Comparing the ability of subjective quality factor and information theory to predict image quality

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8-1-1994

Comparing the ability of subjective quality factor

and information theory to predict image quality

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Comparing the ability of Subj ective Quality Factor and Information Theory to predict Image quality.

By

Shyi - Shyang Li

B.S. Chinese Culture University

( 1982)

A thesis submitted in partial fulfillment of the requirements for the degree of

Master of Science in the Center for Imaging Science in the College of Imaging Arts and Sciences of the

Rochester Institute of Technology

August, 1994

Signature of Author: _S~h_y_i-S_h_y_a_n_g_L_i _

Accepted by: Dana G. Marsh >

~

~

Ifff

COLLEGE OF IMAGING ARTS AND SCIENCES ROCHESTER INSTITUTE OF TECHNOLOGY

ROCHESTER, NEW YORK

CERTIFICATE OF APPROVAL

M.S. DEGREE TIIESIS

The M.S. Degree Thesis of Shyi-Shyang Li has been examined and approved by the thesis committee as satisfactory

for the thesis requirement for the Master of Science Degree

Dr. E. M. Granger Thesis Advisor

Dr. Dana G. Marsh

Mr. Joseph Altman

THESIS RELEASE PERMISSION FORM

ROCHESTER INSTITUTE OF TECHNOLOGY COLLEGE OF IMAGING ARTS and SCIENCES

Comparing the ability of Subjective Quality Factor and Information Theory to predict Image quality.

I, Shyi - Shyang (Robert) Li., hereby grant permission to the Wallace Memorial Library of the Rochester Institute of Technology to reproduce my thesis in whole to in part. Any reproduction will not be for commercial use or profit.

Signature: _ = - - _

"

Comparingthe_abilityofSubjective_QualityFactorand Information_Theory

to predictImageQuality."

By

Shyi-ShyangLi

SubmittedtotheCenter for_Imaging Science inpartial fulfillmentoftherequirements

fortheMasterofScienceDegreeatthe

ABSTRACT

The purposeofthisproject isto compare the _ability ofthe Subjective_QualityFactor and

Information _Theoryto predict image _quality as a function offilm speed fortwo different

methods of_{exposing film.} Oneexposure holdsthe total number ofphotons constant and

theother allowsthefluxtovary.

This studywill:

1. Determinetherelationshipbetweengrainsizeand imagequalityforconstantflux

whenthe_resultingimagesare reproduced atthesame size.

2. Comparethe_{resultinggranularity}and image_qualityoftheconstantfluxcondition

withthenormal exposure method of_varyingthe shutterspeed as afunctionof filmspeed.

3. Comparethe_abilityofSubject _QualityFactorandInformation_Theoryto

ACKNOWLEDGMENTS

This paper would not have been possible without the support of a number ofpeople.

First, to Dr. Edward M. Granger who provided the _ongoing technical insight and guidance that allowed me to proceed through the difficult

periods. Dr. Granger served as the principal advisor. I must also thank Mr. Joseph _{Altman for serving} on _my thesis committee member as well as

providing technical support.

Special thanks are extended to Dr. Dana G. Marsh for the _continuing

support and encouragement through the highs and lows that went with this

project. Thanks for _being understanding.

A special word of thanks is owed to _{my loving wife,} Liang-Jen.

Thoughoutthe _long period ofthis project she stood _{steadfastly by} me. The

many hours and days she _willingly gave for me to complete this project. Her unwavering patience made this struggle an enjoyable _journey and I will forever be indebted.

Finally, I like to present this work to _{my parent, they} provided financial and emotional support made the completion ofthis work possible.

TABLE OFCONTENTS

CERTIFICATE OF APPROVAL ii

COPYRIGHT RELEASE iii

ABSTRACT v

TABLE OFCONTENTS vii

LIST OFFIGURES ix

LISTOF TABLES x

I. Introduction 1

1-1

.GranularityandImageQuality 1

l-2.Subjective_QualityFactor_(SQF) 4

1-3.Information_Theory(I._T.) 7

1-3-1 General Information 7

1-3-2 PhotographicApplications :Discrete Signals 8

1-3-3 Photographic Applications Continuous Signals 11

n. Methods 15

2-1 Photographpreparation 15

2-1-1 _Settingupand _determiningexposure condition 15

2-1-2_Developingfilmand photographic paper 29

2-2_Evaluatingimage qualityof photographs 32

2-2-1 Instructionsto observers 33

2-2-2 Results from evaluatingimagequalityof photograph 34

2-3 _CalculatingMTFof photographs 36

TABLE OF CONTENTS (CONT.)

2-5 _Calculating SQFofphotographs 39

2-6 _CalculatingInformation_Capacityofphotographs 40

III. Results 41

3-1 MTF ofphotographs 41

3-2 _Granularityanalysis 46

3-3 SQF ofphotographs 47

3-4 Information_CapacityofPhotographs 49

IV Discussion 5 1

4-1 _ComparingtheresultsbaseonSQFandInformation_Theory 51

4-2_Comparingtheresultson T-MAX-400andTRI-X 400films 54

V References 56

VI. Appendices 58

LIST OF FIGURES

FIGURE 1

FIGURE 2

FIGURE 3

FIGURE 4

FIGURE 5

FIGURE 6

FIGURE 7

FIGURE 8

FIGURE 9

FIGURE 10

FIGURE 11

FIGURE 12

FIGURE 13

Subjective_QualityLossVs _Granularity 2

AtypicalvisualsystemMTF 5

MTFofT-MAX 1 00filmw/25 mmlens 3 8

MTFofT-MAX 1 00filmw/25 mmlens 42

MTFofT-MAX 400 filmw/25 mmlens 42

MTFofT-MAX 3200filmw/25 mmlens 43

MTFofTRI-X 400 filmw/25 mmlens 43

MTFofTRI-X 400 filmw/55 mmlens 44

MTFofT-MAX 400 filmw/50mmlens 44

MTF ofT-MAX 3200filmw/ 135mmlens 45

SQF results 48

Information_Theoryand_{SQF ranking}prediction 5 1

LIST OF TABLES

TABLE 1

TABLE 2

TABLE 3

TABLE 4

TABLE 5

TABLE 6

TABLE 7

TABLE 8

TABLE 9

TABLE 10

TABLE 1 1

TABLE 12

TABLE 13

List ofdata 10

Informationcapacities offour films 14

Conditionsusedforthisproject 30

Statistic data for_"GreyCard" 3 5

Statistic data for"Egg"

3 5

Statisticdata for"Flower" 36

Granularityresults 46

Calculated _Granularityresults 47

SQFresults 47

Resultsof prediction_byusing SQF 48

Information_Theoryresults 49

Resultsof prediction_{byusing Information Theory} 50

I. INTRODUCTION

1. GranularityandImage Quality

Whenan emulsionis_uniformlyilluminatedandthen_developed, thenegativeshows _density fluctuations dueto the random distribution ofdeveloped silver particles in the emulsion. This is known as photographic granularity. The effect is to introduce a _small,

unpredictable _uncertainty into the photographic _blackening in each small area of the negative. This uncertaintyisof greatimportancein_{imagingscience,} because it sets alimit to the _quality ofphotographic images. Although the individual _density fluctuations are

unpredictable, their mean magnitude ₍ root mean square _density fluctuation ₎ is a well defined statistical characteristic ofthe grain distribution in a_uniformly exposed _negative,

and determines the photographic noise-level. _Granularity is a measure ofthe random density distribution created _by photographic grain in the _image, and depends onthe size

and distribution ofthe grains in the developedphotosensitive material. It ismeasured _by

scanning, with a microdensitometer, areas ofthe photosensitive material that have been exposed and developed to a uniform density. The granularity measured is a function of the circular aperture used in the _{microdensitometer,} the density distribution of the developedphotographicemulsion, andthe type ofemulsion

_{[fT/.se/-,1986]}

Itis obvious that image qualitywillbe degraded asthe grain noise increases. In a recent

study\Lisson,\983], the loss in image quality was found to be linearwith respect to the

Figure 1 _{SubjectiveQualityLoss}vs. _Granularity

^r o

z

->

m O

_i

2-3 a m

>

3 tn

o

RMSGranularity

In_{this project,} some ofthefilm samples willbe exposedunder constantphotonflux inthe

optical system. Thismeansthat ina given amount of_time, Nphotons will passthrough a

constant diameter lens pupil from a given area onthe original object. As a result ofthis

restrictionforaconstant shutter_speed, thelens focal length andtheimagesizeincrease in direct proportion to thefilm speed. Since the final prints made from different films with

different speeds will be printed to the same _size, the system MTF and _granularity will be

The _following diagram provides information about _{the relationship} of the object lens to

the different sizeimagesthatresultduetofilmspeed.

