optical Tests." This became Section6 on Congress recommendation.

The work on transfer functions continuedduring the 1968-72 quadrennium, primarilyunder Welender. His report2 to the 1972Congress covered theory, MTFs offilm and theproposed U.S. standard for film MTF, currentwork on MTF and application to aerial photog­raphy. His working group recommendedcontinuation of OTF and MTF studies. Norton3

organized a panel on OTF standards submit­ting a report based on international answersto a questionnarie that showed the complexproblems associated with drafting an ISPstandard. The majority opinion was that astandard was not yet timely. Correlating be­tween laboratories showed improvement(1972) but significant variables still existedon off~axis results. Hopkins and Dutton4 re­ported that different design programs alsogave different MTF data.

PRESENT STATUS.

At this date (1974) there is increasing em­phasis on problems of partial coherence,noise, and the evaluation of phase. Inter­ferometric methods are recommended asbeing more accurate, complex scanningequipment and complicated programs arebeing employed.

As the studies on transfer functions ac­cumulate one becomes increasingly aware ofthe boundary conditions that limit and defi nethe test techniques, the test equipment, andthe devices to which they can be applied. IfISP standards are to be written, it is not feasi­ble to limit them to photogrammetric lenses,nor to limit the test equipment and avoidtechniques which are most diverse.

PROPOSAL Fon SECTION 6.

The Working Group therefore proposes torewrite or modify Section 6 of the "Recom­mended procedures for Calibrating Photo­gram metric Cameras and Related OpticalTests" with the purpose of showing MTF andOTF as a means of stating the performance oflenses in a which which can be universallyunderstood. The test result should be capa­ble of being reproduced on different ap­paratus, of different design or priniciple. It isexpected that the precautions to assure accu­racy and the basic definition will be includedin the document. To assist the general read­ers, selected references to national or inter­national standards, expanded definitions,tutorial reviews, etc., will be included.

PRELIMINARY CONCLUSIONS AND REC­OMMENDATIONS.

PROPOSALS CONCERNING ASTANDARD.a. As explained in the previous paragraphs,it is not advisable to produce a pure standard.b. The working group proposes to present anew edition of the present Section 6 of theISP "Recommended Procedures ...."c. The additions and/or modifications to Sec­tion 6 will include:

(1) Basic defInitions.(2) Methods of testing (none specifically

recommended).(3) Precautions or limitation of the equip­

ment and techniques.(4) Calibration tests of test equipment.(5) Photo cell performance referenced to

spectral characteristics of selected or stan­dard film.

(6) Light source - white (mean sun) andone or more narrow band, preferably 525 nm.

(7) Testing of cameras - physical re­quirements.SYSTEM TESTING.

The ability to locate and measure imagesfor photogrammetric purposes dependsprimarily on their quality. Studies should becontinued tying together location andmeasurability as a function ofmodulation andphase_

The 1972 Congress Resolution. The secondresolution of Commission I of the XII Con­gress (August 1972) reads as follows:

"Commission I has found that the results ofthe various Optical Transfer Functions (OTF)testing methods are not in sufficient agree­ment to permit the development of an OTFstandard. However, because OTF has beendemonstrated to be a scientific tool forevaluating the image quality of lenses, it isrecommended that appropriate studies, in­vestigations, and correlation testing of OTFcontinue.

"Furthermore, in accordance with the find­ings and suggestions of the working group onModulation Transfer Functions (MTF), Com­mission I recommends continuation of thisactivity, including establishment of specifi­cations and tolerances for test equipment andquality assessment of imagery." The previ­ous paragraphs recommend continuedstudies by this working group.

Correlat-ion Testing. The most extensivecorrelation testi ng is that recently conductedby SlRA6 A paper covering this testing waspresented at the Symposium in Sweden (Au­gust 1974). Correlation testing should be con­tinued until such time as agreement is satis­factory or causes of disagreement can be iso­lated.

OPTICAL AND MODULATION TRANSFER FUNCTIONS 205

THE OTF/MTF WORKING GROUP

Three people comprise the OTF/MTF Work­ing Group which was organized so that theactivity of work within the image-qualityfield of transfer functions would be reportedand further consideration could be given todeveloping an OTF Standard. Gerald C. Brockhas continued his research work on MTF lenstesting and evaluation (begun at Itek undercontractto the US Air Force5 ) and is presentlyacti ve in SlRA6 as well as at Vi nton Ltd. 7 wherehe has introduced MTF in Quality Control.The involvement with SIRA has kept him ac­tive on the latest studies in correlated testingand the techniques for calibrati ng lab­oratories. He will report on the proposed re­vision of Section 6 and expects to rewrite thatdocument.

Dr. Roy Welch has been developing MTFanalytic techniques for evaluating photo­graphic systems for many years. In his work atGeological Survey he has frequently beeninvolved in the analysis of imagery takenfrom satellites. Since the image quality ofsystems determine the quality (and probablyquantity) of information of our remote sen­sors, Welch will keep us informed onworld-wide system MTF projects. He is pres­ently professor in the Dept. of Geography atthe University of Georiga.

Clarice L. Norton has worked in industryfor several decades at Fairchild Camera dur­ing which she was involved in determiningthe photographic performance quality of aer­iallenses and cameras, becoming interestedin MTF testing when first investigated for theAir Force by Brock (at Itek). Now working inthe Maintenance Director's Camera Calibra­tion Facility and still concerned with testingof aerial cameras, she represents the produc­tion viewpoint of industry and government.Norton will report on the status of presentwork as well as the special project on analyz­ing the imagery of two photograrmnetriccameras now being accomplished atWright-Patterson Air Force Base.

PROGRAM FOR THE WORKING GROUP ON OTM AND MTF

A.O StandardizationA.I National StandardsA.2 I S P Proposed StandardsA.3 Tests for Accuracy and Precision

B.O OTF TestingB.I Methods of TestingB.2 Production TestingB.3 OTF in ResearchB.4 OTF in Lens Design

C.O System TestingC.I Working Group Test at Wright-

Patterson Air Force BaseC.2 Space ImageryC.3 Reports from NationsC.4 Application to Quality Control

D.O Current StudiesD.I Signal to NoiseD.!.I Significance, Methods of Analysis,

ControlD.2 PhaseD.3 CoherenceD.4 Cascadi ng

E.O Interferometric Methods

F.O Practical ApplicationF.I Aerial Photography - Use of Natural

Test EdgesF.2 Cascading of ComponentsF.3 Coherence Problems

G.O Recommendations and Proposals.

MTF SYSTEM TESTING FOR WORKING GROUP

Photographs taken by the Canadian AirForce (The Zeiss & Wi ld cameras bei ng usedby Commission I Image Quality WorkingGroup) under Ziemann is now beinganalyzed at the Dynamics and Environmen­tal Evaluation Branch, Air Force AvionicsLaboratory, Wright-Patterson Air Force Basein the United States. Approximately 50 edgeswill be traced for each camera coveri ng the 23cm x 23 cm format. In addition to MTF otherinformation will include exposure evenness,granularity, aerial contrast, resolution. A fullreport will be available at the 1976 Congressin Helsinki.

