DE19726931A1 - Interferometric method to measure phase difference between superimposed optical waves - Google Patents

Abstract

The method involves feeding a signal wave (3) and at least one reference wave (4), which is coherent with respect to it, together. The waves are measured interferometrically and evaluated in common. The intensity of at least one part-beam coupled out of the signal or the reference waves is measured simultaneously with the interferometric measurement and evaluation. This enables the phase difference between the signal wave and the reference waves to be measured. For a nonlinear sensitivity of the detector, a correction value is calculated according to the sensitivity of the detector value of the part wave.

Description

The invention relates to a method and an apparatus for interferometric determination of the phase difference between superimposed optical waves.

Various methods are known for determining the phase or spatial phase distribution of a signal wave with respect to a reference wave by superimposing both waves. The interference field resulting from the coherent superposition of the two waves with the intensities I _S and I _R and the phase difference Δϕ has the intensity

all sizes generally depend on location and time.

If the intensities I _S and I _{R are} known, e.g. B. by default or by direct measurement before or after the recording of the interferogram, the desired phase difference Δϕ can be determined from the measured variable I _IF according to the above equation.

However, the intensities I _S and I _R in the measurement of I _IF are not known, e.g. B. if the signal wave and / or the reference wave change their intensity temporally in an unknown manner or if each pulse has a different intensity or energy in pulsed operation, this direct method is not applicable. However, several methods enable an evaluation:
In the case of an at least one-dimensional interferogram, at unknown intensities I _S and / or I _R, the phase difference can be determined from the position of the maxima and minima in the interferogram and by interpolation between the extremes. However, this presupposes that the intensity I _S and / or I _R changes sufficiently small locally [J. Schwieder, Advanced Evaluation Techniques in Interferometry, in: Progress in Optics Vol. 28, ed E. Wolf (North Holland, 1990)].

With the Fourier transformation method [Schwieder] you can do with a single interferogram and without knowing the intensities I _S and I _R. The disadvantages here are the high computational effort, the arbitrary removal of information when filtering in the Fourier plane, problems in the marginal area of the interferogram. In addition, the evaluation of interferograms with closed lines, e.g. B. circular structures can be problematic. If the intensity I _S and I _{R are also of} interest, an interferogram is not sufficient to infer these values.

The phase shifting method [Schwieder], in which several interferograms are recorded, between which the phase pushed at least one shaft in a defined or undefined manner becomes. The downside is that multiple shots are needed in sequence, between which the object to be measured is only sufficiently small or may only change in a defined manner. So that z. B. a measurement with pulsed light source often not possible.

In the heterodyne method [P.Hariharan, Interferometry with lasers, in: Pro gress in Optics Vol. 24, ed E. Wolf (North Holland, 1987)] becomes a wave frequency shifted and the beat evaluated in the interference field. This requires additional equipment to generate the Frequency Ver shift and to determine the phase of the beat wave. The The method requires a certain measuring time, within which the  measuring object may only change sufficiently little. At the moment it can only be used for point-by-point evaluation of the interference field.

It is also known [e.g. B. DD-PS 1441 85], signal wave and reference wave as double exposure hologram with spatially separated hologram reference waves. This means that at another point in time both waves can be reconstructed individually, to determine the intensities I _S and I _R , or simultaneously to determine the intensity distribution I _IF . However, the additional mechanical and time expenditure for the recording or reconstruction of the holograms and for the temporally sequential intensity detection of the separately and jointly reconstructed waves is disadvantageous.

In the shearing interferometer [D. Malacara, Optical Shop Testing, John Wieley & Sons, 1992], the reference wave is decoupled from the signal wave and spatially shifted by the vector ν (χ) overlaid with it, with χ indicating the location on the detector . The vector ν can e.g. B. describe a lateral translation, a rotation of the beam about the direction of propagation or an expansion. This gives the phase difference for each location χ in the form of the difference Δϕ (χ) -Δϕ (χ-ν). In order to obtain the curve Δϕ (χ) itself, the displacement ν must be kept sufficiently small so that the approximation

applies and integration is possible. However, this limits the accuracy of the Determination of Δϕ (χ) on. For larger displacements ν must be done in advance certain assumptions about the phase progression can be made by e.g. B. chooses a polynomial approach for Δϕ (χ) to solve. Spatial Fluctuations in intensity in the signal wave lead to errors in the result. Areas that are not overlapping cannot be evaluated.