25mmlens

F#:4

Slowspeedfilm

50mmlens

F*:8

135 mmlens

F#:22

As shown inthe _diagram, with the constant flux _{condition, the} faster the _film, the bigger

the image generated. The negative must be magnified to make the slower film generate

the same size print asthefast film.

2. Subjective _QualityFactor₍ SQF₎

Aperceptible difference in image_qualitycanbeobtained_{bychanging SQFby}7-10%. This

phenomenon ofjust noticeable difference _{(JND) being} related to a constant percentage

change in the stimulus has been observed for _many neural processes. Tasks such as judging weight and loudness of sounds followwhat is known as Weber's Law. This led

Granger _{[Granger,1972]} to hypothesizethat image _quality might in some _wayberelated

to a logarithmic spatial _{frequency weighting} of the system Optical Transfer Function (OTF). If_so, image _qualitymight correlate withthe area underthe system OTF on a_log

spatial _frequencyscale.

The Subjective _Quality Factor ₍ SQF ₎ was developed _by Granger and _Cupery, as the

result ofa search for an objective figure ofmerit which could be _easily calculated and

directlymeasuredinpractice and which would correlatewith subjective rank regardless of

Modulation TransferFunction _(MTF) form. A number ofexperiments were performedto

test the quality factor forawide_variety ofMTF shapes. The results ofthe experimental

program werethat SQF was ableto predictimage _qualitywithin normal reader error and

The qualityof a visualimage isrelated to the scaleoftheimageontheretina. Thehuman

visual systemhas anMTF which peaks inthe region of10-20 cycles/mm at the retina. A typicalvisualsystemMTFis shown plottedVs _{log frequency}inFigure 2.

Figure 2. Atypicalvisual system MTF

0.1 1.0 10.0 100.0

Spatial _Frequency

-Cycles/Degree

By postulating an _{arbitrary bandpass} nature for the _eye, the limits of integration to

stimulatethiseffect have been defined.

Based on these observations, a one-dimensional SQF was defined as the integral ofthe

systemMTF( including lenses and films)betweenthe limits of10-40 cycles/mm when the

MTF has been scaled to the retina ofthe observer _by the magnification ofthe _system,

40

SQF =

k\\T(f)\d(\ogf) (1)

10

r(f) istheOptical TransferFunction.

/ isthe spatialfrequency.

\/k isa_normalizingconstant obtained_byequatingtheabove

integrationto =1.

There is no reason to limit the considerations to one-dimensional MTF descriptions. Because real images involve a two-dimensional _MTF, a two dimensional MTF must be

factored into the system. That _is, the impression of _quality is obtained _{by equally}

weighting information over all directions. The SQF value can be obtained for a general MTF _{by describing} the system MTF in polar coordinates and _performing the _following

integration:

402*

SQF =_kj\\r(f,

ep{loSf)W ₍₂₎

10 0

Where: _/ isthe spatial_frequencyincycles/mm _alonga given azimuth 9 ofline structure.

itistheappropriate_normalizingconstant.

402*

A = JJ<5(log/)<a? (3)

The above formula allows a simple calculation ofthe _quality ofa print which lies within

thelimitsoftheImage Sharpness Scale_{(ISS) [Granger, 1972] quality}range.

It is characteristic of the SQF system and of subjective _evaluation, that a _quality

assessmentisnotintrinsicto the image itself but_onlyto the imageas viewed at aspecified

magnification. _Therefore, it isimportant that theproper system magnification bespecified

when_calculatingthe SQF ofa system.

3 Information_Theory

3-1 General Information

The theorems within the general field ofinformation _theory are based on research _by

Shannon in 1948. These theoremswere developed _largely withinthe context ofelectrical

communication channels but _{they may} be _readily adapted to _any other type of

communication system, such as the optical transmission or photographic _recording of

information.

It is estimated that the total amount of printed information alone is inexcess of

1016

bits

per year and that this figure doubles about each decade. In view ofthese present and

future large-scale _{information-handling} problems, the need for a fundamental analytical

In photographic applications the photographic process is used as the _recording medium

and it is important to achieve the highest information _recording rate. The statistical

structure ofthe _incoming signal is _fairly well _known, and the question becomes one of

howtobest presentthe signalto the photographic_recording element. As a_result, it _may

be desirableto match theWiener spectrum of_incoming signals to the spatial frequencies

in the photographic _recording element which yield the highest _{information capacity} and

rate. These frequencies are determined _bythe system MTF and the Wiener spectrum of

the system noise. This approach demonstrates the _very close _{relationship between}

information_{capacity, recording}rate, andDQE [Dainty&Shaw,l974].

3-2 Photographic application : Discrete Signal

When a specified type of signal (for _example, in _{binary form)} is to be stored

photographically withthe highest information storage per unit area, simplified models of

the photographic process as a storage medium _may prove adequate. Altman and _Zweig

gave a method of analysis based on aunit storage cell inthe image_using a simple model

for the influence ofnoise _{according to} Levi

[Z,ev7,1958]

unit area canbewrittenintheform :

C = N

log2 M ₍₄₎

M =

-^r + 1 (5)

where: c isaconstant.

Cisthe information _capacityofthechannel

Misthenumberof_recordinglevels

Nisthenumberofcells

Risthe_densityrange_(D^

-D^J

Aisthecell size.

N = A~'

TheparameterR maybe assumedto beconstant fora given photographic process and so

fora specified separation_{criterion, K, only A}remains asavariable and equation₍₅₎ canbe

writtenas equation(6):

C=[^]log2

( I A

cA2

+1 ₍₆₎

Investigation of equation ₍₆₎ reveals that C increases as A decreases, so A should be as

small as possible for maximum information capacity. _However, at least two _recording

levels arenecessary, sowe conclude_that, inprinciple, binaryrecording willgive optimum

informationcapacity. Thisconclusionisconfirmed_bytheresults ofAltmanand_Zweigfor

TABLEI

Spread function

diameter

Available levels

Bit capacityfor of 0 x

an

10

imagearea

fjm

M logf M-level _Binary Experimei

Kodak Fine Grain 8 3 0.33 0.11

Cine Positive

Recordak Fine 12.5 6 2.6 1.6 0.64 1.1

GrainType 5454

RecordakFine 15 4 2 0.88 0.44 1.1

GrainType 7456

Kodakplus-X 3 1.6 0.33 0.21

Kodak Pan-X 15 3 1.6 0.7 0.44 0.5

lodak Royal-X Pan 27 2 1 0.14 0.14 0.05

Kodak High 1 2 1 160 160 160

ResolutionType

649

An analysis of _binary and multilevel _{recording by} Altaian and _Zweig

[Altman&Zweig,\_963]concludesthat the gainin information _capacityby

using multilevel

ratherthan_{binaryrecording}isnot substantial. Itfollows fromequation₍₄₎thatan _increase

inMgives _onlyalogarithmicincrease incapacity, andtherefore small cell sizeisthe most

important factor. Thecell size or spreadfunction havinga storage area_of\fjmx\/jm, as

opposed to 100/imx_{100/xw, would give an increase in}

capacity of 104

Where _binary

messages and codes are _{commonplace, recording levels higher} than two _may involve

coding complications and _{difficulties, especially in}view ofthe factthat thelevels have to

be well separated. For all these reasons multilevel _{recording may} offer little practical

advantageoverbinary.

