A heterodyne interferometer arrangement

Abstract: A heterodyne interferometer arrangement (1) comprises a two-frequency light source (LS), an optical reference branch (RB) for producing a reference signal, an optical measuring branch (MB), which includes an interferometer unit (IF) causing a phase rotation of the light beams in response to a length to be measured as well as a measuring transformer means arranged at the output of said interferometer unit, and a phase comparator means arranged subsequent to said reference transformer means and said measuring transformer means. In order to minimize linearity errors, the measuring transformer means comprises first and second optoelectric measuring transformer units, which respond to light components orthogonal to each other and which are followed by two phase comparator means whose output signals represent phase differences between the first and the second measuring signal on the one hand and the refererence signal on the other, and a mean value generation circuit whose output signal represents the mean value of said first and second phase differences.

Description: The present invention refers to a heterodyne interferometer arrangement according to the generic clause of patent claim 1, a heterodyne interferometric metering technique according to the generic clause of patent claim 5, an arrangement for detecting the non-linearity of a heterodyne interferometer according to the generic clause of patent claim 6 as well as a method of detecting the non-linearity of a heterodyne interferometer according to the generic clause of patent claim 7. The basic set-up of a heterodyne interferometer arrangement, which is also referred to as two-frequency interferometer arrangement, is shown in Fig. 18. The heterodyne interferometer arrangement as a whole is provided with reference numeral 1 and includes a light source LS for generating light beams E₁, E₂ having a first frequency f₁ and a second frequency f₂. The two partial beams produced by the light source means LS can be described as plane waves, which can be expressed by the following equations: (1a) E₁ = E₀sin(2πf₁t + ₀₁) (1b) E₂ = E₀sin(2πf₂t + ₀₂) In the light path after the light source LS, a first beam splitter BS1 is arranged, said beam splitter supplying the light produced by the light source LS to an optical reference branch RB on the one hand and to an optical measuring branch MB on the other. An interferometer unit IF having a structure which is known per se is arranged after the first beam splitter BS1 in the measuring branch MB, said interferometer unit IF including, in turn, a first polarizing beam splitter PB1 followed by first and second interferometer arms A1, A2 in orthogonal directions. As is, in principle, known to the person skilled in the art, each interferometer arm A1, A2 is closed by a mirror MR1, MR2, which can, for example, be formed by a prism. The two interferometer arms A1, A2 have a first optical length n₁ · l₁ and a second optical length n₂ · l₂. At least one of the two interferometer arm lengths corresponds to the quantity to be measured by the heterodyne interferometer arrangement. At the optical ouput of the interferometer unit IF, a first polarization filter PF1 is arranged whose polarizing direction is rotated by 45° relative to the directions M₁, M₂ of the two plane waves E₁, E₂. An optoelectric measuring transformer unit in the form of a photodiode D m is arranged after this first polarization filter PF1. A second polarization filter PF2 is arranged in the reference branch RB in the light path after the first beam splitter BS1, the polarization direction of said second polarization filter being, just like that of the first polarization filter PF1, rotated by 45° relative to the directions M₁, M₂ of the two plane waves E₁, E₂. The second polarization filter is followed by an optoelectric reference transformer means in the form of a photodiode D r . The reference signal I r produced by this photodiode satisfies the following equation: (1c) I r ∼ E r ² ∼ I₀cos[2π(f₁-f₂)t + ₀] In this connection, the following relationship exists with regard to the amplitude I₀: (1d) I₀ ∼ E₀² With regard to the constant phase displacement ₀, the following connection exists: (1e) ₀ =  r1 -  r2 The measuring signal I m at the output of the optoelectric measuring transformer unit D m is defined in accordance with the following equation: (2a) I m ∼ I₀cos[2π(f₁-f₂)t +  0m + Δ] In this equation, Δ stands for a phase displacement which can be expressed as follows: (2b) Δ = ₁ - ₂ = 4π(n₁l₁ - n₂l₂)/λ m In this equation, λ m stands for the mean wavelength. An arbitrary initial phase is  0m =  m1 -  m2 . The measuring signal I m and the reference signal I r are supplied to a phase comparison circuit PH, which will form the phase difference between the measuring signal I m and the reference signal I r . As can be seen from equations (1c), (2a) and (2b), the measuring signal I m is subjected to a phase displacement in comparison with the reference signal I r , said phase displacement changing in response to changes in the optical path lengths n₁, l₁ and n₂, l₂ in the first and second arms A1, A2 of the interferometer unit IF. Hence, a length variation in one of the two arms A1, A2 can be detected by measuring a resultant phase difference between I m and I r . If, in the case of one example, the resolution which can be achieved when carrying out a phase measurement is 1°, a length resolution of 0.9 nm can be attained for the detection of the displacement of a mirror MR1 and MR2, respectively, in the case of the interferometer shown in Fig. 18. The above-described phase displacement Δ between the reference signal I r and the measuring signal I m is shown in Fig. 19. Fig. 20 shows the above-described orthogonal direction of the two partial beams E₁, E₂ as well as the arrangement of the polarization filters PF1, PF2 which are displaced by 45° relative thereto. However, the above-described derivation of the connection between the phase displacement Δ and a length L₁, L₂ to be measured is only applicable under the ideal condition that only one of the two frequencies f₁, f₂ occurs in each interferometer arm A1, A2. This ideal condition is, however, not met in practice. Due to various influences, mixed frequencies are found in both interferometer arms A1, A2. The causes of such frequency mixtures are, for example, non-orthogonality of the polarization directions M₁, M₂ of the incident waves E₁, E₂, mixing due to elliptic polarization of the incident waves E₁, E₂, mixing due to imperfect optics in the light path before the first polarizing beam splitter PB1 as well as incomplete frequency separation by said first polarizing beam splitter PB1. These mistakes result in a non-linear relation between the measured phase difference and the displacement to be measured or the change in the optical length of one of the two interferometer arms to be measured. The following literature sources are cited with regard to the technological background of the present invention: Sommargren, G.E.: A new measurement system for precision metrology Prec. Eng. 9 (1987), 179 - 184 Quenelle, R.C.; Wuerz, L.J.: A new micrometer-controlled laser dimensional measurement and analysis system. Hewlett Packard Journ. 34,4 (1983), 3 - 13 Dorenwendt, K.; Probst, R.: Hochauflösende Interferometrie mit Zweifrequenzlasern PTB-Mitt. 90, (1980), 359 - 362 Reinboth, F.; Wilkening, G.: Optische Phasenschieber für Zweifrequenz-Laser-Interferometrie PTB-Mitt. 93, (1983), 168 - 174 Bobroff, N.: Residual errors in laser interferometry from air turbulence and nonlinearity Appl. Opt. 26, (1987), 2676 - 2682 Sutton, C.M.: Non-linearity in length measurement using heterodyne laser Michelson interferometry J. Phys. E 20, (1987), 1290 - 1292 Steinmetz, C.R.: Sub-micron position measurement and control on precision machine tools with laser interferometry Prec. Eng. 12, (1990), 12 - 24 Rosenbluth, A.E.; Bobroff N.: Optical sources of non-linearity in heterodyne interferometers Prec. Eng. 12, (1990), 7 - 11 Taking this prior art as a basis, the present invention is, in accordance with a first aspect of the invention, based on the object of further developing a heterodyne interferometer arrangement as well as a heterodyne interferometric metering technique of the type mentioned at the beginning in such a way that the measuring error of linearity is reduced. This object is achieved by a heterodyne interferometer arrangement according to patent claim 1 and by a heterodyne interferometric metering technique according to patent claim 5. In view of the fact that, in the case of known heterodyne interferometer arrangements and in the case of known heterodyne interferometric metering techniques, linearity errors will occur - as has already been explained hereinbefore - when the phase difference is being measured in response to a displacement of the interferometer arm, it will be important to know the magnitude of the linearity error. Up to now, the linearity error of a heterodyne interferometric