Patent Application: US-201515118877-A

Abstract:
the invention is a system and method that enable obtaining ultra - high resolution interference , phase and oct images at high speed . the system uses neither mechanical moving elements nor any optical / electro optical modulating means for obtaining the oct images . two oct operating modes are available : for ultra - high resolution the system allows either spatial coherence td - ff - oct or temporal coherence td - ff - oct imaging , whereas for high resolution and ultra - high speed the system allows fd - ff - oct imaging with full range imaging . in the td mode , the oct enface images are obtained in real time . in the fd mode , the 2d complex signal is reconstructed in real time . in both cases the method has the advantage of very high speed imaging with great immunity to noise .

Description:
one of the main drawbacks of td - ff - oct imaging is that in order to obtain the oct images few ( typically 4 ) interference images usually have to be grabbed with each image phase shifted with respect to the others ( typically by π / 2 ). the oct images are thus produced by a simple combination of these 4 interference images . apart from the fact that this process reduces the available imaging speed by a factor of 4 , it is also quite problematic since it requires great interferometer stability which is absolutely necessary for accurate phase and amplitude extraction of the interference signal . in the past , it was shown [ 45 ] that by using only three phase shifts , high resolution full field oct images can be produced . the phase shifting was applied using a liquid crystal retarder ( lcr ) which had limited speed and accuracy . also , this method required that the interferometer be very stable between successive phase shifted images . for an exact , fringeless , demodulation of the interference signal envelope , a very accurate and stable technique is required . in the present invention three cameras are used , each equipped with a preferably π / 2 , but not limited , phase shifted enface using very accurate achromatic wave plates so that air turbulences and phase mismatch errors are reduced to minimum . the spatial coherence td - ff - oct signal of a single microstructure located within a weakly scattering medium ( eqs . 1 - 3 ) [ 45 ] are now considered . for simplicity the objective lenses are assumed to be used with index matching material . i c ( x , y ) being the irradiance at the peak wavelength . alternatively the light source can be flat or with any kind of spectral shape ; in which case equation ( 4 ) is modified accordingly . generally speaking , for uniform illumination i c is independent of the lateral sample location ( x , y ). the parameter λ is the wavelength , λ c is the central wavelength ( peak wavelength ) of the source , σ λ is the source bandwidth ( variance ), na is the numerical aperture of the objective lens , n 0 is the sample ( and matching ) refraction index , δ z is the scanning distance , l ( x , y ) is the distance of the microstructure from the focal plane which is coincident with the top surface of the sample at the beginning of the scan , r scat ( x , y ) is non - interfering back scattered field , r r is the reference mirror reflectivity and r s ( x , y ) is the sample reflectivity . the coordinates ( x ′, y ′) are at the image plain and β is the phase delay provided by the wave plates arrangements . by providing three phase shifted images , each to a different ccd camera ( see fig1 ), the envelope and phase of the interference signal are obtained ( see fig6 for the simulation results ). in the case of a narrow bandwidth the obtained signal is the so called spatial coherence gating oct signal , see equation 5 . there are several ways to present the oct images ; the most common approach is the logarithmic scaling . equation 5 is the so called linear display and equation 6 is the so called log scaling display : note that if the temporal coherence contribution is to be considered ( temporal coherence gating ffoct ), equation 5 should be integrated for the wavelength band to yield : another implementation of the method of the invention is to extract the phase of the interference signal . for example , the phase of the interference signal can be retrieved using equation 9 : using the extracted phase , very accurate surface and depth profiling can be performed . see an exemplary experimental result in fig1 and fig1 . generally , when the phase difference between each signal is mπ & lt ; β & lt ;( m + 1 ) π instead of π / 2 as in eq . 9 , the general equation for obtaining the phase is given by eq . 