The object of the invention is the apparatus or process engineering Reduce effort to determine the phase differences. In particular not all should be used to calculate the phase difference according to formula (1) known sizes immediately with the inclusion of the signal and Interferogram to be formed by a relatively simple reference wave Equipment and can be obtained in the simplest possible way.

According to the invention, the signal wave and / or at least one Reference wave, from which the superimposed interferogram is formed, a partial steel is coupled out via a beam splitter and over Beam deflecting elements separate from the detection of the merged Signal and reference waves on another detector sub-area of the same Detector or directed to another detector. The interferogram of the superimposed signal and reference waves as well as the intensity of the decoupled partial beams can thus on a single or on Several detectors are detected simultaneously and fed to an evaluation unit become. In this way, the evaluation of the interferogram also determined the as yet unknown quantities from the formula (1) in order to obtain the To be able to calculate the phase difference of signal and reference waves. For Determining these unknown intensity quantities is not an additional one Measuring method and no complex equipment required. The effort consists only in the decoupling of the partial beam or beams and their separate detection.

Subclaims 2-10 contain advantageous design features the invention for the beam detection, the detector signal evaluation and for defining the optical paths of the main and the decoupled Partial beam of the signal and / or reference waves.

In principle, the invention is applicable to various basic types of interferometer applicable, e.g. B. Mach-Zehnder interferometer, Michelson interferometer  or Sagnac interferometer, and is shown below using three in the Exemplary embodiments shown as Mach-Zehnder Interferometer are explained in more detail.

Show it:

Fig. 1 Principle structure of the interferometer according to the invention, in which the signal and reference wave are imaged on one and the same intensity detector

Fig. 2 Principle structure according to FIG. 1 with additional coupling out of a part of the reference wave to a further intensity detector

Fig. 3 basic structure according to Fig. 1, in which in addition a part of the reference wave is separately coupled to the only existing intensity detector.

In Fig. 1 the basic structure of the interferometer is shown. An input wave 1 is divided by means of a beam splitter 2 into a signal wave 3 with an intensity I _S and into a reference wave 4 with a known intensity I _R , via a beam deflecting element 5 or a beam deflecting element 6 and after merging via a semitransparent mirror 7 are guided onto a detector surface 8 by a detector unit 9 . The signal wave 3 can be modified after the beam splitter 2 by an object (not shown here) in the phase and intensity distribution and carries the information sought in the intensity distribution and in the phase distribution with respect to the known properties of the reference wave 4 .

The merged waves hit a partial detector surface 8 a of an at least one-dimensional intensity detector 10 . The interferogram detected in this way is fed to an evaluation unit 12 via a line 11 .

According to the invention, part of the signal wave 3 is coupled out with a beam splitter 13 and directed via two beam deflection elements 14 , 15 to a partial detector surface 8 b of the detector unit 9 .

The interferometer arrangement is constructed so that the optical paths from the beam splitter 13 on the one hand via the semitransparent mirror 7 to the detector partial surface 8 a and on the other hand via the beam deflecting elements 14 , 15 to the detector partial surface 8 b are each of the same length. Thereby, the part of the wave fronts of the signal wave 3 to the detection sub-faces 8 a and 8 b are each identical and are a structure contained in the signal wave 3 is therefore on both detection sub-faces 8 a, 8 b distribution similar intensity. With the reference wave 4 simultaneously striking the detector unit 9 , the interferogram with an intensity distribution I _IF is obtained on the detector sub-area 8 a.

In order to calculate the desired phase difference Δϕ for each point on the detector sub-area 8 a according to equation (1), the still missing intensity I _{S of} the signal wave 3 is calculated from the intensity I _S 'measured at the detector sub-area 8 b of the part coupled out at the beam splitter 13 Signal wave 3 determined. For this purpose, both to each point r on the detector surface portion 8a by the optical system (ray deflection 14, 15, beam splitter 13 and half mirror 7) have predetermined conjugate position r '= τ _S (r) b on the detector surface portion 8 and the division ratio β _S = I _S '/ I _{S of} the corresponding conjugate rays.

The local transformation τ _S is either known from the precise knowledge of the shape and position of the elements of the optical system or can be determined from a calibration measurement (once or at certain intervals) by introducing spatially defined structures into the beam path of the signal wave 3 (or are already present), the reference wave 4 being hidden. These defined structures are identified in the images of both the detection sub-face 8a and the detector sub-area 8b, whereby an assignment is made. The assignment could also be carried out by cross-correlating the images on the detector subareas 8 a and 8 b or by other suitable methods.

