Patent Application: US-52339808-A

Abstract:
the present invention relates to an apparatus and a method combining achromatic complex fdoct signal reconstruction with a common path and dual beam configuration . the complex signal reconstruction allows resolving the complex ambiguity of the fourier transform and to enhance the achievable depth range by a factor of two . the dual beam configuration shares the property of high phase stability with common path fdoct . this is of importance for a proper complex signal reconstruction and is in particular useful in combination with handheld probes such as in endoscopy and catheter applications . the advantages of the present invention are in particular the flexibility to choose arbitrarily positioned interfaces in the sample arm as reference together with the possibility to compensate for dispersion .

Description:
fig1 . concept of a common path configuration . a prominent reflection ( r 1 ) close to the sample structure ( r 2 ) is used as reference signal . δz is the optical path difference between the sample interfaces r 1 and r 2 . fig2 . ( a ) dual beam principle . the output of an interferometer with a relative delay of 2δz iils between the two light beam intensities i r and i s ( interferometric light source ) is pre - compensating for the relative distance between r 1 ( reference surface ) and r 2 ( sample ). the configuration presents a small relative distance δz between reference surface ( r 1 ) and sample ( r 2 ) and up to four cross correlation terms might occur . the blue beam can be considered as the reference beam . ( b ) dual beam configuration presenting a large relative distance δz as compared to the depth range of the spectrometer ( or swept source respectively ) and only one cross correlation term occurs . fig3 . scheme illustrating the filling of a camera pixel in case of dual beam and standard fdoct respectively . fig4 . dual beam heterodyne fdoct . inlet a depicts synchronization of the line detector (( b ) trigger and ( c ) exposure time ) with ( a ) the beating signal . inlet b shows the reference arm added ( same fiber length as in sample arm ) and used for phase stability comparison (§ 4 ) between the dual beam and the standard configuration . see text for details . fig5 . ( 2 . 2 mb ) time sequence of 500 depth scans per tomogram at same position , using the setup depicted in fig4 . the movie is shown at 5 fps ( 7 × reduced speed with respect to original acquisition rate ). the dual beam signal ( red ) remains stable even if the fiber is perturbed whereas the signal peak corresponding to the standard setup ( blue ) is heavily perturbed . the dashed line indicates the standard deviation σ std of the phase fluctuations over one tomogram . the shown tomogram depth is approximately 400 μm ( in air ), snr ≈ 26 . 5 db . fig6 . tomogram of human fingertip with sweat gland , slice from 3d stack of fig7 ( a ), indicated by red frame . ( a ) direct fft on measured data , ( b ) with background correction employing averaging before fft , ( c ) differential complex reconstruction and ( d ) standard complex reconstruction with background correction . frame size : 2 . 5 mm lateral × 1 . 92 mm depth , in air . fig7 . ( a ) tomogram of human finger tip ( structure size : 2 . 5 mm × 2 . mm ×˜ 1 . 1 mm , in air ) with the lower wavy grey line delimiting the dermis - epidermis border and the grey frame indicating the position of the 2d tomogram shown in fig6 . ( b ) thickness map of epidermis in ( a ) ( top view , size : 2 . 5 mm × 2 mm , corrected for n tissue = 1 . 34 ). a dual beam configuration is an extension of a common path setup presented in the previous paragraph . instead of a single light beam travelling the common path to the reference ( r 1 ) and the sample ( r 2 ) as illustrated in fig1 , two beams delayed by an optical path length 2δz ils enter the common path and travel together to the reference and sample ( see fig2 ( a )). in this case , again , both reference and sample light share the same path and exhibit therefore high relative phase stability . this concept has been adapted for time domain oct in particular for precise eye length measurements in order to remove artefacts due to axial probe and motion [ 22 , 23 ]. in the simplest case , a single reflecting sample surface and one reference reflector cause four light fields with relative respective delays . depending on the optical distance δz between reference r 1 and sample r 2 and the introduced delay δz ils