3-3 Photographic Application: Continuous Signal

It is important to know that the results obtained for information capacity when _using a

continuousapproach will notbethe same as_usingofthediscrete _approach, butinpractice

they may turn out to be quite close. The results are different because _they concern

differentquestions, ortypesofinformation input. Thegreatbenefitofthis approachisthat

itallowsthe_{information capacity}tobeexpressed asafunctionof spatial _frequency, andin

turn the close _{relationship between information} transfer rate and DQE then become

apparent. For applications in scientific _photography where overall _{systems, including} the

photographic_{recording element,} mustbe designed toachieve thehighest informationrate

foran_incomingsignal, thisspatial_frequencyapproachis_usuallytakenastheresultforthe

continuous channel with average mean-square limitation and Gaussian noise. In fact the

photographic process is more _nearly a peak-limited channel, with its _operating region

between _{fog density} and Dmax. A difficulty arises due to the _{non-linearity} of the

photographic process andthe widevariationofits_imagingpropertiesovertherangeofits

Accordingto _Dainty [Dainty&_Shaw,197_4] the result for the _{information capacity} ofa

continuouschannelwith anaverage "power" limitation is :

C =

Af log2 P

+ N

N (7)

Ifthe signal and noisepower are _{approximately}constant overtwo adjacent regions Aand

B, eachof width 1/2_f, thenthe_{capacity for}the totalbandwidthapproximatesto :

C=|A/(log2(l+

P/N)

%J)

Ifwe usethe power spectrum of_{the signal, WN}(/)for P and the power spectrum ofthe

noise _WN(f) for_N, then

f

flog2

V wN{f\

de ₍₉₎

Since signal and noise aretwo dimensionalfunctionsof_space, forphotographicimages

77 ( Ws(u,v)

dudv ₍₁₀₎

Sincethe statistical properties ofthephotographic _process, including image_{noise, may}be

assumedtobe isotropic, and sinceforoptimum_codingthesignal willalso havethenature

of an isotropic noise _pattern, it is convenient to work in terms ofthe one-dimensional

spatial_{frequency, w, where}w2 =

u2 +

v2

, leadingto

o V WN{w\

wdw (H)

Ifwe assumethatanatural scenehasa power spectrum proportionalto 1/wthen

2/,..\A

r ( MTF2(w)

C=x _\og2 1+ \> d>v ₍₁₂₎

since _Ws(w) MTF2(w) w

Equation ₍₁₁₎ illustrates the dilemma of _evaluating the _{information capacity} of the

photographic process. Due to _{non-linearity} the S/N ratio in terms of power spectra will

only be constant over a limited input/output, _{exposure/density} range. To _keep equation

(1_{1) "exact",} it is_necessarytorestrictitto smallsignalscondition.

In an attemptto calculate the maximuminformation capacity ofthe photographic process

as constrained between fog density and Dmax, Jones [./owes,1961] used Shannon's

theoremforapower-limited channelandthen made variousadhoccorrectionsto account

forthe respectiveinformationcapacities. _{His results, along}with othercomparative values

of_interest, aresummarized_{in Table II.}

Table II. Informationcapacitiesoffour_films, andvariouscomparative_values, as

estimated_byJones.

Film Information Area for 1 Information Exposure Comparative Filmarea

capacity bit rate foronebit timefor Hi-Fi equiv.to

system oneTV

frame

bits cm 2

fjm2

bits _erg ' photons sec cm 2 em2//frame

(xia-)

K")

(x,0-)

R.oyal-X 0.449 200 26.5 8.18 3.01 2.98

Tri-X 0.845 118.4 7.35 29.4 5.1 1.76

Plus-X 1.86 53.8 6.45 33.6 11.2 0.8

Pan-X 2.85 35.0 7.45 29.2 17.2 0.52

Although manufacturers offilm provide a speed _{rating for} each_{film, usually} no _rating of

image _quality is given. While the speed _rating is _usually a _satisfactory guide for the

ordinaryphotographer, it isinsufficientwhenchoosing afilm forscientific purposes where

thegreatest possible amount ofinformationhastoberecordedbythefilm.

We have defined Information _Theory and we will use this powerful tool to obtain the

capacityofafilmtoreceive and storeinformation.

n METHODS

Theexperimental _setupprocessis basedonthe_followingsteps:

2. 1 Photographpreparation:

2.1.1 _Settingupand_determining exposuretime.

Fourfilmswere used in_{the study, they}are: T-MAX _100, T-MAX_400,

T-MAX 3200andTRI-X 400. T-MAX 100 hasthefinestgrain, T-MAX 400

andTRI-X 400 have medium_grain, andT-MAX 3200has thelargestgrain of

allfour films. Itwouldbe_interestingto know how_theyperform under normal

exposureand constantflux.

Kodak T-MAXprofessionalfilmsare newer_products, and TRI-X 400is

an "older" product ofEastman KodakCompany, soit is_interestingto find if

thereis_{any difference between}these two products.

Beforewe_actuallytake a picture ofthe_object, wemust selectthelens andfilm

combination and alsotheshutter speed. Thefollowingequationsare usedto

illustratethevariables_needingto becontrolledintheexperiment.

(F-y

IM ₍₁₃₎

t : shutter speed

L luminanceincdls/cm2

S : filmspeed

F#

: numerical aperture

where _F#=f I D ₍₁₄₎

f: lens focal length

D : lens diameter

Whenthe shutterspeed andthe totalfluxare_{constant, thefollowing}

relationshipcanbe established:

4ASA

Ifwelet F*

=4 when_ASA=100,thenitfollowsthat _F#=8; whenASA=400

and _F#=22;whenASA=3200. Also, Dmustbe constant(i. e. D=6 mm)inorderto

have a proper range offocal length. When F#=4we use a lensoffocal length

25 mm, afocal lengthof48mm when _F#=8, and afocal lengthof132whenF#=22.

Inordertohaveconstantflux,theshutter speed _setting(f,) needstobe the

same, while new shutter speeds _t3 and t2 are setfornormalexposure and

f, > _h > _tr

Accordingto theabovediscussion,thefollowingexposureconditionscanbe

determined:

(1)ForT-MAX100 film:

(a)Alensof25 mmfocal lengthand F# of4was usedtotakea picture of each

object.

(2)ForT-MAX400 film:

(a)Alens of50 mmfocal lengthand

F#

of8was usedto takeapicture of each

object.

(b) Alensof25 mmfocal lengthand

F#

of4was usedto takepictureof each

object. _{This step}producedthesame image _{size, in}orderto _studytheeffect

ofdifferent magnification on each print.

(3) For TRI-X 400film:

(a) Alensof50mmfocal lengthand

F#

of8was usedto takeapictureof each

object.

(b)Alensof25 mmfocal lengthand

F*

of4was usedto takeapicture of each

object. This stepproducedthesameimage_size,inorderto_studytheeffect

ofdifferent magnificationoneach print.

(4)For T-MAX 3200film:

(a)Alensof135 mmfocal lengthand F# of22was usedto takea pictureof

each object.

(b) Alensof25 mmfocal length and F* of4was usedto takeapicture of each

object. This stepproducedthesameimage_size, inorderto _studytheeffect

ofdifferentmagnification on each print.

To summarizetheabove statementthefollowingcombinations have beenusedfor

(1). Conditionstoproduce constantflux (fixedamount of photons):

T-MAX 100

T-MAX400

TRI-X400

T-MAX 3200

Focal Length

25 mm

50mm

50 mm

135 mm

F#

Shutterspeed _(r,)

4

8

8

22

(2). Conditionsto give normal exposure:

Focal Length F#

T-MAX 400 25mm 4

TRI-X 400 25 mm 4

T-MAX 3200 25 mm 4

1/30sec

1/30sec

1/30sec

1/30 sec

Shutterspeed_(/,)

1/250 sec

1/250 sec

1/1000se

(3). The orders ofthepicturestakenforthescenes are : _graycard, "simple" _scene,

graycard,

"busy"

scene.

