Interferometric measurement device and method for determining the surface topography of a measurement object - Patents.com

Abstract

The present invention relates to an interferometric measuring device and an interferometric measuring method for determining the surface topography of a measuring object (1). Importantly, the value z assigned to the detector element p (6b) of the measuring device p To determine the light intensity I of this detector element p, p (z i ), as well as the light intensity I of at least one other detector element q of the multi-element detector (6). q (z i ) is also used.

Description

[Technical field]

[0001] The present invention relates to an interferometric measurement device and an interferometric method for determining the surface topography of a measurement object. [Background technology]

[0002] Interferometric measuring devices are known for determining the surface topography of a measurement object, in which a portion of the light of a light source is directed to the surface of the measurement object, reflected back therefrom as measurement light and subsequently combined with another portion of the light of the light source, which is used as reference light, by means of suitable interference optics, so that an interferogram is formed by interference of the measurement light and the reference light, from whose fringe structure the surface topography of the measurement object can be deduced. In measurement technology, the surface topography describes the geometric form of the surface to be examined, in particular in the form of a one- or two-dimensional surface profile.

[0003] There are many embodiments of such interferometric measuring methods in the prior art. In many of them, the optical path length difference OPD existing between the optical path of the measuring light and the optical path of the reference light is changed when recording the interferogram. This allows a specific interferogram to be drawn for different path length differences OPD. In this way, an intensity profile is obtained for each individual point of the interferogram as a function of the adjusted OPD. Such intensity profiles, which are scanned for different OPD values, are usually called "correlograms" for the associated points. In many cases, each point of the interferogram is assigned to an associated point on the surface of the measurement object, for example by optical imaging, so that in this case it is also possible to assign the corresponding correlogram to a specific measurement point on the measurement object. Using the correlograms associated with the measurement points, the respective difference between the optical path lengths of the measuring light and the reference light and therefrom the surface topography of the measurement object are then determined during the subsequent evaluation.

[0004] The surface topography of the object is usually calculated by dividing the surface by the level values ​​h of a number of surface points p. p i.e., by their spatial position relative to a known reference plane, often a plane. When the surface topograph exists in this form, it can be easily expressed relative to any other reference plane, provided that the spatial absolute value of the first reference plane relative to this other reference plane is known.

[0005] For the sake of simplicity, therefore, in interferometric measuring devices, a plane is often assumed as a reference plane, in which in a given reference state of the interferometer the optical path length difference OPD between the measurement light and the reference light is zero. This reference plane is often represented by a plane that is optically conjugate to the reference plane of the interferometer, usually a mirror, and often, but not always, a plane in the object space of the measurement object. Based on the above, for all further discussions, this plane can be consistently used as a reference plane for the surface topography, without limiting generality, since conversion to other reference planes is easily possible.

[0006] In the reference state of the interferometer, the OPD for each measurement point p on the measurement object is usually -2*n*h p That is, it corresponds to the negative double of the level value of the associated measuring point p by the light going round trip, possibly corrected by the refractive index n of the material between the reference surface and the measuring surface. For the sake of simplicity, this refractive index is generally assumed to be 1 below, without limiting generality, since the description of other values ​​with slight mathematical modifications is clear to the person skilled in the art.

[0007] Current interferometric methods for determining the surface topography of a measurement object are, on the one hand, phase-shifting interferometry (PSI) and, on the other hand, low-coherence interferometry, in particular scanning white light interferometry (WLI).

[0008] In either case, for every relevant measurement point p on the measurement object, z1, z2, ..., z nStrength of membership for different OPDs changed by I p (z1), I p (z2),...I p (z n ) is recorded in the interferogram, so that for each measurement point p an associated correlogram c p =(c p (1), c p (2),...,c p (n)), where the light intensity measured at the ith point of the correlogram is c p (i)=I p (z i ).

[0009] Preferably, the OPD is varied in a predetermined manner during the recording of the correlogram, often by z1, z2, ..., z n are equally spaced with a known interval Δz. For this purpose, for example, the length of the measurement arm or the reference arm of the interferometer is changed mechanically or by incorporating a material with a different refractive index. In many cases, the measurement object is also slid relative to the interferometer or the interferometer is slid relative to the measurement object, which is essentially equivalent to changing the measurement arm length. The length change is selectively performed continuously or stepwise. It is important that the respective OPD change is known as accurately as possible, since the accuracy of the further evaluation and thus of the specific surface topography essentially depends on accurate knowledge of the respective OPD change. This is also advantageous in the invention described below.

[0010] In phase-shifting interferometry (PSI), the phase difference PD between the measurement light and the reference light is varied and a correlogram is recorded depending on the adjusted phase difference. In principle, the phase change is achieved by changing the optical path length as described above. However, this can also be achieved by changing the wavelength of the illumination light used, as described in patent document 1. All the considerations made below are easily transferred to the latter in the present invention described below. Therefore, for a simpler representation, the further description is limited to the general case of phase change by changing the optical path length, without limiting generality. By using an illumination light with a sufficiently large coherence length or by scanning only a short period of the interference signal, it is achieved that the intensity of the measurement light varies sinusoidally with the adjusted phase. By determining the phase position of the recorded sinusoidal signal depending on the adjusted path length for the various measurement points, the difference in OPD between the various measurement points is determined and, finally, the surface topography of the measurement object compared to the reference surface is determined.

[0011] In low-coherence interferometry, especially scanning white light interferometry, the OPD is likewise changed during the measurement. However, since low-coherence light, i.e. spectrally broad light, is used here, the correlogram only shows a modulation if the measurement light and the reference light pass through approximately the same optical path length, i.e. if the path length difference is small. On the other hand, if the OPD is larger than the coherence length of the light used, the modulation disappears. Typically, the general function correlogram curve c(OPD) is depicted by a slowly varying envelope that approaches zero for large absolute values ​​of the OPD values, depending on the OPD adjusted by a sinusoidal modulation. c(OPD)=A+B*env(OPD)*cos(φ(OPD))

[0012] where env(POD) is a slowly varying envelope, e.g. a Gaussian curve env(OPD)=exp(-a*OPD 2), where φ(OPD) is the phase which varies depending on the OPD, and in the simplest case φ(OPD)=2π / λ*OPD, where λ is the effective wavelength of the illumination light and 2π / λ refers to the carrier frequency of the modulation. The constants A and B represent the signal offset or the associated modulation amplitude, both of which are influenced in particular by the reflectivity of the object at the measurement point. Both constants are not of significant relevance in the following description of the invention, with respect to the following considerations, but are very complicated to explain. Therefore, for simplicity of explanation below, and without limiting generality, it is assumed that A=0 and B=1, and the measurement signal is easily incorporated into this formula, if necessary, for example by subtracting the mean value and by appropriately normalizing the signal.

[0013] To this extent, in what follows we assume, without limiting generality, a general function correlogram course c(OPD) such that: c(OPD) = env(OPD) * cos(φ(OPD))

[0014] Correspondingly, in the following, for the sake of simplicity and without limiting generality, the light intensity I p (z i )=c p (i) = c(z i -2+h p ) are also assumed to be corrected by their offset, which is realized by simply subtracting the offset of the respective correlogram. This offset can in the simplest case be taken from the edge regions of the correlogram where no or little interference occurs, or in another simple way, for example the average light intensity of the correlogram (I p (z1)+I P (z2)+...+I p (z n )) / n. However, if necessary, one can resort to more sophisticated possibilities, for example to consider the phase positions of the individual points together. Correcting the light intensities by their offset is just a matter of subtracting I p (z i ) is the n-dimensional light intensity vector (Ip (z1), I p (z2),...,I p (z n It should be noted that the term "rescale" or "normalize" refers to the transformation of (a) or (b) of (c) in a manner that is consistent with the present invention and should be understood in the context of the following description and particularly the claims.

[0015] It is usually assumed that, to a good approximation, the correlogram curve for all measurement points assumes a defined general functional shape after subtraction of offsets and normalization. In practice, small deviations therefrom may exist, for example due to different material scattering on the light paths to the various measurement points and the associated reference points. In order to take this effect into account and correct its influence on the measurement result, relevant procedures are known, for example, in which this effect or the effects resulting therefrom are measured using a known measurement object, for example a precision plane mirror, and are appropriately taken into account when evaluating the measurement of the measurement object. Measures of this kind are of course also carried out, if necessary, in connection with the inventive procedure described below.

[0016] Typically, during the so-called "envelope evaluation", it is assumed that the envelope maximum is reached when the optical paths of the measurement arm and the reference arm are of the same length, i.e. when the OPD takes the value zero. Correspondingly, for each correlogram, the envelope maximum is determined as the value z at which the correlogram envelope maximum exists for the OPD change relative to the reference state of the interferometer. p According to what has been said so far, the OPD of the affiliation is zero there, i.e. z p -2*h p = 0, from which the level value h p In unusual circumstances, when the OPD at the envelope maximum is different from zero, the procedure is the same, only the right hand side of the above equation is different from zero, and the level value h p is still found in the same way as before. In either case, the multiple level values ​​h p from which the spatial position of the measurement point p is finally obtained and thus the surface topography of the measurement object compared to the reference surface.

[0017] There are various procedures for determining the envelope maximum. In a frequently used approach, the envelope itself is first determined from a correlogram whose envelope is first sinusoidally modulated. For this purpose, for example, a composite correlogram s(OPD)=env(OPD)*sin(φ(OPD)) with a carrier frequency phase shifted by 90° is squared from the correlogram c(OPD)=env(OPD)*cos(φ(OPD)) using the Hilbert transform, and the desired envelope env(OPD) is obtained after adding both correlograms c(OPD) and s(OPD) and subtracting the square root. Alternatively, the envelope env(OPD) can also be determined by fitting sinusoidal functions one by one to the correlogram and evaluating the corresponding amplitudes point by point. In this case, the position of the envelope maximum is often determined by fitting a suitable curve course to the previously determined envelope env(OPD).

[0018] An alternative approach to determining the location of the envelope maximum is to first use a Fourier transform of the correlogram to determine the linear slope of the phase at the carrier frequency in Fourier space, plotted over spatial frequency, and from there determine the location of the envelope maximum as well.

[0019] Once the position of the respective envelope maximum has been determined, in many cases a very accurate determination of the surface topography of the measurement object can be made immediately therefrom, which is particularly the case for measurement objects with rougher surfaces.

[0020] In certain cases, especially when the measurement object has a smooth surface, the accuracy of the surface topography determination can be significantly improved by using the so-called "phase evaluation". This is done by using the sinusoidal modulation of the correlogram in the vicinity of the envelope maximum for the evaluation in addition to the evaluation of the position of the envelope maximum. Here, the initially determined position of the envelope maximum is not used directly as a reference point with an explicitly and / or implicitly set value for the OPD or PD, but instead a much more accurately determinable position closest to the envelope maximum and with a specific phase position of the sinusoidal oscillation, for example the position of their nearest descending zero crossing, is used. Comparing the OPD differences of the positions determined in this way with the various measurement points results in a much more accurately determined surface topography than if the position of the envelope maximum were used alone. For practical implementation, it is often sufficient for this purpose to simply determine the phase position of the sinusoidal modulation at the determined position of the envelope maximum. Therefrom, for any phase position of the sinusoidal modulation in the vicinity of the envelope maximum, the associated position can be obtained with sufficient accuracy if the variation of the OPD over the entire correlogram measurement is known.

[0021] It is worth pointing out here that the methods of correlogram evaluation are closely related to each other whether in low-coherence interferometry or in phase-shifting interferometry. The general function course of the correlogram in low-coherence interferometry is written as follows: c(OPD) = env(OPD) * cos(φ(OPD)) The corresponding correlogram in phase-shifting interferometry has a constant envelope env(OPD)=const and a phase proportional to OPD, φ(OPD)=2π / λ*OPD, where λ is again the wavelength of the illuminating light. This is therefore c(OPD) = const. * cos(2π / λ * OPD) which is finally a special case of the correlogram of low-coherence interferometry, i.e. a special case where the finite coherence length is so large that it is not necessary to take this coherence length into account for the measurements performed. This allows many of the considerations or statements given below in relation to low-coherence interferometry to be directly transferred to phase-shifting interferometry as well, without always going into detail about it.

[0022] The procedures and observations described have been known for a long time and are used in many different ways with many types of interferometers to determine surface topographies. Finally, all types of interferometers known can be used for this purpose, and in particular for implementing the invention described below, where particular mention should be made of the Michelson interferometer, the Mach-Zehnder interferometer, the Mirau interferometer, the Linnick interferometer and the Fizeau interferometer, although other types of interferometers can also be used.