Standards

A review ofthe world-wide situation on OTFstandards is considered essential to theWorking Group studies and the basis for rec­ommendations on standards. This sectionlists the OTF. MTF. and related standards whichare now in use in member nations or arebeing developed and it discusses the activityassociated with the establishment of thosestandards as contained in private letters ofcommunication and publishings. (It shouldbe noted that this is an interim report and thatall national standards are not included at thistime.)

Interest in standards began as far back as1961 when the International Commission onOptics agreed on definitions for Optical,Modulation, and Phase Transfer Functions.Since then other definitions and concepts re­lating to Optical Transfer Function testing

206 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSI G 1975

and evaluation have been reviewed and pub­lished.

Simultaneous with the development of testequipment and test techniques was the in­terest in standards which are only useable iftests on different apparatus produce similarresults. As correlation testing betweenlaboratories emphasized the differences be­tween test values, testing requirements andtest equipment were refined. Today severalcountries have OTF specifications differing incomplexity; yet well-controlled correlationstudies using the same lens are still showingdifferences in test values particularly at off­axis angles. Although it is true that these dif­ferences have been decreased relative tosome of the early studies, the situation is stillsomewhat confused.

The information in the following para­graphs will provide a better understandi ng ofthe status quo, problems which have beenmet in developing and using standards, andsome of the solutions.

GREAT BRITAI1\:

STA1\:DARDS ACTIVITY

Government and commercial agencieshave been using photo-electric techniquesfor over a decade for measuring the line­spread function from which the on is ob­tained by Fourier analysis. The method de­veloped at the Royal Aircraft Establishment(RAE) has resulted in British Standard 4779:(1971); "Recommendations for Measurementof the Optical Transfer Function of OpticalDevices." The RAE equipment for measuringon is now organized in collaboration withthe ational Physical Laboratory as the stan­dard of reference for OTF measurements con­ducted under the control of the British Cali­bration Service. This Service issued publica­tions 0702 and 0751 which set out the generalconditions for testing and approval of alaboratory's equipment and techniques cer­tifying their capability to perform opticaltransfer function measurements.

These critiques rate laboratory capabilityin accordance with their ability to meet thevalues set by the reference laboratory (RAE)for the on testing ofstandard lenses. In addi­tion, there are specified requirements, suchas the necessity that the test equipment bemechanically accurate and repeatable, theenvironment be controlled, the spectralcharacteristics of the source and sensor beknown, and Ii nearity be proved or calibrated.

The RAE is now writing specifications fornew aircraft lenses which greatly reduce test­ing time. The MTF evaluation is for a single,carefully selected spatial frequency. The re-

lationship between this and other reduced~ITF criteria and the corresponding differ­ences in picture quality under typical flightconditions are currently being studied.They assume at present, that a 20 percent fallin MTF at this single frequency is barely per­ceptible as a change in picture quality andcan be used as the tolerance for acceptabilityin production specifications. An experimen­tal study is in progress to verify this assump­tion. The evaluation includes use of photo­graphic emulsion threshold modulationcurves.

In many tests the computed value of the~ITF using monochromatic light has been thecriterion of accuracy. A new polychromaticon computer program is now being studiedfor use in setting the absolute MTF level towhich the acceptance figures ina productionspecification will be related.

INVESTIGATION OF EQUIPMENT AND METHOD~

SIRA Institute Image Assessment Group isa U.K. collaborative activity which hasheaded many qualitative investigations onOTF. Their findings, frequently written inconjunction with RAE are published in paperswhich are excellent references for those es­tablishing or controlling an OTF test labora­tory. These papers include:

• Accuracy in Image Evaluation: Setting upan OTF Standards Laboratory.

• Influence of Optical Bench Errors on Accu­racy of OTF Measurements.

• The Use of Si mple Optical Systems for ver­ifying the Accuracy of OTF Equipment.

• The Use ofStandard Test Lenses for Verify­ing the Accuracy of OTF Equipment.

• Specifications for Checking the Perfor­mance of ~ITF Equipment at Large FieldAngles using a Gimbal Mounted f/4,200-0101 doublet lens.

• Dimensions, Tolerances, and OTF Charac­teristics of the SIRA Group 200-0101 DoubletTest Lens.

• Significance of OTF Methods in AssessingLenses to be Used with Partially CoherentIllumination.

• AWorkshop Instrument for Testing Binocu­lar and Other Sights Using the MTF Criter­ion.

• OTF Standards for Aerial Mapping Lenses.

RESEARCH & CURRENT STATUS

An extensive program of work on the accu­racy and reproducability of OTF measure­ments made in eight different Europeanlaboratories has just been completed and ananalysis is in draft. A paper was presented onthe results of this analysis at the Symposiumin Stockholm, August 27-29, 1974.

OPTICAL AND MODULATION TRANSFER FUNCTIONS 207

STANDARDS IN THE U.S.A.

Ai'SI PH2.36

Proposed American National StandardTerms, Symbols, and Notations for OpticalTransmission and Reflection Measurements(Optical Density).

Many different optical systems are used inphotographic practice, and the number ofdif­ferent spectral and geometric conditions incvolved are increasing. It has, therefore, be­come important to expand ~he scope and ver­satility of standards that pertain to the meas­urement of optical transmission and reflec­tion characteristics of photographic materi­als.

This standard identifies three modes ofpropagation (one of which is the generalmode propagation), three kinds of referenceflux, and two mathematical forms, a total of 18different measurements of modulation. Thesystem of specification provides a standardway of specifying geometric conditionswhich are closer to practice, as well as theextreme situations, permitting their precisedescription. It standardizes on measure­ments such as diffuse transmission density,specular density, the range between the two,projection density, 45° and 0° reflection den­sity, and transmission micro-density, thelatter affecting the response of microden­sitometers and photometers in OTF and MTFanalyses.

ANSI I'H2.39

Proposed American National StandardMethod for Determining the PhotographicModulation Transfer Function of Transpar­ent Photographic Films (Monochrome - Con­tinuous Tone for Still Photograph).

This standard was reported by the MTFWorking Group 1968-72. As the result of cir­culation for voting further modifications areto be made. The basic standard is alreadybeing used by film manuhlcturers and cus­tomers, particularly government, in reportingphotographic MTF values and in verifyingthem.

