Patent Abstract:
method and system for determining the optical temporal response of a medium to a short optical pulse excitation , by sending light that comprises spectral frequencies which make up the fourier transform of the short pulse to be emulated through the medium . the relative amplitude and phase change of each of the spectral components light exiting the medium is determined with respect to that of the illuminating light source and the spectral response of the medium is obtained from the relative amplitude and phase change . an inverse fourier transform is then computationally performed on the spectral response to obtain the temporal response of the medium to the emulated short pulse .

Detailed Description:
in this specification the terms “ turbid medium ”, “ scattering medium ”, “ optically scattering medium ”, “ optically turbid medium ”, and other terms having a similar meaning are used interchangeably . fig1 describes a transmission system used for seeing through a turbid optical medium to acquire an image of an object obscured by the medium . in the preferred embodiment shown in fig1 , a cw frequency - tunable laser 10 is modulated at an rf frequency ω through the use of a rf modulation source 17 , which modulates the laser with the electronic sinusoidal signal 18 . in the weak modulation regime , the modulated light field 11 is e in ⁡ ( t , ω j ) ≅ ⅇ ⅈ ⁢ ⁢ ω j ⁢ t ⁡ ( 1 + a ⁢ ⁢ cos ⁢ ⁢ ω ⁢ ⁢ t ) = ⅇ ⅈ ⁢ ⁢ ω j ⁢ t ⁡ [ 1 + a 2 ⁢ ( ⅇ ⅈ ⁢ ⁢ ω ⁢ ⁢ t + ⅇ - ⅈ ⁢ ⁢ ω ⁢ ⁢ t ) ] [ 1 ⁢ a ] where ω j is the optical carrier frequency and α & lt ;& lt ; 1 ( for simplicity , unit amplitude at the carrier frequency is assumed ). it should be noted that the weak modulation regime is neither an essential nor a simplifying assumption ; similar conclusions are obtained for deep modulation , where expression ( 1 ) takes a simpler form e in ( t , ω j )≅ e iω j t ( e iωt + e − iωt ). [ 1b ] a portion of this beam is directed through the turbid medium 12 , which includes an embedded object 13 . the output field 14 is : e out ⁡ ( t , ω j ) = a ⁡ ( ω j ) ⁢ ⁢ ⅇ ⅈ ⁢ ⁢ ω j ⁢ t ⁡ [ ⅇ ⅈ ⁢ ⁢ φ j 0 + a 2 ⁢ ( ⅇ ⅈ ⁡ ( ω ⁢ ⁢ t + φ j ( + ) ) + ⅇ - ⅈ ⁡ ( ω ⁢ ⁢ t - φ j ( - ) ) ) ] . [ 3 ] the added phases φ j 0 , φ j (+) and φ j (−) for the three spectral components at ω j , ω j + ω and ω j − ω respectively , are due to the effective optical path length difference at these three frequencies . these path length differences are mainly due to material dispersion and frequency - dependent scattering paths . the factor a ( ω j ) represents frequency - dependent attenuation and is real - valued . for simplicity , it is assumed for now that this factor is constant over the frequency range ω j ± ω . the phases as well as the amplitude can also change due to the electronic system , cables , detector , etc ., however these factors are independent of the scattering medium and embedded objects , so that they are determined and accounted for . therefore , the output intensity at 14 which is detected by detection system 15 is i out ( ω j )≅ a 2 ( ω j )·[ 1 + 2 αc cos ( ω t + δφ ( ω j ))], [ 4 ] δ ⁢ ⁢ φ ⁡ ( ω j ) ≡ φ j ( - ) - φ j ( + ) 2 ⁢ ⁢ and ⁢ ⁢ c ≡ cos ( φ j 0 - φ j ( + ) + φ j ( - ) 2 ) . [ 5 ] electronic processor 19 compares rf signals i out ( eq . 4 , 16 in the figure ) to i in ( eq . 2 , 18 in the figure ), so that the amplitude and phase values a ( ω j ) and δφ ( ω j ) ( 20 in the figure ) can be determined . 19 can be a phase detector , network analyzer , lock - in amplifier , or other electronic processor known in the art . the laser frequency is tuned in steps of δω over a frequency range δω and the values of a ( ω j ) and δφ ( ω j ) are acquired for every frequency ω j . fig3 schematically shows the modulation and frequency scanning scheme for a preferred embodiment of the spebi system . in the figure the top line 30 shows the phases of the jth step and the bottom line 31 the phases of the ( j + 1 ) th step . the arrows 32 show that φ j (+) = φ j + 1 (−) for every step j . if the frequency steps δω fulfill the relation shown in fig3 , i . e . then , the spectral response of the medium , within the range δω , can be