The local transformation τ _S is available to the evaluation unit 12, for example, as a table or as an analytical function (e.g. constant or location-dependent translation vector).

The division ratio β _S is known from the precise knowledge of the properties of the optical system (beam deflection elements 14 , 15 , beam splitter 13 and semitransparent mirror 7 ) or can be determined from a (one-time or at certain intervals) calibration measurement by using the aforementioned calibration measurement for Determining the spatial transformation τ _S the intensity ratio for conjugate points or conjugate areas is determined. It is also possible to determine the division ratio β _S from a (one-off or at certain intervals) calibration measurement by registering and evaluating the signal wave 3 without said defined structures in the signal beam path and with the reference wave 4 hidden on both partial detector surfaces 8 a and 8 b .

The division ratio β _S is available to the evaluation unit 12, for example, as a constant factor, location-dependent function or as a table.

In FIG. 2, the basic structure according to the invention according to FIG. 1 is expanded in that a further detector unit 19 is provided, which has an intensity detector 21 with a detector surface 20 . A part of the reference wave 4 is coupled out via a beam splitter 16 and directed via two beam deflection elements 17 , 18 to a partial detector surface 20 b of the detector unit 19 . Simultaneously, a coupled-on half-mirror 7 of the signal wave is 3 surface onto a detector part 20 a of the detector surface 20 directed, the optical paths from the beam splitter 16 on the one hand elements via the semi-transparent mirror 7 to the detection sub-face 20 a as well as other, on the Strahlumlenk 17, 18 to the detector partial surface 20 b are each of the same length.

The detector unit 19 is also connected to the evaluation unit 12 via a line 22 . An interferogram with an intensity distribution I _IF 'is registered on the detector partial surface 20 a of the detector surface 20 , to which a part of the signal wave 3 coupled out at the semi-transparent mirror 7 is directed. Thus, 9 β _S .I _S and I _{IF are registered} on the first detector unit and 19 β _R .I _R and I _IF 'are registered on the second detector unit 19 . According to ( 2 ), I _IF 'runs in phase opposition to I _IF .

With the measured variables, the values τ _S , β _S , β _R and β _R and the equations (1) and (2), the phase difference Δϕ can be determined, the redundancy due to the over-determination of equations (1) and (2) Correction of errors, e.g. B. non-linearity of the detectors or interference effects allowed and thus increases the robustness of the system.

FIG. 3 shows a further exemplary embodiment, in which, as an extension of the basic structure according to FIG. 1, a part of the reference wave 4 is additionally coupled out by a beam splitter 23 and, via two beam deflection elements 24 , 25, onto a third partial detector surface 8 c of the detector surface 8 from the detector unit 9 is passed so that all the quantities required in equation (1) for determining the phase difference Δϕ are registered by a single detector unit (for example a CCD or CMOS camera).

For the evaluation, the local transformation τ _S and the division ratio β _S for the signal wave 3 as well as the local transformation τ _R and the division ratio β _R for the reference wave 4 must be known. The local transformation τ _R and the division ratio β _R are in principle obtained as in the first embodiment of FIG. 1.

The invention described using the example of two-beam interferometry is in principle also applicable to multi-beam interferometers, whereby on at a suitable point, part of one or more shafts are coupled out and in their intensity can be determined (not shown in the drawing).

Instead of the detector units 9 , 19 , photosensitive materials can also be used for storing the intensity distribution (eg photo plate) or the wave field (holographic memory). The stored information can then be called up at a later time (after the necessary process steps such as developing the photo plate) and brought into a form suitable for the evaluation unit, e.g. B. by means of an intensity detector.

The optical system, in particular with the semi-transparent mirror 7 , the beam splitter 13 and the beam deflecting elements 14 , 15 , can advantageously be implemented as a module with a connection thread for a standard CCD camera.

On the measurement and evaluation of the drawing files as well as on the intermediate ones results in the calculation, e.g. B. in the calculation of cos (Δϕ), can various filter operations known per se can be used, e.g. B. Smoothness processing, edge lifting, spin filtering.

When using intensity detectors or photosensitive Materials with a nonlinear sensitivity characteristic can be used in the Evaluation the corresponding parameter (e.g. the gamma factor) or a specific characteristic can be taken into account.  