Photographsattached:

V

Image from TRI-X400film / 25 mmlens

ImagefromT-MAX 3200film /25 mmlens

Image from T-MAX 3200 film / 135 mmlens

22

Imagefrom T-MAX3200 film / 25 mmlens

Imagefrom T-MAX400film /50mm_lens

Image from T-MAX 100 film/ 25 mmlens

26

Image from T-MAX400 film/ 50mmlens

Imagefrom TRI-X400 film /50mmlens

Image from T-MAX3200film/ 135 mm lens

2.1.2 _Developingfilmand photographic paper.

(1)AllfilmsweredevelopedattheRI.T. campus,_usingtheKodakVersamat

Film ProcessorV-5Nfor_developingthefilms.

(a)Process speed for T-MAX 100was2.2ft /min.

(b)Process speedforT-MAX 400was2.75 ft /min.

(c) ProcessspeedforTRI-X 400was 1.5ft/min.

(d)ProcessspeedforT-MAX 3200was2.2ft /min.

(2) The_followingconditions wereusedtoprojectimages fromnegativeto

Table ILL Conditionsusedforthisproject

(1) When 25 mmlenswasused:

#,& H2: 371/2"

& 53/4"

Films Objects Filter

T-MAX 100 _Gray Card 3.5

T-MAX 100 _Egg 4.0

T-MAX 100 Flower 4.0

T-MAX 400 _GrayCard 4.0

T-MAX 400 _Egg 4.5

T-MAX 400 Flower 4.5

TRI-X 400 _GrayCard 3.5

TRI-X 400 _Egg 4.0

TRI-X 400 Flower 4.0

T-MAX 3200 _GrayCard 4.0

T-MAX3200 _Egg 4.0

T-MAX 3200 Flower 4.0

Exposure Time X

Magnification

27 sec 631.9

44 sec 760.8

48 sec 860.4

38 sec 608.8

27 sec 597.3

27 sec 632.2

28 sec 601.4

46sec 784.0

46 sec 632.2

37 sec 711.5

31 sec 784.0

33 sec 632.2

(2)When50mm_lenswasused:

//,& H2: 371/2"

&53/4" Films T-MAX 400 T-MAX 400 T-MAX 400 TRI-X 400 TRI-X 400 TRI-X 400 Objects Filter

GrayCard 4.0

Egg 4.0

Flower 4.0

GrayCard 3.5

Egg 3.5

Flower 3.5

ExposureTime X

Magnification

11.5 sec 190.4

10.0 sec 196.0

10.0sec 215.1

9.0sec 190.4

7.5 sec 196.0

7.0sec 215.1

(3)When 135mmlenswas used:

H,& H2:371/2"

& 53/4" Films T-MAX 3200 T-MAX 3200 T-MAX 3200 Objects Filter

GrayCard 4.5

Egg 4.0

Flower 4.5

ExposureTime x

Magnification

7.7sec 21.1

6.3 sec 21.5

7.1 sec 21.4

(3). Allphotographic paper was developedattheR.I.T. campus_byusinga

Kreonite B/W Process

2-2_Evaluatingimage_quality ofphotographs

The successive categories method wasusedinthisprojectforstatistical analysis.

The_underlyingassumptionsofthelawofsuccessivecategoricaljudgmentshave been

stated_byTogerson ₍₁₉₅₈₎

_{[Togerson,\95S]}

(1) Thepsychological continuumofthesubjectcan_{be divided into} aspecified number

oforder categoriesorsteps.

(2) Owingtovarious and _{sundryfactors,} a given_{categoryboundary}isnot

necessarilyalwayslocated ataparticular point onthecontinuum. _Rather,it

also projects a normal distributionofpositionsonthecontinuum. _Again,

different category boundariesmayhave differentmeanlocations and different

dispersions.

(3) Thesubjectjudges agiven stimulustobe belowagiven_{categoryboundary}

wheneverthevalue ofthestimulusonthecontinuumis lessthan thatofthe

categoryboundary.

There are_manyformsof_{categoryscaling}and awide_varietyofexperimental

techniquesanddatareductionalgorithmsthathavebeenusedin_categoryscaling. A

common experimental method of_{category scaling}wasusedinthis projectto gather

dataabouttheimage_qualityoftwenty-onephotographs. Thirty-threeobservers

participated inthisproject. _Theywere askedtoratetheoverallimage_qualityof each

photograph ona7-point scale. The instructions and results were asfollows:

2-2-1 Instrustionstoobservers

INSTRUCTIONS TO OBSERVERS

Youwillbeshown anumber of photographs. We wouldlikeyou to make ajudgment on

theimage _qualityofthe_photograph,and give a_ratingfortheprint.

Pleasedonot _directlytouch thephotographs.

Do notconsider composition.

Ignorescratches, dirt, and_anyphysicaldefectsinthephotograph.

The viewingdistance shouldnotexceed 12 inches.

Please express your opinion _using a scale of number from 1 to 7 where 7 represents

unusable and 1 represents excellent image quality. Numbers between 1 and 7 represent

equalintervalsofimagequality. Thecategories usedintheseexperiment are:

(1)Excellent

(2)VeryGood

(3)Good

(4)Acceptable

(5)Unsatisfactory

(6)Poor

You may not use fractions or _decimals; you must use integers. The integers should be

from 1 to_7;nootherintegers_{may be}used.

2-2-2Results from_evaluatingtheimage_qualityof photographs

(1)Animage _qualityassessment_bytheobservers wasperformed ina period of

threemonths. The observerwere_{randomlychosen, among}themwere:

professional_{people, students,}and_ordinaryobservers. Thephotographs

were_randomlypresentedto each observerforevaluation. Therandomness

ofthephotographis important. Thisprocess allowed control of_accuracyof

the_ratingdata. _{After collecting} allthedatafromtheviewersa statistic

analysisisperformedto generate mean value_(m) and standarddeviation (S)

(2) Thirtythreeviewers were askedto make ajudgmentontheimage_qualityof

thephotographand a_ratingwas giventothephotograph. A ratingof"1"

means _excellent, and "7" means unusable.

(3)Data: Appendix 1

Theabbreviations areas follow:

graycard: _G, Egg:E, Flower: F

T-MAX100/25 mm: _1, T-MAX 400/25 mm: _2, T-MAX 3200/25mm: _3,

TRI-X 400/25 mm: _4, TRI-X 400/50mm: 5, T-MAX 400/ 50mm: 6,

T-MAX3200/ 135mm: 7

(4) Astatistical analysiswas performedto evaluatethedata.

(5) Theoriginalresults weretransferred toanew scalewheretheoriginal 1 is

represented_by 1 andoriginal7 isrepresented_by0. Thesenew numbers are

identifiedas "Ranking"

Ranking (R)= _{116.666-16.666 x}

mean _{(m) (15)}

Table TV Statistic datafor_"GreyCard"

Gl G2 G3 G4 G5 G6 G7

Mean_(m) 3.55 4.15 5.30 4.52 3.0 2.30 1.79

Ranking (R)

StandardDeviation

_w

0.575 0.99 0.475 1.08 0.283 1.34 0.413 1.13 0.666 0.85 0.783 0.90 0.868 0.73

TableV Statisticdatafor"

Egg "

Mean_(m)

TableVI Statistic data for"

Flower "

Fl F2 F3 F4 F5 F6 F7

4.52 5.39 4.97 3.18 3.21 1.91

1.13 1.13 1.19 1.03 1.01 0.71

Mean(m) 3.52

StandardDeviation_(S) 0.93

2-3 _CalculatingMTFofphotographs

Many studies in the field of image _{quality definition} have noticed that a perceptible

difference in image _quality can be obtained _{by changing} the scale ofthe point spread

function. _{The quality}of a visualimage is related to the scale ofthe image onthe retina.