10 : ψ ( x ′, y ′, λ )= tg − 1 ( tg ( β / 2 ){[ i ( 0 )− i ( 2β )]/[ 2 i ( β )− i ( 0 )− i ( 2β )]})− β ( 10 ) although to demonstrate the disclosed system and methodology the inventors concentrated on three phase shifted signals arriving to three detectors in parallel , it should be mentioned that its generalization to the case of any number ( n & gt ; 3 ) of phase shifted channels using the same number n of detectors in parallel is straightforward using phase shift extraction algorithms known in the art . in many cases of oct the sample reflectivity is significantly smaller than the reference mirror reflectivity . under these circumstances equation 1 can be rewritten accordingly , as equation 11 : i ( x ′, y ′, δz , β , λ )≈ i 0 ( x , y , λ ){ r r + 2 √{ square root over ( r r r s ( x , y ))} a [ δz − l ( x , y ), λ ] cos { 2π f z [ δz − l ( x , y )]+ β }} ( 11 ) in this case , the spatial coherence gate td - ff - oct signal can be obtained using only two cameras in accordance with the description of fig2 . the signal is obtained by first saving one image with only the reference arm imaged i r ( x ′, y ′)≈ i 0 ( x , y , λ ) r r . then , by subtracting this image from each one of the full field interference images grabbed by the two cameras , the in phase and quadrature signals are obtained in parallel . by taking the square of these two signals the envelope of the interference signal is extracted , whereas by dividing these two signals the interference phase is obtained . the above description is formulated using equations 12 and 13 : in the case of temporal coherence gating td - ff - oct , equation 12 is integrated over the entire optical bandwidth in similar fashion of equation 7 . here too , the oct signal may be presented using logarithmic , as well as linear , scaling . as previously explained in the background section of this application , the fd - ff - oct approach is the only method that does not require any form of scanning in order to obtain the 3d oct images . as such , it has the potential to be the ultimate solution for high speed 3d oct imaging . referring now to fig9 , the interference field projected onto each pixel , at each parallel detector and in each wavelength / frequency is as follows , see equation 14 : in equation 14 the reference and sample back reflected fields are interfered . the parameter r r is the reflectivity of the reference field , e 0 ( k ) is the field amplitude at any given wave number k , ω is the optical radial frequency , f is the focal length of the objective lenses , l r is the length of the reference arm , r m is the reflectivity of each microstructure in the sample , z m is the optical path length from the principle plain of the sample objective lens to the m th microstructure , l 0 is the length of the sample arm , β = β e − β o is the retardation provided by the wave plates and { right arrow over ( n )} a is a unit vector in the direction of the analyzers in front of the cameras . equation 14 disregards any losses or non - ideal conditions set forth by the optical components comprising the system . in particular it disregards the losses due to splitting and polarizing at the different bs and analyzers . more specifically , equation 14 is derived using the following assumptions : ( 1 ) contributions of multiple reflections at the sample are negligible , ( 2 ) refraction at the sample is negligible due to the relatively low na of objective lenses used , ( 3 ) reflection coefficients are very small as n m ˜ n m + 1 ˜ n avg ( 4 ) the depth of field of the objective lenses is large in comparison with the sample thickness , ( 5 ) the model disregards diffraction , and ( 6 ) the model assumes that the paraxial ray approximation holds . also , for keeping the discussion as general as possible , it is assumed that each spectral line is coherent . when using led with a tunable filter the spectral lines are not coherent and coherent noise is transformed into additional dc noise which is simpler to eliminate ; this is the reason that each spectral line can be regarded as being purely coherent . the incident irradiance at each pixel at each wavelength is given by the time average poynting &# 39 ; s vector , see equation 15 : in equation 15 , { right arrow over ( s )} is the poynting &# 39 ; s vector which reflects the provided power density of the propagating interfering fields , t is the time period of the optical wave , { right arrow over ( e )} is the interference electrical field of equation 14 , { right arrow over ( h )} is the magnetic interference field , μ 0 is the free space magnetic permeability , ∈ 0 is the free space dielectric permittivity and { right arrow over ( n )} z is a unit vector in the direction of the propagation fields . equation 14 is simplified using a simple trigonometric identity by taking the dot product of the unit vector of the detector surface and equation 16 the irradiance incident at each pixel of the sensor is obtained , see equation 17 . in equation 17 i 0 ( k ) has been substituted for e 0 2 ( k )/ 2z 0 and d set equal to 0 for simplicity . in an effort to further simplify the method , a few more simple substitutions are