small - angle light scattering ( sals ) 
 techniques offer a number of advantages for the investigation of the nature and 
 behavior of polymer materials .
nonintrusive characterization of the 
 flow field of transparent film 
 is an essential step toward an implementation of a structural control system 
 that can regulate the structure development during processing .
a combination of in situ 
 birefringence and depolarized light - scattering experiments was used to study 
 the formation of an ordered cylindrical microstructure in a 
 polystyrene - block - polyisoprene copolymer melt under a shear flow field .
a new multivariable measurement 
 approach   for 
 characterizing and correlating the nanoscale and microscale morphology of 
 crystal - amorphous polymer blends with melt - phase behavior is described .
a 
 vertical small - angle light scattering 
 instrument optimized for examining the scattering and light transmitted 
 from structures ranging from 0.5 to 50 m , thereby spanning the size range 
 characteristic of the initial - to - late stages of thermal - phase transitions 
 ( e.g. , melt - phase separation and crystallization ) in crystal - amorphous polymer 
 blends , was constructed .
the present paper explores an 
 effective means of characterizing structural changes of 
 poly(vinyl chloride ) ( pvc ) particles during gelation and fusion of pvc 
 plastisols with small - angle light scattering .
the sals method was shown to 
 provide an in situ observation of swelling of pvc particles as well as 
 quantitative information of average size of swollen particles while they are in 
 progress of gelation and fusion .
in addition , the sals method enabled one to 
 evaluate the relative solvent power of plasticizers from the manner of increase 
 in the correlation distances .
recently , there has been increasing interest in understanding 
 the complex processes that take place during the processing of polymer blends [ 46 ] . for this purpose ,
the small - angle 
 light scattering technique is a very efficient method [ 79 ] .
one of the important 
 characteristics of light scattering is that it is a nondestructive test .
this makes 
 it possible to 
 follow the time evolution of the phase separation process .
the scattering pattern 
 is a direct reflection of 
 orientation , shape , and size of the structure .
another advantage is that with 
 an appropriate choice of instruments , one can follow extremely fast events having 
 a low optical contrast [ 10 , 11 ] . for optimum mechanical and optical 
 properties ,   fine - structured 
 morphologies on a submicron scale
are generally desired , as   fine dispersions or 
 cocontinuous morphologies with a low volume fraction of one component .
the light 
 scattering method is valid for giving information about overall structures but 
 is difficult to use for extracting local information on morphology .
recently , a 
 digital image processing technique has shown its utility in analyzing the 
 pattern formation in polymer systems .
various light scattering and optical techniques have been investigated as potential candidates for characterization of 
 multiphase polymeric materials .
sals is one of the tools that can be used to 
 study a phase separation .
it is shown that sals can be used to discriminate 
 between nucleation and growth ( ng ) and spinodal decomposition ( sd ) even when 
 both give a pattern composed of a ring . the gelation mode as a function of 
 time
was analyzed 
 for polymers and polymer - carbon fiber composites by using polarized microscopy 
 and polarized light scattering in terms of the formation of polymer spherulites .
endoh et al .   aimed at elucidating the influence of shear - induced 
 structures ( shear - enhanced concentration fluctuations and/or shear - induced 
 phase separation ) , as observed by rheo - optical methods with small - angle light 
 scattering   under shear flow ( shear - sals ) and shear - microscopy , on viscoelastic 
 properties in semidilute polystyrene ( ps ) solutions of 6.0 wt% concentration 
 using dioctyl phthalate ( dop ) as a  solvent and tricresyl phosphate ( tcp ) as a 
 good solvent .
small - angle 
 light scattering was used to determine the binary interaction parameter in a 
 molten blend of linear polyethylene ( lpe ) ( mw   =   52 kg / mol , pdi   =   2.9 ) and linear 
 low - density polyethylenes ( lldpes ) based on homogeneous ethylene-1-butene 