within the interferometric light source ( ils ) ( see fig2 ( a )), a perfect match between the two fields can be achieved , as illustrated in fig2 ( a ) for δz ils = δz 0 . as a matter of fact , all light fields present within the unambiguous depth range of the fourier domain system ( spectrometer - based or swept source ) are coherently summing up and contribute to the detected interference signal . this clearly has a strong adverse effect on the achievable system dynamic range . however , the potential of the dual beam configuration lies in the possibility to choose an arbitrarily distant interface in the common path as reference by matching the respective delay δz ils of the interferometric light source as illustrated in fig2 ( b ). in the most general way , the intensity of the total optical field impinging on the camera array in case of a single reflecting sample surface can be written as : being the detected reference and sample light fields respectively , with i r , s ( r , s ) = i r , s ρ r , s 2 being the light intensity contributions at the detector and ρ r being the amplitude reflectivity of r 1 in fig2 and ρ s the sample amplitude reflectivity ( r 2 in fig2 ), both accounting also for coupling losses , additional losses on optical elements and the diffraction grating efficiency . the upper indexes ( r ) or ( s ) indicate whether the contribution is coming from the reference beam i r or the sample beam i s of the ils respectively . k stands for the wave number and z r , s are the integral optical path lengths travelled by the respective light fields . the shading in eq . ( 1 ) visualizes the different contributions to the signal generation : the green shaded elements correspond to the four dc terms ; the yellow elements are the complex conjugates to the ones on the bottom left side of the dc terms ; the red shaded elements are zero if the reference surface is placed far away from the sample surface ( see fig2 ( b )) such that the coherence function becomes zero and no interference will occur anymore ; for the same reason the blue shaded elements would vanish as well due to the matched delay δz ils ≈ δz between the two fields e r and e s . hence one is finally left with the dc components as well as the actual sample - reference cross - correlation term in the lower left corner of eq . ( 1 ) together with its complex conjugate . the delay δz ils can be used to adjust the position of the sample structure within the unambiguous depth range . in case of the reference interface being close to the actual sample structure one encounters all terms given in eq . ( 1 ). one could introduce a dispersion unbalance between the reference ( r 1 ) and the sample ( r 2 ) field , and place double the dispersion into the reference arm of the ils . different undesired cross correlation terms would then be attenuated since they experienced double or quadruple dispersion whereas the actual structure terms were dispersion corrected . nevertheless one still suffers from the complex conjugate mirror terms that lead to a reduced maximum system depth range and might obstruct the structure reconstruction . the concept of heterodyne spectrometer - based fdoct was already discussed by bachmann et al . [ 11 ]: slight detuning of two acousto - optic frequency shifters in the reference and sample arm of the interferometer causes an achromatic beating signal of frequency ω =| ω r − ω s | detected by the sensor . by quadrature detecting this timely varying signal the full complex signal can be reconstructed and the unambiguous depth range is doubled . for this purpose the detector is locked to four times the beating frequency , resulting in π / 2 phase shifted copies of the time dependent interference signal components . the frequency - shifted light fields can be written as : with ω 0 being the light frequency and ω r , s the frequency shift induced by the acousto - optic frequency shifters . the resulting signal detected by the line scan camera therefore becomes , for the case where reference and sample are well separated ( see fig2 ( b )): i ccd ( k , t )= i r ( r ) ( k )+ i r ( s ) ( k )+ i s ( r ) ( k )+ i s ( s ) ( k )+ 2 √{ square root over ( i r ( r ) ( k ) i s ( s )( k ))}{ square root over ( i r ( r ) ( k ) i s ( s )( k ))}{ square root over ( i r ( r ) ( k ) i s ( s )( k ))}{ square root over ( i r ( r ) ( k ) i s ( s )( k ))} cos ( ωt − ψ ), ( 3 ) with ψ containing all time - independent phase terms . beside the additional dc terms i r ( s ) ( k ) and i s ( r ) ( k ), this signal is equal to a standard heterodyne fdoct configuration and has the same properties with respect to the suppression of mirror terms . dual beam heterodyne fdoct therefore allows for displacing the actual sample structure along the full doubled depth range by adjusting the distance δz ils . the dc and auto - correlation terms due to internal interferences between sample structure fields can be further eliminated using a differential complex signal reconstruction according to [ 11 ]: being the complex reconstructed interference signal of two adjacent spectra recorded at an arbitrary time instance t 0 . sensitivity and dynamic range ( dr ) are important issues in spectrometer - based fdoct . in practice , the dr depends on the reference light power being set close to the saturation level of the detector in order to achieve maximum sensitivity . it is evident that the dual beam configuration will present smaller sensitivity than standard fdoct due to the presence of a second strong dc signal i s ( r ) ( k ) not serving as reference signal for coherent amplification but reducing ccd dynamics . we would therefore like to comment more in detail on dr and sensitivity of the dual beam configuration as compared to the standard configuration in spectrometer - based fdoct . in § 2 . 1 we defined the beam intensities in the ils ( see fig2 ( a )) to be i r and i s respectively . the corresponding amount of generated photoelectrons [ 2 , 5 ] is then as the photon conversion factor with the reduced planck constant h , the vacuum light speed c , τ the integration time of the camera , η ( k ) the detector quantum efficiency , h kc the photon energy in vacuum , and a pixel the size of a detector pixel . we further express the total spectrally integrated number of photoelectrons as function of the spectral peak value as n tot = αn ( k 0 ), with k 0 being the center wave number where the detected spectrum is assumed to have its maximum . for a gaussian spectrum with the spectral fwhm being imaged onto nlm pixels , i . e . δk fwhm ( n ) = n / m , we have α gauss = δk fwim ( n ) √{ square root over ( π /( 4ln2 ))}, where n is the total number of detector pixels , and m defines the ratio of n to the fwhm . in case of a rectangular spectrum α rect = n . according to eq . ( 3 ) the signal term can be written as : n signal ( k )= n ac ( k )= 2 √{ square root over ( n ref ( k ) n sample ( k ))}{ square root over ( n ref ( k ) n sample ( k ))} cos ( ω t − ψ ). ( 5 ) with n ref ( k )≡ β ( k ) i r ( k ) ρ r 2 a pixel and n sample ( k )≡ β ( k ) i s ( k ) ρ s 2 a pixel . an additional assumption we make is that the presence of a reference surface in the sample arm does not influence the ratio of sample to reference reflectivity ρ s / ρ r , significantly , which means that the transmittance of the reference surface is high . with the approximation ρ r 2 & gt ;& gt ; ρ s 2 , we consider only those fields for the dc term that are reflected at the reference interface r 1 : where we define a load factor y as the ratio between dc level and the pixel saturation level n sat . this definition will be useful for our dynamic range discussion since the maximum sample signal will clearly depend on the remaining pixel capacity . we would further like to find the optimum ratio ξ between the ils intensities i r and i s . with the definition i s ≡ ξi r and eq . ( 6 ), the number of photoelectrons corresponding to the sample signal becomes : the signal - to - noise ratio ( snr ) can be defined as snr = s oct 2 /{ umlaut over ( σ )} 2 , with • being the time average , s oct = ft { n d ( k )}| z 0 being the signal peak at the position z 0 = δz − δz ils after fourier transform ( ft ) and { umlaut over ( σ )} the noise variance after ft . following [ 2 ] the squared oct signal reads s oct 2 =( αn ac ( k 0 )/( 2n )) 2 . the noise variances before and after ft are related via { umlaut over ( σ )} 2 = σ 2 / n . for shot - noise limited detection it can be expressed by the pixel - averaged total dc signal with eq . ( 6 ) as { umlaut over ( σ )} 2 ≈( 1 / n )( αγn sat / n ). together with eq . ( 7 ), the snr in this case becomes : we observe firstly that the snr increases linearly with the load factor γ . secondly , the snr expression reaches a maximum for ξ = 1 , or i r = i s . in words , the two interferometer arms of the ils should have the same intensity in order to achieve a maximum snr in dual beam interferometry . this is an important conclusion