RU2507487C2 - Method to determine amplitude of nanovibrations by signal of laser autodyne - Google Patents

Abstract

FIELD: measurement equipment.

SUBSTANCE: method to measure amplitude of nanovibrations ξ, consists in the fact that an object is illuminated with laser radiation, they convert radiation reflected from it into an electric (autodyne) signal, the signal is decomposed into a spectral row, and they measure the value of amplitude of the harmonic S_x at the frequency of object oscillation Ω. At the same time additional mechanical vibrations are imposed onto the object at the frequency Ω₁ with minimum amplitude, they measure the maximum value of the harmonic S_1max, at the frequency Ω₁ as the amplitude of additional mechanical oscillations increases, they increase the amplitude of additional mechanical oscillations until there are interference maxima and minima appear on the autodyne signal on the dedicated interval of time between points that correspond to extreme positions of object displacement, they calculate the ratio of time of decay t_dec of the autodyne signal to the time of its increase t_inc in the dedicated interval of time. In the case when the value t_dec/t_inc is more than 1, they calculate t_inc/t_dec, on the basis of the dependence t_dec/t_inc(C) or t_inc/t_dec(C) they determine the level of the external optical feedback C, they calculate S_x/S_1max, according to the dependence S₁/S_1max(ξ, S) with the previously determined C they find ξ.

EFFECT: higher accuracy of measurement of amplitudes of nanovibrations.

17 dwg, 1 tbl

Description

The invention relates to the field of instrumentation, can be used to determine the amplitudes of vibration of objects in tens of nanometers and can be widely used in precision engineering and electronic engineering.

A known method of measuring the amplitudes of vibrations, the essence of which is to obtain the interference field of the reference and measuring beams of coherent radiation. The method consists in the fact that after receiving the interference field, the radiation frequency of one of the beams relative to the other is shifted by an amount less than ω / 2, where ω is the vibration frequency of the controlled object, a signal is obtained proportional to the brightness of the interference field, the signal is filtered and judged by its nature about the amplitude of the vibration. When filtering the signal, harmonic components are left in it with frequencies included in the interval nω ± Δ, where n = 1, 2, 3, ..., and Δ <ω, the signal amplitude is measured before and after filtering and the vibration amplitude is determined by the formula (see patent for invention No. 2217707, IPC G01H 9/00).

The disadvantage of this method is the difficult technical implementation, the need to measure the brightness of the interference fields, the need to change the radiation frequency of one of the light beams and control it.

There is also a method for determining the amplitude of an object’s oscillations from the ratio of even or odd harmonics of the spectral series of an autodyne signal (Usanov D.A., Skripal A.V., Skripal A.V. Physics of semiconductor radio-frequency and optical autodyne. Saratov University Press, Saratov, 2003 ., 312 p.).

However, this method does not take into account the influence of external optical feedback and is not applicable for cases when only two harmonics are clearly distinguishable in the spectrum of the autodyne signal.

The closest is a method for determining the amplitude of vibration by two harmonics of the spectrum of the autodyne signal (RF patent for the invention No. 2300085). The method consists in irradiating an object with laser radiation, converting the radiation reflected from it into an electrical signal, decomposing the signal into a spectral range and measuring the amplitude of the selected harmonics, select two adjacent harmonics in the spectral series, the vibration amplitude of the object is determined from the relation:

$$\frac{{\mathrm{from}}_{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="00000017.png,00000018.png"\; state="\{\{state\}\}">n</figure-callout>}}^2}{\mathrm{four}{J}_n^2(\frac{\mathrm{four}\pi }{\lambda }\xi )}+\frac{{\mathrm{from}}_{n+\mathrm{one}}^2}{\mathrm{four}{J}_{n+\mathrm{one}}^2(\frac{\mathrm{four}\pi }{\lambda }\xi )}=\mathrm{one}$$

where ξ is the vibration amplitude of the object, λ is the wavelength of the laser radiation, n is an integer, J _n is the n-th order Bessel function, with _n is the spectral component of the Fourier series at a frequency n · ν, ν is the vibration frequency of the object. (Patent for the invention of the Russian Federation No. 2300085. A method for determining the amplitude of vibration from two harmonics of the spectrum of the autodyne signal / Usanov D.A., Skripal A.V., Kamyshansky A.S. Publ. 05.27.2007. Bull. No. 15. Application No. 2005134749 November 9, 2005. The patent holder is SSU.)