made , namely : k = 2πν / c , z m = δz m n + f + δz 1 ( 1 − n ), τ m = 2δz m n / c , τ 0 = 2 [ δz 1 ( 1 − n )+ d ]/ c , τ mn = 2 ( z n − z m )/ c with δz m being the thickness of the m th layer of the multilayer sample . using these substitutions , equation 16 becomes equation 18 . note that τ m is positive for structures located after the zero delay line and negative for structure located before the zero delay line . also , note that although the entire image is shifted by τ 0 , the distances between structures are not influenced by this shift . therefore , the constant time shift can be disregarded by setting it to zero ; as it has no influence on the total sample structure . also note that for incoherent light source such as a led , the autocorrelation term vanishes ; the method of the invention is described using equation 17 to avoid any loss of generality in the case of a swept laser source . in normal fd - ff - oct , after recording interference images with different wavelengths , the 3d image is obtained by taking the inverse fourier transform ( ift ) of each pixel of the stored interference images . it is clear from equation 18 that an ift operation of the equation results in what is usually termed by those familiar with the art as dc noise , autocorrelation noise and mirror image obscuring . in this invention a method and a system are disclosed that solves these problems using the system depicted in the figures and described herein above . for example , referring now to fig2 and to fig4 , each camera is optionally equipped with π / 2 phase difference provided by the wave plates arrangement and the polarimetric configuration of the linnik / twyman - green / michelson interferometers . therefore , by using equation 19 the mirror image , the dc noise and the autocorrelation parasitic noise can be eliminated . then , by taking the ift of equation 19 the fd - ff - oct signal is obtained with full range imaging and obscuring by mirror images , dc noise , as well as autocorrelation noise , are eliminated . see equation 20 . in equation 20 the fact that the ift of a complex phase is simply a shifted time impulse has been used . the ift of the irradiance of the source is designated by i ( t ). from equation 20 it is clear that the resulting signal is a train of impulses shifted by a time delay τ m , which is typical to the location of the m th structure , and convolved with the ift of the source spectra . note that each time delay τ m is easily interpreted into the sample axial morphology by using the previous substitution δz m = cτ m / 2 n . as equation 20 is obtained at each point of the image of the sample , the 3d morphology of the sample has thus been obtained . the above model doesn &# 39 ; t take into account that the optical components are not ideal . for example , the beam splitters may not have exactly a 50 / 50 splitting ratio and may not have the same splitting ratio for each wavelength . also , the analyzers may not be exactly oriented at 45 degrees to the axes of the wave plates . the retardation wave plates may not have exactly π / 2 and π phase retardation and do not have exactly the same delay for each wavelength . the transmission efficiency of the optical components , the collecting efficiency of the light source , as well as the quantum efficiency of the optical sensor , are not brought into consideration in equation 20 . a detailed and accurate derivation of the output expression from this system should take into account the polarization transmission and reflection at each optical element and the exact retardation provided . the simulation results in fig1 and fig1 , as well as the simulation results for the td mode as depicted in fig7 and fig8 , have taken into account all the above factors using the optical specifications provided by the manufacturers ; demonstrating that the current invention is valid and can be very well realized . another important feature of the invention is depicted in fig3 and fig5 using only two cameras to obtain the full range fd - ff - oct signal . in oct the reflectivity of each microstructure is most often much smaller than the reflectivity of the reference mirror , that is r r & gt ;& gt ; r m . under these circumstances , equation 18 may be approximated accordingly , see equation 21 : by saving an image of the reference mirror only i r = i 0 ( ν ) r r 2 , at each one of the illuminating wavelengths , the complex signal can be reconstructed accordingly , see equation 22 : then , by taking the ift of equation 22 , the fd - ff - oct signal is obtained with complex conjugate ambiguity resolved . another embodiment of the invention uses the polarized mirau common path interferometer . this interferometer is similar to the mirau objective but with slight modification to allow integration into the system of the invention . fig1 a shows this common path interferometry unit that replaces the non - common path linnik and tywman - green interferometers depicted on fig2 - 5 . it is a modified mirau type objective with the internal flat beam splitter ( fbs ) replaced with a flat polarized beam splitter such as a wire grid polarizer or a stack of qwp / fbs / qwp . this type of objective already exists in the prior art ( see us2010 / 0309476 a1 and u . s . pat . no . 