[0023] In order to be able to determine the surface topography accurately using such an interferometer and the procedure described above, it is important, according to known prior art techniques, to control as accurately as possible the OPD changes which are adjusted or occur during the recording of the correlogram: small deviations of the true OPD changes from the expected or adjusted OPD changes usually lead to large deviations of the determined surface topography compared to the true surface topography.

[0024] This fact is generally known and therefore appropriate measures are usually taken for this purpose when using interferometers in order to avoid unwanted and uncontrolled OPD influences during measurements or, if this is not possible, to at least determine them as well as possible and take them into account in the evaluation.

[0025] Correspondingly, the interferometers used are usually constructed and built in such a way that they are as little influenced as possible by ambient vibrations, since such vibrations usually have different effects on the measurement and reference arms of the interferometer, which leads to unknown and uncontrolled OPD changes. In many cases, vibration-proof or even active vibration-compensated tables are used as base platforms for the construction of the corresponding interferometers. For high-precision measurements, even air eddies, which are accompanied by refractive index fluctuations in the measurement and reference arms, are disruptive and must be prevented. This is done, for example, by keeping the air temperature in the interferometer as constant as possible and / or by guiding the air flow as laminar as possible, or even in extreme cases, by operating the interferometer under vacuum conditions. Of particular importance are the positioning or displacement units, with which the OPD and the associated guiding and fixing elements are changed during the measurement. Since inaccuracies here significantly affect the measurement accuracy of the entire system, expensive and costly components are usually used here.

[0026] Nevertheless, in many cases, this measure is not sufficient to stabilize the OPD sufficiently well. In this case, in addition to the actual interferometer, a further measuring device is integrated into the overall system, which has the exclusive task of measuring the OPD fluctuations occurring during the actual measurement as precisely as possible, so that their influence can be taken into account when evaluating the correlogram. An extensive disclosure of the measuring devices used for this purpose and possible procedures for appropriately taking the determined results into account for the evaluation of the correlogram is given in US Pat. No. 5,399,433.

[0027] All of the above mentioned measures to avoid and / or determine unwanted or uncontrolled OPD effects during interference measurements are complex, cumbersome and / or expensive. [Prior art documents] [Patent documents]

[0028] [Patent Document 1] U.S. Pat. No. 4,594,003 [Patent Document 2] U.S. Patent No. 8,902,431 Summary of the Invention [Problem to be solved by the invention]

[0029] The object of the present invention is therefore to provide an interference measuring device and an associated method which is sufficiently robust against OPD variations and which therefore makes it possible to largely avoid the previously mentioned complicated measures for avoiding the disruptive effects of OPD, in that it is not necessary to determine disruptive OPD variations or take them into account in the evaluation method. [Means for solving the problem]

[0030] This problem is solved by a method according to claim 1 and by a device according to claim 20. Preferred configurations are set out in the dependent claims.

[0031] The method of the present invention for interferometrically determining the surface topography of a measurement object includes the steps of forming an illumination light and a reference light by at least one light source and illuminating the measurement object with the illumination light, combining the illumination light reflected back from the measurement object as measurement light with the reference light to form an interference pattern in a detection area, varying the optical path length difference and / or phase difference between the measurement light and the reference light, and determining a light intensity I of the interference pattern on a plurality of detection elements p of a multi-element detector in the detection area. p (z i ) with different absolute values ​​z i detecting at least two optical path length differences or phase differences that have been changed by an absolute value z of the change in optical path length difference or phase difference for a plurality of detection elements p of the multi-element detector; pdetermining the absolute value at which the optical path length difference or the phase difference between the measurement light and the reference light, respectively, reaches a value explicitly and / or implicitly set for the detector element p; and measuring the surface topography of the measurement object by the absolute values ​​z p and determining the amount of the compound from the above.

[0032] The value z assigned to detector element p p To determine the light intensity I p (z i ), in addition to the light intensity I of at least one other detector element q of the multi-element detector. q (z i It is important to also use

[0033] Therefore, the light intensity I p (z i ) and I q (z i ) is determined by at least two different detector elements p and q, which are assigned different points of position on the measurement object by optical imaging and / or different points of position on an optical surface, preferably an optically conjugate plane, conjugated to the multi-element detector. This surface optically conjugated to the multi-element detector is preferably a reference plane of the interferometer, a surface in the space of the measurement object, an intermediate image plane of the optical imaging, a pupil and / or an aperture plane of the optical imaging.

[0034] In the method of the present invention, the light intensity I of the interference pattern is measured on a plurality of detection elements p of the multi-element detector in the detection region. p (z i ) but with different absolute values ​​z i Advantageously, at least two optical path length differences or phase differences are detected which are changed by different absolute values ​​z i The detection is carried out for a relatively large number of optical path length differences or phase differences, which are changed by at least three, preferably at least 10, particularly preferably at least 20 different z iDetection is carried out for different absolute values ​​z. Typically, fewer measurement points are sufficient for PSI methods than for WLI methods. Therefore, when the method according to the invention is configured as a WLI method, it is advantageous to i The detection is carried out for a relatively large number of optical path length differences or phase differences, which are changed by at least 5, preferably at least 20, particularly preferably at least 50 different z i Perform detection on.

[0035] It is also within the scope of the present invention that analog variables are used for the variables used to describe the method of the present invention, which, optionally together with further variables or parameters, have the information content of said variables and can therefore be converted as required. This means that the variable z and the absolute value z assigned to the detector element p Thus, for example, with knowledge of the constant rate of change of the optical path length difference and / or the phase difference, the measurement time t p You can specify the absolute value z p This also applies to the inventive device and to the preferred embodiments of the inventive method and the inventive device described below.

[0036] The inventive apparatus described below is preferably adapted to carry out the inventive method, in particular the preferred embodiments thereof. The inventive method is preferably adapted to be carried out by the inventive apparatus described below, in particular the preferred embodiments thereof, such as the advantageous configurations described below.

[0037] The inventive interferometric measuring device for interferometrically determining the surface topography of a measuring object has the following characteristics: The inventive interferometric measuring device comprises at least one light source, e.g. laser, LED, superluminescent diode, incandescent lamp, gas discharge lamp, arc lamp, plasma light source, etc. The measuring object is illuminated with a portion of the light of the light source, preferably using suitable illumination optics, particularly preferably illumination optics which images the light source onto the aperture plane of the objective, e.g. coherent illumination optics. A reference light is formed with a portion of the light of the light source, preferably by splitting the light of the light source by means of a beam splitter, e.g. a neutral or polarizing splitter, into a first portion for illuminating the measuring object and a second portion used as reference light.

[0038] By means of the interference optics, the illumination light reflected or scattered back from the measurement object as measurement light is combined with the reference light. This is preferably done by combining the measurement light and the reference light with one another by a beam splitter, but at least by directing the measurement light and the reference light to a common detection area, so that an interference pattern is generated by the interference of the measurement light and the reference light. Interferometric measuring devices of this kind are well known and are used in various ways. Ultimately, all known types of interferometers can be used to realize the invention, and in particular the Michelson interferometer, the Mach-Zehnder interferometer, the Mirau interferometer, the Linnick interferometer and the Fizeau interferometer are mentioned here. However, the invention is not limited to these interferometer types. Any other interferometer types can also be advantageously used within the scope of the invention without any restrictions. The interference optics therefore preferably comprises one or more optical elements from the following list of optical lenses (beam splitters, filters, diaphragms, mirrors, polarizing filters, retardation plates and other elements that affect the polarization of light):

[0039] The inventive interferometric measuring device further comprises at least one adjustment unit, by means of which the optical path length difference OPD or the phase difference PD between the measuring light and the reference light can be changed by an absolute value z. For this purpose, the optical path length of the measuring light or the reference light or both can be changed. For example, the measuring object can be moved relative to the interferometric measuring device or, equivalently, the interferometric measuring device can be moved relative to the measuring object. The optical paths of the illumination light and / or the measuring light can also be changed in such a way that the OPD and / or the PD change. For this purpose, for example, movable mirrors, movable lenses or other movable beam-guiding elements can be used. It is also possible to accommodate elements in the beam path of the measuring light, which change the optical path length by changing the refractive index. Such elements can be, for example, various flat plates made of optical material or, if a continuous change of the optical path is desired, wedge-shaped plates made of optical material that can slide relative to one another. Similarly, optical elements, such as, for example, LCD elements, Pockels cells, in which the refractive index changes when a voltage is applied, are also conceivable.

[0040] For changing the optical path length of the reference light, similar possibilities exist and are preferably used in the same way: particularly preferably, an assembly is used in which the reference light is reflected or scattered from a reference surface, very particularly preferably a reference mirror, which reference surface can be moved and whereby the optical path length of the reference light is changed.

[0041] In order to change the optical path length of the measurement light and / or the reference light, it is particularly advantageous within the scope of this document to use mechanical adjustment units for moving components. Step motors or DC motors with or without encoders and speedometers, linear units, piezoelectrically driven adjusters or stepping motors, as well as many other drive units are suitable for this purpose. Particularly preferably, the adjustment units used contain or are provided with a suitable measuring system, by means of which the respective position of the adjustment unit and thus the change in the optical path length difference OPD and / or the phase difference PD can be controlled or determined as precisely as possible. For example, in order to achieve a precise positioning of the adjustment unit or a translational movement as good as possible, regulating and control systems, for example PID controllers, are also quite advantageous. In a simple embodiment, in the case of a more or less constant adjustment speed, knowledge of the start and end points of the adjustment unit is also necessary in order to be able to estimate the time when the OPD change and / or the PD change, respectively, reaches a certain desired explicitly and / or implicitly set value or to be able to estimate the absolute value z of the OPD or PD change, which exists at the respective time of the adjustment to be determined.

[0042] If only the phase difference PD between the measurement light and the reference light is changed, but not the optical path difference OPD, then the wavelength of the light of the light source is preferably changed. In the case of many light sources, such as for example laser diodes or LEDs, this can be achieved by changing the operating temperature and / or by changing the applied current, or in the case of lasers, for example by changing the length or by the influence of a spectrally filtering element in the laser cavity. Light sources with a variable wavelength of this kind are commercially available in many implementations. In the case of broadband light sources, the wavelength can also be influenced by the use of a variable spectral filter.

[0043] Regardless of which of the many different possibilities is used for adjusting the path length difference and / or phase difference between the measurement light and the reference light, it is important to control or at least know the absolute value z by which the OPD or PD, respectively, is changed. For this purpose, advantageously, a relationship is established between the adjustment parameters or adjustment parameters of the adjustment unit and the corresponding change in the OPD or PD. This is usually easy if the system parameters are known. If, for example, a piezoelectrically driven reflective mirror is used as an adjustment element for the path length of the reference light in the reference arm, this relationship is obtained on the one hand by calibration of the piezoelectric adjuster, and the voltage U, which is preferably applied by the piezoelectric adjuster, is converted into the shift distance w(U) of the mirror. On the other hand, in the case of a shift w(U) of the mirror, it is obtained by the knowledge that the path of the reference light is affected on the round trip and therefore changes by 2*w(U) or, for example, by 2*n*w(U) if the refractive index n of the passing medium, such as air, is not negligible. Considerations of this kind can also be carried out very easily in many other cases and are well known to those skilled in the art, so that, without limiting generality, they will be omitted and only the following will be mentioned here. If the relationship between the adjustment parameter or the adjustment parameter of the adjustment unit and the absolute value z of the change in OPD or PD cannot be easily or accurately established, an additional measuring system is preferably provided, by means of which the absolute value z of the change in OPD or PD is directly measured and / or controlled, for example by means of a suitable length or speed measuring system.

[0044] In all cases it is assumed that the absolute value z by which the optical path length difference OPD or phase difference PD between the measurement light and the reference light is changed by the adjustment unit is known to a certain degree, often with sufficient accuracy.

[0045] It should be noted in particular that the precision with which the absolute value z of the OPD or PD change is known in a truly performed measurement is always finite. That is to say, although there is respective knowledge of this absolute value z, this known value never corresponds exactly to the truly existing value. Nevertheless, within the scope of the present invention, exactly as in the prior art, this finitely accurate value of z is used for the evaluation, at least as long as a better value is not known. In particular, the inventive device and the inventive method differ from the prior art in that the inventive evaluation is significantly more insensitive and robust to inevitable deviations of the known value of z from the true value of z. This is further described below.

