SPIE Proceedings [SPIE Interferometry '89 - Warsaw, Poland (Monday 8 May 1989)] Interferometry '89 - Application Of Single Beam Speckle Interferometry In Macromolecular Physics

Application o

1lnstitute o

2lnstitute o

f single beam speckle interferometry in macromolecular physics

Jaroslav Holoubek1 and Herbert Krug2

f Macromolecular Chemistry, Czechoslovak Academy of Sciences,162 06 Prague 6, Czechoslovakia

f Physical Chemistry, 6500 Mainz, Federal Republic of Germany

ABSTRACT

An application of one -beam speckle interferometry to polymer systems is presented withemphasis on measuring of speckle pattern correlation. The system for an interactive pictureanalysis useful for the extraction of various types of physical information from "speckled"images is described.

1. INTRODUCTION

The scattering of coherent light from a rough surface or during passage through an opti-cally heterogeneous material gives rise to a speckled structure, sometimes perceptible bythe naked eye, of light and dark grains called the speckle pattern1-3(SP). Many polymersystems display remarkable bright SPs in transmission due to inherent heterogeneous struc-ture (supermolecular morphology comparable to or larger than the wavelength of visible light,heterogeneity in composition, variety of additives etc.). While several polymeric materialsproduce sufficiently visible SPs both in the transmission and reflection mode, for some ofthem general surface preparation is required because of the relatively low reflectivity ofsolid polymers. Retroreflective paint has been successfully used2 as the application ofa quick drying black acrylic enamel sprayed onto a surface or white paints with ballotini.The bright SPs are known from small -angle laser light scattering from polymer films4,5,polymer blends6'7, optically heterogeneous gel systems8,9, amorphous polymers10, etc.Generally, the methods in which this phenomenon is utilized can be characterized as tech-niques based on measurements of the intensity correlation of scattered light11, such asholographic interferometry12, speckle interferometry1 -3,12 speckle photography1 -3,12, laserDoppler velocimetry or photon correlation spectroscopy 13,14. While the former three tech-niques predominantly analyze spatial aspects of intensity changes, the latter two deal withthe time or frequency dependences of the intensity fluctuations of light scattered froman inhomogeneous medium. In this paper we restrict ourselves to the SPs created by propa-gation of the coherent light through an optically heterogeneous polymer system with singlebeam illumination in an arrangement usually called one -beam speckle interferometry orspeckle photography, although in more recent measuring set -ups photography is usuallya superfluous step. As stated above, the basis of the speckle techniques is the measure-ment of correlation between SPs. In this contribution we present the methods of speckle cor-relation measurements together with examples of application that include the determinationof 1) the displacement vector and Poisson's ratio of polymer films, 2) optical path fluctu-ations of scattered light which has passed through the polymer films with different concen-tration of additives, 3) the coherence factor of two polarized SPs caused by light scatteringfrom solid polymers, 4) "smoothing" of SPs during the space -time integration process,5) slow correlation time measurement, 6) structural aspects of non -Gaussian SPs connectedwith the small number of scatterers in the illuminated volume. Recently, the digital imageprocessing technique has developed rapidly with the advance of computer science. In thispaper we describe an interactive picture analysis system used in an evaluation of SP para-meters. Although the present examples of application are limited to polymer systems, thetechnique of interactive picture analysis is useful for a quantitative evaluation of infor-mation from real and Fourier -space images of arbitrary structure15.

2. STATISTICAL PROPERTIES

Since speckles play an important role in many physical phenomenal- 3,16,17 it is essentialto fully understand their statistical properties. Most often, the amplitude of the electricfield A(x,y,z) consists of a large number of contributions from various scattering regionsand the resulting field A has the Gaussian probability (the amplitude A of the scatteredfield is a circular complex Gaussian random variable). The corresponding statistical pro-perties of intensity are described by the probability density function p(I) (where p(I) isthe probability that a speckle has intensity between the values I and I + dI, and isthe average intensity) which has the form of a negative exponential1,2,18 (Fig.].)

p(I) = (11 )exp(-I/) (1)

400 / SPIE Vol. 1121 Interferometry '89

Application of single beam speckle interferometry in macromolecular physicsl 2 Jaroslav Holoubek and Herbert Krug

1Institute of Macromolecular Chemistry, Czechoslovak Academy of Sciences,162 06 Prague 6, Czechoslovakia

Institute of Physical Chemistry, 6500 Mainz, Federal Republic of Germany

ABSTRACT

An application of one-beam speckle interferometry to polymer systems is presented with emphasis on measuring of speckle pattern correlation. The system for an interactive picture analysis useful for the extraction of various types of physical information from "speckled" images is described.

1. INTRODUCTION

The scattering of coherent light from a rough surface or during passage through an opti cally heterogeneous material gives rise to a speckled structure, sometimes perceptible by the naked eye, of light and dark grains called the speckle pattern1 " 3 (SP). Many polymer systems display remarkable bright SPs in transmission due to inherent heterogeneous struc ture (supermolecular morphology comparable to or larger than the wavelength of visible light, heterogeneity in composition, variety of additives etc.). While several polymeric materials produce sufficiently visible SPs both in the transmission, and reflection mode, for some of them general surface preparation is required because of the relatively low reflectivity of solid polymers. Retroreflective paint has been successfully used2 as the application ojf a quick drying black acrylic enamel sprayed onto a surface or white paints with ballotini. The bright SPs are known from small-angle laser light scattering from polymer films4 ' 5 , polymer blends6 / 7 , optically heterogeneous gel systems 8 '^, amorphous polymers10 , etc. Generally, the methods in which this phenomenon is utilized can be characterized as tech niques based on measurements of the intensity correlation of scattered light11 , such as holographic interferometry1 2, speckle interferometry1 " 3 * 12 , speckle photography1 " 3 / 12 , laser Doppler velocimetry or photon correlation spectroscopy13 ' 14 . While the former three tech niques predominantly analyze spatial aspects of intensity changes, the latter two deal with the time or frequency dependences of the intensity fluctuations of light scattered from an inhomogeneous medium. In this paper we restrict ourselves to the SPs created by propa gation of the coherent light through an optically heterogeneous polymer system with single beam illumination in an arrangement usually called one-beam speckle interferometry or speckle photography, although in more recent measuring set-ups photography is usually a superfluous step. As stated above, the basis of the speckle techniques is the measure ment of correlation between SPs. In this contribution we present the methods of speckle cor relation measurements together with examples of application that include the determination of 1) the displacement vector and Poisson's ratio of polymer films, 2) optical path fluctu ations of scattered light which has passed through the polymer films with different concen tration of additives, 3) the coherence factor of two polarized SPs caused by light scattering from solid polymers, 4) "smoothing" of SPs during the space-time integration process, 5) slow correlation time measurement, 6) structural aspects of non-Gaussian SPs connected with the small number of scatterers in the illuminated volume. Recently, the digital image processing technique has developed rapidly with the advance of computer science. In this paper we describe an interactive picture analysis system used in an evaluation of SP para meters. Although the present examples of application are limited to polymer systems, the technique of interactive picture analysis is useful for a quantitative evaluation of infor mation from real and Fourier-space images of arbitrary structure15 .

