RU2531764C2 - Method of forming of equidistant by optical frequency readouts at spectral interference reception of backward scattered of ultrabandwidth radiation - Google Patents

Abstract

FIELD: physics, optics.

SUBSTANCE: method includes recording of optical spectrum of the sum of interfering waves at different values of mutual delay, separation of modulating functions corresponding to mutual delays, determination of nonlinearity of distribution of their phase, calculation of the correction table, registration of optical spectrum of the sum of interfering waves with unknown mutual delays, application of the correction table to the optical spectrum. The segmented correction table with decreased number of determined readouts of registered optical frequencies is calculated, the registered array is divided into the respective segments, the spatial distributions for each segment are calculated using Fourier transform, each distribution is additionally multiplied by values of the segmented correction table, the restored values of amplitude of an optical spectrum are calculated using the inverse Fourier transform and combined by adding of restored values for obtaining of spectral readouts, equidistant by an optical frequency.

EFFECT: avoidance of aberrations of the shape of spread function due to the use of Fourier processing of registered values of optical spectra.

2 cl, 2 dwg

Description

The invention relates to optical spectrometry (spectroscopy) and can be used to generate samples that are equidistant in optical frequency with spectral interference reception of ultra-wideband backscattered radiation.

The well-known technique for recording spectral components equidistant in optical frequency in a diffraction grating spectrometer allows one to compensate up to two orders of non-linearity of the relationship between the wave number of the received spectral component k and its location on the plane of photodetectors x. This allows, when reconstructing the profile of the scattering structure of the object, to avoid broadening of the hardware function by more than two times at the maximum realizable depth of observation. However, when visualizing OCT images, as a rule, a logarithmic scale is used, which is due to the exponential nature of the dependence of the amount of radiation returned in the opposite direction on the depth of the diffuser in the medium. In this case, the broadening that occurs in the hardware function at the level of 0.1 maximum value and below becomes visually noticeable. To eliminate this broadening, a comprehensive method is proposed for correcting the nonequidistance of a diffraction grating spectrometer using an additional compensating element.

The non-equidistance of the spectrometer and the effect of material dispersion in the arms of the interferometer can be represented as the nonlinearity of the dependence of the modulation phase of the envelope of the optical spectrum of two interfering waves - the reference and scattered by a single scatterer. In this case, the spectrum of the interfering waves turns out to be modulated according to the harmonic law, and from the sequence of spectral readings we can obtain the dependence of the argument:

2z ₀ k (x) = φ (x, z).

In this consideration, the received spectrum can be represented as a normal signal, digitized with the fulfillment of Kotelnikov's theorem, having constant and modulated components. The modulation frequency of the latter is proportional to the optical path difference in the interferometer. Using the registration mechanisms of the complex amplitude of the optical spectrum or the search algorithms for Hilbert-conjugate signals, it is possible to restore the value of the argument for each photodetector. This makes it possible to determine the dependence of the nonequidistance of the received spectral components on the number of the photocount and to oversample the received values. In the general case, the dependence of the argument φ (x, z) on the parameters x and z can be represented as a power series in the parameter z / δz:

, $$\varphi \left(x,z\right)=A\left(x\right)+B\left(x\right)\frac{z}{\delta z}$$

,

where δ _z is the longitudinal resolution of the OCT system, and the parameter z / δz acts as a discrete dimensionless modulation frequency of the envelope of the optical spectrum. The first term A (x) has the meaning of the material dispersion characterizing the optical path of the OCT setup. The second term B (x) is the non-equidistance of the registration of spectral components in the spectrometer, which leads to the greater the error in determining the location of the scatterer, the higher the modulation frequency of the envelope of the spectrum and, accordingly, the greater the optical path difference between the reference and object waves.

There is a known method of generating optical frequency equidistant samples, known in the article "Real-time resampling in Fourier domain optical coherence tomography using a graphics processing unit", Jornal of Biomedical Optics, May / June 2010. V.15 (3), P. 030511 -1, authors Sam Van der Jeught, Adrian Bradu, and Adrian Gh. Podoleanu. The formation of samples that are equidistant in optical frequency is as follows. The nonlinearity of the phase distribution of the modulating functions is determined, the position of the points of the new discretization is established by the obtained distribution. The value of the function at these points is determined using interpolation algorithms. The method has limited applicability, since when registering spectra with inhomogeneities having a spectrum close to the limiting (Nyquist criterion), reconstruction is performed with significant distortions, which are manifested in the appearance of a high quasi- noise base in the inhomogeneities.

