SU1357712A1 - Method of determining phase difference - Google Patents

Abstract

The invention relates to a measurement technique and can be used to determine the total phase difference in interferometers when using optical methods to determine the surface relief, deformations, vibrations. The purpose of the invention is to enhance the functionality by measuring the distance by eliminating phase ambiguity. For this, additional interferograms are obtained on another wave of radiation selected in such a way that the wavelength values do not have integer common divisors. A complete phase difference is found. according to phase differences, determined within the same period, obtained at different wavelengths. Phase differences determined within one period are determined from a series of interference patterns obtained by changing the phase of one of the interfering waves by a controlled amount. Tunable-wavelength coherent light source 1 is used in interferometer 2 to measure two pairs of interferograms, the intensity of which is determined by block 4 for determining the brightness of the light wave. Interferograms are taken at two phase values, which is determined by the block 3 of the introduction of a controlled phase shift. 2 Il. about € (L with SP yu Fig. 1

Description

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The invention relates to a measurement technique and can be used to determine the total phase difference in interferometers when using optical methods to determine the surface relief, deformations, vibrations.

The purpose of the invention is to enhance the functionality by measuring the distance by eliminating phase ambiguity. For this, additional interferograms are obtained on another wave of radiation, chosen in such a way that the values of wavelengths do not have integer common divisors.

FIG. 1 shows a block diagram of a device implementing the method; in fig. 2 - graphs of the phase dependence of the light waves on the spatial coordinates, explaining the essence of the method.

The device (Fig. 1) contains a source of coherent light with tunable wavelength, the output of which is connected to one input of the interferometer 2. The unit 3 for the introduction of a controlled phase shift is connected to another input of the interferometer 2, and the output of the latter is connected to the input of the brightness determining unit 4 light wave.

. The specific implementation of the device implementing the method may be as follows.

An ionic or dye laser can be used as a source of coherent light with tunable wavelength.

The interferometer can be both optical and holographic and assembled according to any scheme.

The controlled phase shift application unit can be made, for example, on the basis of a mirror, the offset of which is determined by the deformation of the piezoceramics.

A light wave brightness detection unit can be implemented, for example, on the basis of photomultiplier tubes, optical fibers or other photoelectric converters.

Consider integers in connection with the remainder of dividing them by a given positive integer L, which we will call a module.

Each integer corresponds to a certain remainder of dividing it by L. If two integers a and b correspond to the same residue g, then

122

they are called equiolate modulo L or comparable modulo L, the comparability of the numbers a and b modulo L is written a b (mod L). Numbers comparable in modulo L form a class of modulo L.

Looking from each class with one deduction, we get a complete calculation system modulo L, most often the smallest non-negative deductions O, 1, ..., L-1 or the absolutely smallest deductions are used as a complete deduction, in the case of an odd L, , ..., -1.0, 1,. ..,

L-1

-J-, in case of an even

of two ranks

Q + 1, ... j - 1, and, 1, ..., -s-

2 L

-1 n 1 i. -, ..., i, u, i,.,., „

Consider a system of comparisons with one unknown, but with different and, moreover, pairwise simple modules

X b (mod L); X 5 b .. (mod L ,,).

(2)

Solve system (2), i.e. it is possible to find all the values satisfying it by applying the following condition: let the numbers Mg and M be defined

, ...,, (mod L)

let it go

x ,, + M2MH + ..., b ,.

Then the set of values of x, satisfying system (2), is determined by comparing x Xjj (mod L, Lj, ..., L). The uniqueness of the solution of the system follows from the following theorem

if b.j, bj, ...,

) independently friend

complete systics run from each other "; we have residues modulo L, L ,. .., L |, then X р runs over the full residue system modulo L, L, ..., L.

Example. Consider the system:

X 5 b (mod 4),

X E bj (mod 5).

The solution of this system is recorded as

X H 5 L., + 16 bi (mod 20) (3)

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These combinations (b ,, b) do not repeat until X runs through the total residue system modulo 20.

To determine the phase difference within one period of its change is to determine the remainder of dividing the total phase difference by the wavelength. Let be

X P D, + G,

where r is the phase, determined to within 2 n; n is the number of total wavelengths;

X is full phase.

If it is possible to determine r with a sufficiently high accuracy, one can put in correspondence with the real values of the wavelength and phase, determined with an accuracy of up to 2 P, integer numbers with a certain number of significant signs and go to the considered comparison system (2). The greater the number of significant digits, the greater the dynamic range.

a region in which by combinations of b and b, taken at different wavelengths, it is possible to determine the total phase difference,

In the considered example, L -, L 5 dynamic range for

20 5 wavelengths (- / -), dL

20 wavelengths (-). If we take two

characters, L 41, L 53, k% 50, kj a40 / 1j.

In the graphs (Fig. 2), the phase t / has a repetition period of 4, and the if-5 phase. From the graphs it is seen, as follows from the theory, that each pair of numbers (tf, 1 /) corresponds to a single value of the full phase tji, period the repetition of which is equal to 20, which in this case constitutes the limit for determining the total phase. For example, a pair of numbers (,

if 4 corresponds to cc 19, and to a pair of numbers if 1, i (3 corresponds to a full phase (f 13.

The method is carried out as follows.

With a single wavelength of light from coherent radiation source 1 in

0

five

„

five

0

five

0

five

0

12 4.

Interferometer 2 receives a series of interferograms for different values of the phase shift, specified by the unit 3 of the introduction of a controlled phase shift. The luminance values at the studied points on different interferograms are determined using block 4 for determining the luminance of the light wave and using these values, in accordance with formula (1), the phase difference is calculated within one period of its change. Then the length of the light wave from source 1 is changed in a similar manner to determine the phase difference within the period of its change. Now, the total phase difference of the light waves is determined by two values of the phase difference, as was shown in the example (Fig. 2).

Claims (1)

Invention Formula The method of determining the phase difference, the light waves in the interferometers, concluding that an interference pattern is obtained, change the phase of one of the interfering waves by a controlled value, determine the change in luminance at the point under study, and determine the phase difference within one period of its change, characterized in that, in order to extend the functionality by measuring the distance by eliminating phase ambiguity, an additional at least one interfer is obtained At a wavelength different from the original, the wavelengths at which interference patterns are obtained do not have integer common dividers, and the phase difference within one period of its change is determined for each wavelength, then from the known relationship between the numbers corresponding to the total phase difference and phase differences, determined within one period, determine the total phase difference of the light waves. go l