2. STATISTICAL PROPERTIES

Since speckles play an important role in many physical phenomena1 " 3 ' 16 ' 17 it is essential to fully understand their statistical properties. Most often, the amplitude of the electric field A(x,y,z) consists of a large number of contributions from various scattering regions and the resulting field A has the Gaussian probability (the amplitude A of the scattered field is a circular complex Gaussian random variable). The corresponding statistical pro perties of intensity are described by the probability density function p(I) (where p(I) is the probability that a speckle has intensity between the values I and I + dl, and is the average intensity) which has the form of a negative exponential1 / 2 > 18 (Fig.l)

) (1)


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Figure 1. The probability density function of the SP intensity for deep random -phasescreen; a) polarized SP (eq.(1) or eq.(2), M =1) b) unpolarized SP (eq.(2), M =2)

It has been shown19, that under these conditions the spatial autocorrelation function of SPscan be determined on the basis of the van Cittert -Zernike theorem of the classical coherencetheory, and thus the spatial autocorrelation function has no direct structural significance.Nevertheless, this situation is widely utilized in the deformation measurement, where struc-tural information is obtained from the correlation measurements of two or more SPs, insteadof the statistics of a single SP. Many investigators have studied the statistical propertiesof SPs connected with phase screens18,20. The random -phase screen is a scattering layerwhich introduces randomly fluctuating path differences into an incident electromagneticwave. In the deep random -phase screen path differences are introduced that exceed the wave-length of incident radiation. In many experiments, the intensity measured is an integratedversion of the ideal point- intensity (detector aperture is of finite size) and the SP is inmotion. Most often, an approximate form for the first -order PDF of the integrated intensity(sum of M independent SPs) is used - the so called gamma density distribution1,18 - with twoparameters M (the degree of freedom of light) and (the average intensity value) in theform1,18

p(I) = (MM /r(M))(IM-1

>M) exp( -MI/ ) (2)

where M is the number of degrees of freedom of light and is the average intensity. Theparameter M is related to the contrast C by1,18,21 -23

-1/2(3)

where the contrast C can be obtained at the same time from an experimental analysis as

C = <(I - )2> 1/2 / (4)

Asymptotically, when the time of observation T and dimension of the aperture S are suffici-ently large (T » Ts, S » Sc, Tc and Sc denote the coherence time a coherence area at the de-tection plane, respectively) we have22

M = 2TS /TcSc(1 +P2) , (5)

where P is the degree of polarization. Eq.(3), (4) and (5), make possible a simple deter-mination of the correlation time Tc, evaluating the contrast value of SP as is discussedlater.

3. CORRELATION MEASUREMENT

In the following section we briefly summarize the methods used in the speckle correlationmeasurements.3.1. Temporal and spatial correlation

In many cases of practical interest, light can be regarded as cross -spectrally and polar -izationally pure; the time -space correlation function may then be written as a product ofthree terms, each of which in turn reflects the state of polarization, space and time cor-relation. The general relation for cross -spectrally and polarizationally pure radiation isthen23

M = MpMSMt , (61

SPIE Vol. 1121 Interferometry '89 / 401

1.0-

Q5-

Figure 1. The probability density function of the SP intensity for deep random-phase screen; a) polarized SP (eq.(l) or eg. (2), M=l) b) unpolarized SP (eq.(2), M=2)

It has been shown1 ^, that under these conditions the spatial autocorrelation function of SPs can be determined on the basis of the van Cittert-Zernike theorem of the classical coherence theory, and thus the spatial autocorrelation function has no direct structural significance. Nevertheless, this situation is widely utilized in the deformation measurement, where struc tural information is obtained from the correlation measurements of two or more SPs, instead of the statistics of a single SP. Many investigators have studied the statistical properties of SPs connected with phase screens 18 * 20 . The random-phase screen is a scattering layer which introduces randomly fluctuating path differences into an incident electromagnetic wave. In the deep random-phase screen path differences are introduced that exceed the wave length of incident radiation. In many experiments, the intensity measured is an integrated version of the ideal point-intensity (detector aperture is of finite size) and the SP is in motion. Most often, an approximate form for the first-order PDF of the integrated intensity (sum of M independent SPs) is used - the so called gamma density distribution1 > 18 - with two parameters M (the degree of freedom of light) and (the average intensity value) in the form1 / 18

exp(-MI/ (2)

where M is the number of degrees of freedom of light and is the average intensity. The parameter M is related to the contrast C by1 ' 18 / 21 "" 23

C = M-1/2 ,

where the contrast C can be obtained at the same time from an experimental analysis as

C = <(I - ) 2 > 1/2 /<l> .

(3)

(4)

Asymptotically, when the time of observation T and dimension of the aperture S are suffici ently large (T»TS , S » Sc , Tc and Sc denote the coherence time a coherence area at the de tection plane, respectively) we* have22

M = 2TS/TCSC (1+PZ ) (5)

where P is the degree of polarization. Eq.(3), (4) and (5), make possible a simple deter mination of the correlation time Tc , evaluating the contrast value of SP as is discussed later.

3. CORRELATION MEASUREMENT

In the following section we briefly summarize the methods used in the speckle correlation measurements .3.1. Temporal and spatial correlation

In many cases of practical interest, light can be regarded as cross-spectrally and polarizationally pure; the time-space correlation function may then be written as a product of three terms, each of which in turn reflects the state of polarization, space and time cor relation. The general relation for cross-spectrally and polarizationally pure radiation is then23

M = MpMsMt



where Mp = 2/(1 +P2) and Ms and Mt have the form1,24

Ms = { (S /Sc)1/2 erf( V S /Sc)1/2- /irS) [ 1- exp(- ,rS /Sc) ] } -2 (7)

xerf(x) = 2 /(,r)1 /2 J exp( -z2)dz

0

Mt = { 1/y + (1/2y2) [ exp(-2y)- 1] } -1, (8)

where y= T/T . For random -phase screens there exists20 a simple relation between the ge-ometry of exl5eriments and Sc (the correlation area = speckle size). Eq.(3),(4),(6),(7) and(8) make possible the determination of the correlation time Tc.

3.2. Time correlation

The parameters characterizing the time evolution of SP are measured by using the well -known technique of photon correlation spectroscopy13,14. Generally, the method analyzes theintensity fluctuations detected at a single spatial point (thus, the method follows the timeevolution of an individual speckle). The correlation function is calculated13,14 by

Y ( T ) = < I(t)I(t +T) >/ < I(t) >2 (9)

In the present system17 the time correlation can be measured in the same manner by usinga camera as the detector and a computer as the correlator. The smallest detecting area ischaracterized by one pixel. The time resolution is limited by the frequency of the camera(i.e. 1/30 s) and by the stability of the experimental set -up for long correlation times.

3.3. Spatial correlation of two speckle patterns

3.3.1. Diffraction properties. One of the methods of correlating speckle fields makesuse of their diffraction properties1 -3. If SP is doubled by shifting it as a wholesideways, the double- exposed SP will be locally identical, but displaced by an amountand in a direction related to the movement of the object. Similarly, by recording twosuperimposed SPs, one taken before, and one after deformation of the sample, the displace-ment of the illuminated region of the sample can be found1,2. While in some instancesit might be possible to measure the displacement by identifying the corresponding specklesdirectly25, this is more readily done by examining the diffraction pattern of the recordedspeckle intensity distribution (optically1-3,26 or digitally27-29). The FT pattern will bemodulated in brightness to form light and dark straight parallel equispaced fringes,similar to Young's fringes. In this way a point -by -point record of the variation of SPseparation, both in magnitude and direction, can be built up. The quantitative measureof the correlation of. two SPs is the fringe contrast3Q v(visibility of- fringes).

v = 2(I' ®I2 ') /[(I1 'I') + (I'2I') ] (10)

1 max 1 max 2 max

where II and 12 are deviations of SP irradiance from its mean value and symbol denotes thecross -correlation operation.

