RU2743973C1 - Method for determining frequency and amplitude of modulation of a phase of a wave front generated by vibrations of a cell membrane - Google Patents

Abstract

FIELD: physics.SUBSTANCE: invention relates to the field of interferometry of phase dynamic objects. Method for determining frequency and amplitude of modulation of a wave front phase generated by vibrations of a cell membrane involves dividing the radiation of a coherent source into two beams, one of which passes through the analyzed object and is displayed on the recorder, and the second passes along the reference channel and also falls on the recorder, where both beams interfere, and change in the interference pattern indicates changes in the phase of the wave front. Reference channel of the interferometer during registration of the interferogram is adjusted so that the value of the phase difference in the selected region is equal to zero. Part of the wave front passed through the analyzed cell is directed by the optical system to the phase modulator. By means of the phase modulator the transmitted radiation with frequency ω1and modulation depth m1, then modulator image is projected by optical system on recorder, wherein to compensate for phase displacement caused by external vibrations, selecting a portion of the wave front not passed through the object, and directed by the same optical system to a phase modulator, which modulates this portion of the wave front by frequency ω2and modulation depth m2. Then image of this part of phase modulator is projected onto recorder, obtained two electric signals are multiplied, and the resulting signal is subjected to spectral analysis, wherein from the signal spectrum, selecting a frequency equal to the difference in the optical radiation modulation frequencies passed through the object, and optical radiation that has not passed through the object, and near this frequency, a symmetrical pair of frequencies with an opposite phase value is searched for, by frequency coordinates of which frequency is determined, and by value - amplitude modulation phase of the wave front in the selected cell region.EFFECT: technical result consists in providing the possibility of increasing accuracy of measuring frequency and amplitude of membrane cell vibrations.1 cl, 2 dwg

Description

The present invention relates to the field of optoelectronic measurements, namely, to interferometry of phase dynamic objects and can be used in biology and medicine to study the vibration frequency of the shape and refractive index of living cells, which determine its optical thickness.

As you know, living cells are characterized by local oscillations of the membrane, also called flicker or dynamic fluctuations of the membrane. Despite the long history of studying such oscillations, and numerous works devoted to their spectral analysis and modeling, the molecular and cellular mechanisms of this phenomenon are still being discussed. It is important that the fact that the flicker amplitude is determined by the membrane and depends on the state of the cell cytoskeleton is not questioned: changes in the elastic properties of the membrane and cytoskeleton complex or the formation of local bends (protrusions) of the membrane due to rearrangement of the spectrin network (for example, cleavage from the nodal complex of one of the spectrin strands and the formation of a nonplanar network configuration). It is also possible to analyze the nature of the noise, highlighting certain vibration frequencies and evaluating with their help the dynamic processes occurring in the cells. This process is very complex and requires significant human and machine labor. Understanding the origin of the cell and determining the characteristics of the oscillation of its membrane can provide information about the functional states of erythrocytes under normal and pathological conditions. An equally important task is to change the density inside the cell, associated with the synthesis and decay of protein, which also leads to periodic changes in the phase that has passed through the wavefront object. It is practically impossible to separate the influence of membrane oscillations and density fluctuations inside the cell from optical measurements; therefore, the change in the optical thickness of the cell, which characterizes both of these quantities, is determined. Various methods are used to study the dynamics of living cells, such as phase contrast microscopy, reflected interference contrast microscopy, light scattering, and a technique based on point dark-field microscopy. However, these methods are not inherently quantitative from the point of view of absolute measurements and do not allow one to study the distribution of membrane vibrations and fluctuations of the refractive index inside the cell.

Recently, new imaging techniques called quantitative phase microscopy have emerged and have demonstrated their ability to provide accurate three-dimensional imaging of transparent living cells. The use of this method to study the temporal fluctuations of the membrane and density inside the cell is an urgent problem, the solution of which is being addressed by research teams in various countries.

A number of methods for studying vibrations of the cell membrane are known from the prior art; however, the most convenient and popular are optical methods based on interference microscopy.