The Forward, which is not a part of theproposed standard, draws attention to the factthat "One of the advantages of the modula­tion transfer system ... is cascading ... al­though such cascading would be useful anddesirable in systems which include photo­graphic components, this standard does notclaim that the Standard Photographic Mod­ulation Transfer Function will necessarilygive a representative system response if it iscascaded with other components of the sys­tem. Factors beyond the scope of this stan-

dard have to be included when precise pre­dictions of the density of fine details inphotographic reproduction are to be derivedby cascading ..."8

The user of this standard is further re­minded that photographic MTF is a measure ofthe apparent scattering of light within anunprocessed emulsion and not a measure oftransmittance of the processed image. Thegradient of the density-log exposure curveprovides a very approximate factor relatingthe modulation associated with the light scat­tered within the unprocessed emulsion.Nelson's paper8 gives a more exact relation­ship. Frequencies beyond two hundredcycles/mm are not considered.

PH 3.57 TASK FORCE

The American National Standards Institute(ANSI) PH 3.57 TflSk Force is developing anOptical Transfer Function Standard in threeparts. Part I, Theoretical Background, Defi­nitions, and Concepts, is in draft from for afinal review. Two other sections on Test Pro­cedures and Instrumentation are being writ­ten. The approach is to look at the standard asa living, updatable standard initially cover­ing a body of knowledge with presentmethods and practice, and allowing for issueof addends (without obsolescence of themajor body of work) to cover specific situa­tions, such as interface to CRT, eye, etc., and torecommended practices with regard tocoherence effects, mechanical andtrigonometric precision, documented testlenses for setup and control, trouble zones insetup and measurement, computer needs inanalysis, etc. Present plans follows.

Part II, Methods, will contain sine-waveresponse, square wave, point spread, linespread, pupil function, interferometricmethods. Part III will cover establishingmaster references, (lenses) mounting withfull details, dimensions, angles. There willbe an appendix of important factors, tables,needs to know, etc. Each part will comprise acomplete issue, standing on its own.

If plans materialize this standard willprobably be the most comprehensive of anywritten to date. It may, therefore, take con­siderable time to reach agreement and publi­cation.

INTERLAllORATORY COMPARISONS OF MEASUREMENTSAND COMPUTATIONS

Two extensive studies of interlaboratorycomparisons of MTF measurements and com­putations were made under contract to theUnited States Air Force. The first well knownresults reported by Brock and Attaya9 showed

208 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING 1975

SIgnificant lack of agreement on measure­ments of a 24-inch aerial camera lens, thecause of which was not resolved. A more ex­haustive study by Hopkins and Dutton 10 fol­lowed several years later, the specific pur­pose of which was to provide the Air Forcewith a realistic test of the practicality of mak­ing wider use of ~ITF concepts in the evalua­tion and specification of lenses.

Eight laboratories participated in comput­ing the mF ofa 24-inch,f/6, five-element lensat 0°, 10.4°, and 14.7° field angles. The Uni­versity of Rochester program was used as thestandard.

Results are shown in flve tables with fre­quency values to 100 Iines/mm separated intoradial and tangential scans. The maximumdeviation on axis was 0.03 and +0.02 MTFunits. At 10.4° for a radial scan -0.02 and+0.04, maximum values of deviation occur­red at 10 Iines/mm. (For the standard radialvalues the table shows the MTF dropping from0.74 at 10 lines/mm to 0.00 at40 Iines/mm andthen rising again. At 100 Iines/mm the MTF is0.10.) Variations of ± 0.02 MTF units are nor­mal for this scan and angle at low MTF values.Tangential scan results for the same angle aremuch better. At 14.7° (the corner of a 9 x9-inch format) both radial and tangential scancomputed values showed maximum devia­tions from the selected standard of -0.03 to+0.04 and -0.01 to +0.06.

The authors note that, "Although the com­putation of ~fTF or OTF from lens designparameters is, in principle, a simple andstraightforward matter, many approximationsand simplifications are required in practice tomake the actual numerical calculations man­ageable. Different lens designers adapt dif­ferent kinds of compromises in their pro­grams for evaluating OTF, and in general getdifferent answers." The spread of MTF values,therefore, was attributed to the ways in whichdifferent programs compute the shape of thevignetting aperture, possibly to some varia­tion due to evaluation of the pupil functionmethods of taking into account the foreshort­ening of the aperture, and to small variationsin the incidence angle of the chief ray.

A comparison was also made between twocomputing programs for a 10- element, 3-inchf/4.5 wide-angle lens on axis and at 30° off­axis. There was good agreement on axis but at30° they differed as much at 0.2 MTF.

The same 3-inch lens was tested by sevendifferent facilities. Again "the axial valueswere not too extreme but beyond a frequencyof 40 lines/mm the spread was 0.1 or greater.At 30° field, spreads of0.4 (and higher) occur­red between 20 and 40 lines/mm."

Not all of the important features of this ex­tensive report can be contained here andthose concerned with standards and monitor­ing of an OTF testing laboratory would do wellto review the many tables and graphs. Thisauthor (Norton) believes that only extensivethrough-focus tests at specified angles andazimuths (costly for both computing andmeasuring) could have provided more infor­mation, isolating (a little further) the met­rological problems which appear to have con­tributed to much of the scatter.

STAl':DARDS IN THE NETHERLANDS.

Standard for the Measurement of the Opti­cal Transfer Function or the ModulationTransfer Function of Linear Optical andElectro-Optical Imaging Devices (1974).(Philips Co. Standard). Van Leuwen (the au­thor) references the British Standard BS 4779(1971) for the measurement of space­invariant-lens and mirror-optical systems,noting that "due to the restriction of thisstandard (BS 4779) to space-invariant de­vices, which are not afflicted with a consider­able amount of veiling glare, the scope of thisstandard is too small to cover the lion's shareof the industrially interesting optical andelectro-optical devices. There is still a needfor a generally valid standard with a solidphysical and mathematical basis, so thatspace-variant, and devices afflicted with aconsiderable amount of veiling glare, canalso be covered."

In the instance of space-variant devices,the same OTF equipment used for space­invariant devices, may give three differentresults if line-spread functions, edge re­sponses, or sine-wave response supply OTFdata. The most important deviations occur atthe low spatial frequency part of the OTF;however, it is not generally justified to neg­lect the low fi'equency because of a boundedoutput field or a considerable amount of veil­ing glare which may appear as a suddenchange of OTF at these low frequencies. Inelectro-optical devices, Van Leuwen notes.the output fleld is always bounded and theveiling glare can cause a decrease in MTF val­ues by more than ten percent.

The OTF is therefore defined starting withthe image cf of a point source (actually a slitwith length and width selected to provideadequate energy, spatial frequency range,and to satisfy demands of the space-varianceod the device under test) introducing theconcept of local line spread function (LLSF).The Fourier transform ofthe LLSF is obtained,starting from the OTF, by taking the spatialfrequency equal to zero in a direction corre-

OPTICAL AND MODULATION TRANSFER FUNCTIONS 209

spondi ng to the orientation ofthe line source.The resulting one-parameter function willalso be called ow. In the event of anisotropy,the one-dimensional ow depends on theorientation of the light source. Specifyi ng theFourier transform of the LLSF as a function ofthe orientation of the corresponding linesource is equivalent to specifying the com­plete (two-dimensional) ow.

