SU1619033A1 - Method of determining phase difference of light waves - Google Patents

Abstract

This invention relates to instrumentation technology. The aim of the invention is to increase the information content by determining the total phase difference by eliminating phase ambiguity. The positive effect is based on the use of the properties of integers. At least two interference patterns are formed, corresponding to the angle between the directions of the interfering beams, chosen from the condition that the interference fringes chains do not have intact common dividers. For each interference pattern, the phase difference at the studied points is determined within one the period of its change. Taking into account that determining the phase difference within one period of its change is equivalent to determining the remainder of dividing the total phase difference by the wavelength, and having the ability to accurately determine the phase of the wave under study within the period of the wave of the coherent radiation source the bands are mutually simple integers, which allows one to proceed to the determination of the total phase difference by solving a system of comparisons with one unknown. The dynamic range, in which the total phase difference is determined, is given by the number of significant digits in the integers assigned to the prices of the fringes. 2 Il. J

Description

The invention relates to the field of instrumentation technology and can be used to determine the total phase difference in optical and holographic interferometers when measuring surface relief, deformations, vibrations, etc.

The aim of the invention is to increase the information content by determining the total phase difference by eliminating phase ambiguity.

Fig. 1 shows a block diagram of a device for implementing the method; on

figure 2 - graphical dependence of the phases of the light waves from the spatial coordinates.

The method for determining the phase difference is as follows.

At least douf interference patterns are formulated, corresponding to the angle between the directions of the interference beams, chosen from the condition that the interference fringe prices do not have integer common dividers. In addition, for each interference pattern, change the phase of one of the interfering waves to a controlled value of CN

Yu O

SA)

WITH

Well, by the change in brightness at the point followed, the phase difference is determined using one of the known ratios within one period of change. The total phase difference of the light waves is determined from a known relationship between the numbers corresponding to the total phase difference and phase differences determined within one period.

The phase difference Au within one period of its change is determined by three interference patterns obtained as a result of the phase shift of one of the interfering waves by a controlled value having values of e (p,, (, from the ratio

Ap "arctg

(L - b) cos Lyi + (And - 1d) with i fn + (r - t (1z- I) sindpi + (And -12) lndfj + (b h) slndfs

where and, h and s are the luminance values at the same point in the three interference patterns corresponding to the phase shifts AUi, AU2 and Diz.

The determination of the total phase difference is based on the use of the properties of integers.

Let us consider a system of comparisons with one unknown X, but with different, pairwise simple modules Li, L.2, ..., Lk:

fX bi (),

t b2 (), (2)

I XHbK (modLk).

It is known that the solution of system (2), i.e. the set of values of X satisfying this system is determined by comparing:

(modLiL2 ... Lk), (3)

where XoHMiMi1 bi + M2M2 b2 + ... + MkMk bk. (4) and the numbers MI and Mi1 (, 2, ..., k) are determined from the conditions

LvL2 ... MiLi, 7 MiMi l (modLi). J (5)

At the same time, the uniqueness of system (2) follows from the theorem: if bi, 02, .... bk independently of one another run through complete residue systems modulo Li, L2, .... Lk, then Ho runs through the complete residue system by

module Li, L2Lk.

Determining the phase difference within one period, its change equivalent to determining the remainder of dividing the total phase difference by the wavelength.

Let be

X m At + n, where X is full phase;

P - phase, determined up to 2n :;

0 5

0

five

0

.

five

°

five

0

five

Aj is the length of the wave;

P | - NUMBER OF FULL WAVES.

If it is possible to determine P with a sufficiently high accuracy, then it is possible to put in correspondence to the wavelength and phase values, determined to an accuracy of In, integer numbers with a certain number of significant digits and go to the comparison system (2) considered. The greater the number of significant digits, the greater the dynamic range in which, by a combination, for example, bi and b2, taken at different wavelengths, one can determine the total phase difference.

From the graphs (Fig. 2), where, for a specific example, the phase (p has a repeat period of 4 and phase pi is -5, it is clear that, as it follows from the theory, each pair of numbers (p, p2) corresponds to a single value total phase p, the repetition period of which is equal to 20, which is the limit for determining the total phase.

An apparatus for implementing the method comprises a source of coherent light 1, an interferometer 2, a unit 3 for introducing a controlled phase shift and a unit 4 for determining luminance. The inputs of the interferometer 2 are connected respectively to the outputs of the source 1 of coherent light and the control insertion unit 3. phase shift, and the output is with the input of the luminance determination unit 4.

The method is implemented as follows.

At a certain angle between the directions of 2 beams interfering in the interferometer, a series of interferograms is obtained for different values of the phase shift, specified by the block 3 for the introduction of a controlled phase shift. The luminance values at the studied points on different interferograms are determined using the luminance determination unit 4 and using these values, in accordance with formula (1), the phase difference is calculated within one period of its change. Then the angle between the interfering beams is changed and the phase difference is determined in a similar manner within the period of its change. Then, the diurnal phase difference of the light waves is determined from two values of the phase difference.

Thus, according to a series of interferograms obtained with a controlled change in the phase of the reference wave, the phase of the wave under study is within sufficiently accurate within the period of the wave of the coherent radiation source so that when choosing a certain accuracy, the integers assigned to the prices of the interference fringes are mutually simple, determine the total phase difference across the field in diaa3OHev given by the number of significant digits in integers assigned to the prices of the bands.

Claims (1)

Invention Formula The method of determining the phase difference of the light waves, in which the interference pattern is formed, changes the phase of one of the interfering waves by a controlled amount, determines the change in brightness at the point being studied, and determines the phase difference within one period of its change, which differs by that, in order to increase the information content by determining the total phase difference by eliminating phase ambiguity, they form in addition at least one interference pattern with the values of waiting for the directions of the interfering beams, which differ from the original, while the phase difference within one period of its change is determined for each value of the angle between the directions 0 interfering beams, and the values of these angles are chosen from the condition that the prices of the interference fringes do not have integer common dividers, and the total phase difference of the light waves is determined by 5 of the known relationship between the numbers corresponding to the total phase difference and phase differences determined within one period FIG. one 20