metering technique has been determined by comparing the phase characteristic during the measurement of a heterodyne interferometer arrangement to be tested with the phase characteristic of a reference interferometer. This type of check is complicated on the one hand and affected by mistakes of the reference interferometer on the other. It follows that, in accordance with a second aspect of the invention, the present invention is based on the object of providing a simplified arrangement for detecting non-linearity of a heterodyne interferometer as well as a simplified method of detecting the linearity of a heterodyne interferometer. This object is achieved by a non-linearity detection arrangement according to patent claim 6 and by a non-linearity detection method according to claim 7. Preferred further developments of the invention are disclosed in the subclaims. In the following, preferred embodiments of the present invention will be explained in detail while making reference to the drawings enclosed, in which Fig. 1 shows a representation of the plane light waves in the case of non-orthogonality for explaining the frequency mixing which results therefrom; Fig. 2 shows a representation of the light beam components; Fig. 3 shows a representation of the periodic, non-linear phase characteristic of the measuring signal depending on a displacement to be measured; Fig. 4 shows a representation of the linearity error depending on the displacement to be measured; Fig. 5 shows a representation of the phase characteristic with compensated linearity error in the case of the heterodyne interferometer arrangement according to the present invention as well as in the case of the heterodyne interferometric metering technique according to the present invention; Fig. 6 shows an arrangement for detecting the linearity error of a heterodyne interferometer; Fig. 7 shows a representation of the linearity error; Fig. 8 shows a graphic representation of the residual error in the case of the compensation carried out according to the invention in response to the phase error, which occurs without the compensation according to the invention; Fig. 9 shows an embodiment of the heterodyne interferometer arrangement according to the invention; Fig. 10, 11 and 12 show receiver components of the heterodyne interferometer arrangement according to the invention; Fig. 13 shows a measuring set-up for checking the method according to the invention; Fig. 14 to 17 show phase characteristics and phase error characteristics, respectively; Fig. 18 shows a schematic circuit diagram of a known interferometer; Fig. 19 shows a graphic representation of the variation with time of a reference signal and of a measuring signal in the case of the interferometer arrangement according to Fig. 18; and Fig. 20 shows a representation of the idealized orthogonal position of the two plane waves and of the position of the polarization filters in the case of the interferometer arrangement shown in Fig. 18. Fig. 1 shows the non-ideal case that the two polarizing directions of the incident radiation E₁, E₂ are not orthogonal to each other at the first and second frequencies f₁, f₂, respectively, so that frequency mixing will occur in the interferometer arms A1, A2. The deviation of the two polarization directions from orthogonality be α. As a result, in addition to the radiation component having the first frequency f₁, part of the radiation having the frequency f₂ will also enter the first interferometer arm A1 in the direction towards the first mirror MR1. The resultant radiation in this plane of polarization can be expressed as follows: (3a) E m1 = E₀sin(2πf₁t+₀₁+₁) + E₀sinαsin(2πf₂t+₀₂+₁) Accordingly, the radiation component, which is orthogonal to the above radiation and which enters the second interferometer arm A2, can be expressed as follows: (3b) E m2 = E₀cosαsin(2πf₂t+₀₂+₂) The following relation then results for the measuring signal I m , which corresponds to the a.c. output signal of the measuring photodiode D m : (3c) I m ∼ A*I₀cos[2π(f₁-f₂)t+ 0m +Δ-γ] (4) γ = tg⁻¹ sinαsinΔ cosα+sinαcosΔ (5) A* = 1 + sin2αcosΔ On condition that α is much smaller than 1 - said condition being fulfilled in the case of the relation α < 5° - the systematic phase error γ can be expressed by the following equation in first approximation. (6) γ ≃ αsinΔ A comparison between equations (2b) and (3c) shows that the phase measurement carried out by means of the known interferometer arrangement shown in Fig. 18 is affected by a systematic