[0046] The interferometric measurement device of the present invention further includes at least one multi-element detector with a number of detector elements p, which are arranged to detect different absolute values ​​z i For at least two optical path differences or phase differences that are changed by P (z i ) on detector elements p of the detection area. A camera, preferably a CCD camera or a CMOS camera, is particularly suitable for this purpose. Photodiode arrays or photodiode lines are advantageously used, particularly when a high speed is more important than a large number of detector elements. The detector elements measure the light intensity emitted by them in terms of their respective absolute values ​​z iIt is important to detect at each time point, as precisely as possible, the time when the optical path length difference or the phase difference is changed relative to the reference state of the interferometer. For this purpose, it is preferable to first position the adjustment unit in each case and then provide the multi-element detector with a trigger signal, for example from the adjustment unit or from a control unit controlling it. However, in an advantageous embodiment, it is also possible, for example, to move the adjustment unit continuously and, when the adjustment unit passes a defined point, the adjustment unit or its control unit or a measuring system assigned to the movement of the adjustment unit sends a trigger signal to the multi-element detector, which triggers image recording. Alternatively, it is also conceivable that the multi-element detector is automatically controlled in its image recording or that the image recording is controlled by a third unit. In this case, the signal of the multi-element detector or the third unit is used to read out the position of the adjustment unit at the corresponding time point directly or by a suitable measuring system. There are also numerous further possibilities, such as the possibility of realizing a synchronization of the image recording with the adjustment position, all of which can be used within the scope of the device according to the invention. What is important is to convert the light intensity detected by the multi-element detector as accurately as possible into the absolute value z of the optical path length difference or phase difference corresponding to the change in the reference state of the interferometer. i In order to achieve the best possible resolution when determining the surface topography of the measurement object, the multi-element detector preferably has a large number of detector elements, particularly preferably more than 100, preferably more than 10,000, very particularly preferably more than 100,000 detector elements.

[0047] It should be noted here that each detector element p of the multi-element detector is often assigned a corresponding point on the surface of the object to be measured by optical imaging using interference optics. For simplicity, this corresponding point is also called p, but this does not usually lead to confusion. If this assignment exists, the absolute value z p The level value h of point p on the surface of the measurement object is calculated from the absolute value when the optical path length difference or phase difference between the measurement light and the reference light for the detection element p reaches a predetermined value.p The procedure according to the invention can also be used if there is no such direct assignment between detector elements p of the multi-element detector and the associated points on the surface of the measurement object, since the detector elements are not imaged by the interference optics on the measurement object, but elsewhere, for example in the pupil of the imaging optics, but in particular in that case the determination of the surface topography is carried out by the value z p The level value h of the object point p to which p Instead, the surface topography is determined by a level profile or phase profile h determined in a plane optically conjugate to the detector element. p to the measurement object, the corresponding procedures being known to the person skilled in the art and therefore not described further here. The procedure according to the invention is used in this case as well as in the obvious case where a measurement object point p is directly assigned to each detector element p.

[0048] The inventive interferometric measuring device further comprises at least one evaluation unit, which is connected to the multi-element detector. Particularly preferably, the evaluation unit is additionally connected to the adjustment unit, its control unit and / or a measuring system assigned to the adjustment unit or to the movement of the adjustment unit, so that the evaluation unit can use information about the changes carried out by the adjustment unit. The evaluation unit is preferably a computer, a calculation module, a microprocessor, a DSP, an FPGA, etc. It is important that the evaluation unit determines, for a number p of detector elements of the multi-element detector, the absolute value z of the change in the optical path length difference or phase difference relative to the standard state of the interferometer. p The present invention is configured to determine an absolute value when the optical path length difference or phase difference between the measurement light and the reference light reaches a predetermined value, and to obtain a surface topography of the measurement object from the absolute value.

[0049] For this purpose, the light intensity I of the interference pattern determined by the detector element p of the multi-element detector for a number of adjustment positions of the adjustment unit, but at least for two adjustment positions, is p (zi ) is transmitted to the evaluation unit. The evaluation unit then receives the different absolute values ​​z1, z2, ..., z n Correlograms c corresponding to a number of optical path length differences or phase differences between the measurement light and the reference light, which are changed by p =(c p (1), c p (2),...,c p (n))=(I p (z1), I p (z2),...,I p (z n )) exists.

[0050] Usually, from these correlograms, according to the procedure already described in the prior art, the absolute value z of the change in the optical path length difference or phase difference with respect to the reference state of the interferometer is obtained. p The absolute value is determined when the optical path length difference or phase difference between the measurement light and the reference light reaches a predefined value, particularly preferably a predefined value of zero, and from there the surface topography of the measurement object is determined.

[0051] The predetermined values ​​can be set explicitly or implicitly and are described below.

[0052] The predetermined value is preferably set as a constant value, particularly preferably set to the value zero as described above. It is also within the scope of the invention to set a different value for each detector element p. Preferably, the same value is set for a number of detector elements, particularly preferably for all detector elements, in particular the value zero.

[0053] Therefore, it is within the scope of the present invention to explicitly set constant values, such as "zero" (for the path length difference) or "0°" (for the phase difference), p is z=z p It is sought to achieve exactly this value when z=z. Likewise, it is within the scope of the invention to set this value implicitly, and the setting is pIn this case, the optical path length difference or phase difference is set, even if it is not explicitly known at the time of setting or is determined later.

[0054] The evaluation unit measures the optical path length difference or phase difference with respect to the reference state of the interferometer as a light intensity I p (z i ) absolute value of change during measurement i This information is usually given by the absolute value z i is present in the evaluation unit by being known by a defined control of the adjustment unit of the interference measuring device or by the adjustment unit and / or the measurement system assigned to it outputting this information to the evaluation unit via a suitable data line or trigger line. If the adjustment unit and / or the measurement system assigned to it trigger the data recording of the multi-element detector by means of a trigger line, this information can be provided to the evaluation unit, for example, by the configuration at the trigger time being known to the evaluation unit as a function of the adjustment position of the adjustment unit or being defined by the evaluation unit. In addition to the above-mentioned realizations, the evaluation unit can also be configured to calculate the correlogram c p =(c p (1), c p (2),...,c p (n))=(I p (z1), I p (z2),...,I p (z n )) the absolute values ​​z1, z2, ..., z n There are numerous further possibilities, such as being able to arrive at information about the

[0055] At least when using the prior art procedures for further evaluation, the absolute values ​​z1, z2, ..., z nIt should be noted that as accurate a knowledge of z1, z2, ..., z2 is important for the quality of the results. n are also their true values, and these values ​​are used for further calculations. This is particularly problematic, for example, when Fourier or Hilbert transforms are used in connection with the determination of the envelope and / or envelope maximum and / or phase of the correlogram. There are mathematical methods that can also carry out such a transformation on a signal curve scanned at non-equidistant support points, but these too lead to erroneous results just like conventional transformations if the assumed support points of the signal curve to be transformed do not correspond to the true support points. In all other known procedures for determining the envelope, envelope maximum and / or phase positions of a correlogram, similar problems exist if the assumed support points do not correspond to the true support points, regardless of whether the support points are equidistant or not. For example, fitting a curve, in particular a sinusoidal curve, to the signal curve of the correlogram can lead to large deviations if the support points at which the fitting function and its deviation to the measurement data are calculated are incorrect.

[0056] Of course, the absolute values ​​z1, z2,...,z n It is also advantageous for the procedure of the present invention that z is known as accurately as possible. i For known values, the true but unknown z i It is much more robust to deviations from the value of

[0057] Such deviations may be due to, for example, (i) uncontrolled influences on the measurement arm and / or the reference arm of the interferometer during the measurement due to vibrations or movements, (ii) uncontrolled influences on the measurement due to changes in the density and / or refractive index of at least one of the media through which the light passes, in the measurement arm and / or the reference arm, or (iii) the absolute value z i This may occur due to inaccuracies and / or errors in the determination of the

[0058] In the inventive interference measuring device, the evaluation unit determines the value z p To determine the light intensity I p (z i ), in addition to the light intensity I of at least one other detector element q of the multi-element detector. q (z i ) is also configured to use

[0059] The advantage of this becomes very clear based on a simple but relevant consideration: in many cases, the level values ​​h of directly aligned surface points p and q of the measurement object p and q is not exactly the same but very similar.

[0060] Corresponding correlogram of affiliation c p =(I p (z1), I p (z2),...I p (z n )) and c q =(I q (z1), I q (z2),...I q (z n )) The individual values ​​of c p (i) to (c) q (i) Using the general function correlogram progression c(OPD) c p (i) = c(z i -2*h p ) or c q (i) = c(z i -2*h q ) It is expressed as: h p and q Since the differences are small, h q is the formula h q =h p +Δ, where Δ is very small. Therefore, c q (i) = c(z i -2*h q )=c(z i-2*h p -2*Δ) ≒ c(z i -2*h P )-2*Δ*c'(z i -2*h p ) where c'(z i -2*h p ) is the part z i -2*h p is the derivative of the general function correlogram course c(OPD) in q and c p By subtracting the derivative of the correlogram with respect to the measurement point p, we can calculate the derivative of the correlogram with respect to the measurement point z, where the correlogram itself was also recorded. i -2*h p This means that a decision can be made immediately on the matter.

[0061] Then, in the typical general function correlogram curve c(OPD) = env(OPD) * cos(φ(OPD)) of low coherence interferometry, it can be assumed, to a good approximation, that the envelope changes much more slowly than a sinusoidal modulation. This is due to the derivative function formed according to the product and chain law: c'(OPD)=env'(OPD)*cos(φ(OPD))-env(OPD)*sin(φ(OPD))*φ'(OPD) Under the realistic assumption that the first term can be neglected and therefore φ(OPD) approximately depends linearly on OPD, i.e. φ'(OPD) is constant, the derivative c'(OPD) is the composite correlogram phase shifted by 90° at the carrier frequency. s(OPD)=env(OPD)*sin(φ(OPD)) The correspondence is of course not only true for low-coherence interferometry but also for phase-shifting interferometry, since here the conditions env'(OPD)=0 as well as the constancy of φ'(OPD), which are only approximately valid for low-coherence interferometry, apply rather exactly.

[0062] This means that, in summary, the correlogram c p and c q By simply subtracting p A composite correlogram phase-shifted by 90° at the carrier frequency s p =(s p (1),s p (2),...,s p (n) =f*(Q p (z1), Q p (z2),...Q p (z n )) =f*(I q (z1)-I p (z1), I q (z2)-I p (z2),...,I q (z n )-I p (z n )) This means that we obtain p (z i )=I q (z i )-I p (z i ) is the light intensity I p (z i ) represents a signal whose modulation is phase shifted relative to the carrier frequency. p is the original correlogram c p The same point z was scanned. i To generate this composite correlogram, i This makes it possible to obtain the correlogram c p Synthetic correlograms belonging to p The generation of the parameter z i This makes the evaluation much more robust against all forms of disturbances compared to previously known methods.

[0063] In particular, the direction vector or tangent vector determined as described further below is expressed as the light intensity I p (z1), I p (z2),...,I p (z n ) with respect to the phase shifted signal Q p (z1), Q p (z2),...,Q p (z n ) to determine the p (z1), I p (z2),...,I p (z n ) for determining the corresponding associated phase-shifted signals for vectors resulting from the projection and / or transformation.

[0064] Therefore, the light intensity I p (z1), I p (z2),...,I p (z n ) and the phase-shifted signal Q p (z1), Q p (z2),...Q p (z n ) are used to carry out further steps known from the prior art, in particular to determine the envelope and / or phase position of the signal curve given by the light intensity. p (z1), I p (z2),...,I p (z n ) to the phase-shifted signal Q p (z1), Q p (z2),...Q p (z n ) along with the light intensity I p (z1), I p (z2),...,I p (z n ) to determine the envelope and / or phase position of the signal curve given by or corresponding to I p (z1), I p (z2),...,I p (z n) to the vectors and the associated phase-shifted signals resulting from the projection and / or transformation. Particularly advantageously, the determined phase positions and / or envelopes are used to calculate the absolute value z of the change in the optical path length difference or phase difference for an element p of the multi-element detector. p is used to determine the absolute value at which the optical path length difference or phase difference between the measurement light and the reference light reaches an explicitly and / or implicitly set value.

[0065] For further evaluation, preferably, a scaling factor f is further determined, so that the correlogram s p is the correlogram c p There are many possibilities for doing this. A relatively simple one is to set the coefficient f to the square of the envelope of the correlogram (c p ) 2 +(s p ) 2 The goal is to optimize the process so that c p However, the correlogram must of course be adjusted by this offset, which in the simplest case is taken from the edge region of the correlogram where no or little interference occurs, or alternatively the offset is determined by a suitable averaging of the individual correlogram values. Instead of optimizing the coefficient f so that the square of the correlogram envelope has a maximally flat course, it is of course also possible to correspond to the square root resulting from the envelope itself or from any other suitable function therefrom. If such a simple case does not exist, the optimal value of f can be determined directly from the existing data, for example via an equation, for which purpose it is advantageous to use any mathematical optimization method, for example the gradient method, to determine the parameter f so that an evaluation function b(f), which evaluates the deviation from a flat course in an appropriate way, is minimized. An advantageous example for such an evaluation function is to determine for each point i of the correlogram the deviation from the envelope squared of the preceding point i-1 by means of the sum b(f) (formula below), which is squared and subsequently added over all points. For an optimal coefficient f, this b(f) is minimized.

number

[0066] Here, I p (z i It should be noted that (c) is the intensity of the correlogram at point p, corrected for its offset as before. It is even simpler to use only the points near the correlogram maximum for the determination of the coefficient f. In this case, for these points, (c p ) 2 +(s p ) 2 is assumed to be approximately constant, and therefore the evaluation factor is preferably the value I determined from a point in the vicinity of the envelope maximum. p (z i ) 2 +(f*Q p (z i )) 2 Or the square root of the standard deviation is used.