 copolymers ( lldpe-1 , 18.7 mol% butane branches , mw   =   58.1 kg / mol , and lldpe-2 , 5.9 mol% butene branches , mw   =   70 kg / mol ) .
our results 
 are significant because they show that the low optical contrast between 
 coexisting phases in polyolefin blends does not limit the determination of 
 phase boundaries by sals as was previously assumed .
the quantitative analysis software system can be integrated 
 into the picture archiving and communication system .
the combination of advances in charge - coupled - device 
 ( ccd ) fabrication , camera design , digital interface technology , and software 
 development has enabled scientific imaging device manufacturers to overcome the 
 challenges created by the wide range of requirements . the software kits , which include 
 pci device driver and image processing package , are developed based on windows 
 os . in our study , the transparent film 
 is viewed through crossed polarizers to reveal the light scattering pattern .
a 
 high - speed ccd camera is used to record the sals signal in real time with different process conditions for 
 subsequent analysis .
an optical image real - time analysis software has 
 been developed for accurate modeling and simulation of the structural 
 information of the transparent film .
visualization is performed via a 
 high - performance analysis software which allows on - line data acquisition and 
 processing the sals signal .
the experiments yield information regarding the 
 trend of the maximum light intensity of the transparent film that can be compared under different processing 
 conditions .
wavelets have been used successfully in numerous applications ranging 
 from analysis of flotation froth to countertops [ 23 , 24 ] .
lambert et al .   aims at 
 developing a more accurate measurement of the physical parameters of fractal 
 dimension , and the size distribution of large fractal aggregates by small - angle 
 light scattering .
the theory of multiple scattering has been of particular 
 interest in the case of fractal .
outline how the wavelet transform , a hierarchical 
 averaging scheme , can be used to perform both spatial and topological 
 coarse - graining n systems with multiscale physical behavior , 
 such as ising lattices and polymer models .  
a brief description is   given of 
 a methodology that exploits guided ultrasonic waves , lasers and   fiber optics , and 
 simultaneous time - frequency analysis to interrogate the state of a material , 
 component , or structure .
the propagating ultrasound interrogates the host 
 material in a manner providing a wealth of information when coupled with 
 application of the gabor wavelet transform to broadband dispersive waveforms .
recent 
 results are presented pertaining to delamination detection within layered 
 copper / polymer films .
wavelet analysis ( wa ) is typically 
 suited in applications where data contains both large and small scales of 
 variation , such as small - angle light signal .
we presented 
 a new technique 
 that can be 
 used to analyze the 
 structural information of transparent film 
 on - line and nonintrusively while 
 the material is 
 processing .
the technique is 
 based on sals , 
 optical signal real - time analysis software , 
 and wavelet transform 
 method .
it is shown that the 
 proposed technique is easy to implement and provides more flexibility , approximating the relation between the intensity signal and the corresponding 
 variation time . applying this 
 method to analyze 
 structural information of transparent 
 film
will be of 
 great interest , since it will 
 contribute information on optical prosperities that have been proven 
 to be useful 
 for obtaining deep insights into the molecular and structural 
 parameters of transparent 
 film .
in our experiments , the sals signal denoised by wavelet analysis is 
 better than the signal denoised 
 by inducing kf   factor .
the variation trend of the sals signal becomes clear , and 
 the exceptional sals signal can be accurately detected by wavelet 
 decomposition . in this paper ,
the method will be evaluated on the basis of light scattering measurements for 
 a small range of scattering angles .
these measurements have been taken with a 
 fast ccd line scan camera and appropriate optics .
an attempt is made to derive 
 information from these measurements only . with the continuous wavelet transform , sals image 
 analysis methods are used to process the sals signal . 