determined unambiguously : h ⁡ ( ω j ) = a ⁡ ( ω j ) ⁢ ⁢ ⅇ ⅈ ⁢ ⁢ φ ⁡ ( ω j ) , [ 7 ] where ⁢ ⁢ φ ⁡ ( ω j ) = 2 ⁢ ⁢ ∑ m = 0 j ⁢ δ ⁢ ⁢ φ ⁡ ( ω m ) - δ ⁢ ⁢ φ ⁡ ( ω o ) - δ ⁢ ⁢ φ ⁡ ( ω j ) [ 8 ] is the accumulated phase , and ω 0 is the lowest laser frequency to be used . if the frequency steps are larger , i . e . δω & gt ; 2ω , eq . ( 8 ) should be interpolated : φ ⁢ ( ω j ) = [ 2 ⁢ ⁢ ∑ m = 0 j ⁢ δ ⁢ ⁢ φ ⁡ ( ω m ) - δ ⁢ ⁢ φ ⁡ ( ω o ) - δ ⁢ ⁢ φ ⁡ ( ω j ) ] ⁢ ⁢ δ ⁢ ⁢ ω ω . [ 9 ] in the above derivation , it is assumed that the amplitudes a ( ω j ) are constant over the frequency range ω j ± ω . this is not a necessary requirement . if they differ , then the output intensity ( eq . 4 ) will have a dc value and a peak - to - peak ac value , which is dependent on the amplitudes , so that the amplitude values can be determined from a measurement of the dc and peak - to peak values . referring to eq . 4 , it is to be noted that the phase variable c , which affects the modulation depth of the modulated light at the output , is also dependent upon the added phases of the spectral components . therefore , the phases φ ( ω j ) can also be determined by measuring the modulation depth of the output signal . a computational inverse fourier transform of h ( ω ) will give the temporal response of the medium to an input pulse whose spectral bandwidth is δω . the ‘ first - light ’ signal can be extracted from this information by computationally filtering out the bulk of the temporal response and retaining the ‘ first - light ’ response ( in analogy to the task of the fast shutter in a real short - pulse measurement ). note that the computational work , which may form the bulk of the acquisition time , can be done ‘ off - line ’, either simultaneously , or after the spectral data is collected . other holographic methods [ 10 ] are in some sense similar to aspects of the current invention , since in both methods the measurements are done in the spectral domain , and both amplitude and phase are measured . however , there are two crucial differences between the two techniques : 1 ) the holography methods are based on interference of two beams that pass through two totally different trajectories . this type of interferometric measurement is highly sensitive to system noise , and difficult to implement in non - laboratory systems . in the present invention , on the other hand , the two beams copropagate along common paths , and therefore the measurement is extremely robust ; 2 ) moreover , since in both methods the phase and amplitude must be measured , the methods of arons et al [ 10 ] consists of two scans : wavelength and time delay , while the present invention requires only a wavelength scan , since the measurements of amplitude and phase are done simultaneously . fig2 shows schematically a preferred embodiment for acquiring the image of an object obscured by an absorbing layer in a reflection - illumination configuration . elements 10 , 11 , 15 , 16 , and 17 to 20 are identical to those of fig1 . in fig2 , the laser output 11 is directed towards a target , which consists of multiple scattering layers , two are depicted in the figure as 22 and 23 . layer 23 is also the object , hidden behind the front scattering layer 22 . a portion of the light 21 transverses the first layer and is reflected back by the object at small enough angles with respect to the optical axis that it is collected by the detection system . much of the light is scattered in a wide angle by all of the layers , shown as 26 . a beam splitter 24 deflects the returning light 25 into detector 15 . the laser modulation and signal processing is identical to that of fig1 . as in the transmission case , the temporal response is computed , and the ‘ first light ’ response is determined , so that the image information of the hidden object can be extracted . as in time - gated imaging , as well as other imaging techniques , it is difficult to extract information on objects deeply embedded within a scattering volume when using the reflection configuration . this is due to the accumulated backscattering of light from the scattering volume in front of the object , which