"If the imaging device is linear, the cor­rected result of a correctly executed analysisofthe spatial frequency content of the spatialdistribution of the radiance or radiant emis­sion in the image of a static, incoherentlyradiating, short, narrow slit, given as a func­tion of the orientation of the slit, it will beclose to the exact value of the (two­dimensional) OTF of the device under testunder the circumstances prevailing duringthe measurement." Thus the dependence ofthe OTF on the prevailing circumstances isdifferent for different kinds of imaging de­vices.

In order to obtain useful measuring results,the relevant measuring conditions during themeasurement must be chosen as close as pos­sible to those during normal operation. Inthis document, sets of measuring conditionshave therefore been standardized for a groupof devices or their special applications. Thisstandard particularly treats certain devicesspecifying the sets of measuring conditionsand accuracies required. (It seems probablethat more types will be added to the standardtests being tailored for production qualitycontrol.) The tests presently standardized arefor: .

* Image intensifiers for passive image­intensifying systems.

* Eyepieces for image-intensifying system.* Front optics for passive image-intensifyingsystems.

* Passive 1mage-intensifying systems.For each of these devices the standard de­

scribes the device, conditions which applyduring normal operation and the dependenceof the OTF on these conditions, the relevantmeasuring conditions and corresponding tol­erances, and recommendations for methodsand techniques for measurement.

The Philips Co. standard extends the use ofOTF and MTF which they consider the mostinformative of test criteria for electro-opticalequipment, but the bounds and the testequipments are well defined such that re­sults of tests give realistic values.

STAt DARD OF OTF I 'JAPA

A working group of the Japan Optical En­.gineering Research Association (jOERA) was

organized early in 1974 having as a goal theproduction of an OTF standard by 1976. Thestandard will cover: (1) optical systems to betested, (2) definition of OTF and ~ITF, (3) stan­dard graphical representation of OTF and ~ITF,

and (4) inspection standard for the accuracyof ~ITF measuring instruments.

The optical system will be limited tophotographic objectives with TV, motion pic­ture, aerial, and copy lenses being consid­ered in the same class. Definitions of ~ITF andOTF will be similar to those in British standardBCS 0751 and the West German standardDIN 58185. A method of graphic representa­tion of data will be selected from five recom­mended forms.

The use of iso-~nF curves of certain fre­quencies have also been recommended, butbecause of the large amount of data involvedfor through-focus tests, such curves are sel­dom used. Japan manufactures a largenumber of amateur cameras in which colorfilm is used and a standard will probably bedeveloped for color.

The working group has investigatedmethods of inspection for the accuracy OLITFmeasuring instruments. They considered astandard grating but this is useable only fortest equipment based on scanning methodsand a difhaction limited lens which has alarge f/number with a small angular field.The overall characteristics of the equipmentare therefore not tested with such a lens.They are therefore proposing to use lenseswith known lens data as is being done by theBritish Calibration Service, and the papergives graphs of three such I~nses with meas­ured MTFs using the e-line compared withthree methods of calculation. All the axialcurves and the one curve at 20° show goodagreement.

JAPAN - RECENT TRENDS IN OTF MEASUREMENT

A group of scientists and researchers fromUniversities and Optical companies beganstudies of OTF measurements as far back as1954. The last decade has seen the develop­ment of many Japanese instruments formeasuring ow, most being based on theanalog Fourier transform method.

The Committee of OTF and the Committeeof Lens-Measuring Instruments of jOERA con­ducted comparison OTF tests on ten typical,domestic (Japanese) equipments, amongwhich five were of the same design. A50-mm,f/2.8 len was used at 0° and 15° ang­les, radial and tangential. The light sourceswere monochromatic (e-line) and white light.Emphasis was placed on spatial frequenciesup to 40 lines/mm .

210 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING 1975

If the setting errors of the reference imageplanes were removed, the five C-4 typeequipment of the same design, tested withthe monochromatic light agreed within ap­proximately 5 percent of the calculated ~ITF.

The two units of different design if testedwith the e-line light source showed largerdifferences between the calculated andmeasured ~ITF which appeared to be about 10percent. If illuminated with white light theresults were similar. Mechanical problemsremain to be investigated so that the focusingposition will agree. A digital Fourier trans­form method using a knife-edge was studied.It was found that the pitch error of the micro­screw that moves a knife edge could be verysignificant and must be avoided.

The JOEHA instrument detects the lateralshift of the knife-edge by a moire scale detec­tor in intervals of one micron. The Canon,Inc. instrument is pushed or pulled, step bystep at intervals of 0.25 Mm by an elec­tromagnetic vibrator.

"The influence of Noise on the Measure­ment ofou by the Digital Fourier TransformMethod", a paper presented by Ose, T., andTakeda, M., Institute of Industrial Science,University of Tokyo, Japan, was presented atthe SPIE·OSA meeting in the U.S.A. in May1974. This theoretical study concludes that:(a) for stationary noise the multi-slit method iseffective in reducing error of the OU; (b) theknife-edge method can also be used effec­tively provided the sampling interval isselected closer than one-third of that re­quired by the sampling theory; (c) for shotnoise, the multi-slit gives a slightly largererror than that of the single slit, but muchsmaller than that of the knife edge method;(d) the experimental comparison of themulti-slit and knife-edge show that themu lti-slit methods has an advantage if used tomeasure the ou of dark-line images. Thestudy finds that in applying this method it isnecessary that the step of the scan preciselyequal the width of the elementary slit. Thismethod can be used for measurement of OTF

oflenses used in infrared imagery where thedominant source of noise is detector noise,which is independent of the signal intensityand consequently stationary.

In 1973, Mr. T. Asaeda, et al. (Canon, Inc.)produced an instrument in which a slit isused as a 'scanning aperture. In this instru­ment, a mini-computer works not only for adigital Fourier transform of the measuredline-spread function but for data processings.The influence of noise is reduced by repeat­ing the measurement of intensity at eachsample point and the fluctuation of dark cur-

rent is avoided by the subtraction of a con­stant current from each sampled output cur­rent. The constant current is the averagedone at several sampled points on the foot ofline-spread function. The lens assessment inthe recent lens design technique, needs ~ITFs

in high-spatial frequency domains. The digi­tal Fourier transform method will be appliedmore and more in ~ITF measurement.

A new instrument designed to measure anddisplay the OTF and based on analog Fouriertransform method has been produced by

ippon Kogaku Kogyo K.K. according to thespeci fications of the Japan Camera and Opti­cal Instruments Inspection and Testing Insti­tute (JCll) in 1973. A rotating Siemens'star-type square-wave chart is used as an ob­ject target in this instrument. Special atten­tion is given to the precise production ofopti­cal bench and mechanical parts, and sophis­ticated electronic circuitry process the sig­nals fed into the X-Y recorder. Now, this in­strument is regarded as a standard instrumentof OTF measurement in Japan, both MTF andOTF being obtained with accuracies.