the purpose of the 
 present work is to apply the optical image technique to characterize the structural 
 informal of transparent 
 film .
in particular , we attempt 
 to on - line the analysis of 
 the light intensity signal .
when   a light beam passes through a diffusion surface , the 
 variation of propagation direction of the beam can not be determined by the 
 principle of geometrical optics because of scattering function of light beams 
 on diffusion surface . a transparent fluid is an optical phase object . in the 
 experimental set - up for measuring flow fields in fluid flows by using speckle 
 interferometry ,
the part of the arrangement for the object light beam is just 
 like a subjective photographic system .
the speckle displacements can change the intensity 
 distribution of spatial speckle fields . as a result
, the intensity distribution 
 of a speckle interferogram is also changed . in this paper ,
this is advantageous to improve the quality of the speckle 
 interferogram . in our experiments
, device performs real - time image 
 analysis of the evolving light scattering signal .
the experimental device 
 incorporates an he - ne laser generator , optics , a ccd camera , and a personal 
 computer as its major hardware components .
software designed specifically for 
 this application performs real - time analysis of the light scattering pattern . 

figure 1 shows an experimental set - up for small - angle light - scattering 
 measurement device .
a polarizer and an analyzer are 
 placed before and after the polymer melts .  
the laser light first passes the 
 polarizer , which removes one orthogonal component of the light .
the other component of light 
 passes through the polymer melts with resulting scattering due to the 
 orientation of molecular chain .
the analyzer removes the second component since 
 it is placed 90 out of phase with respect to the analyzer . 

therefore , any light that comes out of the analyzer is entirely due to the 
 scattering within the polymer melts .
the depolarized intensity of light that 
 passes through the polarizer , polymer melts , and analyzer is recorded and related to 
 the orientation of polymer melts .
a ccd camera captures the image , and the total intensity 
 of the image is determined in every 5 seconds .
we assume that each column of the following matrix represents 
 the intensities of one observed raman spectrum at the selected wave shifts :   ( 1)d=[d1,1d1,2d1,nd2,1d2,2d2,ndm,1dm,2dm , n ] ,  drmxm .
therefore ,   each spectrum is 
 represented by ( m ) number of spectral intensities , and a total of ( n ) 
 spectrum exists . 

the dispersion matrix z   that represents the variation in the 
 data is computed as ( 2)z = dtd ,  zrmxm .  
the diagram of multiple scattering is shown in figure 2 . according to the effect of the 
 sample on the incident light
, the sample can be divided into a surface layer , a 
 first scattering layer , a second scattering layer , and so forth .
the incident 
 light first impinges on the surface of the sample of the first scattering layer ( random reflection ) 
 of the medium .
the second one comes from the first scattering layer ( because of 
 the internal heterogeneity ) and the third in turn .
,  is the angle of incident light , and d is the thickness of the sample . because of multiple light scattering 
 caused by the thickness of the sample , the light scattering images will be dispersion and distortion 
 models
the measurable intensity of scattered 
 light is and the factual intensity of scattered light is have the relationship   ( 3)is = kfis,where kf   is the correcting factor that can be written 
 as   ( 4)kf = e(d / cos  )d(cos11  ) { e[d(cos11)1]}1,where  is the scattering angle , and  is the turbidity of the sample . in a specific point
supposed  ( the turbidity of the sample ) is the same , so 
 correcting factor kf is only with relation to d ( the thickness of the transparent film ) .
spectral analysis and time series 
 methods are the most commonly used signal processing techniques .
however , these 
 methods were reported to provide a good solution only in the frequency domain 
 and poor solution in the time domain .
like the fourier transform ( ft ) , the wavelet transform 
 ( wt ) can be used to measure the frequency content of a signal .
however , the wt differs from 
 the ft in that it yields frequency 
 information in a time - localized fashion [ 35 , 36 ] .
this makes the wt far more effective 
 than ft in identifying time - based phenomena .
given a 
 time varying signal f ( t ) , wts 
 consist of computed coefficients of 
 inner products of the signal and a family of wavelets .
in a continuous wavelet 
 transform ( cwt ) , the wavelet corresponding to scale ( a ) and time 
 location ( b ) is ( 5)a , b=1|a|(tba ) ,  a , br ,  a0 ,    where ( a ) 
 and ( b ) are the dilation and translation parameters , respectively .
the 
 cwt is defined as follows : ( 6)cwt{x(t);a , b}=x(t)a , b*(t)dt ,    where  denotes the complex conjugation . in this 
 paper ,
morlet 
 wavelet function   was used , which can be represented as ( 7)(t)=et2/2ejw0 t .
its cwt is ( 8)a , b=1ae1/2((tb)/a)2ejw0((tb)/a ) . in ( 8) , ( a ) and ( w0 ) can be changed , each way yields 
 a different type 
 of wt .
the sample frequency of the wavelet function and the signal is ( fw ) and ( fs ) , respectively ; the relationship 
 of the parameter a and w0 is ( 9)a = w0fs2fwf0 ,    where ( f0 ) is the frequency focused signal 
 energy . when a = 2 ,    b = k2 ,    j , k  z ,   the wt becomes ( 10)j , k=2j/2(2jtk ) .
the discrete wavelet transform ( dwt ) is defined as ( 11)cj , k=f(t)j , k*(t ) ,    where ( cj , k ) is a time frequency map of the original 
 signal f ( t ) .
a multiresolution analysis approach is used in this work , in which ( 12)j , k=2j/2(t2jk2j),dj , k=f(t)j , k*(t ) ,    where ( j , k ) is a discrete scaling function , and ( dj , k ) is a scaling coefficient . 
 when j = 0 ,    j , k is the   sampled version of the original signal . 