is usually much stronger than the ballistic backreflection from the desired object . therefore , spebi , like other first - light techniques , works best with discrete scattering layers , as shown in fig2 , or in situations where the objects are not deeply embedded within the scattering volume . the ballistic light , which is reflected from each layer would appear temporally separated , so that the information on the object layer can be extracted . acquisition of a complete two - dimensional ( 2d ) image of the desired object requires the computation of the ballistic light components within the entire 3d volume . this can be done by scanning the input light and detector throughout the 2d input and output planes , and performing the spebi measurements for each coordinate . alternatively , the entire input plane of the scattering medium can be illuminated simultaneously , while performing parallel measurements using a detector array at the output plane . the light sources and / or detectors may include lenses , optical fiber , mirrors or other optical components for light expansion , collection , focusing , steering , etc . as is well - known in the art . the above discussion leads to the conclusion that the main parameters to be determined to enable the spebi measurements to be carried out are the desired spectral resolution δω , laser modulation frequency ω and the required tuning range δω . these parameters and the method used to determine them will now be discussed . the tuning range is optimally the spectral bandwidth of the input pulse width τ p , which is to be emulated with the tunable cw laser . a good rule of thumb is that for a dense optical medium of length l , the pulse width should be significantly smaller than the ‘ flight time ’ of a ballistic photon t b = nl / c through the medium , so that τ p ≈ 0 . 01 nl / c , where n is the effective index of refraction . assuming a gaussian pulse , so that δω = 4 / τ p , gives δω = 400 c / nl . the required spectral resolution δω is dependent upon the characteristic diffusion time of the medium . in order to obtain full reconstruction the spectral resolution of the measurement should be better than δω ≈ 2π / t d where t d is the diffusion time , which can be approximated by t d ≅ l 2 / d ≅ 3 μ s ′ nl 2 / c . d is the diffusion constant and μ s ′ is the effective scattering coefficient ( the reciprocal of the random walk length ). as an example , for ordinary human tissues t d ≅ 10 ns . assuming 100 resolution points , or δω / δω ≧ 10 2 , gives δω = 4 c / nl and ω = 2 c / nl . assuming , for example , a length of 10 cm and n = 1 . 5 , leads to the following required operating parameters for a tunable laser with a center wavelength of 1530 nm : a wavelength tuning range of 1 . 0 nm , tuning resolution of 10 pm , and modulation frequency of 640 mhz . this will emulate the performance of a 5 ps laser pulse . tunable lasers having these parameters are commercially available . for example , the tunics - pri - 1530 supplied by nettest photonics fulfills the above requirements . this laser has the following specifications : wavelength tunability range 1480 - 1580 nm , wavelength resolution = 1 pm , and power modulation frequency ω / 2π to 1 ghz . the tuning range of 100 nm means that a minimum pulse length of approx . 50 fs can be emulated . the 1 pm resolution capability means that the lowest δω / 2π = 128 mhz and that up to 10 5 resolution points can be measured . skilled persons will realize that the number of resolution points can be lowered to a limit where δω / 2π = 2ω / 2π = 2 ghz . an important advantage of the tunable laser is the ease with which its power can be amplified . since it operates at the optical communication wavelength band and is fiber - coupled , its power can be easily ( and relatively cheaply ) amplified from 3 mw to over 500 mw using an erbium - doped fiber amplifier ( edfa ). for medical and other applications , it may be advantageous to employ wavelengths in the 800 nm - 900 nm band . other types of tunable laser sources , e . g . ti : sapp ., diode lasers , that are known in the art can be used in spebi . alternatively , a