Two working groups of JOERA are conduct­ing studies on methods of checking the ac­curacies of measured and calculated OTF.

Three kinds of standard lenses are being de­signed and fabricated for tests of on-axismeasurement, off-axis measurement, andcondition of illumination. All of the OTF

measuring instruments will be tested againusing these standard lenses in 1974.

REVIEW.

A review of the standards, supplementarycontrols, and testing activity associated withthe standards shows a number of importantfacts that must be considered by the ISPCommission I Working Group on Optical andModulation Transfer Functions. These are:

• There is increasing use of OTF and MTF inevaluating optical and electro-optical de­vices.

• Correlation testing results show good cor­relation on axis (current tests) and impor­tant differences off-axis. Many differencesappear to be due to meauring equipment(or bench accuracy) and the sensitive focus.

• Through-focus tests at many off-axis anglesand two or more azimuths (similar to pres­ent resolution tests) are time consumingand expensive. For manufacturing or ac­ceptance testing, much shorter tests areneeded which are still adequately selec­tive.

• Testing methods and equipment will haveto vary in accordance with the device beingtested. Standards should be provided for alloptical and electro-optical devices. .

OPTICAL AND MODULATION TRANSFER FUNCTIONS 211

• For the manuf'lcturer who has a specilka­tion in terms ofaTF or ~ITF on an operationalsystem, methods of testing elements andsubassemblies that go into that system (andwhich may have been purchased and there­fore require acceptance on a separate testprior to use in the system) will have to befound so that quality tests can separate outthe unacceptable, such that they do not de­grade the system. This is where cascadingis useful.

• In all instances only a scientist or engineerf'1Il1iliar with the requirements of precisionequipment (mechanically, electronically,optically, thermally, the problems of partialcoherence, noise, phase, etc.) armed withproved computer programs can specify thetest and test equipment.

• I I' the results of the theoretical design are tohe used as' the criteria of accuracy, design­ers should agree on the approximationswhich simplify the computing; or con­trariwise, the most rigorous program shouldbe used so that the most exact results arecomputed. In the first instance, tolerancesshould be estimated to form a basis forphysical tolerances.

• Camera systems generally use sources ofillumination with long spectral ranges. Foraerial cameras the range varies with thefi Im of the sensor. It seems necessary thatthe lens be tested using the same spectralrange and amplitude if the tests are to pro­duce values which are useable for the sys­tem. Results using monochromatic sourcescan perhaps be more easily compared withdesign data as a means of control, but thecolor aberrations affect both lateral spreadand focus and it would be difficult, if notsomewhat indeterminate, to cascade ~ITF,

to wide band system performance usingmonochromatic data.

lsI' STA1\DAHDS PROPOSAL

Based on the above (which is doubtfully allinclusive) the Working Group has elected toexpand Section 6 of the Calibration of Photo­gram metric Cameras to include, if possible,all ofthe techniques presently known. It is notexpected, however, that this can be trulycomprehensive.

DE\'LLOP~IE'\TAOJACE:\CY EFFECTS (ll.S.A.)

A study 12 at the Kodak Research Lab­oratories shows that only in the absence ofadjacency effects does the ~ITF of the filmrepresent the effect oflight scatter that occurswithin the emulsion during the exposure.The authors call this unique curve the optical.\/7'1' noti ng that it depends only slightly on theexposure level and the modulation of thetarget input. Adjacency effects must be con­sidered in an effective .117'1-' because resultsnow depend on exposure level and inputmodulation.

A formula has been developed relatingoptical .\/7'1-' and a hlmily of effective ~IT

curves. The mass of silver produced by theaverage exposure of the sine-wave targetmust be used in conjunction with the chemi­cal spread functions. The chemical spreadfunction derived in this article predicts thebehavior as a function of exposure and mod­ulation.

The theoretical derivations were testedexperi mentally usi ng Kodak Panatomic-Xfilm, the series of film-development combi­nations exhibiting chemical adjacency ef~

fects being measured for ~ITF,. In these exper­iments the ~ITF significantly increased as themean density of the sine-wave exposures.For a given density the lower modulationtarget gives a greater ~ITF.

A further complication exists if one wishesto predict which of two negatives, whose ~ITF

curves are known, will produce the betterprint because the harmonic distortion of theinput signal due to nonlinearity in the trans­mittance versus the exposure curve of thefilm may cause significant loss of informa­tion. This is because the higher harmonicscreated in a negative cannot be resolved inthe printing stage unless the optical ~ITF ofthe printing system and the optical charac­teristics of the print material are perfect.Thus, what may be gained in micro-contrastdue to edge effects, may be lost if the gammaof the negative is so high that harmonic dis­tortion becomes excessive.

FIGURE OF M EHIT Ai':D M EHIT CURVE (FRAi':CL)

I n the paperl2a presented by Pauleau atthe1972 Congress, he suggested a generalizedmethod of evaluating the ~ITF for a number offield angles. He bases the method on theArea-Weighted-Average Resolution (AWAR)used in the U.S. substituting a fixed modula­tion M for R. The formula then became:

Optical, Modulation, Phase TransferStudies, Figures of Merit,Microdensitometry, Noise.

A number of studies show that cautionmust be observed in cascading of functionsand in obtaining accurate MTF and OTF values.Suppression or smoothi ng of noise, partialcoherence effects, phase, as well as the testequipment must be evaluated for the applica­tion of the system being tested if values otherthan locally relative must be known.

AWAM = [ . ~ Ait = 1 A ]

V2MRiM Ti

212 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSI G 1975

where A is the area of the format, Ai is thesub-area usually the annulus ring, MRi is themodulation on the radial line at an angle cen­tered in the sub-area, and MTi is the modula­tion on the tangential line at an angle cen­tered in the sub-area. A single curve is ob­tained by using selected frequencies.

M ICHODE"SITmIETRY (U.S.A.).

The problems of microdensitometry ascaused by partial coherence and flare lighthave been considered by Swing andGrimes. 13 Grimes 14 proposes a LinearMicrodensitometer where the sample is il­luminated by a slit focused on a sample by ahigh-quality condenser, baffles between thecondenser and the slit acting to control straylight. Approximately all of the light transmit­ted .through the sample is collected by anoptical element. The system has a number ofadvantages:

... The output is independent of the partialcoherence of the source;

... There are fewer focusing and alignmentproblems;

... Because there is no sampling slit, the over­all system transfer function is improved;

... The measurement of singly diffuse densitymakes interlaboratory comparison easier.