The disadvantage of this method is the inability to take into account the influence of the level of external optical feedback on the measurement accuracy and the associated high measurement error.

The objective of this method is to determine the amplitude of nanovibrations from a laser autodyne signal, taking into account the level of external optical feedback to increase the accuracy of measurements.

The technical result consists in a significant increase in the accuracy of measuring the amplitudes of nanovibrations.

The problem is solved due to the fact that the object is illuminated with laser radiation, the radiation reflected from it is converted into an electric (autodyne) signal, the signal is laid out in a spectral series, and the harmonic amplitude S _{x is} measured at the object’s oscillation frequency Ω, the difference between the proposed method consists in that additional mechanical vibrations are imposed on the object at a frequency of Ω ₁ , the maximum value of harmonic S _{1max is measured} , at a frequency of Ω _1, when the amplitude of the additional mechanical vibrations is changed, the amp litudu additional mechanical oscillations until the autodyne signal interference maxima and minima on the selected interval of time between the points corresponding to the extreme positions of the object displacement is calculated the ratio of the decrease of t _dec autodyne signal to time its increase t _inc on the selected interval of time, wherein if the value t _dec / t _{inc is} greater than 1, then t _inc / t _{dec is} calculated, according to t _dec / t _inc (C) or t _inc / t _dec (C) the external optical feedback level C is determined, S _x / S _{1max is calculated} , according to the dependence S ₁ / S _1max (ξ, C) at the previously determined C, the amplitude of nanovibrations ξ is found.

The invention is illustrated by drawings.

Figure 1, 2, 3 and 4 shows the variable components of the autodyne signal for the vibration amplitudes of the object ξ1250 them, 125 nm, 400 nm and 650 nm, respectively. Curves a 1, a 2, a 3 and a 4 shown in figures 1, 2, 3 and 4, respectively, are plotted at the feedback level C = 0, 1; curves b1, b2, b3 and b4-C = 0.5; curves c1, c2, c3 and c4-C = 0.9. Figure 5 shows the dependence of the ratio of the decay time to the rise time of the autodyne signal function on the feedback level C. Figures 6, 7, and 8 show the isolines of the harmonic amplitude of the spectrum of the autodyne signal S ₁ (ξ, θ) at the object oscillation frequency at levels external optical feedback C = 0.0001, C = 0.5, C = 0.9, respectively. Figure 9 presents sections A, B and C of the contour graphs presented in Fig.6, 7 and 8, respectively. Figure 10 shows the dependences of the amplitude of the first harmonic S _{1 of the} spectrum of the autodyne signal, normalized to its maximum value S _1max , on the amplitude of nanovibrations of the object at different levels of external optical feedback: a 10-С = 0.0001, b10-С = 0, 5, c10-C = 0.9. Figure 11 shows the experimental setup: 1 - a semiconductor laser powered by a current source 2, 3 - a reflector mounted on a piezoceramic 4, 5 - a generator of sound vibrations, 6 - photodetector, 7 - filter of an alternating signal, 8 - amplifier, 9 - analog-to-digital converter, 10 - computer. On Fig presents the measured autodyne signal of the vibrations of the object with an amplitude of vibrations corresponding to the maximum value of the first harmonic of its spectrum, presented in Fig.13. On Fig presents the measured autodyne signal with micro-vibrations of the object to determine the level of feedback. On Fig presents the measured autodyne signal of vibrations of an object with an unknown nanometer amplitude, on Fig - its spectrum. On Fig presents the dependence of the amplitude of the first harmonic S _{1 the} spectrum of the autodyne signal, normalized to its maximum value S _1max from the amplitude of the vibration ξ, at feedback levels C = 0.19 - curve a17 and C = 0.0001 - curve b17.

The theoretical basis of the method.

To determine the vibration amplitude of an object, taking into account the level of external optical feedback, the following theoretical premises are used.

