CN1047443C - Double-Rayleigy air refraction interferometer - Google Patents

Abstract

Double Rayleigh air refractive index interferometer, with laser source S, beam expander lens A1, divides the clear aperture into upper, middle and lower parts, each part has a diaphragm D for two beams, and a first vacuum is set in the upper optical path Chamber T1, a second vacuum chamber T2 is set in the lower optical path, and the two beams of the upper and lower parts are respectively formed on the CCD photoelectric conversion device of the camera through the lens A2 and the cylindrical mirror A3 and move with the measured air refractive index The different measured interference fringes, the two light beams in the middle form fixed interference fringes on the photoelectric conversion device, the output of the photoelectric converter is input to the computer, and the air refractive index value is obtained after data processing. The instrument has a simple structure and can be used for real-time correction.

Description

Air Refractive Index Double Rayleigh Interferometry Method and Device

The invention relates to a double Rayleigh interferometric method and a device for air refractive index, belonging to the interferometric technology in the metrology field.

In the interferometric measurement of length, the importance of air refractive index measurement is needless to say, and the measurement error of air refractive index has often become a main source of error in length measurement.

Industrial production often requires the accuracy of length measurement to be better than 1×10 ^-7 , while in the measurement of some precise physical constants or other scientific research, higher measurement accuracy is often required, so the uncertainty is 2-5×10 An air index of refraction value of ^-8 is often required.

The measurement methods of the air refractive index can be roughly divided into two categories, by measuring the air pressure, temperature and humidity of the air, and then calculating the air refractive index with a formula, or directly measuring the air refractive index with an interferometer.

1 formula calculation method

The refractive index of air is related to parameters such as air pressure p, temperature t, and humidity f, as well as air composition. B.Edlen published a set of air refractive index formulas based on experimental data in 1966 (Journal Metrologia, 1966, No. 2, pages 71 to 80). After the pressure, temperature and humidity of the air are known, the following formula can be used Calculate the refractive index of air for the standard composition:

(n-1) _s ×10 ⁸ =8342.13+2406030/(130-σ ² )+15997/(38.9-σ ² )

(n-1) _tp =[p(n-1) _s /720.775]×[1+p(0.817-0.0133t)10 ^-6 ]/

(1+0.0036610t)

n _tpf -n _tp =-f(5.7224-0.0457σ ² )×10

The subscript "S" in the above formula indicates the refractive index of air in the standard state, which corresponds to p=760mmHg (1mmHg=133.32Pa), t=15°C dry air, and the subscript "tp" indicates the dry air in the general state ; and the subscript "tpf" indicates the air in general state; σ is the vacuum wave number (μm ^-1 ).

Corresponding to standard air, the uncertainty of the above formula is about 5×10 ^-8 . The so-called standard air means that the molar percentages of the main components in the air are: nitrogen 78.09%, oxygen 20.95%, argon 0.93% and carbon dioxide 0.03%.

The method of calculating the refractive index of air through the Edlen formula is still widely used today, such as the dual-frequency laser interferometer of HP Company in the United States, the laser interferometer of Ranishaw Company in the United Kingdom, and most domestic laboratory interferometry.

It has also been reported recently that carbon dioxide sensors can be used to measure the content of carbon dioxide in the air to further correct the refractive index (author Birch KPand DownsM.J, Metrologia, 1993, No. 30, pages 155 to 162), so that the calculation formula can be calculated accurately degree increased to 3×10 ^-8 .

The main disadvantages of the formula calculation method are:

(1) The air refractive index is related to the air composition, and the air refractive index calculated by empirical formula is only applicable to the standard air condition. When the air composition of the measurement environment deviates from the standard air, the error of the formula will exceed the uncertainty given above. In the usual measurement environment, due to the increase of carbon dioxide content and the pollution of various oil vapors, there may be a large difference between the actual value and the calculated value of the air refractive index, usually the actual value is slightly larger than the calculated value, and the difference The value varies with environmental conditions, often up to 1×10 ^-7 , sometimes even as high as 2×10 ^-7 . This limits the application of the formula calculation method in high-accuracy length measurement.

(2) By measuring the content of carbon dioxide in the air, the refractive index of the air can be further corrected, and it is reported that the uncertainty of the formula can be reduced to 3×10 ^-8 (Owen JC, Appl.Opt., 1967, p. 6 Issue 51 to 59), but the article also points out that in practical applications, due to the measurement uncertainty brought by each air parameter sensor, the total error calculated by the formula increases to 1×10 ^-7 . Considering the verification of the carbon dioxide sensor, the investigation of its stability, and the high price of the carbon dioxide sensor (the unit price is about 6,000 US dollars), the practical value of this method is greatly reduced.