The human visual system has a modulation transfer function _(MTF) with broad peak

response at 6 cycles perdegree (cpd). Image quality rank canbe computed ifthe "true"

eyeMTFisusedinthecalculationof_qualityrank. In_fact, computationsthatuse_onlythe

one-dimensional MTF have proven quite successful in _{predicting quality} rank for

two-dimensional imagestructure. These successes suggestthatthe one-dimensionaltreatment

includes theproper_weighting function to describe thetwo-dimensional visual properties

ofthe image. Subjective _Quality Factor _(SQF) tells us that image _quality is related to

logarithmic spatial _{frequency weighting} ofthe system optical transfer function (OTF).

Specifically, image _qualitycorrelates with the area underthe system OTF whendisplayed

ona_logspatial_frequencyscale.

ACrosfield Magnascan 636 reflection drum scanner was used to scan seven ofthe _gray

card photographs. All photographswere_carefully aligned and scannedat 18 pixels /mm.

The datawerethen readin_Photoshop 4-5 to generate rawdata for_granularityand MTF

calculation. MTFs' ofeachprintwerecalculated _accordingto the_following equations:

4*)=

^

md07F(f)=]i(x)ea'*'& (17)

oo

MTF{f)=

\OTF(f\

A routine was written inMathcad 4.0 and used to do the calculation. The program and

calculations are showninAppendix-3.

The MTF curve for the print generated from T-MAX 100 film and 25 mm lens

Figure3 MTFoffinalprint_{byusing T-Max 100}filmw/25 mmlens

1.5 2 2.5

Frequency (lines/mm)

2-4_{Determininggranularity}

Photoshop4-5 was usedto obtainthe_{granularitydata,} one set ofdatawas

obtained withalowpassfilterandthesecondsetdatawas obtained withoutafilter.

The digitaldatawere scaled as anintegers between 0 and255. Amean of128 was

usedintheequationbelow. Thefollowingequationwas usedtotransform original

granularity datato

"New"

granularitydata:

^New logNoise(p)

White ,

+log2 (19)

No^y-hlfpl

(20)

Vpixels vofpixels

where white=₂₅₅

A_{linear relationship}was_{developed betweenInformation}

Theoryand _aDto

predictthe subjectsaveraged responseforeach set ofprints. Asecondlinear

relationship was_{developed betweenSQF and}

oD to predictthesubjects averaged

responseforeach set of prints.

2-5 _CalculatingSQFofphotographs.

A Subjective_QualityFactor_(SQF)was_developed astheresultofasearchforan

objective figureof meritwhichcouldbe_easilycalculated and_directlymeasured in

practice andwhich wouldcorrelatewithsubjectiverankregardlessofMTFform.

The SQF meritfunctionpredictsimageappearance_linearlywhentheactionsof

the eye_includingthemagnification oftheimagearetakenintoconsideration.

A_{linear relationship}wasdevelopedbetween SQFand _aD topredictthesubjects

averaged responseforeach set ofprints. _{Image quality}isrelatedtoboth MTFand

granularity. _Theyact_{independently}as whenincreasein granularitythenweexpect a

loss in image_qualityand alsowhenalossofMTFwecanexpect alossofimage

/ Q. = SQF

-aaD

(21)

Aroutinewaswritten_{in Mathcad}4.0 andusedto calculated SQF. Programs and

calculationsare shownonAppendix-4. An_{image quality}assessmentwasperformed

byusing SQF.

2-6_CalculatingInformationCapacity.

Information_capacityof anemulationdependsonthemodulationtransferfunction

(MTF) andthe_granularityoftheemulsion. Inthis_{study MTF}of each system was

obtained_first, thenalinear relationshipwasdevelopedbetween Information_Theory

and _<jd topredictthesubjects averaged responseforeach set of prints.

I.Q.=

a0+b0(lC)

Aroutine was writtenin Mathcad 4.0and usedto calculateInformation

Capacity. Programsand calculationsareshownonAppendix-5. Information_Theory

was also usedtopredictimage_qualityby_{calculating information capacity}and_taking

granularity into consideration.

m. Results

3- _{1 MTFofthefinal prints was calculated:}

(1)Allofthe seven_graycardphotographswere scanned anddigitized_byusing

CrosfieldMagnascan 636reflection drumscanner. Anedgetracewas_performed,

and a_scanningof18 pixels/mm wasused.

(2). MTF'sof eachprintwere calculated_accordingto the_followingequations:

4x)= *x)

dx.

otfw)= J(xy2^ac

n=l

MTF{f)=

\OTF{fl

Aroutine was writteninMathcad 4.0and usedtodothecalculation. The MTF's

Figure 4 MTFoffinalprint_{byusing T-MAX 100} filmw/25mmlens

1.5 2 2.5

Frequency (lines/mm)

Figure 5 MTFoffinalprint_{byusing T-MAX 400 film}w/25 mmlens

1.5 2 "

Frequency(lines/mm)

Figure6 MTF offinalprint_{byusing T-MAX 3200}filmw/25 mmlens

1.5 2 2.5

Frequency (lines/mm)

Figure 7 MTFoffinal print_{byusing TRI-X 400} filmw/25 mmlens

1.5 2 2-5

Figure8 MTFoffinalprint_{byusing TRI-X}400filmw/50mmlens

Frequency (lines/mm)

Figure 9 MTFoffinalprint_{byusing T-MAX 400}filmw/ 50mmlens

1.5 2 2.5

Frequency (lines/mm)

Figure 10 T-MAX3200filmw/ 135mmlens

0.98

0.96

0.94

-0.92

-0.9

0.88

-15 2 2.5

Frequency (lines/mm)

3-2 _Granularityanalysis

Photoshop4-5was used to obtainthe_{granularity data}fromthefinal prints. Therefore

thismeasurement contain a systemslevel of_{MTF, including}MTFof_film,paper, lens

andscanner usedformeasurement. Oneset ofdatawasobtained with alowpassfilter

andthe secondset ofdatawas obtainedwithout afilter. Thedigital datawere scaledas

anintegers between0and255 andmean of128was usedforcalculation. _Granularity

TableVII _Granularityresults

T-MAX 100 T-MAX 400 T-MAX 3200 TRI-X 400 TRI-X 400 T-MAX 400 T-MAX 3200

25mm

Print_GranularityW/filter 5.1

Print_Granularityw/o 9.4

25mm 25mm 25mm 50mm 50mm 135mm

9.3 10.3 8.0 4.6 5.4 5.1

9.7 19.1 15.3 8.7 9.6 14.6

Byusingequation:

New

'log^M)+,g2

V White

wehavenew_granularitydataas:

Table VHI Calculated_Granularityresults

T-MAX 100 T-MAX 400 T-MAX 3200 TRI-X 400 TRI-X 400 T-MAX 400 T-MAX 3200

25mm 25mm 25mm 25mm 50mm 50mm 135mm

Print_GranularityW/filter 0.0183 0.0322 0.0353 0.028 0.017 0.0196 0.0187

print_Granularityw/o 0.0325 0.0334 0.0486 0.0507 0.0303 0.0331 0.0621

3-3 SQFofphotographs

Image qualitywasdetermined_byusingthecorrelation ofSQF & _aDF subjectdata for

each photograph.

(1). Aroutine was writtenin Mathcad4.0to calculatetheSQF.