the dwt computes wavelet coefficients cj , k for j = 1 ,  , j , and 
 scaling coefficients dj , k
are given by ( 13)cj , k=n  x[n]hj[n2jk],dj , k=n  x[n]gj[n2jk ] ,    where x[n ] are discrete time signals , hj[n  2k ] are the discrete wavelets , the discrete equivalents 
 to 2(2(t  2k ) ) ,    gj[n  2k ] are called scaling sequence .
at each resolution j > 0 , the 
 scaling coefficients and 
 the wavelet coefficients are ( 14)cj+1,k=n  g[n2k]dj , k , dj+1,k=n  h[n2k]dj , k . from a mathematical point of view , the structure of computations in a 
 dwt is exactly an octave - band   filter band . 

the terms ( g ) and ( h ) are high - pass and low - pass filters derived 
 from the analysis wavelet (t ) and the scaling function (t ) . hence , cj ,
k represents the high - frequency components of 
 the signal f ( t ) .
the results reported in this 
 study were obtained with polystyrene ( ps ) and high - density polyethylene ( hdpe ) . 

as they are commercial polymers that melt at high temperatures , they enabled 
 the study to be performed under quasi - industrial conditions .
optical system 
 and the polarization analyzer are detected by a ccd connected to a computer .  
we used two kinds of material ( ps and hdpe ) , 
 three kinds of rotate speed ( 20 rpm , 24 rpm , and 32 rpm ) , five kinds of vibration 
 amplitude ( 0.04 mm , 0.08 mm , 0.12 mm , 0.16 mm , and 0.20 mm ) , and five kinds of 
 vibration frequency ( 5 hz , 8 hz 10 hz , 12 hz , and 15 hz ) . in the experiments ,
second , we changed the amplitude and frequency of the 
 screw , respectively . at the same time , a ccd camera captured the light scattering image of each 
 processing condition .
finally , the optical image real - time analysis software characterized the flow field of polymer melts .
the optical image real - time processing software for sals ( see figure 5 ) , which provides a user - friendly 
 interface already familiar to the users , is based on personal pc platform 
 running under ms windows operating system .
hardware specifics of a / d and 
 digital i / o boards which are connected on pc motherboard impose some 
 constraints and partly determine real - time software structure , especially 
 disposition of its components at processors .
real - time 
 visualization of various scattered light image and light intensity matrices is 
 performed by the host application .
the next step is setting parameters using 
 corresponding dialog - boxes provided by the host application .
some of these 
 parameters are vibration parameters ( frequency , amplitude ) , display parameters 
 ( sizing grid , display scale , image translation , and rotate angle ) , and other 
 parameters ( rotate speed , material , sampling time ) . the light intensity matrix 
 can be saved on disk of main workstation for further analyses . the software 
 can measure the signal intensity of light scattering images , draw the 
 frequency - intensity curves and the amplitude - intensity curves to indicate the 
 variation of the intensity of scattered light in different processing 
 conditions , and estimate the hydrodynamic parameters .
so , the system brought 
 the qualitative analysis of the structural information of transparent film 
 success . 

figure 6(a ) shows a 3d light intensity image of hdpe at 24 rpm screw rotate speed 
 without vibration .  
figure 6(b ) shows light intensity image of hdpe at the same rotate 
 speed with vibration frequency of 10 hz and vibration amplitude of 0.20 mm . in comparison 
 with 3d light intensity image without vibration , 3d light intensity image with 
 vibration has stronger light intensity .
it is illustrated that the orientation 
 of molecular chain increases because light intensity is proportional 
 to orientation of molecular chain . 

figure 7 
 shows the variation trend of maximum intensity projection area with the 
 increase of vibration frequency of ps at 20 rpm rotate speed .
as shown in figure 
 8 , with the increase of vibration frequency , the maximum intensity projection 
 area becomes larger .
it is because with the increase of vibration frequency , 
 the molecular orientation of polymer melts also increases . as a consequence , 

figure 8 
 shows the relationship between maximum intensity projection area and vibration 
 amplitude of hdpe at 24 rpm screw rotate speed . from figure 8 , it is clear that with the increase 
 of vibration amplitude , the maximum intensity projection area becomes larger . 