which will facilitate the following comparison of dual beam to standard fdoct . fig3 shows in an intuitive way the signal contributions on camera pixel level at spectral position k 0 with equal load factor γ ( detected signal when sample light is blocked ) where we assume the cosine in eq . ( 3 ) to be 1 . since maximum snr is achieved for both arms of the ils at equal intensity ( ξ = 1 ) we can write i r = i s = i / 2 . the dotted region indicates the light intensity reflected by the reference surface r 1 which does not contribute to coherent amplification — but still contributes to shot noise and burdens the sample with additional light power . hence , the effective reference signal for dual beam is only half that of the standard configuration with equal noise floor which results in a decreased snr . according to fig3 the snr can be expressed as : snr dual ∝ ρ s 2 i , and snr std ∝ 4ρ s 2 i , thus snr dual = snr std / 4 . ( 9 ) however , the maximum snr is the same for both configurations as it is limited by the saturation value of the camera pixel . this implies the relation for the maximum sample reflectivity assuming equal reference signal : the sensitivity σ on the other hand is defined as the inverse of the smallest detectable sample reflectivity ( ρ s ( min ) ) 2 i . e . σ = 1 /( ρ s ( min ) ) 2 for snr ≡ 1 . from eq . ( 9 ) and with the same load factor γ for both configurations , we can write : which is equivalent to a − 6 db disadvantage in sensitivity for dual beam as compared to standard fdoct . together with eq . ( 10 ) we can deduce the following relation : i . e . the ratio between maximum and minimum sample reflectivity remains the same . this relation leads us directly to the implications to dr which is defined as the ratio between the maximum to the minimum snr . for a given reference intensity and load factor γ , the maximum snr is achieved for the maximum sample reflectivity ( ρ s ( max ) ) 2 . since the minimum snr depends on the minimum sample reflectivity and considering eq . ( 12 ), the dr will remain the same for dual beam and standard fdoct : one could be tempted to increase snr by increasing the load factor γ ( cf . eq . ( 8 )). however , changing γ from e . g . 0 . 7 to 0 . 8 increases the snr by less than + 1 db while decreasing the dr already by − 4 db ( cf . eq . ( 13 )). the situation becomes even worse for larger load factors . a mach - zehnder like interferometer setup as shown in fig4 was built . the spectrometer consists of a collimator with a focal length of 80 mm , a transmission diffraction grating ( 1200 lines / mm ), an objective ( cl ) with a focal length of 135 mm and a line scan camera ( atmel aviiva m2 , 2048 pixel , 12 bit ) driven at 17 . 4 khz line rate . the light source ( ls ) is a ti : sapphire laser with center wavelength at 800 nm and a bandwidth ( fwhm ) of 130 nm . the effectively by the spectrometer detected bandwidth ( fwhm ) is 90 nm due to spectral transmittance losses along the total system , i . e . coupling losses . the maximum depth range ( after complex signal reconstruction ) is 4 mm and the axial resolution in air is 4 μm . the signal drop - off along the depth range is approximately − 7 db / mm with a sensitivity close to the zero delay of about 95 db with 2 × 1 . 1 mw light power incident on the sample and a load factor γ of 0 . 8 . using eq . ( 8 ) the theoretical sensitivity is calculated to be σ dual ≈ 101 db with ξ = 1 , α = 800 , γ = 0 . 8 , n sat ≈ 1 . 2 · 10 5 and ρ r 2 ≈ 1 . 4 · 10 − 3 . the reference arm length can be adjusted by means of a translation stage ( ts ). beam splitting and recombination is realized by a fiber coupler ( fc ) and a 50 : 50 beam splitter ( bs ) respectively . the peculiarity of the proposed system is the light source module comprising an interferometer with two acousto - optic frequency shifters ( aofs ) ( aa opto - electronic sa with optical packaging by cube optics ag , ω r = 2π · 100 mhz , ω s = 2π · 100 mhz + 4 . 35 khz ). since our acousto - optic elements are based on a birefringent crystal ( tellurium dioxide ( teo 2 )) light has to enter these devices in a controlled , linear polarization state . in addition , in order to maximize interference contrast , the light field states at the common path input have to be oriented accordingly , employing polarization control paddles ( pc ) ( see fig4 ). the sample is finally illuminated by two frequency shifted copies of the original light field . the dispersion compensation ( disp ) in the reference arm of the ils pre - compensates for the additional dispersion induced by the wedge plate and the lens f 2 of the hand piece . the hand piece consists of a scanning unit based on a single mirror tip / tilt scanner ( x / y scan ) [ 24 ]. it is placed in the back focal plane of lens f 2 , allowing for two - dimensional transverse scanning of the sample . the glass wedge with a deviation angle of 2 ° ( θ ≈ 3 . 