The closest analogue of the developed method is a method of generating samples that are equidistant in optical frequency, known in the article "Signal processing with unequally spaced data in Fourier-Domain Optical Coherence Tomography", SPIE Proc. 2010. V.7554, P. 75542W1-4, authors Sebastien Vergnole, Daniel Levesque, Sherif S. Sherif, Guy Lamouche. The optical spectrum of the sum of the interfering waves is recorded for at least two different preset values of the mutual delay, the modulation functions corresponding to the preset mutual optical delays of the interfering waves are extracted in the obtained optical spectrum, the phase distribution of the modulating functions is nonlinear, the correction table containing the values of the complex factors for all recorded optical frequencies of the spectrum and all possible delays between the interfering waves within the range of observation. The optical spectrum of the sum of the interfering waves is recorded with a set of unknown mutual delays and the correction table is applied to the optical spectrum of the sum of the interfering waves with a set of unknown mutual delays. The article discusses the work of three algorithms for numerically correcting the nonequidistance of the distribution of the values of the spectral amplitude of the optical field by the wave number of the separately recorded spectral component. An effective decrease in the artifact broadening of the reconstructed hardware image function is shown. However, the quality of restoration does not satisfy the conditions for displaying the restored distribution on a logarithmic scale in intensity (a substantial broadening is observed in the restored profile at the base).

The problem to which this invention is directed is to develop a method for generating samples that are equidistant in optical frequency with spectral interference reception of backscattered ultra-wideband radiation, in which spectral samples are obtained that are equidistant in optical frequency. In addition, this method is designed to effectively suppress artifacts in the OCT image due to the broadening of the hardware function that is restored during nonequidistant Fourier transform corresponding to the deep scattering profile of the medium under study. Using this method eliminates the distortion of the shape of the hardware function in studies related to the need for Fourier processing of the recorded values of the optical spectra.

The specified technical result is achieved due to the fact that the developed method of generating samples that are equidistant in optical frequency with spectral interference receiving backscattered ultrawideband radiation, as well as the method that is the closest analogue, involves recording the optical spectrum of the sum of the interfering waves with at least two different preset the values of the mutual delay, the selection in the obtained optical spectrum of modulating functions corresponding to updated mutual delays of the interfering waves, determination of the nonlinearity of the phase distribution of the modulating functions, calculation of a correction table containing the values of complex factors for all recorded optical frequencies of the spectrum and all possible delays between the interfering waves included in the observation range, registration of the optical spectrum of the sum of interfering waves with a set of unknown mutual delays, applying a correction table to the optical spectrum of the sum of interfering waves with a set of nei known mutual delays.

New in the developed method for the formation of samples that are equidistant in optical frequency for spectral interference reception of ultra-wideband backscattered radiation is that a segmented correction table is calculated with a reduced number of independently determined samples of recorded optical frequencies, a recorded array of optical spectrum amplitudes of the sum of interfering waves with a set of unknown mutual segment delays in accordance with the partition adopted for a segmented correction table, then the spatial distributions for the values of each segment are calculated using the Fourier transform, then each distribution is multiplied by the values of the segmented correction table and the reconstructed values of the amplitude of the optical spectrum of the sum of the interfering waves are calculated using the inverse Fourier transform, the reconstructed amplitude values are combined by adding optical spectrum of the sum of interfering waves to obtain spectral tschetov, equidistant from the optical frequency.

New in the developed method for generating samples that are equidistant in optical frequency with spectral interference receiving backscattered ultra-wideband radiation according to claim 2, is that the correction table is segmented in the space of mutual delays of the interference waves included in the observation range, and a segmented correction table with a reduced number is calculated independent samples in the space of mutual delays of the interfering waves included in the observation range I, then the obtained values are subjected to the Fourier transform, the resulting array of values is partitioned into segments in accordance with the partition adopted for the segmented correction table, after which the restored values of the amplitude of the optical spectrum of the sum of the interfering waves are calculated for each segment using the inverse Fourier transform, multiply each distribution by values of the segmented correction table and combine, by adding, the restored values of the amplitude of the optical spectrum Ummah interfering waves to obtain spectral samples at equidistant optical frequency.

Figure 1 presents a schematic optical diagram of an experimental setup that implements the simultaneous registration of quadrature components in spectral OCT.