[0067] In particular, a suitable procedure for determining the scaling factor f in phase-shifting interferometry is to simultaneously obtain a value for f as well as a correlogram c p To do this, we simultaneously optimize the two parameters f and o by one of the known mathematical optimization methods: p (z i )-o) 2 +(f*Q(z i )) 2 Or the function is optimized so that it exhibits a curve as flat as possible as a function of i, or in the case of phase-shifting interferometry, is even as constant as possible, for which purpose, as previously described, a suitable evaluation function is preferably used which evaluates the deviation from the flat curve or constant that is sought to be obtained.

[0068] Another suitable approach for determining the coefficient f is to fit a practical envelope function, e.g. a theoretically known envelope function or an envelope function determined and / or approximated from measured data, to the envelope determined in dependence on the coefficient f, and use the squared corresponding deviation ("chi-squared") as an evaluation function in dependence on f. In addition to the already mentioned possibilities for determining the scaling factor f, any further possibilities exist which provide a sufficiently accurate value for the required scaling factor f, and it is within the scope of the invention to utilize these, provided that they provide a sufficiently accurate value for the required scaling factor f.

[0069] Therefore, Q p (z i ) is the composite correlogram s up to the scaling factor f p Corresponds to.

[0070] Each correlogram c p After determining the appropriate scaling factor f for , the corresponding composite correlogram s, correctly scaled and shifted in carrier frequency, p If is determined, a further evaluation is preferably carried out accordingly, based on procedures known from the prior art.

[0071] Thus, the direction vectors, tangent vectors and / or the determined phase-shifted signal Q p (z1), Q p (z2),...Q p (z n ) whose carrier frequency amplitude and / or envelope is the optical intensity I p (z1), I p (z2),...,I p (z n ) to correspond to the amplitude or envelope of the carrier frequency.

[0072] For example, both correlograms c p ands pIn a preferred embodiment, the correlogram envelope is determined by squaring, adding and subtracting the square root. The position of the envelope maximum is then determined by fitting a suitable curve profile to it. In the context of the inventor's research, it has been shown that the envelope profile determined by the inventive procedure is much smoother and more realistic than in the case of the previously known procedures, particularly when one of the abovementioned obstacles is present, and the position of the envelope maximum is much more accurate.

[0073] A more accurate phase estimation of the correlogram, in which in addition to estimating the location of the envelope maximum, the sinusoidal modulation of the correlogram in the vicinity of the envelope maximum is also utilized for the estimation, provides significantly better results using the procedure of the present invention. p (i) The corresponding point s of the correlogram shifted by 90° in the carrier frequency p (i) is the OPD change or phase change z adjusted by the adjustment unit i Regardless of knowledge of the absolute value of z i By determining φ p (z i )=φ p (i) = unwrap(arctan2(s p (I C p (i))) Using each OPD or PD change z i The exact phase value φ for p (z i ) where arctan2 is the variable of the arctangent function covering a value range of 360° and therefore spanning all four quadrants of the unit circle, and unwrap() represents the phase unwrapping performed after the arctangent formation, which is preferably performed using the previously determined envelope maximum φ p The (z) position is selected to be as close to 0° as possible.

[0074] Next, z i A phase transition φ that rises or falls monotonically with a relatively constant slope as a function of p (z i) is known, it can be easily obtained from there via linear regression (or possibly curve fitting, if necessary, in cases where deviations from linearity occur, e.g. due to scattering) and further the value z at which the OPD or PD reaches the explicitly and / or implicitly set value. p This can be done, for example, by determining φ p (z) is therein determined to take an explicitly and / or implicitly set value, e.g. 0° for the maximum of the sinusoidal modulation closest to the envelope maximum, or 90° for the falling zero crossing of the sinusoidal modulation closest to the envelope maximum.

[0075] Therefore, advantageously, the value z p To determine the function I, which depends on the change z in the optical path length difference and / or phase difference between the measurement light and the reference light, p Information regarding the envelope and / or phase position of (z) is sought, which in particular requires the light intensity I p (z i ), in addition to the light intensity I of at least one other detector element q of the multi-element detector. q (z i ) is also used.

[0076] z p In this determination, the value z i Since the imprecision introduced into is very small, this makes the invention very robust against disturbances and ultimately yields superior results.

[0077] For completeness, let us consider the coordinates (z i ,φ p (z i )) from the regression line or from the fitted curve, preferably z i Correction for Δz i This is then used to determine the exact z i It should be noted that a value can be obtained, for example, at a point (z i +Δz i ,φ p (zi )) is just on the regression line or fitted curve. i In particular, the correction values ​​Δz obtained for the various detector elements p are i By combining these, for example by a suitable averaging method with appropriate weights, the true z i The original z values ​​provided may deviate significantly from the i The values ​​are corrected so that known evaluation methods also give good results. When the procedure of the invention is combined with previously known procedures, improved results are also achieved there.

[0078] In principle, of course, the z i The values ​​can also be used as a new starting point for the evaluation according to the present invention and can be developed into an iterative method by repeating. However, the inventors' work in particular has focused on the corrected z i It has been shown that calculating and using these values ​​in connection with the procedure of the present invention offers little notable advantage, since the procedure according to the present invention is in any case very robust against disturbances, and therefore can typically be omitted.

[0079] It should be mentioned again that the procedure described so far has been explained for the example of low-coherence interferometry, but can also be very easily transferred to phase-shifting interferometry. Of course, in phase-shifting interferometry the correlogram envelope does not exist or is constant, but this simply eliminates the step of determining the envelope maximum, and all the approximations that were necessary within the context of low-coherence interferometry still apply exactly. However, the original procedure of combining the correlograms of the different detector elements p and q with one another remains completely intact in all details and effects, so that the procedure of the invention, in particular the procedure according to the described preferred embodiment, fully covers phase-shifting interferometry as well as low-coherence interferometry.

[0080] Here again, the composite correlograms obtained as described above and below are p =(s p (1),sp (2),...,s p (n)) can be approximated to a very good, and often useful, extent by the correlogram c p It should be noted that the correlogram with the carrier frequency phase shifted by 90° with respect to φ(OPD) is shown by the same envelope, but this is not exactly correct. As shown previously, this is only true if the envelope env(OPD) varies infinitely slowly over the general function correlogram course c(OPD), as in phase-shifting interferometry, and the phase derivative φ'(OPD) is constant. The composite correlogram s obtained as explained previously p and correlogram c p The previously determined synthetic correlogram s is obtained even if the deviation between the original correlogram of the same envelope, with the carrier frequency phase shifted by 90° with respect to p Instead, we obtain a correspondingly corrected composite correlogram and use this as s p This can be solved by using instead of

[0081] In this regard, the equation c'(OPD)=env'(OPD)*cos(φ(OPD))-env(OPD)*sin(φ(OPD))*φ'(OPD) Using s(OPD) = env(OPD) * sin(φ(OPD)), s(OPD)=-(c'(OPD)-env'(OPD)*cos(φ(OPD))) / φ'(OPD) and use c(OPD)=env(OPD)*cos(φ(OPD)). s(OPD)=-(c'(OPD)-env'(OPD) / env(OPD)*c(OPD))) / φ'(OPD) This means that the corrected composite correlogram is p This means that the derivative vector c'(OPD) (or (c p)') is determined, and from this the original correlogram c(OPD) (or c p ) and divide the difference by φ'(OPD).

[0082] The parameters env(OPD), env'(OPD) and φ'(OPD) are preferably determined from a model of the general function correlogram curve, which model is known based on the characteristics of the measuring device or is determined from the measurement data. The position of the model relative to the measurement data is determined, for example, by the original correlogram c p and uncorrected composite correlogram s p Empirically, no particular precision is required for the model or its exact location for a concrete correlogram, and the procedure is very robust to any form of deviation, so that the possible iterative procedures are very rarely required in practice for the determination of an accurate composite correlogram.

[0083] This shows an advantageous procedure: in the simplest case, the synthetic correlogram s p If the approximation for the determination of is too coarse, the original correlogram c p Using this and a relatively easy-to-obtain model, the correlogram c p A correct composite correlogram is obtained in which the carrier frequency is phase shifted by 90° with respect to the correlogram s p are used entirely within the framework of the procedures of the invention described above and below, without further restrictions.

[0084] Up to this point, for the sake of clarity, it has been shown very simply by way of example how the inventive configuration of the evaluation unit can be used in determining the surface topography of a measurement object in order to achieve more robust results compared to the prior art known up to now.

[0085] An important feature according to the invention of the evaluation unit of the method according to the invention and of the device according to the invention is the value zp To determine the light intensity I on the detector element p, p (z i ), in addition to the light intensity I of at least one other detector element q of the multi-element detector. q (z i ) can be advantageously constructed and used in a much wider range of applications.

[0086] First, according to what has been said so far, the value z assigned to the detector element p p When determining, it is not necessary to be limited to the additional information of one individual further detector element q, but advantageously at least two, preferably at least three, preferably at least 10, very particularly preferably at least 20, detector elements q of a multi-element detector are used for this purpose.

[0087] Advantageously, its light intensity I q (z i ) is the value z assigned to detector element p p At least one other detector element q used for detection of p is selected to have a predetermined proximity characteristic with respect to detector element p.

[0088] Therefore, the value z assigned to detector element p p For the determination of , it is advantageous not to simply use an arbitrary detector element q and the associated correlogram, but to use a detector element q that has some favorable neighboring properties with respect to the detector element p. Such favorable neighboring properties are, for example, often of course, the spatial neighboring properties between the detector elements p and q or between the associated object points, but the similarity of the associated correlograms, respectively, can also determine the neighboring properties, on the basis of which the point q can be advantageously selected. At that point, the value z assigned to the detector element p p Advantageously, at least one detector element q used in the determination of {overscore (q)} is selected to have a predetermined neighbourhood property with respect to at least one predetermined metric with respect to detector element p.

[0089] It is therefore particularly advantageous if the neighbourhood characteristic is defined at least in part by means of a metric, which particularly advantageously comprises the spatial spacing of the detector elements p and q and / or the spatial spacing of the points assigned to these detector elements on the measurement object and / or on an optical surface conjugate to the multi-element detector.

[0090] Such a metric for determining the adjacency of detector elements p and q can include determining the spatial spacing of detector elements p and q and / or the spatial spacing of points belonging to them on the measurement object and / or on the optical surface conjugate to the multi-element detector. This is advantageous since spatially adjacent detector elements are often assigned to object points with similar level values. Furthermore, the disturbances suffered by spatially adjacent detector elements are very often also very similar. In particular, in the case of disturbances due to changes in density and / or refractive index of at least one medium through which light passes in the measurement arm and / or reference arm, for example due to eddies caused by different air temperatures, the disturbances are usually locally different and are therefore best taken into account by a corresponding local evaluation with the spatially adjacent detector element q for detector element p.

[0091] Correlogram c p =(I p (z1), I p (z2),...,I p (z n )) and c q =(I q (z1), I q (z2),...,I q (z n It is advantageous if the vectors (I p (z1), I p (z2),...,I p (z n )) and (I q (z1), I q (z2),...,I q (zn )) or in a vector space resulting from a projection and / or transformation therefrom. Such metrics can be, for example, q -c p or correspondingly, the length of the projected vectors in the subspace, in which case it may similarly involve using the correlogram points in the vicinity of the respective envelope maxima for the adjacency determination.

[0092] Advantageously, the metric for determining the adjacency of detector elements p and q is the level value h determined by a first coarse determination. p and q We also use an interval metric based on

[0093] Basically, the value z p In selecting the detector elements q used to determine p and c q It is highly advantageous to use detector elements q for which there is a large similarity between the correlograms c p and c q It may be disadvantageous for q to be too similar or identical, since in this case little or no additional information is gained. Therefore, in many cases, when selecting detector elements q to be used, it may be advantageous to exclude those that are considered to be too adjacent in terms of their neighboring properties.