1 °) is used in order to create a single well defined reference reflex at the front surface . such a configuration can be seen as auto - collimation and the reference signal intensity is adjusted by slightly tilting the glass wedge . the theoretical beam width on the sample is 26 . 5 μm ( 1 / e 2 - intensity ) with a rayleigh range of 1 . 3 mm and is defined by the ratio of the focal lengths ( f 1 = 15 mm , f 2 = 75 mm ) used in the handheld probe and the mode field diameter of the one meter single mode ( sm ) fiber . with a transverse scanning speed across the sample of 40 mm / s the resulting transverse over - sampling is approximately 12 ×. in order to properly reconstruct the complex signal as described in § 2 . 2 , special attention has to be paid to the synchronization of the camera with the resulting beating frequency ( cf . inlet a of fig4 ). the complex differential reconstruction needs two pairs of complex reconstructed spectra ĩ ( k ) ( thus in total four by 90 ° retarded acquisitions ) which is realized by externally triggering the camera frame grabber ( see ( b ) in inlet a of fig4 ). frequency shifters and trigger signal generators are linked and synchronized via a common 10 mhz time base . the exposure time τ ( see ( c ) in inlet a of fig4 ) is 45 μs . the complex spectra ĩ ( k ) ( see § 2 . 2 ) are finally reconstructed using two successively recorded spectra as indicated by ( d ) in inlet a of fig4 . with the extension shown in inlet b of fig4 we had the flexibility to compare the phase stability of the following three configurations : common path : by blocking the dual beam arm and placing a thin glass plate instead of the mirror in inlet b . dual beam : by blocking the external reference arm ( inlet b ). for phase stability measurement a mirror was used as sample without x / y scanner . standard : cross - correlation between mirror of inlet b and mirror at sample position of the dual beam arm ( top right corner in fig4 ). dual beam and standard fdoct could be measured simultaneously by adjusting the two respective reference signals r 1 ( for dual beam ) and mirror of inlet b ( for standard ) to 0 . 4 each . in order to demonstrate the advantage of dual beam versus standard fdoct in terms of phase stability , the previously described three configurations were used ( fig4 ). for each configuration the snr of the signal peak was adjusted to approximately 26 . 5 db . the phase fluctuations at the signal peak position were measured while the system was unperturbed and perturbed respectively . the perturbation consisted in bending and moving the sample arm fiber guiding during measurement . the resulting standard deviations of the phase fluctuations σ δ , φ are shown in table 1 . the measured values are close to shot noise limited phase stability defined by the relation σ δ , φ =( snr ) − 1 / 2 [ 25 ]. for the perturbed case of the standard fdoct configuration no clear value could be measured since the phase fluctuations are strongly varying ( see fig5 ). the phase signals were extracted after fft at the mean signal peak positions . by touching and bending the sm fiber , the signal of the standard setup is heavily perturbed , even resulting in up to 100 μm signal peak shift in depth . this displacement is caused by a change in optical path length due to a stress - induced change in refractive index . both signal peaks were again adjusted to approximately the same snr = 26 . 5 db . the strong fluctuations of the standard signal peak intensity are mainly due to fringe washout and stress - induced polarization state changes in the perturbed fiber , resulting in reduced interference fringe contrast . these measurements proof clearly the advantage of dual beam fdoct over standard fdoct for employing fiberized handheld applicators . in the following we demonstrate the feasibility of the introduced dual beam fdoct principle to perform in - vivo imaging of human skin on the finger tip of a male subject . for this task we employed a fiberized handheld probe with a single mirror tip / tilt scanner . the reference reflex was realized by placing a wedge glass plate into the collimated beam before the scanner , generating a stable reference light intensity . attention had to be paid to the positioning of the beam with respect to the scanner pivot since slight misalignment introduces unwanted phase shifts during scanning . the total distance δz between reference and sample was 200 mm which had to be pre - compensated by adjusting δz ils within the ils . the recorded tomograms consist of 1100 depth scans each , covering a transverse range of 2 . 