Table TX SQFresults

T-MAX 100 T-MAX 400 T-MAX 3200 TRI-X 400 TRI-X 400 T-MAX 400 T-MAX 3200

25mm 25mm 25mm 25mm 50mm 50mm 135mm

SQF 0.57 0.51 0.48 0.54 0.77 0.79 0.97

(2) The_followingequation was usedto take_granularityintoconsideration:

2

{l\Pr^on){N)-aSQF{N)-ba0{N))

=i

a=l andb=-3.6

then

TableX Resultsofprediction_byusing SQF

R,

(prediction)

'(measured)

T-MAX 100 T-MAX 400 T-MAX3200 TRI-X 400 TRI-X 400 T-MAX 400 T-MAX 3200

25mm 25mm 25mm 25mm 50mm 50mm 135mm

0.51 0.40 0.36 0.44 0.71 0.72 0.91

0.57 0.51 0.48 0.54 0.77 0.79 0.97

Fig 11 SQF results

1

0.9

0.8

0.7

0.6

O 0.5

0.4

-0.3

0.2

--0.1

--0

4 Films

3-4 Information_Capacityof photographs

Image qualitywas obtainby_{using Information}Theoryforeachprint:

(1)Aroutine waswrittenin Mathcad4.0to calculate_{information capacity}withthe

granularitytakeninto consideration. Theresults are asfollows:

Table XI Information_Theoryresults

T-MAX 100 T-MAX 400 T-MAX 3200 TRI-X 400 TRI-X 400 T-MAX 400 T-MAX 3200

25mm 25mm 25mm 25mm 50mm 501 135r

I.C. 30.9 30.0 24.8 31.1 47.1 63.2 63.5

(2)The_followingequation was usedto take_granularityintoconsideration:

%^M=00884+00119*IC

Table XII Resultsof prediction_{byusing InformationTheory}

T-MAX 100 T-MAX 400 T-MAX 3200 TRI-X 400 TRI-X400 T-MAX 400 T-MAX 3200

R_{prediction)

D

(measured)

25mm

0.46

0.57

25mm

0.44

0.51

25mm

0.38

0.48

25mm

0.46

0.54

50mm

0.65

0.77

50mm

0.84

0.79

135mm

0.84

TVDISCUSSION

4-1 Comparison of results_using SQF andInformation Theory.

JudgingtheresultsfromFigure₍₁₂₎we can_saybothSQFandInformation_Theory

canproduce_veryreasonable results. But overall the SQFdoes abetter jobof

predicting imagequality.

Figure12 I.T. and _{SQF ranking}prediction

0.3

.

. /

s

_il.

/

I.T.

SQF

0.4 0.5 06

Ranking-_Measured

Theprediction oftheimage_{quality Vs}measured_granularity

(crD)

Is Image_Quality a , ? -JASA

(a)When constantflux isusedfor_exposure,thefast film has better imagequality.

Itis becausethegaininMTF morethan offsetsthegrain_{effects;also,}becausethe

fast filmsare_usuallysensitizedbetter.

(b)Undernormal exposuretheslowerfilmhas better imagequality.

Table XIII _Summaryoftheresults:

T-MAX 100 T-MAX 400 T-MAX 3200 TRI-X 400

25mm 25mm 25mm 25mm

TRI-X 400 T-MAX400 T-MAX3200

50mm

Note:

(1) Constantfluxcondition:

G5: TRI-X 400film / 50mmlens

G6: T-MAX 400 film/ 50mmlens

50mm 135r

SQF 0.57 0.51 0.48 0.54 0.77 0.79 0.97

Information Cap. 10.16 9.98 10.55 9.8 15.21 21.73 27.72

Granularityw/fil. 5.1 9.3 10.3 8.0 4.6 5.4 5.1

Granularityw/o 9.4 9.7 19.1 15.3 8.7 9.6 14.6

^(prediction/_SQF) 0.51 0.40 0.36 0.44 0.71 0.72 0.91

(2)Normalexposure condition:

G2: T-MAX400film /25 mmlens

G4: TRI-X 400 film /25 mmlens

Figure 13 _Comparisonof_{granularityby}

using I. T. and SQF

0.05

.& 0.04

C

O 0.03

4

Films

Photoshop4-5 was usedtoobtainthe_granularitydatafromthefinal prints. Thereforethis

measurement contain a systems level of_{MTF, including} MTF of_{film, paper,} lens and

scanner used for measurement. One set ofdata was obtained with a low pass filter and

the second set of data was obtained without a filter. The digital data were scaled as

integers between 0 and 255 and a mean of 128 was used for the calculation. When we

compare the _granularity on each photograph _{by using SQF} and Information _Theory, we

reachthe_followingconclusions :

(a)WhenSQFisusedforprediction:

Underconstantfluxthe_granularityintheprint shows no_bigchanges,butunder

normalexposure _aDvaries inproportionto thegranularity.

(b)When Information_Theory isusedforprediction:

FromFigure_(13), it isobviousthat it is_{very difficult}to predict_granularityby_using

InformationTheory.

(c)Thereasonthat SQFcan predictfilm granularity isbecause SQFusesa

lowpassfilterto simulatethehumanvisual system andInformationTheorydoesnot.

(d)Fromthisproject welearnthatwhenafixedamount of photonfluxandafixedprint

size are usedit isbettertouseafast film. Intheotherwords, under normal

conditions, aslowerfilmwouldbeabetterchoice.

4-2 ResultsonT-MAX400,andTRI-X 400films

ComparedwithTRI-X400, T-MAX 400 filmisanewer productfromEastmanKodak

Company. Inthis_studywe usedboth SQFandInformationTheorytopredictimage

quality, andto _studythedifferences betweenthesetwo films.

(a)Underconstantfluxcondition:

The scanningwas done fromthefinalprintsinthisproject. Therefore this

measurementcontainasystemslevelof_MTF,includingMTF offilm, paper,lens

and scannerusedformeasurement. Accordingtotheresultsfromthisproject and

byusing thedata intableXIII, when under constantfluxit isclearthat

either with

thanTRI-X 400film. Intheother_words,theT-MAX 400 film isafinerfilmwhen

comparedtoTRI-X400film.

(b)Undernormal exposure condition:

Byusingthe sameTable_XIII,undernormal_exposure, theresultof_granularity

without_using afilter it isobviousthat theT-MAX 400 film hasfiner_grain,when

comparedto TRI-X 400film. Whenthefilter isused, TRI-X 400film hasa

granularityof8.0Vs9.3 for T-MAX400. Itispossiblethat thisiscaused_bythefilter

usedinthesystem orthe truncationofdata_duringthe_scanningprocess. _Possiblythe

photographic paper used isa cause.

(c)Wecanmake abriefconclusionforthisproject as:Whentheprint sizeis fixedand a

fixed amount ofphotonswere usedina_system, it is bettertouseafast film.

VREFERENCES

James A. _Wisner, Film_GranularityandtheEffecton_SubjectiveImage _Quality,

Master_{Thesis, R.I.T.,} 1986

Lisson, G,DigitalImage_ModelingofFilm_GranularityandEffecton Subjective

Pictorial _Quality,Master_{Thesis,R.I.T.,} 1983

Granger,E. M. _{&, Cupery,} K. N. An Optical Merit Function_(SQF), whichcorrelates

withSubjective Image_Judgments, Photogr. Sci.Eng. 16 ,221 (1972 )

J.C._Dainty, &R. Shaw. Image Science 10 Academic Press Inc. _California, 1974.

Jones, R. C._{Information capacity} ofphotographicfilms. J. OPSoc.Amer.,51.1159. ₍₁₉₆₁₎

Levi,L. Ontheeffect of_granularityondynamic rangeandinformationcontentof

photographic recordings. J. Opt. Soc. Amer. , 48 , 9

,(1958)

Altman, J. H. and_Zweig, H. J. Effectof spread functiononthestorageofinformation

W.S. _{Togerson, "Theory}andMethodofScaling" John_Wilyand _Sons,New_York,

1958.

G. P _Corey,M. J. _Clayton, and K. N. Cupery. SceneDependenceofImage_Quality

Photogr. Sci. Eng. ₍₁₉₈₂₎

M. C._Davidson, J. Opt. Soc.Am. _58, 1300 (1968).

VIAPPENDICES

APPENDIX- 1

Thefollowingsaresubjective ratingsof21photographsfrom33 differentviewers.