error γ , said systematic error γ being a periodic error which varies with the phase difference Δ. The maximum error is 2α. If α = 5°, for example, the maximum error of phase measurement will be 10°. This corresponds to an error of 9 nm in the length measurement in the case of the heterodyne interferometer according to the prior art which has been described at the beginning. It should also be noted that the amplitude of the measuring signal I m is no longer constant in contrast to the ideal case (cf. equation (2a)), but represents a periodic signal modulated by α and Δ (cf. equation (5)). Also the other causes of failure, which have been mentioned at the beginning and in view of which mixing occurs, cause similar results. When there is frequency mixing in both arms, the phase errors behave additively. But a simple rotation of the polarization directions of the incident light wave relative to those of the interferometer theoretically do not cause first order phase errors. Mixing errors due to leakage of the first polarizing beam splitter PB1 can mostly be neglected, because the leakage flux retains its polarization and must pass the first polarizing beam splitter PB1 at least once more before mixing of the leakage flux can take place at the location of the receiver. The first polarizing beam splitter PB1 normally has a rejection ratio of 0.3 % in intensity. The resulting phase error leads to a maximum error in the length measurement of 0.17 nm in the case of the heterodyne interferometer arrangement shown in Fig. 18 and 0.001 nm for differential interferometers. Non-ideal non-polarizing or polarizing optics behind the first polarizing beam splitter PB1 do not cause the error of non-linearity. In the case of the heterodyne interferometric metering technique according to the present invention, two measuring signals I m1 and I m2 are produced, which represent light components orthogonal to each other at the output of the interferometer unit. The following equations are obtained for the two measuring signals: (7) I m1 = I m ∼ A*I₀cos[2α(f₁-f₂)t +  0m + Δ - γ] (8) I m2 ∼ -B*I₀cos[2π(f₁-f₂)t +  0m + Δ + γ′] The negative sign in equation (8) for the second measuring signal I m2 corresponds to a constant phase displacement of π relative to the first measuring signal I m1 , and that has no influence on phase measurement. In the eighth equation, the following relationships exist: (9) B* = 1-sin2αcosΔ (10) γ′ = tg⁻¹ sinαsinΔ cosα-sinαcosΔ On the basis of an approximation, which corresponds to the approximation described with reference to equation (6), the following relationship between the two deviations of linearity of the two measuring signals I m1 , I m2 is obtained: (11) γ′ ≃ αsinΔ = γ It can be seen that the two measuring signals I m1 , I m2 have opposite deviations of linearity. When it is assumed that (12) Δ₁ =  0m + Δ - γ (13) Δ₂ =  0m + Δ - γ′ the following connection will be obtained provided that α << 1: (14) Δ₂ - Δ₁ = γ′ + γ (15) γ′ + γ = sin⁻¹ sin2αsinΔ 1-sin²(2α)cos²(Δ) ≃ 2αsin Δ Fig. 5 shows the graph of the arithmetic mean of the phase displacement Δ₁ of the first measuring signal I m1 as well as of the phase displacement Δ₂ of the second measuring signal I m2 in response to the length variation ΔL to be detected. When this graph is compared with the non-compensated graph according to Fig. 3, it will become evident that, with the exception of a residual error, the periodic linearity error has been compensated almost completely. In the case of the method of detecting the non-linearity of a heterodyne interferometer according to the present invention, the first and second measuring signals I m1 , I m2 , which have already been mentioned and which represent two light components orthogonal to each other at the output of the heterodyne interferometer, are produced, whereupon the phase difference between these measuring signals is detected, without there being any necessity of carrying out a comparison of said measuring signals with a reference signal for the method of measurement according to the present invention. Nor is it necessary to carry out a comparison with a reference interferometer for the purpose of detecting non-linearity. The phase difference calculated is shown in Fig. 4, whereas Fig. 7 shows the phase difference measured in the case of the embodiment of a non-linearity measuring arrangement according to Fig. 6, which still has to be explained hereinbelow. In both cases, the amplitude of the periodic phase difference signal represents the maximum