3.3.2. Subtraction and clipping. Recent investigations have addressed the prospect ofusing clipped laser speckle to make correlation measurements31. The clipped representationis a 1 -bit digitization of the speckle intensity defined as

if Ii>ci

iotherwise

The absolute value of <1 I1 - I2 V> depends on the correlation between subtracted SPs andon the clipping thresholds ci. As the clipping threshold we used the value ci = <Ii> In 2,which was recommended31 for maximizing the dependence of the clipped correlation functionon pp. It can be shown that the explicit relation between the clipped absolute value ofthe difference in intensities and the parameters c and pp has the form32

<II1 - 22 > - exp [ -c/ (1 - 1pAI 2)1/2 ] , (12)4 

where Ippl is the modulus of the normalized cross -correlation function of speckle amplitudes,which is defined as follows

1/2uA(x1,y1 ;x2,y2). _ < A( xl, Y1)Á( x2, Y2)>/[< A( xi, yl),(xi,Y1) ><A(x2,Y2)Á(x2,Y2)>] (13)

402 / SPIE Vol 1121 Interferometry '89

where Mp = 2/(l+P2 ) and Ms and Mt have the form1 / 24

= { (S/Sc ) 1/2 erf( IT S/Sc ) 1/2 -(Sc /irS) [ l-exp(-irS/Sc ) ]}" 2 (7)

erf(x) = 2/(ir) 1/2 / exp(-z 2 )dz0 _

Mt = { I/Y + (1/2 Y 2 ) [ exp(-2Y ) -I]}- 1 , (8)

where Y= T/T . For random-phase screens there exists20 a simple relation between the ge ometry of experiments and Sc (the correlation area = speckle size). Eg. (3) , (4) , (6) , (7) and (8) make possible the determination of the correlation time Tc .

3.2. Time correlation

The parameters characterizing the time evolution of SP are measured by using the well- known technigue of photon correlation speetroscopyl3 / 14. Generally, the method analyzes the intensity fluctuations detected at a single spatial point (thus, the method follows the time evolution of an individual speckle). The correlation function is calculated13 , 14 by

Y ( T) = < I(t)I(t+T)>/< I(t)> 2 (9)

In the present system17 the time correlation can be measured in the same manner by using a camera as the detector and a computer as the correlator. The smallest detecting area is characterized by one pixel. The time resolution is limited by the freguency of the camera (i.e. 1/30 s) and by the stability of the experimental set-up for long correlation times.

3.3. Spatial correlation of two speckle patterns

3.3.1. Diffraction properties. One of the methods of correlating speckle fields makes use of their diffraction properties1 " 3 , if SP is doubled by shifting it as a whole sideways, the double-exposed SP will be locally identical, but displaced by an amount and in a direction related to the movement of the object. Similarly, by recording two superimposed SPs, one taken before, and one after deformation of the sample, the displace ment of the illuminated region of the sample can be found1 ' 2 . While in some instances it might be possible to measure the displacement by identifying the corresponding speckles directly25 , this is more readily done by examining the diffraction pattern of the recorded speckle intensity distribution (optically1* 3 ,^ or digitally27'29 ). The FT pattern will be modulated in brightness to form light and dark straight parallel eguispaced fringes, similar to Young's fringes. In this way a point-by-point record of the variation of SP separation, both in magnitude and direction, can be built up. The guantitative measure of the correlation of two SPs is the fringe contrast3 ^ v (visibility of -fringes).

where 1^ and 1 2 are deviations of SP ir radiance from its mean value and symbol « denotes the cross-correlation operation.

3.3.2. Subtraction and clipping. Recent investigations have addressed the prospect of using clipped laser speckle to make correlation measurements 31 . The clipped representation is a 1-bit digitization of the speckle intensity defined as

T ,^l, if I.> c± (n)

0, otherwise

The absolute value of <| 1^ - 12 | f > depends on the correlation between subtracted SPs and on the clipping thresholds cj_. As the clipping threshold we used the value Ci = <I^ > In 2, which was recommended31 for maximizing the dependence of the clipped correlation function on PA- Ifc can be shown that the explicit relation between the clipped absolute value of the difference in intensities and the parameters c and ^ has the form32

- 1.2 l'> . -c/(l - K| 2 ) 1/2 ] , (12)4

where ju^l is the modulus of the normalized cross-correlation function of speckle amplitudes, which is defined as follows

M» 1/2 , (U )



where the complex field A(x,y) represents the speckle field at the point with spatialcoordinates (x,y) and the angle brackets designate the average value.

3.3.3 Statistical properties.

A statistical analysis based on the measurement of the probability density function of addi-tion of two correlated SPs provides the degree of correlation between the contributions. Wehave derived32 the resulting probability density function of the sum of two correlated SPsand their first two moments for speckle fields with the following statistical properties:

(1) let A1(x11y1) and A2(x2,y2) represent samples of the complex field at point (xl,y1)and (x2,Y2) in a speckle pattern; the Al and A2 are circular complex Gaussian randomvariables

(2) Al and A2 are statistically correlated with the correlation specified by the complexcoherence factor u A

(31 the mean values of the corresponding intensities of the components are equal, i.e.<1 A1 V > = <IAi 12>

By fitting the experimental data to the theoretical probability density function32

p(W) = ( 1/ 2I uAI)[ exp(- W/((1 +IPAI))- exp(- W / (1- I11AI)) ] , (14)

the modulus of the normalized cross -correlation function of speckle amplitude IuAI can beobtained.

4. Device description

The technique of interactive image analysis is useful for a quantitative extraction ofinformation from both real -and Fourier -space images 15-17. In this part we shortly summarizel7the hardware and software package. The hardware system is shown in Fig. 2. The image is

10

9

11

1 2

8

3

7 6 5 4 3

Figure 2. Schematic diagram of the experimental arrangement:(1) Laser (2) neutral- density filters (3) mirrors (4) diaphragm (5) a/2 wave - plate(6) sample (7) analyzer (8) CCD camera (9) microcomputer (10) monitor (11) printer

taken by a CCD camera and fed to the image processor of the computer. The digitized videosignal is sent to the monitor or can be stored in the image storage device. If real -timeinformation is necessary, the image can be recorded in the video -recording system with a timeresolution of 1/30 s. The videorecorder is a 3/4" tape semi- professional recorder (SonyVO- 5850P). The videocamera (Sony XC -37) has a resolution of 384x 491 elements. The micro-computer is a 16 -bit Eltec E3 with 12MHz frequency and 1Mbyte memory capacity. By the imageprocessor an image is converted to digital interlaced form in 40 ms. The memory capacity of512 kbyte of the image storage device allows storage of two pictures of 8 bit resolutionof each pixel (corresponding to 256 grey levels). The final resolution of the whole systemis limited by the time -resolution of the videocamera, i.e. 1/30 for a picture.From the software package17 we mention mainly operations that are important from the pointof view of further application in this paper. The intensity of the stored picture can beunderstood as a 1 -bit digitalization of the intensity. The following quantities can be de-termined: intensity variation along a user definable line or several lines, the averageintensity of the whole picture, the contrast, the probability intensity function, additionand subtraction of two pictures, double- exposure of two pictures in a different memorylocation, 2D FFT of a part of the picture up to 128x128 pixels, addition or subtraction ofa constant grey value for the whole picture, some low and high pass filtering functions,

SPIE Vol. 1121 /nterferometry '89 / 403

where the complex field A(x,y) represents the speckle field at the point with spatial coordinates (x,y) and the angle brackets designate the average value.