8 , 072 , 610 b1 ) but in the present invention it is integrated with a parallel phase retardation imaging system in which the incident beam polarization is linearly polarized at 45 degrees to the axis of the flat polarized beam splitter . the light coming from the illuminator is directed with the ordinary non - polarizing beam splitter 601 towards the modified mirau objective lens system 602 , hits the flat pbs ( e . g . wire grid polarizer ) 603 , splits into te polarized beam towards the reference mirror 604 and into tm polarized beam towards the sample 605 . the two beams then recombine in reflection and continue to the rest of the system to unit 2000 of fig1 or starting from component 133 , 233 , 333 and 433 in fig2 - 5 , respectively . another preferred embodiment is depicted in fig1 b in which a nomarski or differential interference contrast interferometer unit is shown . the wollaston prism 613 produces the two orthogonally polarized beams , which are collimated by microscope objective 616 , hit the sample 617 at different locations , are reflected and recombined back upon traversing the wollaston prism 613 in the opposite direction and continue towards the imaging and phase retardation units 2000 of fig1 or starting from component 133 , 233 , 333 and 433 in fig2 - 5 , respectively . another embodiment is shown in fig1 c , which consists of a polarized fizeau interferometer in which the incident beam 621 is directed towards an optical flat 623 . the top surface of optical flat 623 is anti - reflection coated while the bottom surface acts as a polarization beam splitter such as a wire grid polarizer or a stack of qwp / fbs / qwp . in the latter case the beam preferably linearly polarized and oriented at 45 degrees to the qwp optic axis . the bottom surface of the optical flat 623 optionally has small spacers 624 in order to maintain a constant gap with the sample surface . alternatively these small spacers maybe removed and optionally some proximity sensors can replace them . one linearly polarized beam gets reflected from the bottom surface of optical flat 623 while an orthogonally polarized beam is transmitted to sample 625 and gets reflected . the two beams are recombined with beam splitter 622 and transmitted towards the imaging and phase retardation unit 2000 of fig1 . another preferred embodiment uses the orthogonally polarized interferometer described in fig1 . the orthogonally polarized two beam interferometers in this case are non - common path configurations ( linnik , michelson and twyman - green interferometers ) in which the illuminating light beam 701 first passes through a non - polarization beam splitter 702 while the interferometer uses a polarizing beam splitter 703 to generate the two orthogonally polarized beams . the two orthogonally polarized beams recombine in reflection at the pbs 703 and directed with the non - polarizing bs 702 towards the imaging and phase retardation unit . another important embodiment of the invention is an interferometric microscopy unit built based on the same concepts described before but with the detectors replaced by three photodiodes or any other fast detectors , made of single pixel or multiple pixels . this embodiment is important for dynamically monitoring the position of a moving stage carrying a sample with high precision such as to help maintain the sample at the focal plane of an imaging system . another important embodiment of the invention is to convert the system into a multimodal imaging system . for this purpose the incident polarized light from the illumination unit 1700 is rotated , mechanically or electronically using an electrooptic or a magnetooptic modulator , so that the whole beam is forwarded towards the sample arm of the interferometer unit and nothing is transferred to the reference arm . this way a bright field imaging mode is produced and multimodal operation of the microscope system becomes possible such as fluorescence , dark field , and phase contrast , in addition to the 3d interference microscopy mode . another option is to rotate the incident polarization from the illumination unit 1700 so that the intensity reflected from the reference mirror matches the intensity reflected from the sample to obtain optimum contrast . the phase shifts between the three cameras are produced in the present invention by using two slightly different approaches to arranging the wave - plates . in the first approach element 33 , 133 , 233 , 333 and 433 in fig1 - 5 , respectively , is used as a zero