The variable normalized component of the autodyne signal, taking into account the feedback level, is written as (Usanov D.A., Skripal Al.V., Skripal An.V. Physics of semiconductor radio-frequency and optical autodyne - Saratov: Publishing house of Sarat. Un-that, 2003 . 312 s)

$$P(t)=\cos (\omega (t)\cdot \tau (t)),\left(\mathrm{one}\right)$$

where ω (t) is the radiation frequency of the semiconductor laser autodyne, which is found from the phase equation

$${\mathrm{<figure-callout\; id="0"\; label="\omega "\; filenames="00000008.png,00000009.png"\; state="\{\{state\}\}">\omega </figure-callout>}}_0\tau =\omega \tau +C\cdot \sin (\omega \tau +\psi ),\left(2\right)$$

$$C=\tau \cdot z\cdot \sqrt{\mathrm{one}+{\mathrm{<figure-callout\; id="2"\; label="\alpha "\; filenames="00000017.png,00000018.png"\; state="\{\{state\}\}">\alpha </figure-callout>}}^2},\left(3\right)$$

C is a coefficient characterizing the level of external optical feedback, ω ₀ = 2πс / λ ₀ , λ ₀ is the laser radiation wavelength without feedback, c is the speed of light, Ψ = a rctg (α), α is the broadening coefficient of the generation line, z is the feedback coefficient.

When an object moves in harmonic law, the time by which the laser radiation bypasses the external resonator changes according to the law

where Ω is the frequency of harmonic vibrations of the object, τ ₀ = 2L / c, τ _a = 2ξ / s, ξ is the amplitude of the vibrations of the object, ε is the initial phase of the vibrations of the object. The numerical solution of transcendental equation (2) taking into account relation (3) allows us to obtain the dependence ω (t) for various feedback levels C.

The results of numerical simulation of the autodyne signal P (t), normalized to the amplitude of the autodyne signal at C = 1, for different feedback levels are shown in Fig. 1. In this case, the following parameters were used in the calculations: ξ = 1250 nm, L = 8.5 cm, ε = π / 6, Ω = 4 Hz, α = 5, λ ₀ = 654 nm.

From the simulation results shown in figure 1, it follows that with a change in the level of feedback, the amplitude and shape of the autodyne signal change. As the feedback level increases, the amplitude of the autodyne signal P increases and the appearance of sections with an asymmetric slope relative to the extreme values of P when the reflector moves. This slope can be characterized either by the value of the ratio of the decay time t _{dec of the} autodyne signal P to its rise time t _inc between the points A1 and A2 corresponding to the first interference minima (maxima) relative to the extreme positions of the object’s displacement, or by the ratio of the rise time t _inc to its decay time t _dec in the region tB between points A3 and A4, corresponding to the first interference minima relative to the extreme positions of the object's displacement (Fig. 1). In figure 1, the times t1, t2 and t3 correspond to the extreme positions of the displacement of the object during vibration. The interference minima A1, A3 are the first on the right with respect to the extreme positions of the displacement of the object t1 and t2, respectively, the interference minima A2 A4 are the first on the left with respect to the extreme positions of the displacement of the object t2 and t3, respectively. It should be noted that at small amplitudes of nanovibrations, there are no time sections tA and tB with interference minimums on the autodyne signal (Fig. 2). The appearance of these areas is observed with an increase in the amplitudes of vibrations (Figs. 3, 4). The dependence of the ratio of t _dec to t _inc when choosing a plot of tA with a characteristic slope to the right from C and the dependence of the ratio of t _inc to t _dec when choosing a plot of tB with a characteristic slope to the left of C are the same. These dependencies are shown in figure 5.

Theoretical analysis showed that the ratio of the time of the decrease in the amplitude of the autodyne signal to the time of its rise does not depend on the parameters of the object’s motion and the parameters of the autodyne system, but is determined only by the level of external optical feedback. Therefore, the ratio of the decay time to the rise time of the autodyne signal function at a given time interval uniquely determines the level of external optical feedback. The curve shown in FIG. 5 is a relationship from which the level of external optical feedback can be determined.

For the analysis of the autodyne signal, it is convenient to use spectral methods in which the ratio of the values of the spectral components or their quantity found from the measurements is used to determine the vibration amplitude (Usanov D.A., Skripal A.V., Skripal A.V. Physics of semiconductor radio-frequency and optical Avtodinov - Saratov: Publishing House of Sarat.University, 2003.312 s; Pernick B.J. Self-Consistent and Direct Reading Laser Homodyne Measurement Technique Appl. Opt, 12, 607-610 (1973)).