3.3.3 Statistical properties.

A statistical analysis based on the measurement of the probability density function of addi tion of two correlated SPs provides the degree of correlation between the contributions. We have derived^2 the resulting probability density function of the sum of two correlated SPs and their first two moments for speckle fields with the following statistical properties:

(1) let Ai(xi,yi) and A2<X2,y2) represent samples of the complex field at point and (X2/Y2) in a speckle pattern? the AI and A2 are circular complex Gaussian random variables

(2) AI and A2 are statistically correlated with the correlation specified by the complex coherence factor y A

(3) the mean values of the corresponding intensities of the components are equal, i.e. 2 > =<

(14)

By fitting the experimental data to the theoretical probability density function32

p(W) = (1/2 |y -exp(-W/ (1-

the modulus of the normalized cross-correlation function of speckle amplitude |yA | can be obtained.

4. Device description

The technique of interactive image analysis is useful for a quantitative extraction of information from both real-and Fourier-space images15 " 17 . In this part we shortly summarize17 the hardware and software package. The hardware system is shown in Fig. 2. The image is

Figure 2. Schematic diagram of the experimental arrangement:(1) Laser (2) neutral-density filters (3) mirrors (4) diaphragm (5) A/2 wave - plate (6) sample (7) analyzer (8) CCD camera (9) microcomputer (10) monitor (11) printer

taken by a CCD camera and fed to the image processor of the computer. The digitized video signal is sent to the monitor or can be stored in the image storage device. If real-time information is necessary, the image can be recorded in the video-recording system with a time resolution of 1/30 s. The videorecorder is a 3/4" tape semi-professional recorder (Sony VO-585OP). The videocamera (Sony XC-37) has a resolution of 384x 491 elements. The micro computer is a 16-bit Eltec E3 with 12MHz frequency and IMbyte memory capacity. By the image processor an image is converted to digital interlaced form in 40 ms. The memory capacity of 512 kbyte of the image storage device allows storage of two pictures of 8 bit resolution of each pixel (corresponding to 256 grey levels). The final resolution of the whole system is limited by the time-resolution of the videocamera, i.e. 1/30 for a picture. From the software package^ we mention mainly operations that are important from the point of view of further application in this paper. The intensity of the stored picture can be understood as a 1-bit digitalization of the intensity. The following quantities can be de termined: intensity variation along a user definable line or several lines, the average intensity of the whole picture, the contrast, the probability intensity function, addition and subtraction of two pictures, double-exposure of two pictures in a different memory location, 2D FFT of a part of the picture up to 128x128 pixels, addition or subtraction of a constant grey value for the whole picture, some low and high pass filtering functions,



contour plot of definable intensity values, zooming of a part of the picture and severalother operations. The following elements were used in the experiment: Spectra Physics 124BHe -Ne laser, Ar laser ILA 120 -1, Spectra Physics a/2 wave -plate, Glan- Thompson analyzer.

5. APPLICATIONS

A number of techniques have been reported1 -3 on the utilization of SPs for measuringstructural parameters.

5.1. Deformation measurement

5.1.1. Subspeckle region. The SP created by small -angle scattered light33 (a semitrans-parent polymer foil is illuminated with a laser beam) is detected in the far -field. Themagnitude of the displacement vector IoxI can be measured by digitally superimposing theintensity profiles before and after deformationZ5 (see Fig. 3). The displacement of intensity

1

4-).,cn

(1)

...,

0 channel 460

Figure 3. Superposition of two intensity profiles; the peak displacementItxI is a measure of the deformation of the sample

peaks is related to the deformation of the sample17,25. It is interesting to note that thespeckle displacement is determined not only by the distance between sample and detectionplane, but also by the curvature radius of the Gaussian illuminating beam and by the ratioof translation to boiling speckles20,25.

5.1.2. Speckle region. The magnitude and the direction of the in -plane movement of theobject point can be obtained by measuring the spacing and direction of the parallel andequispaced fringes1- 3,5,26 (Fig. 4). The displacement d of the object points is related tothe fringe spacing D/m by d = m L /MD, where L is the distance from the sample to the video -camera, M is magnification of the image system and m is the order number of fringe. Thedisplacement is inversely proportional to the fringe spacing, and the direction is perpen-dicular to Young's fringes, that means that the tensor of deformation can be determined by2D -FFT. The detail description of the processing procedure can be found in several papers27 -29.The displacement vector and Poisson's ratio (ratio of displacements perpendicular to exten-sion to those parallel with extension) have been determined for samples of isotactic poly-propylene films in the range of small deformations, and in small consecutive deformationssteps covering the range under investigation5 ,26,

5.3. Measurement of path fluctuations by means of dichromatic SPs

Illumination of an optically heterogeneous sample with light of two near -by wavelengthsgives rise to a SP which has a typical radial -fibrillar appearance34. For different materialsthe regions A,B,C (see Fig.5) are of different size. The SP parameters can be related tothe standard deviation of fluctuations of the optical path oz of light passing througha layer of heterogeneous materia134. The gradual decrease of correlation with increasingox for samples PE 2 -6 is given in Fig.5. The resulting values of oz are summarized in Table 1.

404 / SPIE Vol 1121 /nterlerometry '89

contour plot of definable intensity values, zooming of a part of the picture and several other operations. The following elements were used in the experiment: Spectra Physics 124B He-Ne laser, Ar laser ILA 120-1, Spectra Physics A/2 wave-plate, Glan-Thompson analyzer.

5. APPLICATIONS

A number of techniques have been reportedl"* 3 on the utilization of SPs for measuring structural parameters.

5.1. Deformation measurement

5.1.1. Subspeckle region. The SP created by small-angle scattered light33 (a semitransparent polymer foil is illuminated with a laser beam) is detected in the far-field. The magnitude of the displacement vector |AX| can be measured by digitally superimposing the intensity profiles before and after deformation25 (see Fig. 3). The displacement of intensity

enc0)

channel 460

Figure 3. Superposition of two intensity profiles; the peak displacement |AX| is a measure of the deformation of the sample

peaks is related to the deformation of the sample17 / 25 . It is interesting to note that the speckle displacement is determined not only by the distance between sample and detection plane, but also by the curvature radius of the Gaussian illuminating beam and by the ratio of translation to boiling speckles20 / 25 .