retardation wave plate , that is , the element has no effect on the interference signal emerging from the linnik interferometer and thus can be even completely excluded from the setup . in this case , the analyzers in front of the cameras are aligned at 45 ° with respect to the s and p polarization directions while the optic axes of the retardation wave plates are parallel to the s and p polarization directions of the waves emerging the interferometer . as a result , an achromatic phase shift is produced between the three cameras ; a zero phase shift is generated at the camera which is equipped with the compensating retardation wave plate , a π / 2 phase shift is introduced in the interference signal generated in the camera which is equipped with the precision achromatic quarter wave plate ( pqwp ) and a π phase shift is introduced in the interference signal generated in the camera which is equipped with the precision achromatic half wave plate ( phwp ). alternatively , instead of a π / 2 phase shifts , the phase shifts between the cameras is β where mπ & lt ; β & lt ;( m + 1 ) π and m is an integer , in the second approach the wave plates 22 , 28 and 25 in the detection unit 2000 of fig1 and their respective designations in fig2 - 5 are completely excluded from the setup while element 33 , 133 , 233 , 333 and 433 in fig1 - 5 , respectively , is used as a pqwp retardation wave plate , which is rotated at 45 ° with respect to the s and p polarization waves emerging from the interferometer . as a result , the incident s and p linear polarization waves are converted into circular polarization waves with left and right handedness lh and rh , respectively . the two circular polarization waves are collected by the tube lens , then split by the beam splitters , then linearly polarized by the analyzers and finally projected onto the camera image plane . the analyzers are preferably aligned in 0 °, 45 ° and 90 ° with respect to the s and p linear polarization original directions . as a result , a phase shift of 0 retardation is introduced in the interference signal generated in the camera equipped with the analyzer that is rotated by 0 °, whereas a π / 2 retardation is generated at the interference signal recorded by the camera equipped with the analyzer that is rotated in 45 ° and a π retardation is generated at the interference signal recorded by the camera equipped with the analyzer that is rotated in 90 °. alternatively , instead of a 45 ° analyzer rotation shifts , the rotation shifts are made by α where mπ / 2 & lt ; α & lt ; π ( m + 1 )/ 2 and m is an integer . note that this approach is sometimes preferable because there is no need for the retardation wave plates which are located between the non - polarizing beam splitters and the cameras [ 46 ]. reference : [ s . suja helen , m . p . kothiyal , r . s . sirohi , achromatic phase shifting by a rotating polarizer , optics communications 154 , 1998 , 249 - 254 ] to further clarify this issue the jones matrices formalism is now used to show how the phase shift is generated . consider the jones vectors of rh and lh circularly polarized waves which represent the circular waves exiting the pqwp positioned in front of the tube lens ( element 33 , 133 , 233 , 333 and 433 in fig1 - 5 ): in equations 23 - 24 , φ 1 and φ 2 are the phases of the optical waves coming from the reference and sample arms of the interferometer . after the circular waves split at the beam splitters , they are incident on a linear polarizer which is rotated at an angle α where α is preferably 0 , 45 or 90 degrees . the jones matrix is now written for an analyzer rotated at α degrees with respect to the p polarization direction : the rh circular polarization wave transmitted through the analyzer is then expressed using the jones calculus formalism , giving : clearly , the phase delay introduced between the reference and sample waves is directly related to the rotation angle of the analyzer : δφ =∠ e lh , out −∠ e rh , out = φ 2 − φ 1 + 2α = δφ + β ( 28 ) the constant phase delay δφ appears common to all the interference signals , which are produced at the different cameras , while the β phase delay is different in each camera . for the camera equipped with the analyzer that is rotated at α = 0 °, the phase delay is β = 0 . for the camera equipped with the analyzer that is rotated at α = 45 °, the phase delay is β = 2α = 90 °= π / 2 rad . for the camera equipped with the analyzer that is rotated at α = 90 °, the phase delay is β = 2α = 180 °= π rad . 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 exceeding the scope of the claims . 1 . d . huang , e . a . swanson , c . p . lin , j . s . schuman , w . g . stinson , w . chang , m . r . hee , t . flotte , k . gregory , c . a . puliafito , j . g . fujimoto , “ optical coherence tomography ”, science , 254 , 1178 - 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