Data:

Theabbreviations are asfollow:

Gray Card: G

T-MAX100/25mm: 1

TRI-X 400/25 mm: 4

T-MAX 3200/ 135mm: 7

Egg:E

T-MAX 400/25 mm:2

TRI-X 400/50mm: 5

Flower: F

T-MAX 3200/25mm: 3

T-MAX 400/50mm: 6

Gl G2 G3 G4 G5 G6 G7 El E2 E3 E4 E5 E6 E7 Fl F2 F3 F4 F5 F6 F7

Viewer#1 234422234543223455331

Viewer#2 344432243342324444342

Viewer#3 23 3432344443334444342

Viewer#4 345343234543313454332

Viewer#5 34534 1143542222444332

Viewer#6 34433 1134553122344231

Viewer#7 333411155554214555231

Viewer#8 2232 12 122332112342 121

Viewer #10 _{467642 155775214775 332}

Viewer #11 2 2 2 2 4 2 234322223 334 342

Viewer #12 _{466644356565323 776673}

Viewer #13 4 4 7 6 3 3 366775324 677 533

Viewer#14 54763 1257643125 576321

Viewer#15 45 763 2 145363213 576421

Viewer#16 44 5 422235542324 656433

Viewer#17 3 4643 3 255654324456332

Viewer#18 5 6 5 4 4 4 256665545 666 443

Viewer#19 44653 1146764314565241

Viewer #20 5 66644256665535 565442

Viewer #21 437422145762212363243

Viewer#22 6 6 7 5 44 366674435 577443

Viewer#23 455432246754214567221

Viewer #24 345521124552124454342

Viewer #25 3 44423 244554333 354322

Viewer#26 345533234543223454342

Viewer #27 456642 144654223565421

Viewer #28 456443 145655114565432

Viewer#29 445 53 3 135553223 344232

Viewer#30 555432353443224455332

Viewer#31 3 4 6 5 2 2 344654225 566 542

Viewer#32 336532225662222344223

Viewer #33 446533245654323455332

APPENDIX 2

The_followingLine SpreadFunctiondatawas obtained_byusingPhotoshop2-5.

(a)T-MAX100/25mm:

Line Spread Function

1

2

2

5

8

13

16

22

18

14

6

5

2

3

3

2 Pixel# Edge Reflectance

1 231

2 230

3 228

4 226

5 221

6 213

7 200

8 184

9 162

10 144

11 130

12 124

13 119

14 117

15 114

16 111

(b) T-MAX400/25mm:

Pixel# _{EdgeReflectance Line}

Sp

1 ₂₂₇

2 226 ₁

3 _{226 0}

4 _{223 3}

5 _{220 3}

6 _{215 5}

7 209 6

8 200 9

9 187 13

10 172 15

11 154 18

12 137 17

13 128 9

14 121 7

15 116 5

16 113 3

17 111 2

18 108 3

19 107 1

20 104 3

(c)T-MAX3200 /25 mm:

Pixel# _{EdgeReflectance Line} Sp

1 ₂₂₅

2 _{224 1}

3 _{223 1}

4 221 2

5 218 3

6 213 5

7 206 6

8 196 10

9 180 16

10 159 21

11 137 22

12 121 16

13 110 11

14 103 7

15 98 5

16 96 2

17 92 4

18 88 4

19 85 3

20 82 3

(d)TRI-X400/25 mm:

Pixel # Edge_{Reflectance Line Spi}

1 ₂₂₅

2 _{221 4}

3 218 ₃

4 _{215 3}

5 207 8

6 194 13

7 178 16

8 158 20

9 139 19

10 129 10

11 119 10

12 116 3

13 109 7

14 104 5

15 100 4

16 99 1

(e) TRI-X400/50mm

Pixel# _{EdgeReflectance Line Spi}

1 ₂₂₃

2 _{222 1}

3 _{220 2}

4 218 2

5 _{212 6}

6 194 18

7 162 32

8 129 33

9 109 20

10 101 8

11 97 4

12 95 2

13 93 2

(f)T-MAX400/50 mm:

Pixel # _{EdgeReflectance Line}

Sp

1 ₂₂₉

2 227 2

3 _{225 2}

4 _{215 10}

5 186 29

6 141 45

7 119 22

8 112 7

9 104 8

10 97 7

11 97 0

12 96 1

13 94 2

(g) T-MAX3200/135mm

ixel # Edge_{Reflectance Line Spi}

1 ₂₃₂

2 ₂₃₃

-1

3 _{222 11}

4 150 72

5 _{89 61}

APPENDIX - 3

Written Mathcad4.0program and resultsfor Information MTFs

(a)T-MAX100/25mm:

1 = o.. 11

x .= 0

x,4 = 2.3S

x, =

.79

x,5 = 2.3S

x, = _1.59

x.fi = 1.59

x. = _1.59 x,_ = _1J9

x_. = 3.97 x,. - 1.59

10

x5 = 6.35

x,? =0

x5 = 10.32 x:o =

x. = 12.7

1 *:i

=

^ -- I7-6 x., = 0

x, = 14.29

y X.,

= 0

x10 = 11.11 _x.. =0

x,, =4.76

x., = 3.97

c =

CFFT(x)

N = _{last(c) N} =₇₁

j :=0..N 1.3S9 1.334 1.184 0.984 0.787 0.635 0.534 0.462 0.396 0.327 0.256 0.19 0.13: 0.098 0.076 0.063 0.055 0.052 0.044 0.031 0.032 0.043 0.057 0.051 0.033 0.017 0.022 0.02S 0.028 0.029 0.036 0.045 0.056 0.072 0.09 0.105 0.11 0.105 0.09 0.072 0.056 0.045 0.036 0.029 1.389 0.96 0.852 0.70J 0.566 0.457 0.385 0.333 0.2S5 0.235 0.184 0.137 0.098 0.071 0.055 0.045 0.04 0.037 0.03: 0.023 0.023 0.035 0.041 0.037 0.024 o.oi: 0.016 0.02 0.02 0.021 0.026 0.033 0.041 0.052 0.065 0.075 0.079 0.075 0.065 0.052 0.041 0.033 0.026 0.021 0.79 1.59 1.59 3.97 6.35 10.32 12.7 17.46 14.29 11.11 4.76 3.97 1.59 2.38 2.38 1.59 1.59 1.59 hh 0.017 --- " 0.012 0 0.033 0.024 0 0.051 0.037 0 \ 1 1 1 1 / \ 1 \ / V ^ L^>

50

J

(b) T-MAX400 /25 mm:

i =

&.. n

X

1 := ₀

X,

1 = _2.44

>S = 2.44

X. =_4.07

X4 = _4.88

X5 = 7.32

X. = _10.57

x. = _12.2

Xg := 14.63

x, =

13.32_

x]0 := 7.32

x,. = _5.69

1I

xu = 4.07

xu := 2.44

XH := 1.63

X15 := _2.44

X16 := _0.81

xn := 2.44

x;s = 0

X19 := 0

X20 := 0

X2! != 0

X22:= ₀

X23''

= ₀

X24-= ₀

(c)T-MAX3200/ 25mm:

i = _{o.. n}

x := 4.64

x = ₀

xM := _3.31

x. := _0.66

x]5 := _1.32

x, := _0.66 x .= 2.64

16

x3 = _1.32

xn := _2.64

x4 = _1.99

xlg := 1.99

X5 = 3-31

x19 := 1.99

Xo = _3-97

X20 := ₆₆

x. - 6.62

x2] := 0.66

xg := _10.6

x,2 .= 1.99

x9 := 13.91 Xj3 := 1.32

^4 = ₁₃₂

x10 := 14.57

'Si = _10-6

X12 = _7'28

c =

CFFT(x)