5.1.2. Speckle region. The magnitude and the direction of the in-plane movement of the object point can be obtained by measuring the spacing and direction of the parallel and equispaced fringes1 ' 3 / 5 / 26 (pig. 4). The displacement d of the object points is related to the fringe spacing D/m by d = m L/MD, where L is the distance from the sample to the videocamera, M is magnification of the image system and m is the order number of fringe. The displacement is inversely proportional to the fringe spacing, and the direction is perpen dicular to Young's fringes, that means that the tensor of deformation can be determined by 2D-FFT. The detail description of the processing procedure can be found in several papers27" 29 . The displacement vector and Poisson's ratio (ratio of displacements perpendicular to exten sion to those parallel with extension) have been determined for samples of isotactic poly propylene films in the range of small deformations, and in small consecutive deformations steps covering the range under investigation5 / 26 .

5.3. Measurement of path fluctuations by means of dichromatic SPs

Illumination of an optically heterogeneous sample with light of two near-by wavelengths gives rise to a SP which has a typical radial-fibrillar appearance34 . For different materials the regions A,B,C (see Fig.5) are of different size. The SP parameters can be related to the standard deviation of fluctuations of the optical path oz of light passing through a layer of heterogeneous material34 . The gradual decrease of correlation with increasing AX for samples PE 2-6 is given in Fig.5. The resulting values of az are summarized in Table 1,



Figure 4. Model calculation of speckle displacement in the double- exposure planeunder uniaxial tensile deformation cca 1.5 %, Poisson's ratio u =0.4 being used.

The processing (FT) of one quadrant of SP is shown. The displacement isinversely proportional to the fringe spacing d, and the direction of

displacement is perpendicular to the fringes.

PE 2 PE 3 PE 4 PE5 PE 6

0Figure 5. Dependence of the contrast on as for samples of PE (Table I)

Combination of the following pairs of wavelengths were used:a0 = 496.5 nm, Al = 501.7 nm, a2 = 488.0 nm

SPIE Vol 1121- ldterferometry '89 / 405

elongation

c or*— -«-»

8

4 :*r.- •**• '/TT*' "* */ • "^ '

:r:v^;»^M:. *V "••. t-'ftj** t"' ••'• -*-4 f• -*-' •* •/• *** ;/»••* * "-' •' •."'••»* *-'-^;?»-v'!i rv.V

*.. ;'

Figure 4. Model calculation of speckle displacement in the double-exposure planeunder uniaxial tensile deformation cca 1.5%, Poisson's ratio y=0.4 being used.

The processing (FT) of one quadrant of SP is shown. The displacement isinversely proportional to the fringe spacing d, and the direction of

displacement is perpendicular to the fringes.

A,, A,

PE2 PE 3 PE4 PE5 PE 6

Figure 5. Dependence of the contrast on AX for samples of PE (Table I)Combination of the following pairs of wavelengths were used:

AO = 496.5 nm, A- = 501.7 nm, A2 = 488.0 nm

SPtE Vol. 1121- Inierferometry '89 / 405


Table 1. Some structural parameters of the samples

Type PE2 PE3 PE4 PE5 PE6 PPO PP8 PE50

Volume % ofCaCO3

AbsorbanceA= log10Io /I

Standard dev.of path fluctuationsoz [un]

Thickness [um]

0 3.6 7.8 12.7 18.5

1.77 2.72 3.07 3.22 3.25

4.4 ±1.0 9.4± 1.0 18* 22* 26*

380 380 380 380 380

0 0 0

0.324 0.260 0.227

- - -

40 50 40

*extrapolated values

Experimental results obtained with a series of samples (PE = polyethylene, PP= polypropylene)with and without inorganic additives are in a comparatively good agreement with theoreticalexpectation that for such strong scatterers the standard deviation of optical path fluctu-ations due to the passage of coherent light through a polymer film should be greater thanthe wavelength1,2. The range of measurable deviations path for a combination of the wave-length from an Ar laser lies in the range of 1 -15 I,m.

5.4. Correlation properties of polarized light- scattering SPs

It is very well known that the radiation scattered by a semitransparent medium illuminatedby a plane polarized wave is not plane polarized but consists of both parallel and cross -polarized components that are not necessarily correlated. In order to include the statisti-cal properties of SPs caused by the light scattering from solid polymers into a broader con-text of SPs formed by the propagation of coherent light through a medium with random re-fractive index fluctuations we examine in this paper a) the probability density function(PDF) of polarized and unpolarized SP, b) the PDF of addition of two partially correlatedSPs, c) the subtraction of two SPs and clipping of the difference thus obtained as a measureof their correlation. The correlation between two SPs is usually specified by a value ofthe coherence factor }iA, where Iupl is defined as a modulus of the normalized cross- corre-lation function of speckle amplitudes (see eq. (13)). The form of the probability density

W

as p(W) OS

c

0.5

b

W

W

Figure 6. Fitting of the experimental (crosses) to the theoretical (solid curve)probability density function of speckle pattern intensity of two partiallycorrelated speckle patterns for sample PE6 (Table 1). The orientations ofpolarization plane are (a) parallel, (b) (0,10), (c) (0,20), (d) (0,30)

(e) (0,40), (f) crossed, (0,45)

406 / SPIE Vol 1121 Interferometry '89

Table 1. Some structural parameters of the samples

Type Volume % of

PE2

0

PE3

3.6

PE4

7.8

PE5

12.7

PEG

18.5

PPO

0

PP8

0

PESO

0

AbsorbanceA=log10I0/I Standard dev. of path fluctuations oz [vm]

Thickness [pm ] 380

1.77 2.72 3.07

4.4± 1.0 9.4± 1.0 18*

3.22 3.25

22* 26*

380 380 380 380

0.324

40

0.260

50

0.227

40

*extrapolated values

Experimental results obtained with a series of samples (PE = polyethylene, PP=polypropylene) with and without inorganic additives are in a comparatively good agreement with theoretical expectation that for such strong scatterers the standard deviation of optical path fluctu ations due to the passage of coherent light through a polymer film should be greater than the wavelength1 9 2. The range of measurable deviations path for a combination of the wave length from an Ar laser lies in the range of 1-15 urn.

5.4. Correlation properties of polarized light-scattering SPs

It is very well known that the radiation scattered by a semitransparent medium illuminated by a plane polarized wave is not plane polarized but consists of both parallel and cross- polarized components that are not necessarily correlated. In order to include the statisti cal properties of SPs caused by the light scattering from solid polymers into a broader con text of SPs formed by the propagation of coherent light through a medium with random re fractive index fluctuations we examine in this paper a) the probability density function (PDF) of polarized and unpolarized SP, b) the PDF of addition of two partially correlated SPs, c) the subtraction of two SPs and clipping of the difference thus obtained as a measure of their correlation. The correlation between two SPs is usually specified by a value of the coherence factor y^, where (y/J is defined as a modulus of the normalized cross-corre lation function of speckle amplitudes (see eq. (13)). The form of the probability density

w 6 8

Figure 6. Fitting of the experimental (crosses) to the theoretical (solid curve)probability density function of speckle pattern intensity of two partiallycorrelated speckle patterns for sample PE6 (Table 1). The orientations ofpolarization plane are (a) parallel, (b) (0,10), (c) (0,20), (d) (0,30)

(e) (0,40), (f) crossed, (0,45)



function of addition of two partially correlated SPs (with 0s1jiJ S1) depends on IuAI andthis quantity can be found from an analysis of the probability density function32 or by themethod of subtraction of clipped intensities32 (see eq.(12)). The results of the fittingare given in Fig. 6. In Fig. 7 the results of the measured quantity '111-12r> are plottedversus difference in the orientation of the polarization plane of subtracted SPs.

