Patent Application: US-52701690-A

Abstract:
apparatus is provided for measuring non - absorptive scattering with an exceptionally high degree of accuracy . in the preferred mode , the apparatus can also be used to measure absorptive scattering , thus providing a method of distinguishing absorptive scattering from scattering due to transparent moieties . the approach of the invention promises to significantly expand the use of optical systems in quality control . the general concept of the invention relies on symmetric heterodyne scattering . specifically , two beams at slightly differing optical frequencies are directed to intersect at some arbitrary angle . transparent objects within the intersection volume scatter light from each beam into the other . after intersecting , the two beams are directed to separate photodetectors which mix each transmitted beam with the scattered light from the other beam . because the two beams are at different optical frequencies , the mixing of the light generates heterodyne signals modulated at the difference frequency on each of the photodetectors . these signals can then be combined in various ways to directly measure the absorptive and non - absorbtive scattering from the scattering region .

Description:
shown in fig1 is a laser detection system which can be used to distinguish scattering from absorption in an optical scattering medium , an important process for determining quality of some products . those skilled in the art will realize that such products could be beverages , optical components , gases , or just about any medium for which scattering ( from particulates for example ) would provide some indication of quality , or lack thereof . an incident beam 12 is provided by a laser 11 which impinges on a 50 - 50 beam splitter 13 , thereby creating two beams , 14 and 20 . beam 14 impinges on an acousto - optic frequency shifter 17 that is controlled by an r . f . generator 35 to provide an r . f . frequency shift ( typically on the order of 10 &# 39 ; s of mhz ). a frequency shifted beam 14 &# 39 ; exits the frequency shifter and enters a scattering region 19 . beam 20 is directed by mirror 15 toward scattering region 19 , so that it intersects beam 14 at some arbitrary angle . in the scattering region , light from each beam scatters into the other . after intersecting in the scattering region , the two beam are intercepted by separate high speed photodetectors , 21 and 23 , which for example could photodiodes or photomultipliers . because the two beams 14 &# 39 ; and 20 are at different optical frequencies , the mixing of the light generates heterodyne ( beat ) signals modulated at the difference frequency on each of the photodetectors . the signals from detectors 21 and 23 are then amplified by r . f . amplifiers 25 and 27 . ( further , if desired , the r . f . amplifiers can be used to cut off all but the beat frequency .) the signals from the amplifiers are then directed to r . f . splitters 29 and 31 , each of which splits the incoming signal equally . one of the signals from splitter 29 is then added to one of the signals from splitter 31 using an in - phase r . f . power combiner 37 . similarly , the other signal from splitter 29 is subtracted from the other signal from splitter 31 using an r . f . power combiner 39 . with the above arrangement , the resulting signal from combiner 37 is proportional to the correlated part of the signals from the two splitters , since the correlated signals add while the anti - correlated signals cancel . similarly , the resulting signal from combiner 39 corresponds only to the anti - correlated signals . because the correlated signals are caused by absorption in the scattering region , while the anti - correlated signals are caused by scattering , e . g . by particles that do not absorb , the above arrangement makes it possible to easily distinguish scattering from absorption . in order to measure the correlated and anti - correlated signals from combiners 37 and 39 , it is useful to shift the r . f . and d . c . in the simplest approach , this can be done by multiplying each signal by an r . f . signal from generator 35 , as is illustrated in fig1 by multipliers 41 and 43 . another approach would be to use a phase shifter between r . f . generator 35 and each of multipliers 41 and 43 . then one could use a phase sensitive detector to measure the absorber signal from multiplier 41 by adjusting the phase sensitive detector to obtain the maximum signal . one could similarly determine the anti - correlated signal using another phase sensitive detector in the same way on the signal from multiplier 43 . as alluded to earlier , with the above approach , one can distinguish absorption , e . g . due to absorbing particulates , from scattering due to non - absorbing particulates , i . e . transparent moieties . a good example would be bubbles . hence , one can easily distinguish bubbles , which do not absorb , from absorbing particulates . this is particularly useful in many