THE SIGNIFICANCE OF THE PHASE TRANSFERFUNCTION (u.s)

The phase of the image transform is farmore important than the modulus accordingto Shack15 because an image in which themodulus is drastically altered is still recog­nizable, whereas correspondi ng phasechanges completely destroy recognizability.Many instruments measure only the mod­ulus, it being a matter of great practical con­venience if phase can be neglected. Shackshows that under general circumstances thephase must be considered and, if significant,some method found of incorporating it into aspecification of image quality.

It is principally in the area of image evalua­tion that the question of the significance ofthe phase-transfer fu nction must be faced.Both the spread function and the transferfunction are determined by the complex,fundamental pupil function. The modulus ofthe pupil function is determined by thegeometry and transmission of the pupil,whereas the phase is determined by the aber­rations.

The phase-transfer function is shown asdepending on the location of the origin in thedescription of the spread function. If thespread function is asymmetric and the peak ofthe asymmetric blur is used as the origin (as

would be natural in measuring photogram­metric images), very little harm would bedone in evaluating the MTF, but the asym­metry itself would introduce an error in loca­tion of the object.

One must be careful in dealing with themodulus alone, however, even though thespread function may be symmetrical. This istrue if the nature of the spread function issuch that its Fourier transform, althoughpurely real, has strong negative components.There are situations in which the inversetransform of the modulus does not corre­spond well to the true spread function show­ing the modulus to be overly optimistic. Shackconcludes that for noncoherent image­forming systems, the quality of the image interms of the spread of the spread function isadequately judged by the modulus of thetransfer function as long as the phase-transferfunction referred to the peak (not the cen­troid) of the spread function, is well within aquarter cycle over the range of significantvalues of the modulus. .

NOISE 11\ MTF MEASURDIENTS (U.S.)

Slaymaker16 notes that in MTF measure­ments are three sources of noise which canenter at almostany step which must be consid­ered: those introduced experi mentally,those due to the quantum nature of light it­self, and shot noise from the photocathode ofthe photodetector. Assuming that the firsttwo can be reduced to negligible values, hedeals with shot noise which appears as aperiodic term added to the true value of theOTF. He shows that in making an OTF meas­urement by means of a knife-edge scanner,the effect of the shot noise can be reduced toan acceptable level by establishing a max­imum value for the scan velocity. The seri­ousness of the noise can then be calculated asa normalization error and an upper bound onthe variance of the MTF from known values forthe electrical bandwidth, the time to makethe scan, the gain of the photodetector andthe anode current. To verify the noise calcu­lations experimentally, Slaymaker measuresthe variance in the ~ITF data. He then calcu­lates the mean and standard deviation for thedata at specific spatial frequencies for anumber of repeated scans.

A comparison of the calculated and ex­perimental results obtained with a 0.1 xMicro Tropar lens having a.focallength of26mm, an f/number of f/1.6 and a theoreticalcutoff frequency somewhat above 1200cycles/mm, shows good agreement at spatialfrequencies approaching the theoreticalcutoff. At zero frequency, however, the

OPTICAL AND MODULATION TRANSFER FUNCTIONS 213

measured value for the standard deviation ofthe data is more than twice that of the calcu­lated normalization error. He explains this bypointing to the possibility of other sources ofexperimental uncertainty in addition to shotnoise.

His basic premise that the noise can beheld to an acceptable level is upheld, how­ever, and for the specific lens and testparameters used is 0.0035 \ITI' units at zerospatial frequency and approximately 0.018\ITI' units at 1200 cycles/mm.

hTEBFEROMETHIC METHODS (U.S.)

Interferometric testi ng essentially meas­ures the pupil function from which the opti­cal transfer function, the spread function, andaberration coeHicients may be computed.The pupil function must be used to evaluatecascaded optical systems and systems em­ploying coherent or partially coherent illumi­nation.

Most quantitative interferometric testingsystems are expensive, time-consuming, andrequire operational expertise. The applica­tion ofthe Wavefront Shearing Interferometer(\\'Sl) developed at the U.S. Bureau ofStandards l7 (J\:BS) eliminates some of theseundesirable features, employing an inter­ferometric cube into which the adjustmentsare fixed. The WSI into which the cube is in­stalled is portable and easily set up on anoptical bench.

The resulting interferograms, however,cannot be interpreted by simple inspectionin terms of wavefi'ont aberrations. Hence themajor cost of testing goes into data reductionand analysis.

The lens under test is set on the bench foreither finite or infinite focus. Beyond thefocus, in diverging light, the cube ispositioned. An auxiliary lens photographs thefj'inges on film.

The cube interferometer operates by am­plitude dividing th~ incoming wavefront intotwo equal parts and introducing a small angu­lar shear into one of the beams. For two45°-90°_45° prisms contacted along thediagonals to form a cube, the pivot point ofrotation lies in the plane of the back face ofthe cube. A small shear is then introduced.

As the cube is not used in parallel light,corrections are made for the known aberra­tions which are introduced by the opticalpath differences.

Working with photographic transparenciesofthe interferograms the test data is suppliedin fringe-peak locations. The technique ofautoconvolving the fringe density profile inthe vicinity of a maximum or minimum was

llsed to locate the fj·inge-peaks. (The peak ofthe autoconvolution function corresponds tothe fringe-peak.) This method has the advan­tage of averaging grain-noise effects duringintegration and, according to the authors, ap­pears to be as accurate as the scanning inter­val allows. It is necessary to orient the inter­ferograms orthogonally so the resulting datah'om the scanner is registered in a commoncoordi nate system.

The auxiliary lens that photographs thefringes is located such that its aberrations donot affect the measurement of the fri nge loca­tions.

Comparison tests were made using a50-mm SIBA standard lens. Within a spatialhequency of 100 lines/mm there was goodagreement on MTF values with those certifiedby the British Calibration Service.

The WSI system has been demonstrated atNBS to be a versatile, inexpensive, and simplealternati,ve for interferometric testi ng oflenses. The authors note that further im­provements are possible, particularly to thecomputing techniques and (this author, Nor­ton) would like to see correlation testing atsignificant field angles.

PTF/MTF Applications.

U.S. AlB FORCE hlAGE EVALLTATION PROGRA\1 18

Some of the biggest disadvantages of theuse of MTF have been the cost am.! sensitivityof test equipment and the test and analysistime. These problems were faced by the AirForce Avionics Laboratory at Wright­Patterson Air Force Base by installing high­speed, automated equipment under closequality control, and testing many quantitiesand types of camera systems.

The Dynamics Environmental EvaluationBranch notes in the paper on "Quality Con­trol as applied to Imagery -Analysis" thatimage-quality aspects are becoming increas­ingly important to the Air Force. More carto­graphic and reconnaissance systems are there­fore, bei ng analyzed through an evaluation oftheir recorded photographic performance,some negatives being exposed under un­known environmental conditions and othersin laboratory studies under controlled envi­ronments. Simulated condition, equivalentto the extremes encountered in actual mis­sions are also analyzed with the Mann-DataMicro analyzer to determine image quality.