[0094] Basically, the value z assigned to the detector element p p For the determination of m There are many possibilities to use the correlogram information of . The closest possibility is to simply j Correlogram of c p and c qj As already mentioned, we use pand then average them appropriately, possibly weighted, to obtain z p The goal is to obtain a final value for

[0095] However, advantageously, different detector elements q j The value obtained using z p Instead of averaging over detector element q j Different composite correlograms s obtained using p Then, the resulting averaged composite correlogram is called the correlogram c belonging to point p. p and, for example, z p Determine a value for

[0096] However, the correlogram c p =(c p (1), c p (2),...,c p (n)) and c qj =(c qj (1), c qj (2),...,c qj (n) is a point or vector in an n-dimensional vector space, and the derivative s given up to coefficient f is p =(s p (1),s p (2),...,s p (n) is considered as a direction vector, and this direction vector is the vector c p (c p (1), c p (2),...,c p (n)) and c qj =(c qj (1), c qj (2),...,c qj (n)) or (I p (z1), I p (z2),...,I p (z n )) and (I q (z1), I q (z2),...,I q (z nIt is further advantageous to at least locally approximate the main direction of the point distribution given by

[0097] Correlogram c belonging to detector p p and a single further correlogram c belonging to detector element q q Composite correlograms from p The above determination is also in this sense at least a local approximation of a directional vector to a distribution of points (here consisting of only two points) consisting of correlogram vectors in an n-dimensional vector space.

[0098] Therefore, the value z assigned to detector element p p The approximation used in determining includes determining a direction vector, which is the light intensity vector (I p (z1), I p (z2),...,I p (z n )) or vectors resulting from projections and / or transformations from it, at least locally, p (z1), I p (z2),...,I p (z n )) and (I q (z1), I q (z2),...,I q (z n It is advantageous to approximate the main directions of the point distribution given by vectors resulting from (i) or (ii) by projection and / or transformation.

[0099] In order to be able to perform the evaluation in an n-dimensional vector space as discussed, it is preferable to use the actual measured light intensity vector (I p (z1), I p (z2),...,I p (z n )) and (I q (z1), I q (z2),...,I q (z n)) are used or these are advantageously adjusted by an offset and / or amplitude scaling factor as already mentioned many times. p (z1), I p (z2),...,I p (z n ) light intensity vector, or the expression c p =(c p (1), c p (2),...,c p Where or when the correlogram or correlogram vector of (n)) is used, which are usually the same, preferably both are meant, respectively, unless expressly stated otherwise or clearly meaningless. Further, in all observations and discussions, the formula (I p (z1), I p (z2),...,I p (z n ) or c p (1), c p (2),...,c p It is preferable to restrict the number of correlogram points (n) to a subset of the number of correlogram points (n), which is advantageous, for example, in terms of computational costs. This is also explicitly covered by the specification.

[0100] These are all referred to in particular in the claims as "light intensity vectors (I p (z1), I p (z2),...,I p (z n ) or vectors resulting therefrom by projection and / or transformation”, the concept “projection and / or transformation” can additionally include further aspects.

[0101] The coefficient f explained above is given as a directional vector, and this directional vector is the vector c p =c p (1), c p (2),...,c p (n) and c qj =(c qj (1), cqj (2),...,c qj (n)) or (I p (z1), I p (z2),...,I p (z n ) and (I qj (z1) , I qj (z2),...,I qj (z n A synthetic correlogram s that at least locally approximates the principal directions of the point distribution given by p =(s p (1),s p (2),...,s p There are many more possibilities for determining the vectors (n), the simplest of which is to perform a fitting, advantageously a least-squares fitting or a regression of the gradient in an n-dimensional space, by known mathematical methods, to a given distribution of points, and from there to the direction vectors and then to the coefficients f, to obtain the composite correlogram s p The coefficients f are then determined as already described, and both correlograms c belonging to the detector element p are p ands p , preferably the value z p is required.

[0102] Another particularly advantageous possibility is the synthesis of synthetic correlograms. p Let c be the correlogram vector p and c qj The goal of the method is to determine the vectors that at least locally approximate the distribution of points given by p and c qjThe principal axes of the distribution of points given by are determined, and the direction of the eigenvector belonging to the largest eigenvalue of the covariance matrix is ​​the desired direction vector. As soon as this direction vector exists, the process continues as described above. It should be noted that the principal component analysis does not necessarily have to be carried out completely. It should be carried out until the desired eigenvector exists, and therefore preferably so. This is a very early stage in many known numerical methods for PCA, since the eigenvector usually belongs to the largest eigenvalue that was initially determined.

[0103] Therefore, the value z assigned to detector element p p I p (z i ) and I q (z i ) is given by the n-dimensional light intensity vector (I p (z1), I p (z2),...,I p (z n ) and (I q (z1) , I q (z2),...,I q (z n )) or at least partly by approximating the vectors resulting therefrom by projection and / or transformation.

[0104] But the vector c p =(c p (1), c p (2),...,c p (n)) and c qj =(c qj (1), c qj (2),...,c qj (n)) or (I p (z1), I p (z2),...,I p (z n )) and (I qj (z1) , I qj (z2),...,I qj (z n)) but instead it is very particularly advantageous to at least locally approximate a suitable low-dimensional submanifold of the n-dimensional vector space to this point distribution, for example a maximum three-dimensional submanifold, preferably a maximum two-dimensional submanifold, very particularly preferably a one-dimensional submanifold, i.e. a one-dimensional parameter curve in the associated high-dimensional vector space, to this point distribution.

[0105] This is possible because, for this purpose, the correlogram c p =(c p (1), c p (2),...,c p (n)) and c qj =(c qj (1), c qj (2),...,c qj This can be easily understood using the example of phase-shifting interferometry, assuming that (n)) exists after being offset adjusted and normalized as described above.

[0106] And for example, the correlogram c p =(c p (1), c p (2),...,c p (n)) is c p (i) = cos(2π / λ*(z i -2*h p ) which, according to the addition theorem, p (i) = cos(2π / λ*z i )*cos(2π / λ*2*h p )+sin(2π / λ*z i )*sin(2π / λ*2*h p ) and then this is expressed as a vector in the form c p =(c p (1), c p (2),...,c p (n))=cos(2π / λ*2*h p )*v+sin(2π / λ*2*h p)*w, where vector v=(cos(2π / λ*z1),cos(2π / λ*z2),...,cos(2π / λz n )) and w=(sin(2π / λ*z1),sin(2π / λ*z2),...,sin(2π / λ*z n )) for all possible c p Vector and c qj It is understood that vectors always lie on an ellipse, i.e., on a one-dimensional parametric curve in n-dimensional space, and this ellipse of course lies entirely on a two-dimensional submanifold, in the concrete case on the plane. This means that z i The exact location and shape of this ellipse is determined by the z i It depends entirely on the value of

[0107] This gives us different options for the evaluation. The simplest option is to actually fit an ellipse in n-dimensional space to the measured correlogram c p and c qj Fit the points defined via the correlogram c p Project onto this ellipse and obtain the composite correlogram vector s p Let us consider a one-dimensional differentiable submanifold of the n-dimensional space given by an ellipse as a tangent vector to this submanifold and project the correlogram vector c p The differentiation can be performed very easily in this case, since the ellipse is represented both as a one-dimensional submanifold of the n-dimensional space and as a one-dimensional parametric curve in this vector space. After determining the tangent vector and its scaling factor, we preferably compute s p Further evaluation is performed as described above using

[0108] It is therefore advantageous to determine the tangent vector to a differentiable manifold M by differentiating it.

[0109] As previously assumed, the correlogram to be evaluated is c p =(c p (1), c p(2),...,c p (n)) and c qj =(c qj (1), c qj (2),...,c qj It is possible, but less advantageous, to omit adjusting the n-dimensional vectors c(n) by their offsets and / or scaling, and instead of an ellipse we obtain a two-dimensional or even three-dimensional differentiable submanifold of the n-dimensional space. Again, preferably, this correlogram vector c p is projected onto this submanifold, and the composite correlogram vector s p is the projected correlogram vector c p , and then proceeding as before.

[0110] Particularly advantageously, the approximation is therefore performed by dividing a differentiable submanifold M, in particular a low-dimensional differentiable submanifold, by a set of points (I p (z1), I p (z2),...,I p (z n )) and (I qj (z1) , I qj (z2),...,I qj (z n )) or to a distribution of points of a vector space of vectors resulting from a projection and / or transformation from said points, in particular said differentiable submanifold being a maximally three-dimensional, in particular a maximally two-dimensional submanifold of the corresponding vector space,

[0111] The procedure described is based on the correlogram obtained by low-coherence interferometry. p and c qjIf the offset-adjusted and normalized correlogram in phase-shifting interferometry is used for the evaluation as before, an ellipse no longer results, but instead, based on the changed envelope, another one-dimensional parameter curve or one-dimensional differentiable submanifold results, which resembles an elliptical spiral, but which, unlike the ellipse, is not closed. Here too, however, one proceeds exactly the same as in phase-shifting interferometry, even if the determination of the curve course to be fitted is more complicated and if necessary a model of the envelope and the determination of the relative position of the modulation with respect to the envelope are required, which information can if necessary also be obtained from the measurement data. Furthermore, the correlogram c to be evaluated is p and c qj If one omits adjusting x by their offsets and / or scaling, the procedure becomes correspondingly more tedious, but is still basically feasible.

[0112] Therefore, in an advantageous embodiment, an n-dimensional light intensity vector (I p (z1), I p (z2),...,I p (z n )) and (I q (z1) , I q (z2),...,I q (z n )) are represented by one-dimensional parametric curves in the corresponding vector space.

[0113] Particularly preferably, the light intensity vector (I p (z1), I p (z2),...,I p (z n )) and (I q (z1) , I q (z2),...,I q (z n)), or the vectors resulting from them by projections and / or transformations, are at least locally linear approximations. They are thus approximations to a line, a plane, or another linear subspace of the vector space that has a lower dimensionality than the vector space itself.

[0114] However, the measured, advantageously offset-corrected and normalized correlogram c p and c qj There exists a much more advantageous procedure for evaluating in n-dimensional space a point defined via . This procedure is applicable both to low-coherence interferometry and to phase-shifting interferometry. In the following, this procedure will be described for low-coherence interferometry, since its application in the special case of phase-shifting interferometry can be carried out in exactly the same way, as will be easily understood. For this application, it is again assumed that the envelope of the correlogram varies much more slowly than its modulation. Under this assumption, the spiral is closed in a first approximation even in the low-coherence case, and the one-dimensional curve defined by the correlogram lies in n-dimensional space and in a first approximation in a two-dimensional subspace, i.e. a plane, where the one-dimensional curve is approximately represented by an ellipse (in the case of PSI, everything applies quite exactly). This two-dimensional plane in n-dimensional space is then determined and parameterized by plane fitting or two-dimensional regression, by principal component analysis, or by some of them, etc. Then, the correlogram c p and c qj The points defined by are projected onto this plane, in which they are described by an ellipse. The ellipse is determined in this projection plane by two-dimensional fitting or an equivalent method, after which a corresponding affine map can be defined that maps the ellipse onto the corresponding circle. If the projection plane is determined by principal component analysis, advantageously in an alternative configuration, the corresponding affine map is determined using the two largest eigenvalues ​​or the corresponding eigenvectors of the PCA covariance matrix. The correlogram vector c to be projected is then projected using the affine map present. p and c qj After this transformation has been performed, all points belonging to the different correlograms c p and cqj The spatial angle between two projected and affinely mapped points corresponds to the phase difference between the sinusoidal modulations of the associated correlogram and is therefore used to estimate the phase of the correlogram.

[0115] Advantageously, the determination of the directional vectors is therefore carried out by principal component analysis (PCA) or parts thereof, by eigenvalue determination, by linear regression or by the determination of vectors (I p (z1), I p (z2),...,I p (z n )) and (I q (z1) , I q (z2),...,I q (z n )) or other optimization methods for minimizing the deviation from a given distribution of points by vectors resulting from them by projections and / or transformations.

[0116] For envelope estimation, preferably the correlogram vector c p and c qj The spacing of the points belonging to z with respect to the projection plane is used, which is more or less discrete for all correlograms and takes clearly distinguishable values ​​depending on whether the correlograms take the same phase position or a phase position shifted by k*360° (k is an integer). The evaluations described so far then give similar results for the envelope evaluation and for the phase evaluation, which are correspondingly similarly robust to disturbances. But the advantage of the last described procedure is that the desired value z p Many correlograms c p can be obtained simultaneously for all of the above, which significantly reduces the computational cost.