AHV

& ,e5=,1

v e'm/,gv e/m

0 5 ' e/m/

n /3)/7

/em_i t I I

10 20 30 40

orientation [°]

PE 2e PE 3A pp 8

pp 0PE 50.-® -

A 0

Figure 7. Dependence of <IIi - I21' > /2 on the difference in theorientation of the polarization plane of subtracted SPs for samples from Table 1

It can be concluded that a) the measurements of PDF of SPs for polarized scattered lightconfirm the saturated character of the scattering process i.e. the polymer films under in-vestigation scatter light as strong scatterers with fluctuations of the optical path ex-ceeding the wavelength of light (p(W) function has the form of a negative exponential forpolarized SPs)

b) generally, the SPs of cross -polarized scattered light may be partially correlatedand the degree of correlation as expressed by the coherence factor IPA' can be determined byfitting the experimental PDF to the theoretical one

c) The coherence factor IpAl can be found also more directly by correlation measurementsusing subtraction and clipping of SPs. Both approaches b) c) provide consistent results ingood accord with a theoretical prediction of the form of the density function of two cor-related SPs

d) we assume that the parameter 1u AI will provide a useful characterization of the pre-vailing structural contribution to the process of laser light scattering by optical hetero-geneous media that change the polarization state of incident light during the scatteringprocess

5.5. Space -time integration process

Both an exact and approximate expression for the contrast C of time -varying SPs have beenused. For some structural application it is desirable to minimize the speckle effect and to"smooth" the SP. One of the possible means of doing so is the movement of the sample. Therandom -phase screen theory20 offers a simple relation for the correlation time Tc, namely,

Tc = WI 1v1 , (15)

where W is the radius of the laser beam at the object plane of the focussed beam and; isthe speed of motion at the plane of illumination. Then, using eqs.(3)-(5), the appropriatecontrast can be determined3 (see Fig. 8).

Relations (3),(4) and (6) -(8) were used in model experiments in which slow temporalchanges of SPs caused by the rotation of the polymer film were studied23. The phenomenonof laser speckle makes ossible, at least basically, the determination of slow correlationtimes in the 10-1 to 102 s time scale, by suitably choosing and varying T /Tc and S /Sc (cf.Fig. 9).

SPIE Vol. 1121 Intederometry '89 / 407

function of addition of two partially correlated SPs (with 0 £ |u^l - D depends on |v&l and this quantity can be found from an analysis of the probability density function32 Or by the method of subtraction of clipped intensities32 (see eg.(12)). The results of the fitting are given in Fig. 6. In Fig. 7 the results of the measured quantity <|li-l2 l f> are plotted versus difference in the orientation of the polarization plane of subtracted SPs.

Figure 7. Dependence of <| Ii - 12| f >/2 on the difference in the orientation of the polarization plane of subtracted SPs for samples from Table 1

It can be concluded that a) the measurements of PDF of SPs for polarized scattered light confirm the saturated character of the scattering process i.e. the polymer films under in vestigation scatter light as strong scatterers with fluctuations of the optical path ex ceeding the wavelength of light (p(W) function has the $orm of a negative exponential for polarized SPs)

b) generally, the SPs of cross-polarized scattered light may be partially correlated and the degree of correlation as expressed by the coherence factor |PA| can be determined by fitting the experimental PDF to the theoretical one

c) The coherence factor |y^l can be found also more directly by correlation measurements using subtraction and clipping of SPs. Both approaches b) c) provide consistent results in good accord with a theoretical prediction of the form of the density function of two cor related SPs

d) we assume that the parameter (y^l wil1 provide a useful characterization of the pre vailing structural contribution to the process of laser light scattering by optical hetero geneous media that change the polarization state of incident light during the scattering process

5.5. Space-time integration process

Both an exact and approximate expression for the contrast C of time-varying SPs have been used. For some structural application it is desirable to minimize the speckle effect and to "smooth" the SP. One of the possible means of doing so is the movement of the sample. The random-phase screen theory20 offers a simple relation for the correlation time Tc , namely,

Tc = W/ (15)

where W is the radius of the laser beam at the object plane of the focussed beam and v is the speed of motion at the plane of illumination. Then, using eqs.(3)-(5), the appropriate contrast can be determined35 (see Fig. 8).

Relations (3),(4) and (6)-(8) were used in model experiments in which slow temporal changes of SPs caused by the rotation of the polymer film were studied23 . The phenomenon of laser speckle makes possible, at least basically, the determination of slow correlation times in the 10~1 to 10^ s time scale, by suitably choosing and varying T/TC and S/SC (cf. Fig. 9).



x+.4, -,i

i If

Figure 8. "Smoothing" of the speckle contrast by increasing the number of the temporaldegrees of freedom M (cf. eq.(5))

a) small angle light scattering SP of the polymer film (Hv type, sample between crossedpolarizers), static sample, geometry of "boiling" speckles, time of exposure T= ls,C =1

b) Tc = 0.34 s, T = 1/5 s, C = 1.00 c) Tc = 0.34 s, T = 1 s, C = 0.57d) Tc = 0.34 s, T = 3 s, C = 0.33

015

C

010

005

50 60 70 80ln M

90

Figure 9. The comparison23 of an experimental and theoreticaldependence of the contrast of SP on the number of the degrees of freedom M.The solid curve is the theoretical dependence based on eqs.(3) and (6) - (8)

5.6. Structural significance of non -Gaussian SPs

By limiting the number of a randomly phased contribution, if only a few independent scat-tering areas are present, the speckle statistics do contain information about the scatteringmedium. In that case the scattered field of a single SP does not obey the Gaussian distri-bution. The moments of intensity can be explicitly found and compared with the experiment36,37.

6. CONCLUSIONS

The paper briefly reviews theoretical concepts and experimental methods for performingspeckle -based measurements in polymer systems. Although the present examples of applicationare limited to light scattering speckle patterns of polymer systems, it is hoped thatstimuli may be provided for the generation of new techniques and applications in the fieldof material research.


Figure 8. "Smoothing" of the speckle contrast by increasing the number of the temporaldegrees of freedom M (cf. eq.(5))

a) small angle light scattering SP of the polymer film (Hv type, sample between crossed polarizers), static sample, geometry of "boiling" speckles, time of exposure T=ls,C=l

b) Tc = 0.34 s, T = 1/5 s, C = 1.00 c) Tc = 0.34 s, T = 1 s, C = 0.57d) Tc = 0.34 s, T = 3 s, C = 0.33

015

010

005

50 60

23

70 80tnM

90

Figure 9. The comparison^ J of an experimental and theoretical dependence of the contrast of SP on the number of the degrees of freedom M. The solid curve is the theoretical dependence based on eqs.{3) and (6) - (8)

5.6. Structural significance of non-Gaussian SPs

By limiting the number of a randomly phased contribution, if only a few independent scat tering areas are present, the speckle statistics do contain information about the scattering medium. In that case the scattered field of a single SP does not obey the Gaussian distri bution. The moments of intensity can be explicitly found and compared with the experiment 36 / 37 .

6. CONCLUSIONS

The paper briefly reviews theoretical concepts and experimental methods for performing speckle-based measurements in polymer systems. Although the present examples of application are limited to light scattering speckle patterns of polymer systems, it is hoped that stimuli may be provided for the generation of new techniques and applications in the field of material research.