In order to avoid that the maxima in the interferogram on the detector surface portion 8 a detector unit 9 does not override, the division ratio between the divided shafts is advantageously chosen so that the dynamics of the detector unit is optimally utilized. 9 In general, the sub-beam to the detector sub-area 8 a should therefore be darker than the sub-beam to the detector sub-area 8 b.

With the known by measuring the intensity of the signal wave 3 and / or reference shaft 4 a not shown in the drawing, light modulator in the respective optical path of the signal and / or reference waves may influence this in a defined manner such that on the detector unit 9 optimal intensity resolution or The dynamic range of the detector is optimally used (adaptation to the object to be measured, darkening of particularly bright areas).

The sign of the phase difference Δϕ cannot be determined from the inverse of the cos function. When evaluating at least one dimensional interferograms, this can be done using suitable, well-known methods using additional information about the shape of the wave, e.g. B. with monotonous curvature of the wavefront. The beam splitters 2 , 13 , 16 , 23 shown symbolically in the drawing can be implemented, for example, by partially transparent (metallic or dielectric) mirrors, by polarization beam splitters, by holographic-optical elements or by diffraction gratings.

For use as beam deflection elements 5 , 6 , 14 , 15 , 17 , 18 , 24 , 25 , in particular (metallic or dielectric) mirrors, prisms, holographic-optical elements and diffraction gratings are possible.

Reference list

1

Input shaft

2nd

,

13

,

16

,

23

Beam splitter

3rd

Signal wave

4th

Reference wave

5

,

6

,

14

,

15

,

17th

,

18th

,

24th

,

25th

Beam deflecting element

7

semi-transparent mirror

8th

,

20th

Detector area

8th

a,

8th

b,

8th

c,

20th

a,

20th

b Detector partial area

9

,

19th

Detector unit

10th

,

21

Intensity detector

11

,

22

management

12th

Evaluation unit
I _IF

,

I _IF

'' Intensity distribution
Δϕ phase difference
I _S

Intensity of the signal wave
I _S

'Intensity of the extracted part of the signal wave
I _R

Intensity of the reference wave
r

,

r 'location on the detector surface
τ _S

Local transformation of the signal wave
τ _R

Local transformation of the reference wave
β _S

Division ratio of the signal wave
β _R

Division ratio of the reference wave

Claims (5)

1. A method for the interferometric determination of the phase difference between superimposed optical waves, in which a signal wave and at least one coherent reference wave are merged and jointly measured and evaluated interferometrically, characterized in that at the same time for interferometric measurement or evaluation of the merged signal and reference waves Intensity of at least one partial beam coupled out of the signal wave and / or the at least one reference wave is measured and used to determine the phase difference between the signal wave and the at least one reference wave. 2.Device for the interferometric determination of the phase difference between superimposed optical waves, in which a signal wave and at least one coherent reference wave, for example by a semitransparent mirror, are brought together again and passed to a detector which is used for interferometric evaluation of the after combining signal and Reference waves incident on the detector light are connected to an evaluation unit, characterized in that in the beam path of the signal wave ( 3 ) and / or the at least one reference wave ( 4 ) a beam splitter ( 13 or 23 ) for coupling out a partial beam from the signal or at least one reference wave ( 3 , 4 ) is arranged and that beam deflecting elements ( 14 , 15 , 17 , 18 , 24 , 25 ) are provided, through which the partial beam for intensity measurement on another detector partial surface ( 8 b, 8 c) of the same detector ( 9 ) or another, preferably also connected to the evaluation unit ( 12 ), detector ( 19 ). 3. The method according to claim 1, characterized in that for a non-linear sensitivity characteristic of the detector the detector measured value of the decoupled partial beam is a sensitivity characteristic corresponding correction value is taken into account. 4. The method according to claim 1, characterized in that for the purpose of Selection of an advantageous dynamic range of the detector's intensity the signal wave and / or the at least one reference wave in Dependence of the intensity of the measured by the detector decoupled partial beam, for example by an LCD display optical modulator, is controlled. 5. The device according to claim 2, characterized in that the optical path of the divided signal wave ( 3 ) or at least one reference wave ( 4 ) between the beam splitter ( 13 , 16 or 23 ) and the partial detector surface ( 8 a or 20 a) and the optical path of the decoupled partial beam between the beam splitter ( 13 , 16 or 23 ) and the detector partial area ( 8 b or 20 b or 8 c) is in each case of the same length.