[0117] Further advantageous features and configurations are explained below on the basis of examples and drawings. [Brief description of the drawings]

[0118] [Figure 1]FIG. 1 shows a first embodiment of the apparatus of the invention comprising a Michelson interferometer. [Diagram 2] FIG. 2 is a diagram for explaining an embodiment of the method of the present invention carried out by the device of FIG. [Diagram 3] FIG. 2 is a diagram for explaining an embodiment of the method of the present invention carried out by the device of FIG. [Figure 4] FIG. 2 is a diagram for explaining an embodiment of the method of the present invention carried out by the device of FIG. [Diagram 5] FIG. 2 is a diagram for explaining an embodiment of the method of the present invention carried out by the device of FIG. [Figure 6] FIG. 2 is a diagram for explaining an embodiment of the method of the present invention carried out by the device of FIG. [Figure 7] FIG. 2 is a diagram for explaining an embodiment of the method of the present invention carried out by the device of FIG. [Figure 8] FIG. 2 is a diagram for explaining an embodiment of the method of the present invention carried out by the device of FIG. [Figure 9] FIG. 2 is a diagram for explaining an embodiment of the method of the present invention carried out by the device of FIG. [Figure 10] FIG. 2 is a diagram for explaining an embodiment of the method of the present invention carried out by the device of FIG. [Figure 11] FIG. 2 is a diagram for explaining an embodiment of the method of the present invention carried out by the device of FIG. [Figure 12] FIG. 2 shows a second embodiment of the apparatus of the invention comprising a Michelson interferometer. [Figure 13] 13 is a diagram for explaining an embodiment of the method of the present invention performed by the device of FIG. 12. [Figure 14] 13 is a diagram for explaining an embodiment of the method of the present invention performed by the device of FIG. 12. [Figure 15] FIG. 3 shows a third embodiment of the device according to the invention with a Mirau objective lens. [Figure 16] 16 is a diagram for explaining an embodiment of the method of the present invention performed by the device of FIG. 15. [Figure 17]FIG. 4 shows a fourth embodiment of the apparatus of the invention comprising a Michelson interferometer. [Figure 18] 18 is a diagram for explaining an embodiment of the method of the present invention performed by the device of FIG. 17. [Figure 19] 18 is a diagram for explaining an embodiment of the method of the present invention performed by the device of FIG. 17. [Figure 20] 18 is a diagram for explaining an embodiment of the method of the present invention performed by the device of FIG. 17. [Figure 21] 18 is a diagram for explaining an embodiment of the method of the present invention performed by the device of FIG. 17. [Figure 22] 18 is a diagram for explaining an embodiment of the method of the present invention performed by the device of FIG. 17. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0119] The drawings are schematic and not to scale. In the drawings, the same reference signs represent the same or equivalent elements.

[0120] 1 shows a first embodiment of an apparatus according to the invention comprising a Michelson interferometer, which is used for interferometrically determining the surface topography of a measurement surface 1a of a measurement object 1.

[0121] The device comprises a light source 2, here configured as an LED, having a broadband light spectrum here in the wavelength range 490 nm to 550 nm, with a maximum at 520 nm.

[0122] The light of the light source reaches a semi-transparent mirror 4 via a condenser 3, which guides approximately 50% of the light intensity as illumination light to the measurement surface 1a of the measurement object 1. The illumination light reflected back from the measurement surface 1a as measurement light passes partly through the semi-transparent mirror 4 and is imaged by imaging optics 5, which are here configured as telecentric imaging optics, into the detection area of ​​the device, in which a multi-element detector 6 is arranged. The imaging optics 5 here has optical lenses 5a and 5b for telecentric imaging as well as an optical diaphragm 5c.

[0123] The multi-element detector 6 is configured here as a CCD camera and has a CCD sensor. The CCD sensor is configured as a planar sensor of 1024 x 1024 sensor elements, which are arranged at the intersections of a square grid as a sensor array. Each sensor element is a detector element of the multi-element detector 6.

[0124] Approximately 50% of the light generated by the light source 2 passes through the semi-transparent mirror 4 as reference light and reaches the reference mirror 8 via the optical filter 7. The reference light reflected by the reference mirror 8 passes through the optical filter 7 again, is partially deflected by the semi-transparent mirror 4, and is likewise imaged in the detection area by the imaging optics 5. As a result, an interference pattern is formed in the detection area by the overlap of the measurement light and the reference light, and this interference pattern can be evaluated by the multi-element detector 6. The filter 7 is used here to attenuate the light intensity of the reference light, so that approximately the same light intensity is achieved for the measurement light and the reference light in the detection area.

[0125] The distance of the device to the measurement object 1, i.e. the optical path length difference OPD between the measurement light and the reference light, can be changed by means of the adjustment unit 9. In the present example, the optical path length of the measurement light is changed for this purpose.

[0126] Therefore, the multi-element detector 6 detects different absolute values ​​z i For at least two optical path length differences OPD changed by p (z i ) can be detected.

[0127] The device therefore has an interference optics system for guiding the measurement light together with the reference light and a section for forming an interference pattern in the detection area, the interference optics here having as elements a condenser 3, a semi-transparent mirror 4, an imaging optics system 5, an optical filter 7 and a reference mirror 8.

[0128] The device further comprises an evaluation unit 10, which is configured in the form of a commercially available computer, here a laptop, with a processor, a data memory, a display unit and a keyboard as an input unit. The evaluation unit 10 is connected to the multi-element detector 6 and to the adjustment unit 9, so that the measurement signals of the detector elements of the multi-element detector can be read out by the evaluation unit and the optical path length difference OPD can be changed via the adjustment unit 9 by means of a control signal.

[0129] The evaluation unit calculates absolute values ​​z p and is configured to determine the absolute value at which the optical path length difference between the measurement light and the reference light reaches an explicitly and / or implicitly set value, here 0, and to obtain therefrom the surface topography of the measurement surface 1a of the measurement object 1.

[0130] The important thing is that the value z assigned to the detector element p p To determine the light intensity I p (z i ), in addition to the light intensity I of at least one other detector element q of the multi-element detector. q (z i ) is also used, and examples of the method of the present invention are described in detail below.

[0131] A first embodiment of the method of the present invention is configured as a scanning white light interferometer (WLI).

[0132] First the device is moved to a reference state by the adjustment unit 9. An imaginary reference plane 11, which corresponds to an optical path difference OPD=0 in the reference state, is shown in FIG. 1 by a dashed-dotted line and is perpendicular to the drawing plane of FIG. 1. The exact position of this reference plane 11 is not important for the measurement. The reference plane 11 may therefore pass through the object as in the present example. However, it may equally well be, for example, above the object. What is important is that for a number of measuring elements p height information h pwhereby the relative level differences of the measurement points with respect to one another can be calculated, thereby obtaining a surface topography of the measurement surface 1a.

[0133] Starting from the previously described reference state, the adjustment unit 9 is controlled by the evaluation unit 10 in such a way that the device is moved away from the measurement object 1 in predefined equidistant steps, i.e. upwards in the illustration in FIG. 1. This results in an increase in the optical path length of the measurement light, while the optical path length of the reference light remains unchanged, resulting in a change in the OPD. Here, the respective measured values ​​of all detector elements p of the multi-element detector 6 are detected at 64 positions of the device. In the device shown in FIG. 1, each of the 1024×1024 (=1048576) detector elements p of the multi-element detector 6 is assigned a measurement point p on the measurement surface 1a of the measurement object.

[0134] Thus, the evaluation unit calculates z1, z2,...,z n For all 64 OPDs that were changed relative to the baseline by (n=64), the strength of membership I p (z1), I p (z2),...I p (z n ) is recorded in the interferogram, so that for each measurement point p an associated correlogram c p =(c p (1), c p (2),...,c p (n)), where the light intensity measured at the ith point of the correlogram is c p (i)=I p (z i ).

[0135] Here z i The values ​​are set at equal intervals, i.e., at least according to the setting, two successive z i The interval Δz set between the values ​​is constant.

[0136] After performing this measurement, there is therefore a correlogram with 64 measurements for each detector element p.

[0137] An example for such a correlogram of a detector element p is shown in Fig. 2a. On the x-axis, the given z-values ​​are plotted in [μm], and on the y-axis, the light intensity in arbitrarily selected units is plotted, here preferably normalized to the light intensity outside the interference region of the correlogram, i.e. normalized to the offset of the correlogram. This also applies to the correlograms shown in the further figures, unless stated otherwise.

[0138] Basically, as explained in the introduction to the prior art, the envelope can be determined for the correlogram of FIG. 2a, and the value corresponding to the maximum of the envelope (here, about 5 μm at z position) is taken as z p Therefore, for this measurement point, half the determined z value, i.e., h of 2.5 μm, can be determined. p will be determined.

[0139] However, if disturbances occur, for example in the form of vibrations during the measurement, the measurement will not be performed exactly at the given z-value, but rather the z-value of the actual measurement will be shifted to the right or left in the correlogram display depending on the effect of the vibrations.

[0140] An exemplary impaired correlogram is shown in Fig. 2b. The measurement conditions are essentially the same as those in Fig. 2a, but an impairment has been introduced. This impairment is due to the z i This causes a shift in the values ​​so they are not exactly equally spaced.

[0141] The effects of such impairments are first described below in a prior art evaluation.

[0142] FIG. 3 shows that the evaluation by the prior art is performed in the absence of a fault, i.e., z i The values ​​are shown as evenly spaced.

[0143] FIG. 3a shows the unimpaired correlogram of FIG. 2a.

[0144] The Hilbert transform produces the composite correlogram s shown in Figure 3b. p (z) is generated. As mentioned at the beginning, the original correlogram c p (z) and the synthetic correlogram s obtained via the Hilbert transform p (z) to the envelope env in Fig. 3c p (z) can be obtained.

[0145] This determination of the maximum z-value of the envelope gives us a good approximation already for the absence of disturbances: z p The desired value for h at this measurement point p p A value twice that (approximately 5 μm) can be determined.

[0146] Furthermore, during the evaluation, the original correlogram c p Note that the offset adjustment of (z) was performed. This results in c p The (z) values ​​are now scattered around the zero value as shown in FIG. 3c.

[0147] The correlogram in Fig. 4a corresponds to that in Fig. 2b, but with the disturbance introduced into the measurement due to vibrations, z i The values ​​are not evenly spaced.

[0148] And if we perform a Hilbert transform on the correlogram in Figure 4a, we get the correlogram s in Figure 4b. p Figure 4c shows the original (Figure 4a), but offset-adjusted correlogram c p (z) and the envelope env determined as before. p (z) has an irregular course due to the obstacle. In particular, a clear maximum cannot be determined. Therefore, in the evaluation method according to the prior art, when such obstacles are present, z p The desired value of 5 μm for is not detected or is detected very inaccurately.

[0149] The specificity of the method of the present invention, which enables highly accurate evaluation even in the presence of such obstacles, will be described based on a first example and further embodiments of the method of the present invention with reference to FIGS.

[0150] 5 shows a schematic representation of a part of a planar sensor 6a of a multi-element detector 6. As already mentioned, the CCD chip has 1024×1024 detector elements, of which detector element p is marked by black dots, by way of example, with reference number 6b. It is important to note that the value z p To determine the light intensity I p (z i ), in addition to the light intensity I of at least one other detector element q of the multi-element detector. q (z i ) is also used.

[0151] For this purpose, in this embodiment, adjacent elements are observed in a 3×3 pixel square. The detector element 6b is surrounded by eight adjacent elements q j These are highlighted by thick black frames in Figure 5. From these eight neighbors, one neighbor is selected as follows.

[0152] For each neighbour, we form the difference between the correlogram of the neighbour and that of detector p. For example, for neighbours q1, q2 and q3, the top graph shows the correlogram of this neighbour, and the bottom graph shows the difference between the correlogram of this neighbour and that of detector p (6b).

[0153] By the vector law, the difference vector c qj -c p A scale is assigned to each difference correlogram representing the difference vector c qj (I C p (i) based on the standard deviation formed from the neighboring element q jIf the correlograms of detector element p and detector element p deviate only slightly according to this measure, the correlograms of these two detector elements are very similar, which is disadvantageous here for the evaluation of the present embodiment, since possible signal noise makes it difficult to form an accurate difference. Basically, large deviations according to the above measure are also disadvantageous, since in this case the linear approximation, as explained below, is no longer reliable. However, excessively large deviations are almost impossible in such a measurement situation, since normally only the next adjacent element, whose correlograms differ only slightly, is observed.

[0154] In this embodiment of the method of the present invention, eight adjacent elements q j From among them, the neighboring element whose difference vector has the maximum value according to said measure is selected. In the example of FIG. 5, this is detector element q3.

[0155] Therefore, the value z assigned to the multidetector element p p To determine , the light intensity of detector element q3 is now also used, as will be described in more detail below.

[0156] In Fig. 6a the correlograms of detector elements p and q = q3 are shown with disturbances introduced into the measurement as in Fig. 2b. Since adjacent detector elements p and q are assigned to positionally adjacent measuring points p and q on the measuring surface 1a of the measuring object 1, the correlograms differ only slightly.