408 / SPIE VoL 1121 tnterferometry '89


7. ACKNOWLEDGMENTS

The financial support of the Max -Planck Society is gratefully acknowledged. Part of thiswork was performed during the stay of both authors at the Max -Planck Institute for PolymerResearch, Mainz, FRG.

8. REFERENCES

1. J.C. Dainty, ed., Laser Speckle and Related Phenomena, Springer Verlag, Berlin -Heidelberg (1975).

2. R.K. Erf, ed., Speckle Metrology, Academic Press, New York (.978).3. M. Francon, Laser Speckle and Application in Optics, Academic Press, New York (1979).4. C. Picot, R.S. Stein, R.H. Marchessault, J. Botch and A. Sarko, "Interparticle

interference in light scattering from spherulite systems ", Macromolecules 4, (4) 467 -470(1971).

5. J. Holoubek and B. Sedlácek, "Displacement measurement using double- exposure specklephotography of small -angle scattered light ", J.Polym.Sci., Polym.Phys.Ed. 18(2), 265 -275(1980).

6. T. Hashimoto, J. Kumaki and H. Kawai, "Time- resolved light scattering studies onkinetics of phase separation and phase dissolution of polymer blends. 1. Kinetics of phaseseparation of a binary mixture of polystyrene and poly(vinyl methyl ether) ", Macromolecules16)4), 641 -648 (1983).

7. H.K. Snyder and P. Meakin, "Details of phase separation processes in polymer blends ",J.Polym.Sci., Polym.Symp. 73, 217 -239 (1985).

8. T. Igarashi and S. Kondo, "Rayleigh and Brillouin scattering from linear polymerduring gelation ", in Physical Optics of Dynamic Phenomena and Processes in MacromolecularSystems, B. Sedlácek, ed., W.de Gruyter, Berlin, New York, 165 -175 (1985).

9. D.B. Sellen, "The diffusion of compact macromolecules within hydrogels" Brit.Polym.J.18(1), 28 -31 (1986).

10. P.J. Carroll, G.D. Patterson and S.A. Cullerton, "Light- scattering photography ofpolymers near the glass transition ", J.Polym.Sci., Polym.Phys.Ed. 21(10), 1889 -1896 (1983).

11. H.M. Pedersen, "Intensity correlation metrology: a comparative study ", Opt.Acta29(1), 105 -118 (1982).

12. R.Jones and C. Wykes, Holographic and Speckle Interferometry, University Press,Cambridge 1983.

13. B.J. Berne and R. Pecora, Dynamic Light Scattering with Applications to Chemistry,Biology and Physics, J.Wiley, New York 1976.

14. H.Z. Cummings and E.R. Pike, eds., Photon Correlation Spectroscopy and Velocimetry,Plenum Press, 1977.

15. H. Tanaka, T. Hyashi and T. Nishi, "Application of digital image analysis to patternformation in polymer systems ", J.Appl.Phys. 59(11), 3627 -3643 (1986).

16. J. Holoubek and H. Krug, "Laser speckle techniques: application in polymer physics ",Makromol.Chem., Macromol.Symp. 18, 123 -133 (1988)

17. H. Krug, J. Holoubek and E.W. Fischer, "Application of interactive image analysisto light scattering patterns of some polymer systems ", Colloid Polym.Sci. 265(9), 779 -785(1987).

18. B. Crosignani, P.Di Porto and M. Bertolotti, Statistical Properties of ScatteredLight, Academic Press, New York (1975).

19. J. Holoubek and J. Baldrian, "Speckle patterns in small angle light scattering: thespatial autocorrelation function ", Collect.Czech.Chem.Commun. 50(11), 2873 -2883 (1985).

20. T. Asakura and N. Takai, "Dynamic laser speckles and their application to velocitymeasurements of the diffuse object ", Appl.Phys. 25(2), 179 -194 (1981).

21. J. Pefina, Quantum Statistics of Linear and Nonlinear Optical Phenomena, D. ReidelPubl.Co., Dordrecht 1984.

22. A. Zardecki, "Statistical features of phase screens from scattering data in InverseSource Problem in Optic, H.P. Baltes, ed., pp.155 -189, Springer Verlag, Berlin (1978).

23. J. Holoubek, "Light scattering speckle photography: Determination of slow correlationtimes ", Opt.Acta 31(11), 1283 -1291 (1984).

24. J. Pefina, "Photocount statistics of radiation propagating through random and non-linear media" in Progress in Optics, E.Wolf, ed., Amsterdam, North Holland, Vol.18, 129 -220(1980).

25. J. Holoubek and H. Krug, "Note on the relation between sample and speckle displace-ment: a random -phase screen approach ", Opt.Commun. 58(4), 241 -244 (1986).

26. J. Holoubek and J. R$Cek, "A strain analysis technique by scattered -light specklephotography ", Opt.Acta 26(1), 43 -54 (1979).

27. R. Erbeck, "Fast image processing with a microcomputer applied to speckle photo-graphy", Appl.Opt. 24(22), 3838 -3841 (1985).

28. S.A. Isacson and G.H. Kaufmann, "Two- dimensional digital processing of specklephotography fringes. 2: Diffraction halo influence for the noisy case ", Appl.Opt. 24(10),1444 -1447 (1985).

29. F. Ansari and G. Ciurpita, "Automated fringe measurement in speckle photography ",Appl.Opt. 26(9), 1688 -1692 (1987).

SPIE Vol. 1121 /nteKerometry '89 / 409

7. ACKNOWLEDGMENTS

The financial support of the Max-Planck Society is gratefully acknowledged. Part of this work was performed during the stay of both authors at the Max-Planck Institute for Polymer Research, Mainz, FRG.

8. REFERENCES

1. J.C. Dainty, ed., Laser Speckle and Related Phenomena, Springer Verlag, Berlin- Heidelberg (1975).

2. R.K. Erf, ed., Speckle Metrology, Academic Press, New York 0.978).3. M. Francon, Laser Speckle and Application in Optics, Academic Press, New York (1979).4. C. Picot, R.S. Stein, R.H. Marchessault, J. Botch and A. Sarko, "Interparticle

interference in light scattering from spherulite systems", Macromolecules 4, (4) 467-470 (1971).

5. J. Holoubek and B. Sedlacek, "Displacement measurement using double-exposure speckle photography of small-angle scattered light", J.Polym.Sci., Polym.Phys.Ed. 18(2), 265-275 (1980).

6. T. Hashimoto, J. Kumaki and H. Kawai, "Time-resolved light scattering studies on kinetics of phase separation and phase dissolution of polymer blends. 1. Kinetics of phase separation of a binary mixture of polystyrene and poly(vinyl methyl ether)", Macromolecules 16)4), 641-648 (1983).

7. H.K. Snyder and P. Meakin, "Details of phase separation processes in polymer blends", J.Polym.Sci., Polym.Symp. 73, 217-239 (1985).

8. T. Igarashi and S. Kondo, "Rayleigh and Brillouin scattering from linear polymer during gelation", in Physical Optics of Dynamic Phenomena and Processes in Macromolecular Systems, B. Sedlacek, ed., W.de Gruyter, Berlin, New York, 165-175 (1985).