Selected image edges, traced with the mi­crodensitometer, are recorded on high-speedmagneti.c tape. This recorded data is then op­erated on by a CDC 6600 digital computer toprovide edge-trace data, in either tabular or

214 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING 1975

graphic form, for detailed visual inspection.Various computer programs are then availa·ble. It is routine to obtain information on:

• Exposure• Target detail and contrast• Granularity• Density range with maximum and

minimum exposure, and log exposure datafor obtaining absolute density exposurevalues.

• MTF when operated on by the Fouriertransforms

• There is, of course, much additionalspecialized information available throughthe analysis of the micro-densitometer data.This may be selected as desired.

These routine ~ITF tests and supplementaryanalyses have supported the quality func­tions by proving that quality systems havebeen procured anclJor photographic perform­ance is stable. The equipment and testtechniques being at "the state-of~the-art"arealso used for research studies. The speed ofprocessing, that is available through automa­tion and use ofcomputers, greatly reduce testand analysis time, resulting in lower cost­time per unit test. The nearly real-time foranswers to the question of quality of imagesmakes it possible to make confident equip­ment decisions for an important mission, ordesign development, or to investigate per­formance problems.

Imagery obtained by the Canadian AirForce with the Wild and Zeiss reseau carto­graphic cameras being used in the study con­ducted by the Commission I Working Groupon Image Geometry, will be analyzed by thisfacility. Results will be reported at the 1976ISP Congress.

IMAGE CONTROL AND EVALUATION (U .S.)

In a concerted effort to optimize the infor­mation content ofaerial photography, the AirForce has instituted a service-wide programcalled Sentinal Sigma. The program is de­signed to control quality_ by standardizingprocedures, first black-and-white photog­raphy, and later other types, such as color,nonconventional, etc. The standardizatIonand guidance will set the basic documenta­tion and direction for USAF Commands moreeffectively to manage, utilize, and evaluatetheir photographic production resources andto unify procedures and techniques.

An integral part of the effort is the ImageryEvaluation Working Group. This group is di­rected: (I) toward the establishment of tyingtogether objective and subjective measuresfor determining image quality, and (2) towardestablishing a common technical photo­graphic language between engineers, opera-

tion personnel, users, and project managers.Techniques such as Modulation TransferFunctions, visual edge matching, and holo­graphic models are being used to determineclearly the quality and operational perform­ance of Air Force reconnaissance plat­forms. These and similar techniques arebeing compared to established operationalmethods of evaluation.

MTF ANALYSIS ApPLIED TO SATELLITE hIAGERY(U.s)

Welch 19 has written a number ofpapers forthe U.S. Geological Survey reporting ontechniques and results of analysis of satelliteimagery using resolution and ~ITF criteria.(Welch will present a paper at the Stockholmsymposium on such analysis, so only mentionis made here.) (Attaya and Corbett at Itekhave also used MTF analysis techniques onSkylab photography.)

INDUSTRIAL USES OF MTF

ITEK COHPORATIOK

Itek employs various image analysistechniques20 in both design and testing ofoptics some of which are considered unique.An MTF computing scheme permits the pre­diction of image quality for the most generalcases offield angle, image orientation, spec­tral region and film characteristics. A design2an be adjusted to the optimum with thisprogram allowing, for example, filter charac­teristics to be balanced against aberrationsand exposure time for maximizi ng resolution.The MTF techniques are also used for evaluat­ing fabrication tolerances and for predictingthe effects of thermal variations on systemperformance. Computer support is providedduring optical fabrication through melt-dataadjustment, image-quality analysis, and in­terferometric test data-reduction to providesurface error contours and rigorous-systemimage-quality analyses. Manufacturing proc­essing corrections results.

The lens designed at Itek for the S-I90Amultiband camera of NASA's Skylab21 programwas evaluated in the design stage, the man­ufacturing stage, and the performance stageusing MTF techniques. MTF techniques (withadditional analyses) of the Apollo ISpanoramic space photography showed thatthis unusual camera was functioning close toits predicted quality duri ng its complete mis­sion.

Another MTF evaluation is used on fiberoptics.20 A fiber optics faceplate is composedof an ordered array of small individual lightpipes which transfer images from input to

OPTICAL AND MODULATION TRANSFER FUNCTIONS 215

ouput. Conventional methods of investigat­ing the fiber-optics image-transfer processutilize the spread function and the edge re­sponse as a basis for transfer-function calcu la­tion. Unfortunately, a transfer function calcu­lated hom a fiber-optics spread function doesnot have clear meaning. A holographicmethod is, therefore, employed, photo­graphic recordings being made of the sum­mation of sinusoidal fi'inges at the input sur­hwe and at the output surhlce of the fiberoptics. From these the FraunhoferdilTractionpatterns are produced. Because the ir­radiances of the narrow sine light distribu­tions in the Fraunhofer difhaction patternsare directly related to the amplitude of thesinusoidal irradiance variations, the pairyields a fiber-optics transfer factor, and astatistical ~ITF, the latter being a measure ofthe average perfi))"mance. Tests were con­ducted with techniques that provided addi­tional infilrmation on lateral and rotationaldistortion offibers, missing or broken fibers,and resolution.

FAIRCIIILD CA~IEI1A & INSTHLI~IE1\T COllI'.

At Fairchild Camera, ~rTF and OTF havefound their primary applications in opticaldesign and diagnostics. As an optical designtool evaluation, based on contrast and phase,calculations have proved invaluable in thelarge-scale computer-oriented design proc­ess. Although ~ITF has not yet entered intothe merit function formulation to use in as­sessment of system quality, it typically out­weighs other criteria.

I n the evaluation ofprototype systems a cor­relation between paper design and hardwareexecution is essential to development proc­ess. As ofthis writing (1974) modulation andphase measurements provide the best readi lyavailable measurements for the establish­ment of such correlation.

It has not yet proved possible to utilize MTFand OTF evaluation in routine characteriza­tions of wide-angle lenses such as those typi­cally used for photogrammetric purposes.The difficulties encountered in attempts todo this lie both in physical contortions (thevery precise adjustments and locations ofequ i pment parts) necessary and the u ncer­tainties in the results of subsequent analysisof the data obtai ned.

It is envisioned, however, that routine con­trast measurements with electro-opticalequipment can be made to augment, or even­tually to replace, other forms of testi ng in thescreening, and even perhaps in the finalevaluation, of lenses havi ng more modest angular coverage.

STLIDY OF EDGES FOH THE LOCATIOi': OFPIIOT<lGI1A~I~IETHIC hiAGES (U.S.)

A study made at Ohio State University22 isconcerned with the detection and measure­ment of photographic images, and proposesthe edge as being the quantity most inti­mately related to photographic measuration.The selection of the edge is also consideredvaluable because of its relation to the spreadfunction whose Fourier transform leads tothe ~ITF. The stated objective of the study wasto search for a meaningful specifier of imagequality. Image quality is defined in the termsof photogrammetric application to mappingas the measurabi lity ofan edge as determi nedby the degree ofagreement between the sub­jective edge locations from four experiencedobservers. A secondary objective was to lo­cate where the su bjective edge is determi nedto be located in reference to some measura­ble quantity.