[0157] Thus, in Fig. 6b, a close-up of the area around the z-value of 5 μm is shown. q (z)-c p (z). This difference correlogram can also be understood as a 64-dimensional difference vector. In this example, a further evaluation is performed in 64 dimensions. That is, for all z i A measurement point of the value is utilized.

[0158] It is also within the scope of the invention to use subsets, i.e. lower order difference vectors, e.g. pIt is also within the scope of the invention to select points that are approximately symmetrically arranged around the maximum of the modulation, for example ±16 points, i.e. a total of 33 points. In an alternative configuration, the points around the location of the maximum modulation are selected symmetrically, which is indicated by the maximum absolute value of the difference between two successive points. In a further variant of this embodiment, the correlogram is subjected to a sinusoidal fit, and the value of the maximum amplitude of this fit is determined as the median value for symmetrically selecting a subset of points for the subsequent evaluation.

[0159] In Fig. 7a, the correlogram of the detector element p and the differential correlogram of Fig. 6c are plotted. As explained before, the differential correlogram Q p is the composite correlogram s with a scaling factor of f=1. p =f*Q p It can be regarded as:

[0160] However, to determine the correlogram envelope, we first scale the original correlogram c by a scaling factor f. p The composite correlogram s scaled to have the same amplitude as p is necessary.

[0161] As shown in Fig. 7b and 7d, the correlogram envelope env p (z i ) is decided by (c p (z i )) 2 +(s p (z i )) 2 Through the square root formation of s p (z i ) without the correct scaling of the envelope env p (z i ), which would make the maximum determination impossible or at least lead to a significant risk of errors. Figure 7b shows the case now scaled according to figure 7a with a factor f that is too small.

[0162] In contrast, scaling by an excessively large factor f according to FIG. 7c results in an envelope that is likewise wavy and cannot be estimated or is estimated with a significant risk of error, as shown in FIG. 7d.

[0163] In this embodiment, the correct scaling factor f is determined as follows: First, the correlogram c p By finding the maximum of m Then, to determine the scaling factor f, the exponent i m The offset-adjusted original correlogram c, which exists symmetrically around p and the composite correlogram s scaled by a factor f p =f*Q p Here we use 21 points. For these points, we choose 21 values ​​(c p (z i )) 2 +(s p (z i ,f)) 2 , where i=i m -10,i=i m -9,...,i=i m Specify a standard deviation σ(f) of +10. Then use the gradient method to determine the value for f at which the standard deviation is minimized. Using this value for f, we then compute the correctly scaled composite correlogram s p =f*Q p is requested for further evaluation.

[0164] Figure 8a shows the correlogram c of Figure 6a or Figure 2b. p (z i ) into the correctly scaled composite correlogram s determined as previously described p (z i )=f*Q p (z i ) are shown together with the composite correlogram s scaled by a factor f. p (z i ) is the amplitude of the original correlogram c p (z i)

[0165] Figure 8b shows the envelope env p (z) is shown, and this envelope is the correlogram c p and the correctly scaled composite correlogram s determined as described previously. p Here, the envelope env p (z i ) is, as mentioned above, (c p (z i )) 2 +(s p (z i )) 2 This was found by taking the square root of

[0166] In summary, Fig. 9 shows in subfigure a the correlogram of a detector element p with a faulty z value, and in subfigure b the composite correlogram s scaled by the correct factor f determined as previously described. p This composite correlogram was therefore obtained by additionally using the correlogram of detector q3.

[0167] Partial figure c is the correlogram c of partial figure a p , and the envelope env obtained as described before. p When comparing this envelope determined by the method of the invention with the envelope of FIG. 4c determined according to the prior art, it is striking that a much greater robustness against disturbances is achieved, which makes it possible to detect unevenly spaced z i It doesn't become a value.

[0168] Next, the envelope env p is determined according to FIG. 9c, and z p In the concrete case, this is done for the 21 previously selected points z i The envelope in env p (z i )

[0169] However, the measurement data shows that z p Further improvements in the accuracy of the value determination are possible, as will be explained below in an advantageous development of the described embodiment with reference to FIG.

[0170] Figure 10a shows the correlogram c p and the envelope curve according to Fig. 9c obtained by the synthetic correlogram.

[0171] In Fig. 10b, the predetermined envelope env p A partial enlargement of the maximum circumference of (z) is shown on the horizontal axis z. However, on the vertical axis, instead of the intensity for the associated z value, the phase φ assigned to the z value is shown. p (z) is plotted. As explained before, each correlogram point c p For (i), the points s belonging to each are calculated by the synthetic correlogram. p (i) is sought, and the composite correlogram s p is the correlogram c p Therefore, for each position z i For example, the phase can be determined for each point z i The expanded arctangent for arctan2(s p (z i ),c p (z i ) at the corresponding index i and then perform phase unwrapping.

[0172] As mentioned at the beginning, in this embodiment, the reference state was selected by adjusting the optical path length (OPD=0). The value set for the optical path length difference is therefore 0 in this embodiment. Correspondingly, the absolute value z p The phase value set for the determination of is also 0° here. As shown in FIG. 10b, a straight line is fitted by linear regression, and the z value at which the phase value corresponds to the set value (here 0°) is z p is determined.

[0173] First, the approximate value z p is obtained by determining the maximum of the envelope, and then the z of phase 0° is obtained by the regression line. p This two-stage method of determining the value allows for a significant improvement in the measurement accuracy or even greater robustness against disturbances such as vibrations.

[0174] Finally, FIG. 10c shows how the method of the present invention reduces the z value z by an absolute value Δz. i It has been shown that it is possible to obtain information about whether z has changed due to a fault. In the ideal, fault-free case, the value z i lies on the regression line shown by the dotted line in Figures 10b and 10c. i For the value Δz i , the value z i For each value z i and the z value corresponding to the associated phase value on the regression line. This correction value Δz is shown in FIG. i values, where i=30, 31, ..., 37, are designated by horizontal arrows.

[0175] So basically, z i The correction value Δz obtained according to FIG. i and the evaluation is carried out in particular in a manner known per se, by the corrected z i It is also within the scope of the invention to carry this out by value.

[0176] Furthermore, each z i For z, the correction values ​​for all or selected detector elements are averaged to obtain i It is possible to achieve an accurate correction of the disturbance Δz value, because according to this embodiment, for a fixed value of i corresponding to a measurement point, it is possible to obtain, with a good approximation, the disturbance Δz value for all measurement points and all detector elements. i Therefore, for the subset, preferably for all the detector elements, the correction value Δz iand averaging the correction values ​​over a subset of the measurement points, preferably over all the measurement points, in particular by a weighted average, to obtain the correction value Δz i Calculate all z i It is advantageous to carry out a correction of the values.

[0177] FIG. 11 shows the unscaled composite correlogram Q p =s p / f is a correlogram c q -c p and thus is a direction vector in an n-dimensional vector space, and an n-dimensional light intensity vector (c p (1), c p (2),...,c p (n))=I p (z1), I p (z2),...I p (z n ) and (c q (1), c q (2),...,c q (n))=(I q (z1), I q (z2),...,I q (z n )) , which is shown diagrammatically to consist of specifically only two points in this example.

[0178] For practical reasons, only three dimensions have been chosen for illustration, rather than the 64 that actually exist. In Figure 11, only dimensions 31, 32 and 33 of the 64-dimensional vector space are shown.

[0179] In particular, in a vector space, as previously explained in Figure 6, i A subset of values, here the 64 possible z i The limit to 21 of the values ​​is the z dimension selected. iThis corresponds to a projection onto a subspace corresponding to the number of values. Such vectors resulting from the projection and / or transformation can also be evaluated by the method of the present invention.

[0180] An example for such further transformations is to subtract an offset in each correlogram, for example by determining the offset based on the correlogram points outside the interference region or by averaging the correlogram values ​​and then subtracting. Similarly, scaling or other modifications by normalization of the correlograms are such transformations. Rotations and other transformations can be performed as well.

[0181] The measuring device according to the first embodiment as well as the method according to the first embodiment can also be used for measuring objects which partially reflect the measuring light at multiple planes.

[0182] In such a measuring object with several partially reflecting surfaces, for the measurement with the device of FIG. 1, for example, as an alternative to the previous description of the measuring object 1, the measuring surface 1a of the measuring object 1 can be a coated glass surface facing the device, which only partially reflects the measuring light. Furthermore, the measuring object has further boundary surfaces on the metal-coated back side (away from the device, in FIG. 1, the bottom side) in the volume of the measuring object, at which the components of the measuring light entering the measuring object are reflected inside the measuring object. In this way, by the methods known from the prior art as well as by the method of the present invention, it is possible to obtain two or more values ​​z at one location point p. p Because two or more height positions h p This is because the measurement light is (partially) reflected at different heights h p If the difference between the coherence lengths of the detected measurement and reference light is greater than the coherence lengths of the detected measurement and reference light, interferences belonging to different reflecting layers do not overlap in the correlograms, so that the partial correlograms belonging to different layers are separated in the measurement data and can therefore be evaluated separately, and different z p The method of the present invention can determine the values ​​of points z pThe method is particularly advantageously used even when different partial correlograms of overlap, since in this case too the composite correlogram is accurately determined by the method of the invention, which on the one hand allows known methods to be used for the evaluation of overlapping correlograms, and on the other hand provides additional advantageous evaluation options, since for example the common envelope and the common phase of the different partial correlograms are determined very simply in accordance with the procedure already described.

[0183] In FIG. 12 a second embodiment of the device according to the invention is shown diagrammatically.

[0184] This structure is also based on the principle of the Michelson interferometer, so in order to avoid repetition, only the important differences between the second embodiment shown in FIG. 12 and the first embodiment shown in FIG.

[0185] The measurement object 1, which is to be measured here at a previously elevated temperature, is therefore arranged on a hot plate 1b, which is important, for example, if the curvature of the measurement surface 1a due to thermal effects is to be checked in electronic components.

[0186] The problem here is that air eddies 1c arise in the beam path of the measurement light between the measurement surface 1a and the device due to the heat from the hot plate 1b. These air eddies cause density changes and corresponding inhomogeneities in the refractive index. Even variations in the refractive index of air due to thermally induced density fluctuations can lead to significant measurement errors. This is of course also the case if there are no additional disturbances, for example due to vibrations.

[0187] The arrangement of the optical components of the apparatus is the same as in the first embodiment apparatus shown in FIG.

[0188] In this case, the evaluation unit 10 is connected to the multi-element detector 6 as already described. The multi-element detector 6, which is here configured as a CMOS camera, is connected to the adjustment unit 9 via a trigger line. In the second embodiment, the adjustment unit is provided with equally spaced zi The adjustment unit 9 adjusts the z i It is shown diagrammatically that when the value is reached a trigger signal is sent to the multi-element detector 6 and a camera image is recorded.

[0189] Above the measurement object 1, a reference surface 11 is shown, which represents the reference state OPD=0. In this example, the reference surface 11 is therefore above the measurement object and therefore has a negative level value h for a measurement point p on the measurement surface 1a of the measurement object 1. p This occurs.

[0190] The evaluation unit 10 is configured to carry out an evaluation according to a second embodiment of the method of the invention, which substantially corresponds to the first embodiment, so that, likewise, in order to avoid repetition, only the important differences will be mentioned below.

[0191] In Figure 13, a planar sensor 6a of a multi-element detector 6 is again shown diagrammatically. Comparing Figures 13 and 5, it can be seen that in this second embodiment of the method of the invention a relatively large number of detector elements is utilized.

[0192] In FIG. 13, the detector p of reference numeral 6a is also shown in black. The neighboring detectors to be observed are shown by thick black frames. Here, the 48 neighboring elements q of detector p (6a) in a 7×7 detector square are shown. i is used for the evaluation. In this case, desirable neighbor characteristics are also defined to evaluate the suitability of neighbor elements. As a measure for evaluating the neighbor characteristics, the difference vector c q -c p The length criterion of is formed as a metric. Thus, for each of the 48 neighboring elements, for example, in FIG. 13, the differential correlogram c q -c p, as well as a value formed by the numerical value obtained by the metric length criterion for this difference correlogram. Here, the selection is made such that 10 neighboring elements with similar correlograms are selected from the 48 neighboring elements. Thus, for all 48 neighboring elements, values ​​are calculated corresponding to the metric length criterion of the difference vector, and the 10 neighboring elements with the 10 smallest values ​​are determined. This makes sense, since in this measurement situation, it is assumed that the differences in the correlograms are due definitively to air eddies, and therefore neighboring elements with small differences in terms of the metric length criterion of the difference vector will have similar measurement conditions.

[0193] In the example of Fig. 13, the detector element with the difference vector 1.2153 and the length criterion of 0.8715 does not belong to the group of detector elements with the 10 smallest values, whereas the detector elements with values ​​0.4293, 0.3916 and 0.3444 belong to this group and are correspondingly used for the evaluation (together with seven further detector elements not shown in detail).