non-linearity error. As can be seen in Fig. 6, the arrangement for detecting the non-linearity of a heterodyne interferometer according to the invention serves to check heterodyne interferometers according to the prior art whose structure is knonw per se. Said structure comprises a light source LS and an interferometer unit IF; these are components which have already been explained with regard to Fig. 18. At the output of the interferometer unit IF a λ/2 plate LHP is arranged, said plate being used for effecting rotation of the polarization direction by 45°. A second polarizing beam splitter PB2 is provided in the beam path behind said plate. By means of the combined effect of said λ/2 plate LHP and of the second polarizing beam splitter PB2, orthogonal components of the light at the output of the interferometer unit IF are supplied to first and second optoelectric measuring transformer units D m1 , D m2 , which may be constructed as photodiodes. The output signals of these measuring transformer units are supplied to a phase difference circuit PD, which will form the phase difference as defined in equations 14 and 15. In the following, the residual error occurring in the case of the heterodyne interferometric metering technique according to the present invention is to be determined. It can be obtained from equations 12 and 13: (16) (Δ₁ + Δ₂)/2 = Δ + ε and (17) ε = (γ′ - γ)/2 = 1 2 sin⁻¹ sin²αsin(2Δ) 1 - sin²(2α)cos²(Δ) ≃ 1 2 α²sin(2Δ) (if α << 1) As can be seen in Fig. 8, the residual error ε is mostly negligible so that the measured value obtained by forming the mean value of the phase differences in the case of the interferometric metering technique according to the present invention is virtually free from non-linearity. It is, however, emphasized that in the case of the heterodyne interferometric metering technique according to the invention, the two measuring signals I m1 , I m2 cannot directly be related with each other for forming the mean value of the phases, because the amplitudes of these measuring signals are no longer constant and have opposite phases so that an error would be caused if a simple phase addition were carried out. As has already been mentioned, it will be necessary to compare the two orthogonal measuring signals I m1 , I m2 separately with the reference signal I r and then form the arithmetic mean value of the resultant phase differences. A heterodyne interferometer arrangement suitable for carrying out the heterodyne interferometric metering technique according to the invention is shown in Fig. 9. As far as the arrangement according to Fig. 9 corresponds to the arrangement according to the prior art according to Fig. 18, which has already been explained, identical or similar parts will be provided with identical reference numerals so that a renewed explanation of these components can be dispensed with. In the case of the heterodyne interferometer arrangement according to the present invention, the output of the interferometer unit has connected thereto a receiver unit RU, which generally divides the emergent light into two orthogonal light components and which supplies these components to first and second optoelectric measuring transformer units D m1 , D m2 so as to produce first and second measuring signals I m1 , I m2 , respectively; said optoelectric measuring transformer units may be constructed as photodiodes. The output signals of these measuring transformer units D m1 , D m2 are supplied to first and second phase comparator units PH1, PH2 whose reference input has applied thereto the reference signal I r . The resultant two phase difference signals Δ₁, Δ₂ at the respective outputs of the phase comparator units PH1, PH2 are supplied to a mean value generation circuit MV, which will form the arithmetic mean value of the two phase differences. The receiver unit for a heterodyne interferometer arrangement according to the invention can be realized in different ways. Three possible embodiments are shown in Fig. 10, 11 and 12. A feature which is common to all embodiments of this receiver unit RU is that the light wave coming from the output of the interferometer unit IF is subdivided into two light components, which are orthogonal to each other and which are supplied to first and second optoelectric measuring transformer units D m1 , D m2 . The structural design of the receiver unit according to Fig. 10 corresponds to the relevant arrangement of Fig. 9. It should also be noted that, in the case of the structural design of Fig. 10, the