different industries which require , for example , particulate free liquids . appendix a provides a detailed theoretical analysis in support of the above approach . we consider the situation in fig2 in which two laser beams , with correlated optical powers p a = p b = p , and with optical frequencies differing by an amount δν ≡ ν a - ν b , intersect at some point in space . within the volume of intersection is some arbitrary object that scatters light from each of the two beams into the other beam . we choose the time origin such that at t = 0 the phase difference of the two beams at the scattering object is zero . after passing through the region containing the scattering object , each of the two beams mixes with some of the scattered light from the other beam on high - quantum - efficiency photodiodes which generate photocurrents proportional to the total power in each of the beams . the total photocurrent from the two detectors can be written [ 12 ] ## equ1 ## is the photodetective responsivity , h is the planck constant and ν is the optical frequency . the phase of the heterodyne signal of the ith beam ( i = a or b ) is φ i . σ i is the total fraction of light scatter out of the ith beam , and σ ij is the fractional amplitude of the light scattered from the ith beam that mixes with the jth beam to produce a heterodyne signal . if the scattering is weak , such that σ i & lt ;& lt ; 1 then the photocurrents may be written the relationships between the scattering coefficients σ ba and σ ab and between the ophases φ a and φ b of the heterodyne signals are found using scalar diffraction theory [ 13 ]. for a field propagating along the z - axis , as shown in fig3 the complex phasor μ 0 of an electromagnetic field in the x 0 - y 0 plane is found given a known phasor μ 1 in the x 1 - y 1 plane , where the two planes are separated by a distance z . in the fraunhofer approximation . the complex phasor in the x 0 - y 0 plane is given by ## equ2 ## where f x = x 0 / λz and f y = y 0 / λz are the spatial frequencies in the x o y o plane , and ## equ3 ## the symbol f {} indicates the two - dimensional fourier transform , and bold face implies a complex quantity . in the symmetric scattering geometry shown in fig4 a weakly scattering object , with complex transmission τ , is centered at the origin of the x 1 - y 1 - z coordinate system . we write the transmission of the object as ## equ4 ## where α , the absorptive part of the transmission and β , the phase shifting part of the transmission are both real and small compared to one . without loss of generality , we can decompose both the absorptive and the phase shifting parts of the transmission function into even and odd symmetry functions where the subscripts r and i stand for real and imaginary , and the subscripts e and o stand for even and odd symmetry ( along the x 1 - axis ). two collimated beams with equal amplitudes e propagating in the x 1 - z plane along directions ± θ with respect to the z - axis intersect at the origin and are scattered by the object . if the object is thin , then the phasors of the fields leaving the x 1 - y 1 plane are given by where f o = sin θ / λ . from eq . ( 12 ), the phasors in the x 0 - y 0 plane are given by ## equ5 ## where we have used the fourier transforms shift thereon , and ## equ6 ## each term in eq . ( 21 ) is the fourier transform of the corresponding term of eq . ( 16 ): that is the real parts of representative phasors μ oa and μ ob are shown in fig5 as a function of the spatial frequency f x . the phasors consist of strong unscattered components at f x =± f 0 corresponding to each delta function in eqs . ( 19 ) and ( 20 ), and an associated weak scattered component extending over some range from the unscattered component . for the thin scatterer we have assumed , the phasors μoa and μ ob are identical except for a displacement along the f x axis . the scattered intensity as a function of the spatial frequency , f x , is given by the square magnitude of the field , with the time dependence explicitly included . ## equ7 ## where δν - ν b . from eqs . ( 19 - 23 ), the intensity is written ## equ8 ## where (±) stands for ( f x ± f 0 ). in eq . ( 24 ) we have used the relationship δ (-) δ (+)= 0 , and have also neglected terms of second order in the scattering coefficients t xx . the photocurrent generated by a detector is proportional to the total power p incident on the detector surface . for two detectors with responsivity ρ which are located at positions corresponding to f x =± f o , the generated photocurrents are i . sub . b ( t )= ρp { 1 + 2 ] t . sub . re ( 2f . sub . x )- t . sub . ro ( 2f . sub . x )] cos ( 2π & gt ; νt )+ 2 [ t . sub . io ( 2f . sub . x )- t . sub . ie ( 2f . sub . x )] sin ( 2πδνt )}. ( 26 ) we see by comparison with eqs . ( 9 ) and ( 10 ) that , for example , ## equ9 ## the photo currents from the two detectors , i a and i b , can be added or subtracted in external circuitry . from eqs . 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