To describe the spectrum of an autodyne signal, the normalized radiation power of a semiconductor laser P (t) can be represented as a Fourier series expansion

$$P(t)=\frac{\mathrm{one}}{2}{a}_0+{\displaystyle \sum _{n=\mathrm{one}}^{\infty }\{a_n\cos n\omega t-b_n\sin n\omega t\}}.\left(5\right)$$

The first term in (5) is the constant component of the autodyne signal. The amplitudes of the spectral components of higher orders are determined by the amplitude of the oscillation of the object.

It was previously shown (Usanov D.A., Skripal A.V., Avdeev K.S. Changing the spectrum of the signal of a laser semiconductor autodyne when focusing radiation // News of higher educational institutions. Applied nonlinear dynamics. 2009. Volume 17. No. 2. C. .54-65.) That the amplitudes of the spectral components depend on the vibration amplitude ξ and the level of the external optical feedback C. The amplitude of the spectral component of the autodyne signal at the object oscillation frequency, the value of which also depends on the stationary state, is used to determine the amplitude of nanovibrations. th phase shift θ of the laser diode radiation. Graphs of the dependence of the amplitude of the spectral component of the autodyne signal at the oscillation frequency of the object from ξ, θ and C are shown in Fig.6, 7 and 8.

In the graphs shown in Fig.6, 7 and 8, the smallest amplitude of the first harmonic of the spectrum of the autodyne signal corresponds to the dark region of the graph, the maximum value (points M a 1, Mb1, M a 2, Mb2, M a 3, Mb3) is light chart area. Figure 9 shows sections A, B and C of the graphs presented in Fig.6, 7 and 8, respectively, corresponding to the maximum value of the amplitude of the first harmonic of the spectrum of the autodyne signal at the point Ma 1, M a 2 and M a 3.

As follows from the results shown in FIGS. 6, 7, 8 and 9, with an increase in the feedback level, the maximum values of the amplitude of the first harmonic correspond to the following values of the amplitude of vibrations: for the point M a 1 at C = 0.0001 ξ _Ma1 = 96 nm, which corresponds to section A in FIGS. 6 and 9, at C = 0.5 ξ _Ma2 = 69 nm, which corresponds to section B in FIGS. 7 and 9, at C = 0.9 ξ _Ma3 = 45 nm, which corresponds to section C on Fig and 9; for the point Мb1 at С = 0.0001 ξ _Mb1 = 96 nm ( _Fig.6 ), for the point Мb2 at С = 0.5 ξ _Mb2 = 121 nm (Fig.7), for the point Мb3 at С = 0.9 ξ _Mb3 = 140 nm (Fig. 8). Those. it is seen that with an increase in the feedback level, a significant shift of the maxima of the amplitude of the first harmonic along the abscissa ξ occurs, while along the ordinate 6 the maxima shift slightly.

Thus, in the presence of external optical feedback, the amplitude of the spectral component of the autodyne signal at the oscillation frequency of the object changes, as shown in Fig.6, 7, 8 and 9.

To take into account the level of external optical feedback, it is proposed to construct the dependence of S ₁ / S _1max on the vibration amplitude ξ at various levels of external optical feedback. The dependences of S ₁ / S _1max on ξ are constructed from the relation for the autodyne signal function (1) using the Fourier series (5). These dependencies at different levels of feedback are shown in Fig.10.

The dependences presented in Fig. 10 are plotted with a stationary phase incursion θ = 0.5π corresponding to the maximum value of the first harmonic of the spectrum of the autodyne signal.

The method is implemented as follows

The experimental setup is shown in FIG. 11. The object 3, mounted on piezoceramics 4, is illuminated by radiation from a semiconductor laser 1 recorded from a power source 2, the radiation reflected from the object is converted into an electrical signal using a photodetector 6, an alternating signal filter 7, an amplifier 8 and an analog-to-digital converter 9 signal to the computer 10 and laid out in a spectral series, measure the amplitude of the harmonic of the spectrum S _x at the object’s oscillation frequency Ω. The method is characterized in that additional mechanical vibrations are applied to the object at a frequency of Ω ₁ using a sound oscillation generator 5, the maximum value of harmonic S _{1max is measured} , at a frequency of Ω ₁ when the amplitude of additional mechanical vibrations is changed, the amplitude of additional mechanical vibrations is increased until an autodyne signal appears the interference maxima and minima in the selected time interval between the points corresponding to the extreme positions of the displacement of the object, calculate the ratio of the time loss anija t _dec autodyne signal to time its increase t _inc on the selected interval of time, wherein, if the value of t _dec / t _inc is greater than 1, the calculated t _inc / t _dec, from the dependence of t _dec / t _inc (C) or t _inc / t _dec (C) determine the level of external optical feedback C, calculate S _x / S _1max , according to the dependence S ₁ / S _1max (ξ, C) for the previously determined C find ξ.