Figure 2 presents the U-shaped function of the window with smooth edges.

Figure 1 presents a schematic optical diagram of an experimental setup that implements the simultaneous registration of quadrature components in spectral OCT. The optical scheme is a diffraction grating spectrometer with a compensating element made in the form of an optical prism.

To measure non-equidistance parameters, two values of the optical spectrum of the sum of interfering waves are recorded in which the predefined position of the reflector in the object arm of the device is set different relative to the reference plane of the reference reflector. This can be accomplished both by successive movement of the reflector in the object shoulder, and by using an object having several reflectors spaced by an amount not less than 10 times the resolution of the system. The received signal is filtered out to obtain a quasi-harmonic distribution. In the case of a composite reflector, individual dependencies are formed that modulate the optical spectrum of the function for each of the individual space-separated reflectors.

The values of parameters A (x _i ) and B (x _i ) (where i is the number of the photodetector element) are found by solving a system of linear equations for each x when registering the values of the argument φ (x _i , z _1,2 ) for two different values of the delay z ₁ and z ₂ :

The obtained values are used to form a correction table, the elements of which are determined by the expression

after which the elements of the correction matrix are segmented according to the rule:

where J is the number of elements in one segment of the partition, n is an integer. The elements of the segmented matrix m _{i, j} are used to correct the spectral distributions in 3 stages.

At the first stage, the adopted spectral implementation with a compensated autocorrelation component is reduced to a complex form using known phase methods or the Hilbert transform.

At the second stage, the influence of the parameter A (x _i ) is corrected by multiplying the entire spectral realization by a factor

. Для этого вся спектральная реализация подвергается преобразованию Фурье. Полученная реализация умножается на П-образную функцию окна с центром в точке $$j=\left(n+\frac{1}{2}\right)J$$

и сглаженными краями (фиг.2). Ширина плато функции окна при этом подбирается экспериментально по достижению наименьшей толщины аппаратной функции после коррекции. Сглаженный край формируется таким образом, чтобы в любой точке j выполнялось условиеAt the third stage, segmented correction of the influence of the parameter is performed $$B(x{}_i)\frac{z_j}{\delta z}$$

. To do this, the entire spectral realization undergoes a Fourier transform. The resulting implementation is multiplied by the U-shaped window function centered at a point $$j=\left(n+\frac{\mathrm{one}}{2}\right)J$$

and smooth edges (figure 2). The plateau width of the window function is selected experimentally to achieve the smallest thickness of the hardware function after correction. The smoothed edge is formed so that at any point j the condition

The implementation thus obtained is subject to the inverse Fourier transform. In the space of the optical spectrum, realization is multiplied by a factor

where n is the number of the U-shaped window in the space z. A similar procedure is performed for all segments P _n , as a result of which, after summing over all individual implementations, a resampled optical spectrum that is equidistant in optical frequency is restored. By the repeated Fourier transform, the corrected implementation returns to the space of metric coordinates, while the width of the hardware function is narrowed to the limiting calculated one corresponding to the equidistant spectrum received.

, а также коррекция влияния параметра A(x_i) осуществляются по принципу, описанному выше. Коррекция влияния параметра $$B(x{}_i)\frac{z_j}{\delta z}$$

осуществляется следующим образом.In the particular case, the calculation of the parameters A (x _i ) and $$B(x{}_i)\frac{z_j}{\delta z}$$

, as well as the correction of the influence of the parameter A (x _i ) are carried out according to the principle described above. Parameter Influence Correction $$B(x{}_i)\frac{z_j}{\delta z}$$

carried out as follows.

Elements of the correction matrix are segmented according to the rule:

where I is the number of elements in one segment of the partition, n is an integer.

и сглаженными краями (фиг.2). Ширина плато функции окна при этом подбирается экспериментально по достижению наименьшей толщины аппаратной функции после коррекции. Формирование сглаженного края описано выше.The spectral implementation is partitioned into shorter implementations using multiplication by the U-shaped function of the window centered at a point $$i=\left(n+\frac{\mathrm{one}}{2}\right)I$$

and smooth edges (figure 2). The plateau width of the window function is selected experimentally to achieve the smallest thickness of the hardware function after correction. The formation of a smooth edge is described above.