(3) It is difficult to read conventional mercury barometers, which cannot meet the requirements of today's science and technology for measurement automation. The various pressure sensors that have been widely used in industrial measurement usually have a large drift over time and must be calibrated frequently, so they are not suitable for high-precision length measurement.

In view of the above reasons, it is necessary to directly measure the air refractive index when the uncertainty of the air refractive index is better than 5×10 ^-8 , such as the reference line meter ruler and the first-class mass block verification.

2 direct measurement method

Using an interferometer to directly measure the refractive index of air is the most commonly used method. Since the refractive index of gas is generally very small, it is not much different from the refractive index of vacuum. Taking air as an example, its refractive index is about 1.00027 at normal temperature and pressure. , it only differs from the vacuum refractive index by 2.7×10 ^-4 . When measuring the refractive index of air with an interferometer, the refractive index of vacuum is usually used as a standard, and what is measured is the difference between the refractive index of air and vacuum. Therefore, if the air and vacuum can be measured with an uncertainty of 1×10 ^-5 If the optical path difference between the two optical paths is used, the uncertainty of the obtained air refractive index can reach 2.7×10 ^-9 , that is, the measurement accuracy can be increased by about 3700 times.

Many types of interferometers can be used to measure the refractive index of air, and the measurement uncertainty can reach the order of 10 ^-8 , which can meet the requirements of general precision measurement. However, as far as the existing methods are concerned, some of them have large devices and are inconvenient to move; Expensive and cannot be popularized.

2.1 Vacuum method

The classic method of measuring the refractive index of air with an interferometer is to make one optical path of the interferometer pass through a gas chamber of known length, the gas chamber is filled with the same air as the measurement environment, and then gradually evacuate it into a vacuum, as long as the measured The refractive index of air can be accurately calculated by the change of the order of interference fringes before and after air. Although this method can achieve a measurement uncertainty of 5×10 ^-8 , its operation is complicated and requires the cooperation of a vacuum pump, and it can only measure the refractive index of air at the beginning, and it is difficult to reflect the refractive index of air during the measurement process. possible changes and cannot be corrected in real time.

2.2 Using a sealed vacuum chamber

The inventor of the present invention has invented an improved Rayleigh interferometer. When a 1200mm long vacuum tube is used, it is possible to achieve a measurement uncertainty of 2-4×10 ^-8 . The application of more than 20 years shows that the instrument is easy to use and the measurement accuracy can meet the requirements. Its disadvantage is that the machining accuracy of the instrument is relatively high; it is necessary to regularly use multiple wavelengths to calibrate the instrument through the decimal overlap method; and It can only be observed and read with the naked eye, so that the instrument cannot meet the requirements of measurement automation, especially for real-time correction.

2.3 Beat frequency measurement method

The basic principle is to measure the length of the optical resonant cavity in a vacuum state, and the geometric variation of the cavity length before and after vacuuming, so as to obtain the resonant cavity length of the optical resonant cavity in an inflated state. Using this length as a standard, the laser frequency is locked to the resonant frequency of the gas-filled optical resonator, and the locked laser frequency is measured by the beat frequency method, from which the refractive index of air can be calculated (Xu Yi et al.Proceedings of the 12th Triennial world Congress of the International Measurement Confederation, Beijing, China Sep.5-10.1991, 804-807). The beat frequency method is based on the geometric length of the optical resonant cavity, so the stability of the resonant cavity material will affect the accuracy of the measurement. According to literature reports, even the internationally recognized low expansion coefficient material "Zerodur ”, and its annual relative drift is also 3-10×10 ^-8 . Therefore, in order to achieve the measurement uncertainty of 5×10 ^-8 claimed by the method, periodic verification of the length of the optical resonant cavity must be carried out frequently. The main disadvantage of this method is that the device is extremely complicated and expensive, and it needs expensive equipment such as a precision three-channel optical resonator, a 633nm iodine frequency-stabilized He-Ne laser, a laser frequency locking device, a beat frequency measurement device, and a spectrum analyzer, so it is not practical. big.

Through the above introduction, you can get:

(1) The use of an isolated vacuum chamber is more advantageous than the use of a gas chamber that needs to be evacuated during the measurement process, but the former needs to try to determine the integer order of the interference fringes.