One of the analogues of the proposed technical solution is a method for determining density fluctuations inside a cell, which also leads to modulation of the wavefront phase, implemented in the automated interference microscope "Airiskan" and developed on the basis of the MII-4 microinterferometer according to the Linnik scheme (Tychinsky V.P. Coherent phase microscopy of intracellular processes // Uspekhi fizicheskikh nauk. - 2001. - V. 171. - No. 6.). A He-Ne laser was used as an illumination source. The interference image is recorded using a coordinate-sensitive photodetector - a dissector, which is an image converter with an external photoelectric effect (without charge accumulation) with a photomultiplier tube and magnetic transfer of an electron flux into the plane of the diaphragm with a small hole. A compensation method is implemented for automated interpretation of interferograms. The phase modulation of the reference radiation beam was performed using a mirror with a piezoelectric element. The scanning area varied in the range of 5-50 microns. The maximum image size is 1024 × 1024 pixels. The input time for one pixel is 1 ms. The capture time of the entire image varies from 10 s (5 × 5 μm) - 16 min (50 × 50 μm). Thus, this microscope, which has a long image input time, allows one to study only stationary phase objects, or to carry out local dynamic measurements - at several points for dynamic objects. The main disadvantages of this method are: the need to restore the phase of interferograms, which leads to additional errors in the algorithm; the impossibility of compensating for the intrinsic phase noise of the device, due to local phase measurements only in the area of the object; insufficient discriminating ability in spectral analysis, because it is necessary to determine the local maximum against the background of noise.

As another analogue of the proposed method for determining the frequency and amplitude of the phase modulation of the wavefront created by vibrations of the cell membrane, consider a holographic microscope designed to analyze vibrations of the erythrocyte membrane and described in the work of V. Rappaz, et al., Spatial analysis of erythrocyte membrane fluctuations by digital holographic microscopy, Blood Cells Mol. Dis. (2009), doi: 10.1016 / j.bcmd.2009.01.018. The experimental setup that implements this method is a modified configuration of the Mach-Zehnder interferometer. The light that passes through the object and is collected by the lens forms an object wave that intersects with the reference wave R to produce a hologram, which is recorded by a digital camera. Holograms are recorded in off-axis geometry i.e. the reference wave reaches the recorder with a small angle of incidence (angle 1 °) relative to the direction of propagation of the object wave. The reconstruction procedure consists in the numerical reconstruction of the hologram from the digital standard of the reference beam of off-axis geometry. This reconstruction of the process also allows you to correct the aberration of the wavefront and restore the phase of the wavefront that passed through the object. To reduce the noise, the time summation of four consecutive images reconstructed from the holograms is used. This makes it possible to partially compensate for the experimental noise (time shift, vibration, etc.). To estimate the amplitude of membrane oscillations of the phase, the temporal oscillations are determined by the standard deviation of the phase of the signal point in the image over a certain period of time of registration. Spectral analysis of time series is used to determine the frequency of oscillations. The disadvantage of this method is: firstly, there is practically no compensation for distortions associated with the phase noise of the device, and secondly, the presence of a significant error in the reconstruction of the phase from the hologram associated with the algorithms for digital reconstruction of holograms, which leads to additional phase noise, and thirdly, analyzing the signal spectrum and finding a single peak in the spectrum in the presence of noise is challenging.

The closest analogue or prototype of the proposed method can be considered the following method for measuring phase fluctuations: Optical Measurement of Cell Membrane Tension, Gabriel Popescu, 1 Takahiro Ikeda, 2 Keisuke Goda, 3 Catherine A. Best-Popescu, 4 Michael Laposata, 4 Suliana Manley, 5 Ramachandra R. Dasari, 1 Kamran Badizadegan, 1, 4 and Michael S. Feldl, PHYSICAL REVIEW LETTERS PRL 97, 218101 (2006). In it, radiation from a HeNe laser is collimated and separated into an object (S) and a reference (R) channel to form a modified Mach-Zehnder interferometer. The object beam provides an illumination field for an inverted microscope. The spherical lens is positioned in such a way that the image of the sample is formed in the plane of the CCD recorder. The reference field is collimated and expanded using a telescopic system consisting of another objective of the microscope and the same lens of the plane of the CCD recorder.

Using high-frequency spatial filtering and the Hilbert transform, at each point of the interferogram, a spatially changing phase associated with the cell image is reconstructed. To suppress the intrinsic phase noise, a feedback system is used that blocks the interferometer in the interference band as follows. A small mirror deflects some of the beams before they reach the recorder. Two beams propagating along the axis are spatially filtered by the aperture and detected by a photodiode. After the interferogram processing system, phase changes are determined and a control signal is generated, which corrects the length of the reference arm through the control of the piezo mirror in the reference channel. The disadvantages of this method are that, firstly, phase reconstruction errors, which lead to phase noise, are not excluded, and secondly, the low discrimination of the desired frequency and amplitude of phase oscillations is preserved, since it is necessary to search for a single maximum in the spectrum in the presence of noise.