broadband light source of bandwidth δω can be used to illuminate the sample ; while , at the output , the detector system includes a means of spectrally separating the light components and measuring the amplitude and phase of each spectral component . the actual number of resolution points that will be required in a given type of medium may be lower , and in certain circumstances significantly lower than the result of the above model . for example , if a priori information regarding the medium &# 39 ; s optical characteristics is known , then the number of resolution points can be decreased . in many circumstances , interpolation of the missing data would be sufficient . in certain applications , a data bank of spectral data , e . g . data on breast tissue with and without cancerous growths , could be used in order to efficiently categorize the data of a particular patient , so that a high - resolution measurement would not be required . in fig4 a is schematically shown the spebi set - up 40 for an experiment designed to measure the time response of opal diffuse glass 12 , behind which was place a small absorbing object 13 . the glass was illuminated with light from a tunable laser 10 of the type described above . the effective input pulse length was 1 . 5 ps , the modulation frequency was 1 ghz , and the thickness of the glass was 3 mm . also shown in fig4 a are rf oscillator 41 , modulator 42 , optional optical elements 43 , detector 15 , and electronic processor 19 which provides the amplitude and phase data . fig4 b shows the reconstructed time response of the medium , with and without the absorber , to an input pulse of 1 . 5 ps shown at t = 0 . according to the method of the invention , it is not this pulse , but its fourier transform that is transmitted through the diffusing medium and the object . the inverse fourier transform of the recorded data is then calculated and it is this that is known as the reconstructed optical response of the diffusing medium and the absorbing object which appears between 0 . 5 and 1 . 1 × 10 − 11 seconds after the initial pulse . fig4 c is an enlargement of the features shown between 0 . 5 and 1 . 1 × 10 − 11 seconds in fig4 b . in fig4 c , curve a is the reconstructed optical response of the medium alone and curve b that of the medium with the absorber . curve b has been magnified by a factor of 7 . in the reconstructed optical responses , pulse expansion and deformation due to the scattering medium is clearly seen . in addition , it can be seen how the absorber has blocked the first - arriving light . this experiment demonstrates that a temporal resolution of less than ˜ 1 ps is easily achievable ; that it is possible to separate the ballistic and quasi ballistic (“ snake photons ”) portion of the signal from the diffusive component ; that an obstructed object can be detected ; and , perhaps most importantly , that a relatively noiseless signal can be obtained with this technique . although embodiments of the invention have been described by way of illustration , it will be understood that the invention may be carried out with many variations , modifications , and adaptations , without departing from its spirit or exceeding the scope of the claims . b . b . das , f . liu and r . r . alfano , rep . prog . phys . 60 , 227 ( 1997 ) “ time - resolved fluorescence and photon migration studies in biomedical and model random media ”. j . c . hebden , “ evaluating the spatial resolution performance of a time - resolved optical imaging system ” med . phys . 19 , 1081 ( 1992 ). q . z . wang , x . liang , l . wang , p . p . ho , and r . r . alfano , “ fourier spatial filter acts as a temporal gate for light propagating through a turbid medium ”, optics letters , 20 , 1498 ( 1995 ). e . n . leith et al , “ realization of time gating by use of spatial filtering ”, appl . opt . 38 , 1370 ( 1999 ). a . kuditcher et al , “ ultrafast cross correlated harmonic imaging through scattering media ”, appl . opt . 40 , 45 ( 2001 ). a . yodh and b . chance , “ spectroscopy and imaging with diffusing light ”, physics today , pp . 34 - 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