(2) The use of laser light source is more advantageous than that of white light source. The latter needs to calibrate the position of the compensating mirror of the instrument through the multi-wavelength decimal overlap method in advance, which requires a very precise reading drum. If the zero-order fringe is observed, it is necessary to add a set of auxiliary additional compensation sheets.

(3) If a laser light source is used, the integer orders of the interference fringes need to be measured by the multi-wavelength fractional overlap method.

The purpose of the present invention is to develop a new type of double Rayleigh air refractive index interferometer, which should integrate the advantages of various methods as much as possible and avoid their respective disadvantages. Specifically, it is necessary to develop an air refractive index interferometer with the following advantages:

Avoid using vacuum pumps;

Avoid requiring calibration of compensating mirrors;

It is not necessary to use multiple wavelengths;

The structure of the instrument is simple and easy to move;

The measurement process should be able to be carried out automatically and quickly, and can be used for real-time correction.

The instrument can be matched with various types of laser interferometers for air refractive index correction for precision length measurement.

The double Rayleigh air refractive index interferometer of the present invention adopts the single-wavelength decimal overlap method.

The general formula for interferometry is:

nL=(k+e)λ

In the formula, L is the measured length, n is the refractive index of air, λ is the laser wavelength, k and e are the integer and fractional part of the interference order, respectively.

The usual decimal coincidence method is to use a set of, for example, four known wavelengths for measurement, so the following equations can be obtained:

L=(k ₁ +e ₁ )λ _A1

L=(k ₂ +e ₂ )λ _A2

L=(k ₃ +e ₃ )λ _A3

L=(k ₄ +e ₄ )λ _A4

Wherein, λ _A1 -λ _A4 are four known (air) wavelengths, and K ₁ -K ₄ and e ₁ -e ₄ are integer and fractional interference orders corresponding to different wavelengths, respectively. Using a set of measured decimals e ₁ -e ₄ and the rough value of the measured length L, through a set of fixed calculation procedures, the integer orders K ₁ -K ₄ and the measured length L can be accurately determined from the above equations , which is the general decimal coincidence method.

In the air refractive index interferometer, what is measured is the difference between the refractive index of air and the vacuum refractive index 1, ie (n-1), rather than the geometric length L. At this time, the decimal coincidence method can be changed as follows, that is, the geometric length L of the vacuum tube is changed, and the wavelength λ remains unchanged. If two vacuum chambers with different geometric lengths L ₁ and L ₂ are used, then

n-1=(k ₁ +e ₁ )λ/L ₁

n-1=(k ₂ +e ₂ )λ/L ₂

Since the lengths of L ₁ and L ₂ can be accurately measured, according to L ₁ , L ₂ , and the precise ratio between them, the integer order K ₁ , K ₂ and the measured e ₁ and e ₂ can be obtained. Measure the refractive index n of air.

The following example illustrates the process of the fractional coincidence method for a single wavelength:

The refractive index of air is related to the pressure p, temperature t, and humidity f of the air. For 633nm laser radiation, their effects on the refractive index of air are respectively:

Pressure p:3.6×10 ^-7 /mmHg

Temperature t:9.5×10 ^-7 /℃

Humidity f:5.7×10 ^-8 /mmHg

Taking the Beijing area as an example, the fluctuation of air pressure is generally within ±10mmHg throughout the year. If the ambient temperature does not exceed ±1°C (actually, precision length measurement requires a higher ambient temperature), the total of the two, the maximum change in the air refractive index About 5×10 ^-6 . If a vacuum chamber with a length of 600mm is used, it corresponds to a path difference change of 3 μm in the interferometer, which is equivalent to 5 interference orders, which is the maximum possible change in the interference order in the same area. For a vacuum chamber of 92.308 mm, the maximum path difference change of the interferometer due to the change of the air refractive index is about 0.46 μm, which is equivalent to 0.8 interference orders. now assume

The length of the first vacuum chamber L ₁ =600mm

The length of the second vacuum chamber L ₂ =92.308mm

Assume that the actual air refractive index during measurement is: n=1.000275266, and the air refractive index value under normal conditions (pressure p=760mmHg, temperature t=20°C, humidity f=10mmHg) is: n ₀ =1.000271226, we are about to n ₀ is taken as the predicted value of air refractive index n.