second polarizing beam splitter PB2 corresponds with regard to its polarization direction to the axes M₁, M₂ of the wave originating from the interferometer unit IF. In contrast to the above, the embodiment according to Fig. 11 is constructed such that the second polarizing beam splitter PB2 is rotated by 45° relative to the main axes M₁, M₂ so that the λ/2 plate LHP of the embodiment according to Fig. 10 can be dispensed with. In the case of the embodiment according to Fig. 12, a non-polarizing beam splitter NPB2 is used instead of a polarizing beam splitter, the split light beams being caused to pass through third and fourth polarization filters PF3, PF4, respectively - which are displaced by 90° relative to each other - prior to impinging on the first or the second optoelectric measuring transformer unit D m1 , D m2 . Fig. 13 shows an experimental set-up for the detection and compensation of non-linearities in the case of a heterodyne interferometer arrangement. As will be explained hereinbelow, this experimental set-up is adapted to be used for proving the correctness of the theoretical derivation, which was carried out at the beginning and which underlies the present invention. In Fig. 13, reference numeral A generally refers to a reference interferometer arrangement, whereas reference numeral B is used for a heterodyne interferometer arrangement according to the invention having a structure which corresponds essentially to the structure shown in Fig. 9. The structural design of the reference interferometer arrangement essentially corresponds to the known structure shown in Fig. 18. To the person skilled in the art, it will be obvious that both interferometer arrangements A, B have applied thereto coherent light with two frequencies which comes from a joint light source LS. The light source used can be a two-frequency laser. For reasons of simplification, both interferometer arrangements A, B work with a common reference branch RB. The interferometer arms, which form parts of the two interferometer arrangements and which are variable in length, are secured to a lever LE whose geometry is chosen such that the length variation of the variable interferometer arm of arrangement A is fifteen times as large as that of arrangement B. The displacement of the interferometer arm of the heterodyne interferometer arrangement B to be examined is effected by means of a piezoelectric element PI in accordance with a ramp-shaped control signal, which comes from a signal source SS and which is supplied to an X-Y plotter as X signal. The zero passages of of the phase output P0 of the reference interferometer A furnish equidistant subdivisions for the displacement or variation in length of the interferometer B to be examined. The periodical integer phase is not influenced by potential non-linearities. The phase cycle of interferometer B is provided with 15 equidistant marks, and the phase displacements Δ₁ and Δ₂ are measured at these marks. The outputs of the optoelectric measuring transformer units D m1 , D m2 of the interferometer B to be examined respectively define a first input of first and second vector voltmeters VVM1, VVM2 whose respective other input has applied thereto the reference signal via signal dividers SP1, SP2. Said reference signal is also supplied to the X-Y plotter XYR as y₃ input. The two vector voltmeters VVM1, VVM2 constitute the phase comparator units of the interferometer arrangement B according to the invention which is to be checked. The output signals of these phase comparator units are supplied to the X-Y plotter XYR as y₁ input and as y₂ input. Fig. 14 to 17 show typical measurement results. The measured phase values Δ₁, Δ₂ as well as the mean values have been plotted as a function of the displacement in Fig. 14 and 16 for two different examination arrangements. Fig. 15 and 17 show the associated linearity errors or phase errors without compensation as well as with the compensation on the basis of the method of measurement according to the present invention. The following conclusions, which confirm the theory underlying the invention, can be drawn from the measurements: The traces of the two phase outputs Δ₁ and Δ₂ show sinusoidal deviations from linearity. The deviations from linearity are opposite in phase. The arithmetic mean value indicates a clear improvement in linearity. The residual non-linearity decreases with decreasing phase errors. Constant phase components, such as shift in the direction of the ordinate, do not influence linearity.