Thus, among the main disadvantages of interference systems known from the prior art, used to determine the frequency and amplitude of phase front oscillations, the following three can be distinguished:

1. Determination of the phase change is carried out after the reconstruction of the phase from the interference pattern, which leads to a significant increase in the registration time of one phase front during reconstruction using the method of phase steps or an increase in the measurement error when using the Fourier method (Hilbert transform) and a decrease in the investigated frequency band of oscillations of the wave front.

2. The influence of external influences on the interference pattern, such as vibration and periodic displacements of optical elements, which are called the intrinsic phase noise of the device. They also distort the measurement of the natural frequency of the object. Especially these vibrations have a significant effect when tuning the interferometer to bands of finite width, which is necessary for applying the Fourier method or restoring holograms during phase reconstruction.

3. Poor discriminating ability of the spectrum of the phase fluctuation signal in the investigated area of the object. This is because the spectrum is a local maximum against the background of a wide quasi-white spectrum caused by recorder noise and phase reconstruction errors, which has harmonics associated with the reconstruction algorithm. It is also essential that, when analyzing low frequencies, it is difficult to separate a wide spectrum of zero frequencies and a small local maximum of the desired frequency.

The technical problem solved by the claimed invention consists in the elimination of these disadvantages and at the same time in the expansion of the measurement range of the oscillation frequencies of the phase of the wavefront that passed through the cell and created by the oscillations of the cell membrane.

The technical result, which is provided by the claimed invention, is to increase the accuracy of the measurements of the frequency and amplitude of membrane oscillations of the cell by compensating for the effect of external oscillations and increasing the discriminatory ability of spectral analysis, which is expressed in the possibility of forming a characteristic signal, determined by the amplitude and frequency of phase oscillations, in the form of a double maximum and effective detection of it in the analyzed spectrum.

The claimed technical solution is characterized by the following essential distinctive features

1. The amplitude and frequency of modulation of the phase of the wavefront are determined directly from local changes in the interferogram, which allows avoiding errors associated with algorithms for phase reconstruction from interferograms.

2. External phase noise of the device is compensated by mixing the information and reference signals, which makes it possible to completely exclude its influence directly in the measurement process.

3. Additional phase modulation of the information and reference signals can significantly increase the discriminatory ability in spectrum analysis and determine the amplitude and frequency of phase fluctuations at the noise level.

The inventive method for determining the frequency and amplitude of the modulation of the phase of the wavefront created by vibrations of the cell membrane is carried out as follows (see Fig. 1). The radiation of the coherent source 1 is directed to the beam splitter 2, where it is divided into two beams, one of which passes through the investigated cell 3. The second falls on the controlled mirror 4 and then through the mirrors 9 and the beam splitter 8 to the recorder 10.

The investigated cell 3 is placed in the signal arm of the interferometer, illuminated with laser radiation in such a way that the area of illumination is larger than the size of the object. The interferometer, with the help of mirror 4, is tuned to bands of infinite width. An area is visually selected at the object in which the amplitude and frequency of natural vibrations will be determined. Using a controlled mirror in the reference channel, the phase of the reference wave is set so that the phase difference between the reference and signal channels in this region is equal to zero. In this case, the modulation index of natural oscillations m on the interferogram will be maximum. Outside the object, an area of approximately equal size is selected, the signal from which will serve as a reference.

The image of the object is projected using the optical system 5 onto the spatial phase modulator 6.

The phase modulator modulates the incident radiation in the area of the object selected for the study with a frequency ω _s , and in the area outside the object with a frequency ω _r. The modulated image is projected by the optical system 7 onto the recorder 10. A reference wave with a fixed phase is also directed to the recorder 10.