The resulting implementation is subject to the Fourier transform. In the space of permissible mutual delays of interfering waves, the spatial realization is multiplied by a factor

where n is the number of the U-shaped window in the space k. A similar procedure is performed for all segments P _n . Each corrected implementation is subjected to the inverse Fourier transform, and after summing over all individual implementations, a resampled optical spectrum that is equidistant in optical frequency is restored. By the repeated Fourier transform, the corrected implementation returns to the space of metric coordinates, while the width of the hardware function is narrowed to the limiting calculated one corresponding to the equidistant spectrum received.

In a specific implementation of the method of generating samples that are equidistant in optical frequency with spectral interference receiving backscattered ultrawideband radiation, a broadband radiation source with a central wavelength of 1277 nm and a radiation bandwidth of 70 nm was used; an optical spectrometer consisted of a diffraction holographic luminal volumetric grating with a stroke frequency of 1145 lines per mm and an optical prism made of K8 glass with an angle at the apex of 60 degrees; Spectral values were recorded using a linear photodetector with 512 elements. As a result of using the developed method for the formation of samples that are equidistant in optical frequency with the spectral interference reception of ultra-wideband backscattered radiation, a residual non-equidistance of 0.14% is reached with respect to the initial level of 3.5%.

Thus, the developed method allows the formation of samples that are equidistant in optical frequency with spectral interference reception of ultra-wideband backscattered radiation. In addition, this method allows you to effectively suppress artifacts in the OCT image due to the broadening of the hardware function that is restored by the nonequidistant Fourier transform corresponding to the deep scattering profile of the medium under study. Using this method eliminates the distortion of the shape of the hardware function in studies related to the need for Fourier processing of the recorded values of the optical spectra.

Claims (2)

1. A method of generating samples that are equidistant in optical frequency for spectral interference reception of ultra-wideband backscattered radiation, including recording the optical spectrum of the sum of the interfering waves at least two different preset values of the mutual delay, isolating modulating functions corresponding to the preset mutual delays of the interfering waves in the obtained optical spectrum , determination of the nonlinearity of the phase distribution of the modulating functions, calculation to an adjustment table containing the values of complex factors for all recorded optical frequencies of the spectrum and all possible delays between the interfering waves included in the observation range, recording the optical spectrum of the sum of interfering waves with a set of unknown mutual delays, applying the correction table to the optical spectrum of the sum of interfering waves with a set of unknown mutual delays, characterized in that they calculate a segmented adjustment table with a reduced number of independent of the simulally determined samples of the recorded optical frequencies, the registered array of optical spectrum amplitudes of the sum of the interfering waves with a set of unknown mutual delays into segments is partitioned in accordance with the partition adopted for the segmented correction table, then the spatial distributions for the values of each segment are calculated using the Fourier transform, after which multiply each distribution by the values of the segmented adjustment table and calculate the reconstructed The obtained values of the amplitude of the optical spectrum of the sum of the interfering waves using the inverse Fourier transform are combined by adding the reconstructed values of the amplitude of the optical spectrum of the sum of the interfering waves to obtain spectral samples that are equidistant in optical frequency. 2. A method of generating samples that are equidistant in optical frequency during spectral interference reception of ultra-wideband backscattered radiation, including recording the optical spectrum of the sum of the interfering waves at least two different preset values of the mutual delay, isolating modulating functions corresponding to the preset mutual delays of the interfering waves in the obtained optical spectrum , determination of the nonlinearity of the phase distribution of the modulating functions, calculation to an adjustment table containing the values of complex factors for all recorded optical frequencies of the spectrum and all possible delays between the interfering waves included in the observation range, recording the optical spectrum of the sum of interfering waves with a set of unknown mutual delays, applying the correction table to the optical spectrum of the sum of interfering waves with a set of unknown mutual delays, characterized in that the segmentation of the values of the correction table is carried out in a mutual space of many delays of the interfering waves included in the observation range, a segmented correction table is calculated with a reduced number of independent samples in the space of mutual delays of the interfering waves included in the observation range, then the obtained values are subjected to the Fourier transform, the resulting array of values is divided into segments in accordance with the partition adopted for a segmented adjustment table, after which the restored values of the optical amplitude amplitude are calculated for each segment ktra amount interfering waves using inverse Fourier transform on the multiplied value of each distribution segmented correction table by adding and combining the recovered value of the amplitude of the optical spectrum of the sum of the interfering wave to obtain spectral samples at equidistant optical frequencies.

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