the molecular orientation of polymer melts increases is also the main reason of 
 this optical phenomenon .
a signal 
 including noise can be expressed as ( 15)s(i)=f(i)+e(i ) ,  i=0,  ,n1 ,    where f ( i ) is the real signal , e(i ) is the noise ,  is the coefficient of the noise , and s(i ) is the signal including noise . the useful 
 signal is included in the part of low frequency , and the noise is included in 
 the part of high frequency .
as shown in figure 9 , we used one - dimensional wavelet 
 which decomposed 
 the original signal into three level : ( 16)s = ca3+cd1+cd2+cd3 ,    where s is the original signal , ca1 , ca2 , ca3 are the approximation coefficients of levels 1 , 2 , and 3 , and cd1 , cd2 , cd3 are the detail coefficients of levels 
 1 , 2 , and 3 .
the performance of wavelet denoising is comparable to that of 
 inducing kf correcting factor .  
figure 10(a ) is the normal 
 sals intensity signal .   figure 10(b ) is the 
 sals signal with multiple scattering 
 noise .  
sym6 ,  
 the multiple scattering 
 noise is eliminated and the 
 signal ( see figure 10(e ) ) is 
 becoming more smooth . 
 from figures 10(d ) and 10(f ) , the 
 residuals by wavelet decomposition are smaller than the residuals by inducing kf factor .
wavelet method is more successful in 
 removing multiple scattering noise than that of 
 inducing kf correcting factor .
the   method   of   wavelet transform can reduce the ambiguities and accurately 
 analyze the variation trend of the sals signal .
as shown in figure 11(a ) , 
 the variation trend of the original 
 intensity signal ( s ) 
 is not clear .
sym6 ,  the variation trend of the intensity is obvious as shown in figure 
 11(f ) . as shown in figures 11(b)11(f ) , caj   ( j = 1 , 2 , 3 , 4 , 5 ) are 
 the wavelet approximation 
 coefficients of levels 15 .
it is illustrated that the orientation 
 of molecular chain increases because light intensity is proportional to 
 orientation of molecular chain .
the wavelet transform 
 is used to 
 purify the original sals signal and diagnose the 
 exceptional signal .  
. these 
 coefficients can be feature parameters of the inner structural information of 
 the transparent film for 
 further analysis . as shown in figure 12(h ) , the exceptional signal takes place at 5001000 seconds .
the 
 result shows that this technique provides a new tool for diagnosis of exceptional sals 
 signal .
we 
 presented   a new technique that can be used to characterize the structural 
 information of transparent film on - line and nonintrusively while the material 
 is processing with different conditions .
the technique is based on optical sals 
 image real - time analysis software and wavelet analysis .
visualization is 
 performed via high - performance analysis software which allows real - time data 
 acquisition and processing the sals signal .
it is shown 
 that the proposed technique is easy to implement and provides more flexibility 
 approximating the nonlinear relation between the maximum intensity signal and 
 the corresponding vibration intensity ( frequency or amplitude ) . applying this 
 method to characterize 
 the flow field of polymer melts
will be of great interest , since it will 
 contribute information on optical prosperities that have been proven to be 
 useful for obtaining deep insights into the molecular and structural parameters 
 of polymers . in our experiments with the increase of vibration intensity ,
the 
 light intensity matrix becomes stronger and the maximum intensity projection 
 area becomes larger . because the light intensity is proportional to orientation 
 of molecular chain , it is illustrated that the orientation of molecular chain 
 increases . in conclusion , this technique is 
 believed to be important and promising to on - line characterize the structural 
 information of transparent film in the multiple - scattering regime .
   this paper describes an effective on - line polymer characterization technique by using small - angle light - scattering ( sals ) image processing software and wavelet analysis . 
 the phenomenon of small - angle light scattering has been applied to give information about transparent structures on morphology . 
 real - time visualization of various scattered light image and light intensity matrices is performed by the optical image real - time processing software for sals . 
 the software can measure the signal intensity of light scattering images , draw the frequency - intensity curves and the amplitude - intensity curves to indicate the variation of the intensity of scattered light in different processing conditions , and estimate the parameters . 
 the current study utilizes a one - dimensional wavelet to delete noise from the original sals signal and estimate the variation trend of maximum intensity area of the scattered light . 
 so , the system brought the qualitative analysis of the structural information of transparent film success . 
1. INTRODUCTION
2. THEORETICAL BACKGROUND FOR SALS
3. WAVELET ANALYSIS FOR MULTIPLE
SCATTERING SALS SIGNAL
4. EXPERIMENTAL CHARACTERIZATION FOR
THE FLOW FIELD OF POLYMER MELTS
5. CONCLUSIONS