Ξ can also be found by solving the optimization problem, which consists in finding the smallest value of the difference in the ratio S ₁ / S _1max obtained taking into account the measured C from the relation for the autodyne signal function (1) when using the Fourier series (5) with nanovibrations, and the experimental ratio S _x / S _1max . As a result of solving this problem, the desired value of the amplitude of nanovibrations ξ is found.

The practical implementation of the method was carried out as follows.

Using a generator of sound vibrations in piezoceramics, additional mechanical vibrations were caused, the amplitude of which varied over time. The amplitude of the additional vibrations increased until the amplitude of the first harmonic of the spectrum of the autodyne signal reached the maximum value at which the autodyne signal was recorded. If necessary, the stationary incursion of the radiation phase of the laser diode θ is changed to obtain the maximum amplitude of the first harmonic. From the spectrum, the maximum value of the amplitude of the first harmonic S _{1max was determined} . Fig. 12 shows the shape of the measured autodyne signal at the maximum value of the first spectral component and its spectrum of Fig. 13. The average value of S _1max was 0.131 rel. units

To determine the feedback level, the amplitude of additional mechanical vibrations was increased to micrometer values. On Fig shows the shape of the experimental autodyne signal with microvibrations.

The average ratio of decrease time to rise time was 0.79. This ratio corresponds to the level of external optical feedback C = 0.19 (figure 5).

After the exclusion of additional mechanical vibrations, the autodyne signal of object vibrations with an unknown nanometer amplitude was measured at the calculated feedback level and the known parameters S _1max and ξ _max . The shape and spectrum of the measured autodyne signal are shown in FIGS. 15 and 16, respectively. The average value of the amplitude of the first harmonic S _x amounted to 0.074 Rel. units The ratio S _x / S _1max for the given experimental autodyne signals was 0.56.

For the obtained feedback level C = 0.19, the dependence S ₁ / S _{1 max} on the vibration amplitude ξ was plotted, shown in Fig. 17, curve a 17, from which the amplitude of nanovibrations for the autodyne signal shown in Fig. 15 was determined, which amounted to 30 nm. Without taking into account the level of external optical feedback (Fig. 17, curve b17), the amplitude of nanovibrations measured by the method described above was 36 nm.

The results of measurements of the amplitude of nanovibrations ξ, taking into account the feedback level and without taking it into account for various feedback levels, are given in Table 1. The measurements were carried out repeatedly to increase reliability. In the calculations, the averaged values of the measured values were used. According to the measurement results at various feedback levels, the average value of the amplitude of nanovibrations was 29 nm.

Table I Measured Feedback Level The value of the desired amplitude of nanovibrations ξ, taking into account the feedback level, nm The value of the amplitude of nanovibrations ξ without taking into account the feedback level, nm Relative error in determining the amplitude of nanovibrations δ without taking into account the level of feedback,% C = 0.19 thirty 36 24 C = 0.39 27 40 38 S-0.53 thirty 52 79

Claims (1)

A method of measuring the amplitude of nanovibrations, which consists in illuminating the object with laser radiation, converting the radiation reflected from it into an electric autodyne signal, arranging the signal in a spectral series and measuring the harmonic amplitude S _x at the object’s oscillation frequency Ω, characterized in that the object is superimposed additional mechanical vibrations at a frequency of ₁ Ω, the maximum value measured harmonic S _1max, at the frequency Ω ₁ when changing the amplitude additional mechanical oscillations increases the amplitude d additionally mechanical vibrations until the autodyne signal interference maxima and minima on the selected interval of time between the points corresponding to the extreme positions of the object displacement is calculated the ratio of the decrease of t _dec autodyne signal to time its increase t _inc on the selected interval of time, wherein, if the value of t _dec / t _{inc is} greater than 1, then t _inc / t _{dec is} calculated, according to the dependence t _dec / t _inc (C) or t _inc / t _dec (C) the external optical feedback level C is determined, S _x / S _{1max is calculated} , according to dependences S ₁ / S _1max (ξ, C) at previously determined to C, find the amplitude of the nanovibrations ξ.

Images