N.= _{last(c) N-71}

j := _0..N

(d)TRI-X400/25 mm:

i := _0..71

x13 := 3.97

x .= 0

i

xM := 3.17

xT := 3.17 x15 = 0.79

x, := 2.38 _xis =0

x, = 2.38 xn

= ₀

x. - 6.35

4 X18

=

x5 = 10.32 _X19 =

x, = 12.7

0

^o^0

x_ := 15.87 _X21 "

x8 = 15.03 X22

=

x9 := 7.94 **

=

xio

= 7'94

h*

-xu = 2.38

x12 := 5.56

c :=

CFFT(x)

N.=

last(c) N= ₇₁

j - _0..N

(e) TRI-X400/50mm:

i =0.-71

x. =0 i

= 0.70

x,3 := _1.52

XH =

x,s:S0

Xj -

i---xifi i0

X- = i-32 *

xn = ₀

x = 4.55

-f

xis =

x: - I3\04 TO = _24.24

x; .= 25.0

xie =

X? = _15.15 ^o

=0

Xv =

<3.0<3 X,. = ₀

ii

*to =

3.03

X22 !=

xn := _i.52

x,, = ₀

4rJ

x1; = 1.52

X24 :=

c = _CFFT(x)

N =

last(c) N j = _0..N

(f)T-MAX400 /50 mm:

i = _{0.. 71}

X13 = 0

x - 0

i

X14 = 0

x^ = 1.48 X15 = 0

x, - 1.43 X, . = 0

x. .= 7.41

X17 = ₀

x4 = 21.48 X1S = 0

x. = _33.33

5

X19 = 0

x, = _16.3

il *30

= ₀

x. = _5.19

V. = 0

* s 193 X22

= ₀

x? = _5.19

X23 = 0

xio

'-"

X. = ₀

x = 0.74

x,, = _1.43

c =

CFFT(x)

N = _{last(c) N}= ₇₁

(g)T-MAX3200/135mm:

i = _0..71

xu - 0

x := ₀

4

\ = 0

X9 = 0

X10 = 0

xu = 0

X12 = 0

X14 =0

x^ = _7.59

x,5 := 0

x, = _49.66

xid =

x, = 42.07 _xn = 0

x. = 0.69 x_ = ₀

2

X5 =

X19 = 0

x = 0 x.. - 0 x5 u

20

x, = ₀

x:i = 0

x = ₀

X23 =

x. = 0

c =

CFFT(x)

N :=

last(c) N =₇₁

j = _0..N

c! 1.389 1.371 1.313 1.238 1.14 1.034 0.931 0.837 0.756 0.686 0.625 0.57 0.522 0.432 0.451 0.431 0.419 0.411 0.401 0.3 S4 0.357 0.32 0.274 0.223 0.172 0.125 0.087 0.061 0.043 0.048 0.057 0.069 0079 0.087 0.091 0.092 0.093 0.092 0.091 0.087 0.079 0.069 0.057 1.389 1 0.987 0.949 0.891 0.32 0.744 0.67 0.603 0.544 0.494 0.4:: 0.411 0.376 0.347 0.325 0.31 0.302 0.296 0.289 0.277 0.257 0.23 0.197 0.16 0.124 0.09 0.063 0.044 0.034 0.035 0.041 0.057 0.062 0.065 0.066 0.067 0.066 0.065 0.062 0.057 0.049 0.041 1.43 1.43 7.41 21.48 33.33 16.3 5.19 5.93 5.19 0.74 1.48 0.125 -0.09 0 0.172 0.124 0 0.223 0.16 0 \ 1

"\

APPENDIX- 4

Written Mathcad 4.0_{program and resultsfor SQFs}

(a)T-MAX100/25mm:

i =_{<).. 8 j:=0..4}

vx. :=_i i

-.25

vy0:=l

vyr=.96

vy2=.852

vy3:=.708

vy4:=.566

vy3:=.?57

^6--385

vy7-=333

vy8=.:285

fre% =

.5

freqj =

.707

freq2 =₁

freq3 =_1.414

freq4 =₂

modi^) :=_linteiWvx

vy.freq.)

mod(j)

0.852

0.733

0.566

0.41

0.285

. .5-(mod(0)+mod(4))+mod( 1)+mod(2)+mod(3) sqf :

4

sqf=_0.569

(b) T-MAX400/25 mm:

i:=_{0..8 j:}=_0..4

vx, :=i-.25

vy0:=i

vyr=.957

vy2:=.839

vy. :=.678

vy4=.515

vy5:=.381

vy .=

.288

vy?:=.228

vv :=.189

freV=.5

freqi :=.707

freq2:=₁

freq3 -=1.414

freq4:=2

mod(j) =linterp/'vx,vy,frea

modCj) 0.839 0.706 0.515 0.32 0.189

sqf

sqf=_0.514

.5-(mod(0)+mod(4))+mod( I)+mcxl(2)

~_mod(3)

(c) T-MAX3200/25 mm:

i:=_{0..8 j:}=_0..4

vx. :=i-.25

i

vy0=i

vyr=.927

vy2:=.749

vy3=.568

vy4:=.461

vy5 :=.404

vy6=.34

vy? =.266

vyg:=.209

frev=.5

freq1=.707

freq2 =1 freq :=1.414

freq4=2

mod(j) :=linterp/vx _vy.freaj

mod(j)

0.749

0.599

0.461

0.362

0.209

.

.5-(mod(0)+mod(4))+ mod(l)+mod(2)

4-mod(3)

sqi:=

4

sqf=_0.475

(d)TRI-X400/25 mm:

i:=₀

-8 j:=0..4

vx.:= 1 i-.25

vy0:=₁

vyr=

.965

vy2 =.866

vy3:= .723

vy4:=

.562

vy5:= .412

vy6 =

.295

vy7 = 224

vyg = 194

fre% =.5

freqi =.707 freq2:=1 freq. .= 1.414

freq4:=2

mod(j) =_{linterp (vx}

,vy,frea

mod(j)

0.866

0.748

0.562

0.335

0.194

sqf'=.5-(mod(0)

+

mod(4))+mod(1)+mod(2)4-_mod(3)

(e)TRI-X400 /50mm:

i:=_{0..8 j:=0..4}

vx. -1-.25

i

vy0 =1

vyj =.986

vy2 =.944

vy3=.88

vy4=.802

vy5:=.719

vyg =.638

vy?:=.565

vyg =.503

freq():=.5

freq "=.707

freq2:=₁

freq3 .= 1.414

freq4:=₂

mod(j) =linterpi_vx,vy,frea)

mod(j)

0.944

0.891

0.802

0.666

0.503

sqf _ .5-(mod(0)

4-mod(4))+mod(1)+mod(2)4-_mod(3)

sqf=_0.771

(f) T-MAX400/ 50 mm:

i:=₀

8 j:=_0..4

vx. .=i-.25

vy0 =₁

vyi:=

.987

vy2:=

.949

vy3:= .891

vy4 =

.82

vy5.=.744

vy6 = ₆₇

vy/= ₆₀₃

vyg:= ₅₄₄

freq0:=.5

freqj =.707 freq2 = ₁

freq3 =_1.414 freq. =₂

mod(j) _{=linterp/'vx,vy)freq.)}

mod(j)

0.949

0.901

0.82

0.695

0.544

sqf: .5-(mcxl(0)

4-mod(4))

4-mod(1)4-_mod(2)4-_mod(3)

(g) T-MAX3200/ 135 mm:

i=0..8 j:=0..4

vx. :=i-.25

vy0=i

vy :=.999

vy2:=.994

vy, :=.987

vy4:=.976

vy5 :=.963

vyg:=.947

vy7:=.928

vy =.907

te% =.5

freqr=.707

1

=1.414

2 freq2 freq3 freq4

mod(j) =_{linterp/'vx,vy,frea}

mod(j)

0.994

0.988

0.976

0.953

0.907

f._.5-(mod(0)

4-mod(4))+_{mod(1)+mod(2)}

4-mod(3)

4

sqf=_0.967