Claims: A heterodyne interferometer arrangement (1) comprising a light source means (LS) for producing light beams (E₁, E₂) having first and second frequencies (f₁, f₂); an optical reference branch (RB), which has supplied thereto a part of said light beams (E₁, E₂) and which is provided with a reference transformer means (D r ) for producing a reference signal; an optical measuring branch (MB), which has supplied thereto a part of said light beams (E₁, E₂) and which includes an interferometer unit (IF) causing a phase rotation of said light beams (E₁, E₂) in response to a length to be measured as well as a measuring transformer means arranged at the output of said interferometer unit (IF); and a phase comparator means arranged subsequent to said reference transformer means and said measuring transformer means, characterized in that the measuring transformer means comprises first and second optoelectric measuring transformer units (D m1 , D m2 ) responding to light components which are orthogonal to each other so as to produce first and second measuring signals (I m1 , I m2 ); and that the phase comparator means comprises first and second phase comparator units (PH1, PH2) whose output signals represent first and second phase differences (Δ₁, Δ₂) between the first or second measuring signal (I m1 , I m2 ) on the one hand and the reference signal (I r ) on the other, and a mean value generation circuit (MV) which is arranged subsequent to said phase comparator units (PH1, PH2) and the output signal of which represents the mean value of said first and second phase differences. A heterodyne interferometer arrangement according to claim 1, further characterized in that the measuring transformer means is provided with a polarization direction rotating means (LHP) arranged at the output of the interferometer unit and with a polarizing beam splitter means (PB2) supplying the orthogonal light components to the measuring transformer units (D m1 , D m2 ), and that the polarization direction of the polarizing beam splitter means (PB2) corresponds to the direction of one of the two light components. A heterodyne interferometer arrangement according to claim 1, further characterized in that the measuring transformer means is provided with a polarizing beam splitter means (PB2), which is arranged at the output of the interferometer unit (IF) and the polarization direction of which is rotated by 45° relative to the direction of the orthogonal light components, said polarizing beam splitter means supplying the orthogonal light components to the measuring transformer units (D m1 , D m2 ). A heterodyne interferometer arrangement according to claim 1, further characterized in that the measuring transformer means comprises a non-polarizing beam splitter means (NPB2) arranged at the output of the interferometer unit (IF) and two polarization filters (PF3, PF4) which are displaced by 90° relative to each other with regard to their polarization directions and which are used for filtering out the orthogonal light components supplied to the measuring transformer means (D m1 , D m2 ). A heterodyne interferometric metering technique comprising the following steps: producing a reference signal (I r ) representing a reference phase (₀) of the light beams (E₁, E₂) at the input of an interferometer unit (IF); rotating the phase of the light beams (E₁, E₂) in said interferometer unit (IF) in response to a length to be measured; producing a measuring signal representing the phase of the light beams at the output of the interferometer unit (IF); and comparing the phase of the reference signal (I r ) and of the measuring signal so as to produce a phase difference (Δ) which depends on the length to be measured; characterized in that the step of producing a measuring signal comprises the production of first and second measuring signals (I m1 , I m2 ) representing light components which are orthogonal to each other at the output of the interferometer unit (IF); and that the step of comparing the phases comprises the production of first and second phase differences (Δ₁, Δ₂) between the first or second measuring signal (I m1 , I m2 ) on the one hand and the reference signal (I r ) on the other as well as the generation of a mean value of the two phase differences (Δ₁, Δ₂) as a measure of the length (Δl) to be measured. An arrangement for detecting the non-linearity of a heterodyne interferometer whose input has supplied thereto light beams (E₁, E₂) having first and second frequencies (f₁, f₂), said heterodyne interferometer causing a phase rotation of the light beams between its input and its output depending on a length to be measured, characterized by first and second measuring transformer units (D m1 , D m2 ), which are arranged at the output of said heterodyne interferometer and which are constructed such that they respond to light components orthogonal to each other so as to produce first and second measuring signals (I m1 , I m2 ); and a phase difference circuit (PD) for producing a phase difference signal, which is representative of the phase difference (Δ) between the first and second measuring signals (I m1 , I m2 ) and the amplitude of which is proportional to the non-linearity of the heterodyne interferometer to be tested. A method of detecting the non-linearity of a heterodyne interferometer whose input has supplied thereto light beams (E₁, E₂) having first and second frequencies (f₁, f₂), said heterodyne interferometer causing a phase rotation of the light beams between its input and its output depending on a length to be measured, characterized by the following method steps: producing first and second measuring signals (I m1 , I m2 ) representative of two light components orthogonal to each other at the output of the heterodyne interferometer; and producing a phase difference signal, which is representative of the phase difference (Δ) between the measuring signals (I m1 , I m2 ) and the amplitude of which is proportional to the non-linearity of the heterodyne interferometer to be tested.

Inventors: HOU WENMEI DR, WILKENING GUENTHER DR, HOU, WENMEI, DR., WILKENING, GUENTHER, DR., Wilkening, Günther, Dr.
Applicants: HEWLETT PACKARD CO, HEWLETT-PACKARD COMPANY
Application year: 1991
Main classification: G01J9
IPC codes: G01J9, G01B9