5 mm . the measurements had been performed by first adjusting the focal plane to the zero delay using a mirror and then placing the sample structure across this position . the recorded signal was reconstructed following the differential complex scheme from § 2 . 2 ( see fig6 ( c )). the dynamic range within the tomogram is about 40 db with a system sensitivity of 95 db . one observes that the dc term is strongly suppressed as compared to its original amplitude ( directly after fast fourier transform ( fft )). if we define the dc suppression ratio as dc suppress ≡ dc 2 × 2 / dc fft , with dc 2 × 2 being the dc signal value in fig6 ( c ) and dc fft the one in fig6 ( a ) we have dc suppress =− 47 db . the fact that the dc term is not fully suppressed is explained by the presence of slight intensity fluctuations throughout the tomogram . these fluctuations were measured to be in the khz - range with a standard deviation of 0 . 33 %. in fig6 we compare the differential complex reconstruction technique ( eq . ( 4 )) ( fig6 ( c )) to the standard complex reconstruction based on two adjacent lines ī ( k , t 0 ) with background correction ( fig6 ( d )). the background for the tomogram is obtained by averaging of all transversally recorded spectra . the brightness of the tomograms was adjusted by first normalising the intensity to that of a common bright structure ( sweat gland ) and then setting the minimum of the intensity scale bar to the calculated noise floor . the maximum scale bar value is given by the highest intensity in the tomogram . this results in a linear gray scale spanning over a dr of 28 . 5 db for standard complex reconstruction and 31 db for the differential complex reconstruction . as expected , the snr for the differential complex method is better by approximately + 3 db . as compared to the standard complex reconstruction . it can also be observed that dc suppression works slightly better for the differential complex approach ( fig6 ( c ) and ( d )) the tomogram in fig6 ( a ) shows the measured data with standard reconstruction employing straight forward fft reconstruction . one can clearly see that the structure had been measured across the zero delay due to the presence of mirror structures . fig6 ( b ) finally shows a standard reconstruction as in fig6 ( a ) but with background subtraction in post - processing . again , a slight dc term remains together with sample structure obstructing mirror terms . investigating the mirror term suppression within different 2d tomograms for bright scattering structures , the suppression ratio can be measured to be better than − 15 db . higher over - sampling would increase the suppression ratio as one remains tighter within the speckle pattern [ 25 ]. fig7 ( a ) shows a 3d data set of a human finger tip , consisting of 66 2d tomograms and reconstructed using the differential complex scheme . the total recording time was 4 . 5 s . by performing edge detection on each individual 2d tomogram , the user has access e . g . to a thickness map of the epidermis as illustrated in fig7 ( b ). the grey frame in fig7 ( a ) indicates the position of the 2d tomograms presented in fig6 within the 3d data cube . the rudimentary dc peak at the zero - delay , visible in fig6 ( c ), was removed from fig7 ( a ) by first setting it to zero and afterwards interpolating the intensities in post processing . the demonstrated principle can easily be adapted for endoscopic oct as well as for common path ophthalmic imaging . in particular the phase stability can be enhanced by placing the reference to one of the scanning prism interfaces in an endoscope , or by using actually a sample reflection such as at the cornea front surface as reference [ 26 ]. in the latter case one could achieve complete axial proband motion suppression which is especially interesting for functional imaging extensions such as doppler fdoct [ 27 - 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