The study is detailed in the evaluation ofedges and image quality examining the pub­lished, frequently contradicting statementsof experts.

The conclusions of this study (whichshould be applied to a variety of photo­graphic images for further proof) was that: (1)the observers located the subjective edgeslightly into the less-dense region as meas­ured fi'om the inflection poi nt ofthe intensityedge trace, a normal value being 30 secondsohm.:. At the ratio of 10 seconds ofarc equal 1JLm at the photograph this is ± 3 JLm. (2) Any(lUantity related to density correlated withimage quality better than its correspondingintensity quantity, acutance being an excel­lent specifier. A new quantity decutance, hadthe highest correlation (decutance, De = A//5,where A is amplitude and /5 is dispersion,practical units being in terms ofdensity/micrometer. (3) The position of thepointing did not correlate with image quality(as defined above) which suggests an indi­vidual personal edge preference by each ob­server. Observers point more precisely onsome edges than others, but a particular edgeproducing high-pointing precision may varyaccording to the observer. (4) The higher de­rivatives (2nd, 3rd, and 4th) of the intensityedge trace revealed no information that wasnot already discernible from the edge traceor its first derivative. (5) Neither the modul­ers of the Fourier transform of the intensityspread function nor the cut-off fi'equency ascomputed by Cooley's Fast Fourier Trans­form algorithm displayed any correlationwith image quality.

O'Connor23 had shown in a previous studythat the error connected with centering a

216 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING 1975

measuring mark in a target was less than the± 3 /Lm error of this study. As such, in anyphotogrammetric task where it is possible,Thompson 22 suggests that greater accuracywill be ach ieved if edge measurement can bea\·oidecl.

References

1. Brock, Gerald C., "Image Quality," Report of\VOI'king Group, Commission I, InternationalSociety of Photogrammetry Archives(1964-1968).

2. Welender, Erick, "Report of Working Groupon Modulation Transfer Functions," Commis­sion I, International Society of Photogram­metry Archives (1968-1972).

3. Norton, Clarice L., Secy. Com. I, ISP(1968-1972).

4. Hopkins, Robert E., and Dutton, David, "LensTest Standardization Study," Tech. ReportAFAL-TR-70-97 (July 1970).

5. "Image Evaluation for Eeconnaissance,"Proceedings ofa Symposium April 3 & 4,1963(Sponsored by Air Force Avionics LaboratoryReconnaissance Divi sion, Wright-Patterson AirForce Base, Ohio), ltek Corp., Lexington,Mass.

6. SJH.~, (England) an organization representinggovern ment and industrial filcil ities interestedin testing of optical systems and their stan­dards. SI H.~ Institute I mage Assessment Group.

7. Vinton Ltd, England, mal1ld'lcturers of opticalsystenls, canleras, etc.

8. 'elson, C. l. "Prediction of Densities in FineDetail in Photographic Images." Photo­graphic Science and Engineering, 15 (1), jan.­Feb. 1971.

9..Attaya, 'y\'. L., and Brock, G. c., et al. "Study ofImage Evaluation Techniques," Tech. ReportAFAL-TR-66-343, ltek Corp, for AF AvionicsLab, WPAFB, Nov. 1966.

10. Hopkins, Robert E., and Dutton, David, "LensTest Standardization Study," Tech. ReportAFAL-TR-70-93, Univ. of Rochester, Roches­ter, NY, July 1970. Prepared for USAF.

11. Private communication to C. L. Norton.12. Kriss, M. A., Nelson, C. N., Eisen, F. C.,

"Modulation Transfer Function in Photo-

graphic Systems Containing DevelopmentAdjacency Effects," Soc Photo Sci & Eng, 18(2), Mat·.!Apr. 1974.

12A Pauleau, jacques, "The Modulation TransferFunction ;'vleasurement by The Acofam-MetraApparatus and the Generalization ofa Methodof Evaluating Optical Systems," presentedpaper 1972 ISP Congress, Ottawa, Canada.

13. Various research at National Bureau of Stan­dards.

14. Grimes, D. N. "Linear Microdensitometry,"Journal ofOplical Soc ofAmerica, 16(9), Sept.1971.

15. Shack, Roland V., "On the Significance of thePhase Transfer Function," SPIE-OSA Sym­posium, Rochester, NY, May 1974. To be pub­lished.

16. Slaymaker, Frank H., "Noise in MTF Meas­urements," Applied Optics, 12 (11), Nov. 1973.

17. Nyyssonen, D, and jerke, j. M., "Lens Testingwith a Simple Wavefront Shearing Inter­ferometer," Applied 0 plies, 12 (9), Sept. 1973.

18. Gliatti, Edward L, and Mower, Lt. Col. RolandD. (USAF), "Quality Control as Applied to Im­agery Analysis." Presented at National Aero­space and Electronics Conference, Dayton,Ohio, ~v1ay 1974 (to be published).

19. \Velch, R., "Analysis of Image Definition,"Photogral1ll11etric Engineering, 35 (12),1969.Welch, E., "I'dodulation Transfer Functions,"Photogral1ll1letric Engineering, Mar. 1971.

20. "Optics at Itek," Applied Optics, Vol. 11, Dec.1972.

21. Forkey, E. E., and Womble. D. A., "UniqueLens Design for 1\1 ulti-Spectral PhotographicCameras," presented paper, XII Congress ofInternational Society of Photogrammetry, Ot­tawa, Can. july-Aug. 1972.

22. Thompson, Leon G., "The ses of Edges ofPhotographic Images as Specifiers of ImageQuality." Report No. 179, Dept. Geodetic Sci­ence, Ohio State University Research Founda­tion, Columbus, Ohio, Nov. 1972 Prepared forUSAETL, Ft. Belvoir, Va. USURF Project No.3147-AI.

23. O'Connor, D., "Visual Factors Affecting thePrecision of Coordinate Measurements inAerotriangulation," U.S. Army ETL ResearchNote No. 21, (Jan. 1967).

Articles for Next Month

T. M. Lillesand, E. L. Scm-pace, and}. P. Clapp, Water Quality in Mixing Zones.B. N. Koop111al1s, Variable Flight Parameters for SLAR.Floud M. Henderson, Radar for Small-Scale Mapping.Dennis F. Polis, Fourier Spe<.:tra for Non-Homogeneous Patterns.j. C. Trinder, Autocorrelation Fun<.:tions in Stereoscopy.Robert A. Jones, Accuracy and Photo Nonlinearities.YOllssef 1. Abdel-Azi::., Film Distortion in lon-Metric Cameras.Michael C. -Yo Hall, Independent Models with the A-7 and A-B.