The resulting interferogram is formed in the plane of the recorder 10 and converted by it into an electrical signal, which in a given area of the object can be represented as the following expression:

- дрожание плеч интерферометра,

- амплитуда дрожания плеч,

- ширина спектра дрожания плеч, спектр дрожания плеч имеет максимум в нуле частоты и гауссову огибающую, Ф_s(t) - модуляция сигнального канала, представляет собой одностороннюю пилу с максимумом A_max1, минимумом A_min1 и круговой частотой ω₃, ϕ_s - начальная фаза.where U (t) = U ₀ + U _n (t) is the signal amplitude, U ₀ is the constant component of the amplitude, U _n (t) is the noise addition to the amplitude, m is the modulation index of the useful signal, Ω is the circular frequency of the useful signal,

- trembling of the interferometer arms,

- amplitude of shaking shoulders,

- the width of the spectrum of the jitter of the shoulders, the spectrum of the jitter of the shoulders has a maximum at zero frequency and a Gaussian envelope, Ф _s (t) - modulation of the signal channel, is a one-sided saw with a maximum A _max1 , a minimum A _min1 and a circular frequency ω ₃ , ϕ _s is the initial phase.

In the area outside the object, the interferogram is also converted into an electrical signal, which can be represented as the following expression:

where Ф _r (t) is the modulation of the signal channel, is a one-sided saw with a maximum A _max2 , a minimum A _min2 and a _{rotational frequency ω r} , ϕ _r is the initial phase.

Both signals are fed to the multiplier 11 (mixer), as a result, the measured signal is formed at the output, which is determined by the following expression:

The received signal is analyzed in the spectralizer 12.

Spectral analysis of this signal shows that the spectrum of the signal in the region of the difference frequency contains two pronounced maxima at frequencies (Ф _s -Ф _r ) ± Ω.

At the same time, in this area, noises associated with external vibrations and errors associated with phase recovery from interferograms are fully compensated.

FIG. 2 shows the results of modeling the proposed method.

FIG. 2а The results of modeling of the proposed method are presented at the frequency of oscillations of the optical thickness of the cell Ω = 5 Hz:

The model parameters are shown below:

U ₀ = 1

U _n = 0.01

m = 0.01;

Ω = 2π × 5 Hz

ω _s = 2π × 100 Hz

A _max1 = πA _min1 = -π

ϕ _r = 0.6 π

ω _r = 2π × 200 Hz

A _max2 = πA _min2 = -π

All designations are given above in the text.

FIG. 2b shows the results of modeling the proposed method at a frequency of oscillations of the optical thickness of the cell Ω = 100 Hz:

The model parameters are shown below:

Ω = 2π × 100 Hz

ω _s = 2π × 300 Hz

ω _r = 2π × 420 Hz

The rest of the parameters are the same as in FIG. 2a.

From the graphs shown in the figures it can be seen that the information signal is separated from the noise component and is clearly distinguished by a pair of frequencies (ω ₁ -ω ₂ ) ± Ω which make it easy to determine the frequency and amplitude of oscillations of the optical thickness of the cell.

The simulation results show that the proposed method makes it possible to determine the frequency and amplitude of the phase modulation of the wavefront created by vibrations of the cell membrane in a wide frequency range and small amplitude of vibrations with high reliability.

Although the present invention has been described by the example of specific variants of its implementation, for specialists it will be clear the possibilities of numerous modifications of this invention, which do not go beyond the scope of its legal protection defined by the attached claims.

Claims (9)

A method for determining the frequency and amplitude of the modulation of the phase of the wavefront created by vibrations of the cell membrane, containing the following steps: - the radiation of a coherent source is divided into two beams, one of which passes through the object under study and is displayed on the recorder, and the second passes through the reference channel and also enters the recorder, where both beams interfere, and the change in the interference pattern is used to judge about changes in the phase of the wave front , characterized in that - the reference channel of the interferometer during the registration of the interferogram is adjusted in such a way that the value of the phase difference in the selected area is equal to zero, - a part of the wavefront passing through the cell under study is directed by the optical system to the phase modulator, - by means of a phase modulator, the transmitted radiation is modulated with a frequency ω ₁ and a modulation depth m ₁ , then the image of the modulator is projected by an optical system onto a recorder, - in this case, to compensate for the phase shift caused by external vibrations, the part of the wavefront that did not pass through the object is separated and directed by the same optical system to the phase modulator, which modulates this part of the wavefront with the frequency ω ₂ and the modulation depth m ₂ , - then the image of this part of the phase modulator is projected onto the recorder, - the obtained two electrical signals are sent to a multiplier, where they are multiplied, and the resulting signal is subjected to spectral analysis, while a frequency equal to the difference between the modulation frequencies of the optical radiation that passed through the object and the optical radiation that did not pass through the object, and near for this frequency, a symmetric pair of frequencies with the opposite phase value is sought, according to the frequency coordinates of which the frequency is determined, and according to the magnitude, the amplitude of the wavefront phase modulation in the selected area of the cell.

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