At this time, for the first vacuum chamber T1, the interference order should be:

k ₁ +e ₁ =(n-1)L ₁ /λ=260.919

The estimated value of the interference order is: (n ₀ -1)L ₁ /λ=257.090, that is, the integer interference order K ₁ should be within the range of 257±5. However, if the uncertainty of the actual measured interference order decimal is 0.02, then e ₁ should be within the range of 0.919±0.02, assuming that the actually measured decimal is too large, for example, e ₁ =0.935.

For the second vacuum chamber T2, the order of interference is:

k ₂ +e ₂ =(n-1)L ₂ /λ=40.142

The estimated value of the interference order is: (n ₀ -1)L ₂ /λ=39.552, that is, the integer interference order K ₂ should be within the range of 39±1. And if the uncertainty of the actual measured interference order decimal is 0.02, then e ₂ should be within the range of 0.142±0.02, assuming that the actually measured decimal is too small, for example e ₂ =

0.122. Then, if K ₁ =252, then:

n-1=252.935/L ₁

then,

k ₂ +e ₂ =(n-1)L ₂ /λ=252.935L ₂ /L ₁ =38.913

For different k ₁ values, the following table can be obtained: k ₁ 252 253 254 255 256 257 258 259 260 261 262 e ₁ 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 0.935 k ₂ 38 39 39 39 39 39 39 39 40 40 40 e ₂ 0.913 0.067 0.221 0.375 0.528 0.682 0.836 0.990 0.144 0.298 0.452

It can be seen from the above table that when k ₁ =260, e ₂ =0.144, which is closest to the actual measured value of 0.122. Therefore, k ₁ =260 can be determined. Adding the actually measured fraction e ₁ =0.935, it can be known that the interference order is 260.935. Then, the refractive index n of air is:

n=1+(k ₁ +e ₁ )λ/L ₁

=1+260.935λ/L ₁

=1.000275283

The difference of 2×10 ^-8 from the original assumed value of 1.000275266 is caused by the measurement error of the interference order decimal e ₁ of the vacuum chamber T1.

The above is the process of determining the refractive index n of air with the single-wavelength decimal overlap method.

If the measurement uncertainty of the air refractive index is not high, a shorter vacuum chamber can be used, and different ratios of L ₁ /L ₂ can be selected at this time.

According to the above introduction, when using the single-wavelength fractional coincidence method, it is necessary to use two vacuum chambers with different lengths, one larger and one smaller. Ways to solve this problem are:

(1) Change the vacuum chamber during the measurement.

This makes the measurement process very troublesome and is not practically desirable.

(2) Two refractive index interferometers with different vacuum chamber lengths are used.

This is practically feasible, but the equipment investment has doubled, and the volume taken has also doubled, so this is not an ideal method.

The present invention adopts the following technical solutions in order to achieve the aforementioned object by adopting the single-wavelength fractional overlap method.

The double Rayleigh interferometry method of air refractive index is characterized by:

a) Using a laser light source with a wavelength (λ);

b) After the above-mentioned laser light source is expanded and split, it passes through two

Vacuum chambers with fixed geometric lengths L1 and L2;

c) Measure the interference of the single-wavelength laser light source through the above two vacuum chambers

Decimal order e1 and e2;

d) Calculate K1+e1 according to (n ₀ -1)L1/λ, and determine the estimated value of K1

range of

e) According to the measured e1 value and the calculated K1 estimated value range, respectively

According to K2+e2=(K1+e1)L2/L1, a set of values corresponding to the estimated value of K1 can be obtained

Corresponding K2 and e2 values;

f) Determine the K1 value according to the closest value between the measured e2 value and the calculated e2 value;

g) According to the K1 value determined above, the measured e1 value and the known wavelength λ

and L1 to calculate the refractive index n of the air to be measured.

The double Rayleigh interferometry device of the air refractive index is provided with a laser light source (S), a group of lenses (A1) for expanding the laser beam, and is characterized in that a clear aperture is arranged in the exit light path of the lens (A1) The diaphragm (D) is divided into upper, middle and lower parts, so that two beams are emitted from each part, and the two optical paths in the middle are both air layers; the first vacuum chamber (T1) is set in the upper optical path, The medium in the other optical path is the measured air layer; a second vacuum chamber (T2) with a different length from the first vacuum chamber (T1) is set in the lower optical path, and the medium in the other optical path is the measured air layer , the two beams of the upper and lower parts respectively form different measured interference fringes on the CCD photoelectric conversion device of the camera through the lens (A2) and the cylindrical mirror (A3), which move with the refractive index of the measured air, and the two bracket beams in the middle , On the photoelectric conversion device of the camera, a fixed interference fringe that does not move with the refractive index of the air is formed. The electrical signal output by the photoelectric converter is input into the computer through the interface, and the data is processed according to the single-wavelength overlap method to obtain the air refractive index value.