9. D.B. Sellen, "The diffusion of compact macromolecules within hydrogels" Brit.Polym.J. 18(1), 28-31 (1986).

10. P.J. Carroll, G.D. Patterson and S.A. Cullerton, "Light-scattering photography of polymers near the glass transition", J.Polym.Sci., Polym.Phys.Ed. 21(10), 1889-1896 (1983).

11. H.M. Pedersen, "Intensity correlation metrology: a comparative study", Opt.Acta 29(1), 105-118 (1982).

12. R.Jones and C. Wykes, Holographic and Speckle Interferometry. University Press, Cambridge 1983.

13. B.J. Berne and R. Pecora, Dynamic Light Scattering with Applications to Chemistry, Biology and Physics, J.Wiley, New York 1976.

14. H.Z. Cummings and E.R. Pike, eds., Photon Correlation Spectroscopy and Velocimetry, Plenum Press, 1977.

15. H. Tanaka, T. Hyashi and T. Nishi, "Application of digital image analysis to pattern formation in polymer systems", J.Appl.Phys. 59(11), 3627-3643 (1986).

16. J. Holoubek and H. Krug, "Laser speckle techniques: application in polymer physics", Makromol.Chem., Macromol.Symp. 18, 123-133 (1988)

17. H. Krug, J. Holoubek and E.W. Fischer, "Application of interactive image analysis to light scattering patterns of some polymer systems", Colloid Polym.Sci. 265(9), 779-785 (1987).

18. B. Crosignani, P.Di Porto and M. Bertolotti, Statistical Properties of Scattered Light, Academic Press, New York (1975).

19. J. Holoubek and J. Baldrian, "Speckle patterns in small angle light scattering: the spatial autocorrelation function", Collect.Czech.Chem.Commun. 50(11), 2873-2883 (1985).

20. T. Asakura and N. Takai, "Dynamic laser speckles and their application to velocity measurements of the diffuse object", Appl.Phys. 25(2), 179rl94 (1981).

21. J. Pefina, Quantum Statistics of Linear and Nonlinear Optical Phenomena, D. Reidel Publ.Co., Dordrecht 1984.

22. A. Zardecki, "Statistical features of phase screens from scattering data in Inverse Source Problem in Optic, H.P. Baltes, ed., pp.155-189, Springer Verlag, Berlin (1978).

23. J. Holoubek, "Light scattering speckle photography: Determination of slow correlation times", Opt.Acta 31(11), 1283-1291 (1984).

24. J. Pefina, "Photocount statistics of radiation propagating through random and non linear media" in Progress in Optics, E.Wolf, ed., Amsterdam, North Holland, Vol.18, 129-220 (1980).

25. J. Holoubek and H. Krug, "Note on the relation between sample and speckle displace ment: a random-phase screen approach", Opt.Commun. 58(4), 241-244 (1986).

26. J. Holoubek and J. Ruzek, "A strain analysis technique by scattered-light speckle photography", Opt.Acta 26(1), 43-54 (1979).

27. R. Erbeck, "Fast image processing with a microcomputer applied to speckle photo graphy", Appl.Opt. 24(22), 3838-3841 (1985).

28. S.A. Isacson and G.H. Kaufmann, "Two-dimensional digital processing of speckle photography fringes. 2: Diffraction halo influence for the noisy case", Appl.Opt. 24(10), 1444-1447 (1985).

29. F. Ansari and G. Ciurpita, "Automated fringe measurement in speckle photography", Appl.Opt. 26(9), 1688-1692 (1987).



30. J.A. Mendez and M.L. Roblin, "Contrast of correlation fringes in presence ofa longitudinal displacement between the two exposures ", Nouv.Rev.Opt. 7(1), 105 -112 (1976).

31. J. Marron and G. Morris, "Correlation properties of clipped laser speckle ", J.Opt.Soc.Amer. A2(9), 1403 -1410 (1985).

32. J. Holoubek, H. Krug, J. Kfepelka, J. Pefina and Z. Hradil, "Light scatteringspeckle patterns and their correlation properties ", J.Modern Opt. 34(5), 633 -642 (1987)

33. R.S. Stein, "Optical studies of the morphology of polymer films ", in Structure andProperties of Polymer Films, R.W. Lenz and R.S. Stein, eds., Plenum Press, New York,pp.1 -24 (1973).

34. J. Holoubek, F. Lednickír, B. Sedlácek and J. Mikes, "Light scattering by opticallyheterogeneous materials: Structural aspects of dichromatic laser speckle patterns ",J.Polym.Sci., Part B, 24(8), 1823 -1837 (1986).

35. J. Holoubek and B. Sedlácek, "Speckle patterns in small angle light scattering:A random -phase screen approach ", Makromol.Chem. 185 (9), 2021 -2031 (1984).

36. E. Jakeman, J.G. McWhirter and P.N. Pusey, "Enhanced fluctuations in radiationscattered by a moving random -phase screen ", J.Opt.Soc.Am. 66(11), 1175 -1182 (1976).

37. E. Jakeman, "Speckle statistics with a small number of scatterers ", in Applicationsof Speckle Phenomena, Proc. SPIE 243, 9 -19 (1980).

Dr.Joanna Wójciak (left) and Dr.Maciej Lelniewaki (centre) relaxingwhile Dr.Joseph Lancelot (right) and Dr.Andrzej Spik discussing vi-vidly at the interferometric exhibition.

410 / SPIE Vol. 1121 Interfe. ometry '89

30. J.A. Mendez and M.L. Roblin, "Contrast of correlation fringes in presence of a longitudinal displacement between the two exposures", Nouv.Rev.Opt. 7(1), 105-112 (1976).

31. J. Marron and G. Morris, "Correlation properties of clipped laser speckle", J.Opt. Soc.Amer. A2(9), 1403-1410 (1985).

32. J. Holoubek, H. Krug, J. Kfepelka, J. Pefina and Z. Hradil, "Light scattering speckle patterns and their correlation properties", J.Modern Opt. 34(5), 633-642 (1987)

33. R.S. Stein, "Optical studies of the morphology of polymer films", in Structure and Properties of Polymer Films, R.W. Lenz and R.S. Stein, eds., Plenum Press, New York, pp.1-24 (1973).

34. J. Holoubek, F. Lednicky, B. Sedlacek and J. Mikes, "Light scattering by optically heterogeneous materials: Structural aspects of dichromatic laser speckle patterns", J.Polym.Sci., Part B, 24(8), 1823-1837 (1986).

35. J. Holoubek and B. Sedlacek, "Speckle patterns in small angle light scattering: A random-phase screen approach", Makromol.chem. 185 (9), 2021-2031 (1984).

36. E. Jakeman, J.G. McWhirter and P.N. Pusey, "Enhanced fluctuations in radiation scattered by a moving random-phase screen", J.Opt.Soc.Am. 66(11), 1175-1182 (1976).

37. E. Jakeman, "Speckle statistics with a small number of scatterers", in Applications of Speckle Phenomena, Proc. SPIE 243, 9-19 (1980).

Dr.Joanna W6jciak (left) and Dr.Madej LeSniewski (centre) relaxing while Dr.Joseph Lancelot (right) and Dr.Andrzej Spik discussing vi vidly at the interferometric exhibition*

470 /SHE Vol. 1121 Interfetometry '89

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SPIE Proceedings [SPIE Interferometry '89 - Warsaw, Poland (Monday 8 May 1989)] Interferometry '89 - Application Of Single Beam Speckle Interferometry In Macromolecular Physics