The advantage of the double Rayleigh air refractive index interferometer of the present invention is that the structure becomes very compact. And it is a Rayleigh interferometer without any compensation plate.

The classic Rayleigh interferometer needs to move the upper interference fringes and align the upper and lower fringes, so a phase shift compensation plate is set; and for the convenience of alignment, there should be no gap between the upper and lower fringes, so a Fixed displacement plate. The improved Rayleigh interferometer using white light alignment also adds a set of additional compensation sheets. Because the present invention adopts the CCD camera, and the computer processes the interference image, all the above-mentioned compensation plates and displacement plates can be omitted.

The computer processes the interference image, which improves the measurement accuracy of the fractional fraction of the interference order, greatly shortens the length of the vacuum chamber, and facilitates the handling of the instrument.

The present invention will be described in further detail below through embodiments in conjunction with the accompanying drawings.

Fig. 1 is the optical path diagram of the Rayleigh air refractive index interferometer of the present invention;

Fig. 2 is a schematic diagram of three groups of interference fringes formed on the CCD photoelectric conversion device of the camera of the present invention.

Fig. 1 is the optical path diagram of the Rayleigh air refractive index interferometer of the present invention, S is a laser, through a group of beam expander lenses A1, through the diaphragm D, the diaphragm D divides the entire clear aperture into upper, middle and lower three parts, each Some have two light paths. In the upper optical path, one beam passes through the long vacuum chamber T1 with a length of L1, and the other beam passes through the air layer to be measured. In the lower optical path, one beam passes through the short vacuum chamber T2 with a length of L2, and the other beam also passes through the air to be measured. After passing through the lens A2 and the cylindrical mirror A3, the two beams of light in the upper and lower optical paths form different measured interference fringes 2 and 3 that move with the measured air refractive index on the CCD photoelectric conversion device of the camera. (See Figure 2). The two light beams in the middle optical path pass through the air layer to form fixed interference fringes 1 with zero response of the interferometer on the CCD photoelectric conversion device of the camera (see Figure 2). The output electrical signal of the photoelectric conversion device is input into the computer through the interface, and the measured air refraction index value can be obtained after the data is processed according to the single-wavelength overlapping method of the present invention. At the same time, it can be displayed on the display screen of the computer or printed out on the printer. The measured air refractive index value can also be further processed according to the program in the computer.

Claims (2)

1, two Rayleigh interferometric methods of air refraction is characterized in that:

A) adopt the LASER Light Source of a kind of wavelength (λ);

B) above-mentioned LASER Light Source has been proficient in the vacuum chamber of measuring geometrical length L1 and L2 by two after expanding the bundle beam splitting;

C) record interference decimal level time e1 and the e2 of single wavelength laser light source respectively through above-mentioned two vacuum chambers;

D) according to (n ₀-1) L1/ λ calculates K1+e1, determines the scope of K1 estimated value;

E), calculate one group and corresponding K2 of K1 estimated value and e2 value by K2+e2=(K1+e1) L2/L1 respectively according to the K1 estimated value scope of surveying the e1 value and calculating;

F) determine the K1 value according to surveying the e2 value and calculating e2 value closest value;

G) calculate air refraction n to be measured according to above-mentioned definite K1 value and actual measurement e1 value and known wavelength λ and L1.

2, two Rayleigh interferometric measuring means of air refraction, a LASER Light Source (S) is set, one group of lens (A1) with the laser beam enlarging bundle, it is characterized in that in lens (A1) emitting light path, being provided with the diaphragm (D) that a clear aperature is divided into upper, middle, and lower part, make from every part two light beams of outgoing all, two light paths at middle part are air layer; In the light path on top first vacuum chamber (T1) is set, another light path medium is tested air layer; In the light path of bottom second vacuum chamber (T2) different with first vacuum chamber (T1) length is set, another light path medium is tested air layer, up and down two parts separately two light beams on the CCD of video camera electrooptical device, form the different tested interference fringe that moves with tested air refraction size respectively through lens (A2) and cylindricality mirror (A3), middle part two stands light beam, on the electrooptical device of video camera, form the fixedly interference fringe that does not move with the air refraction size, photoelectric commutator output electric signal is imported computing machine through interface, carry out data processing by single wavelength coincidence method, obtain the air refraction value.

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