[0194] Therefore, the second embodiment is different from the first embodiment in that the light intensity I p (z i ) plus the 10 neighboring elements q1,...,q 10 The light intensity I qj (z i ) is also used to measure the distance between adjacent detector elements q j (Here, 10) is assigned to detector element q, and the value z p They differ in the way they are used to determine

[0195] In an alternative embodiment of the second embodiment, rather than selecting a fixed number of detector elements spatially surrounding, for example, detector element p, it is possible to select from a particular preselected detector element all detector elements for which a particular predefined neighborhood characteristic exists, e.g., a correlogram c qj The correlogram c of detector p is only p All detector elements q that deviate from jTherefore, it may be advantageous to select the value c qj (I C p The standard deviation of (i) corresponds to approximately twice the quantization noise and the camera noise. Here, it is advantageous to set upper and lower thresholds for the values ​​determined by the corresponding metrics, on the basis of which the detector elements to be used are selected. This is because, on the one hand, the correlogram c qj and c p (i) takes into account that the correlograms should not be too different, as this would make linear approximation difficult, but on the other hand they should not be too similar, as the difference correlograms would be very small and would be impaired or even swamped by possible noise.

[0196] In FIG. 14, multiple adjacent elements q j Based on this, the value z assigned to the detector element p is p It is shown diagrammatically how to determine

[0197] For reasons of representation, in Fig. 14 as in Fig. 11, a projection into a three-dimensional subspace is made for illustration, and only dimensions 31, 32 and 33 of the 64-dimensional vector space are shown. As already mentioned, in this example, a selection of 10 neighboring elements is made, so that the correlogram vector c belonging to the detector element p is correspondingly shown in the 64-dimensional vector space. p In addition, 10 correlogram vectors c q which for simplicity are represented by end points shown as points.

[0198] Unlike the formation of difference vectors shown in and described in FIG. 11, here the determination of the direction vectors in the 64-dimensional space is performed by dividing the two correlograms c q and c p Instead, it is done by taking the correlogram c qj and c p The end point of (similarly, for simplicity, q jand p), and further denoted by p. p A direction vector 15 is determined that belongs to a line passing through the end point p of vector q. This can be done by using a line fit and then subsequently finding the direction vector from here in a 64-dimensional vector space. In an alternative embodiment, Principle Component Analysis (PCA) is used to find the direction vector 15 belonging to a line passing through the end point p of vector q. j and p, in which the eigenvector belonging to the maximum eigenvalue of the covariance matrix is ​​the directional vector sought. In many PCA algorithms, the maximum eigenvalue of the covariance matrix and the corresponding eigenvector are determined first, so that it is particularly advantageous to interrupt the principal component analysis if a corresponding eigenvector is found, and in a specific embodiment, the complete principal component analysis can be omitted, and only a partial principal component analysis needs to be performed.

[0199] The found directional vectors are also calculated as the unscaled composite correlogram Q p (z i )=s p Therefore, in Fig. 14, p It is shown as / f.

[0200] According to a second embodiment, an unscaled composite correlogram Q is generated based on a number of detector elements q. p =s p Further evaluation is performed as described in the first embodiment. The scaling factor f for scaling the composite correlogram is again determined by the above procedure. Then the correlogram c p and the correctly scaled composite correlogram of membership s p The envelope is determined from the z-value, and the maximum z-value of this envelope is the z pIf necessary, in addition to the envelope estimation, a phase estimation can also be carried out, all results of which can be used in the above-mentioned manner or in correspondence with known possibilities.

[0201] FIG. 15 shows a third embodiment of the device according to the invention.

[0202] In this exemplary embodiment, the formation of the interference pattern is performed by a Mirau interferometer. Illumination light is generated by a light source 2, which reaches a semi-transparent mirror 4 via a condenser lens 3. The illumination light is therefore partially reflected downwards in FIG. 15 and there impinges on a Mirau objective 12, which is constructed in a manner known per se. In particular, the Mirau objective 12 has a front lens 12a with a central reference mirror as well as a beam splitter 12b.

[0203] The measurement light emerging from the Mirow objective in the direction of the measurement object 1 is at least partially reflected from the measurement surface 1a of the measurement object and enters again into the beam path of the Mirow objective 12. At the same time, the reference light is split off from the illumination light by the beam splitter 12b of the Mirow objective and deflected in the direction of the central reference mirror. There, this reference light is reflected and reflected back to the beam splitter 12b. At the beam splitter 12b, a part of the reference light is reflected again and is thereby superimposed with the measurement light reflected back from the measurement object, passes at least partially together with the measurement light through the semi-transparent mirror 4 and is imaged by the cylindrical lens 13 onto the multi-element detector 6, which here is configured as a CMOS camera. The multi-element detector 6 correspondingly has a CMOS image sensor as a planar sensor 6a and here has an array of 512 × 512 detectors, i.e. a total of 262144 detectors.

[0204] The adjustment unit 9 is configured in this example as a piezoelectric adjuster with a piezoelectric controller 9a, by means of which the adjustment unit 9 configured as a piezoelectric adjuster can be controlled in such a way that the Mirau objective is moved towards and away from the measurement object 1 according to the double arrow shown in FIG.

[0205] In contrast, the remaining devices are not moved by the adjustment unit 9 .

[0206] The apparatus again includes an evaluation unit 10 configured as a laptop, which is connected to the multi-element detector 6. In this third embodiment as well as in FIG. 12 and in the second embodiment, a control unit 9, here a piezoelectric controller 9a, is connected to the multi-element detector 6 via a trigger line.

[0207] Here, the interference optics comprises a condenser lens 3 , a beam splitter 4 , a Mirau objective lens 12 and a cylindrical lens 13 .

[0208] The measuring object 1 is here a MEMS element, which has a readily movable pressure-sensitive diaphragm as measuring surface 1a.

[0209] The measurement sequence is essentially the same as that of the second embodiment described in FIG. 12. By means of the piezo controller 9a and the adjustment unit 9, the Mirau objective is moved continuously at an approximately constant speed. At equal time intervals, trigger signals are sent via a trigger line to the multi-element detector 6 for recording the camera images. The storage and evaluation of these camera images is carried out by the evaluation unit 10 as in the previously described embodiment.

[0210] The evaluation was performed in accordance with a third embodiment of the present invention, which is configured similarly to the second embodiment previously described with respect to FIG.

[0211] However, in the third embodiment, the value z assigned to the multiple detector elements q is p is used to determine

[0212] Detector element q jThe selection of is made here such that all 48 neighbors in the 7×7 field of detector element p are used for the evaluation. In FIG. 16, again for illustration reasons, only the diagrams of dimensions 31, 32 and 33 of the n-dimensional vector space of correlogram vectors are shown. As can be seen in FIG. 16, detector elements q1 to q 48 The cloud of points presented by the correlogram of can be better approximated by a curve than a straight line. In this third embodiment, a curve 15a, here an elliptical segment, in an alternative embodiment a parabolic section, is fitted to the cloud of points. The approximation is therefore done by fitting a low-dimensional differentiable submanifold to the distribution of points, here a one-dimensional differentiable manifold. The approximation is done here by determining the squared deviation and optimizing the free parameters of the curve by one of the common mathematical methods, so that the squared deviation is minimized.

[0213] As can be seen in FIG. 16, the correlogram c p After determining the curve 15a for p =s p / f p is determined as the tangent vector 16a to the curve passing through point p.

[0214] Further evaluation begins with the scaling factor f p is determined at point p, and the correlogram c p and the correctly scaled composite correlogram s p and based on the value z p The method is carried out to determine:

[0215] However, in this third embodiment, the determined curve is advantageously examined not only to determine the tangent vector 16a of point p, but also to determine the tangent vector 16b of point q. j (See, for example, tangent vector 16b to point q1 and tangent vector 16c to point q2.) Thus, once the curve is determined, the value z p Not only the determination of , but also all points q j(j=1,...,48), or at least for a large number of them, the corresponding value z q can be determined.

[0216] A fourth embodiment of the device according to the invention is shown in Fig. 17. This embodiment corresponds essentially to the first embodiment from Fig. 1. However, an adjustment unit 9 is arranged in the fourth embodiment on the reference mirror 8 and moves it back and forth in the direction of the double arrow towards the light source. The adjustment unit 9 thus influences the optical path of the reference light. In contrast, the position of the device relative to the measurement object 1 and in particular the measurement surface 1a remains constant, i.e. the optical path length of the measurement light remains unchanged.

[0217] However, if this is ignored, the functional mechanism is the same as in the first embodiment, and in particular the method described for the first embodiment can also be implemented by the device of FIG.

[0218] Based on the fourth embodiment of the device of the present invention shown in FIG. 17, a fourth embodiment of the method of the present invention will be described below.

[0219] In this regard, the apparatus of Figure 17 has been modified and configured to perform PSI measurements, in this case the light source 2 being configured as a monochromatic laser with a wavelength of 520 nm.

[0220] In this embodiment, the adjustment unit 9 adjusts the phase difference z i is changed.

[0221] Therefore, the light intensity I p (z i ) is the absolute value z of the phase difference changed relative to the reference state of the interferometer i The correlogram is recorded again depending on p =(c p (1), c p (2),...,c p (n))=(I p (z1), I p (z2),...I p (z n )) is obtained, where zi is the phase difference measured, for example, in degrees or radians.

[0222] Specifically, in this embodiment, z i Measurements are performed at six different values ​​for . Thus, the correlogram vector c p are given as vectors in a six-dimensional vector space, and the same considerations are made as in the previous example, except that z i The values ​​are given here as phase differences rather than as OPD differences.

[0223] In this fourth embodiment of the method of the invention, all detector elements are utilized for the evaluation. This is shown diagrammatically in the reduction to dimensions 3, 4 and 5 in Fig. 18. As can be seen in Fig. 18, the point cloud generates an ellipse in n-dimensional space, here in a six-dimensional space, although here only three of the six dimensions are illustrated. As mentioned at the beginning, phase-shifting interferometry is considered as a special case of white light interferometry with respect to the correlogram, where a constant envelope env(OPD)=const is given.

[0224] As further detailed above, point clouds are described in PSI as closed ellipses, as shown in Fig. 21. The case of white light interferometry is also treated later.

[0225] z i Disturbances affecting the values, i.e. non-uniform z i The disturbance that causes the z i The value is unaffected or barely affected by said disturbance.

[0226] According to a fourth embodiment of the method of the invention, an ellipse 15a is fitted to the cloud of points shown in Fig. 18. For this purpose, an ellipse is parameterized in an n-dimensional space, here a 6-dimensional space, with n+5 free parameters, here 11 free parameters: n parameters define the normal vector of the plane in which the ellipse lies, including the distance of this plane from the coordinate origin, two parameters define the displacement of the ellipse in the plane with respect to the collision point of the normal vector on the plane, and three parameters define the length and rotation of the major axes of the ellipse. Then, for each correlogram vector c p or c q For a given vector, the distance to the parameterized ellipse is given by the sum of the squared distances over all correlogram vectors c p or c q is minimized by known mathematical minimization methods over the ellipsoid, thereby obtaining the corresponding parameters that define the ellipse. p For the composite (unscaled) correlogram Q p =s p / f p is determined by determining the tangent vector 16a to the ellipse that passes through point p. This is easily possible since the ellipse is parameterized and exists as a one-dimensional differentiable manifold, and the tangent vector can be determined by differentiation. Continuing, as explained before, the scaling vector f p is determined, and the correlogram c p and the composite correlogram of affiliation s p From Z p As can be seen directly in FIG. 18, this determination of the ellipse is not only an evaluation for the detector element p, but also for all other detector elements, e.g. the associated correlogram c q1 ,c q2 ,c q3 and c q4 The corresponding tangent vectors 16b, 16c, 16d, 16e are also presented. qj =s qj / f qjUsing the scaling factor f qj , the correctly scaled composite correlogram of membership s qj , and the membership value z qj is determined, which gives the value z p and z qj This saves a great deal of computational cost compared to determining each separately.

[0227] In a variation of the fourth embodiment, a principal component analysis is first performed to determine the plane in which the ellipse lies. p For , the points are projected onto this plane, minimizing, among other things, the noise or disturbances. That is, the points c are projected onto the plane so that they lie within the plane. p is shifted perpendicular to this plane. After all points are projected onto the previously determined plane, the determination of the ellipse is carried out subsequently. This achieves high accuracy.

[0228] In Fig. 19, a point cloud is shown diagrammatically for display by projection into a three-dimensional subspace of a six-dimensional vector space given by the light intensities measured at z3, z4 and z5. The point cloud is obtained by determining a plane 14 by PCA and projecting the individual points onto this plane. It should be noted here that the illustrated plane is not a plane of three-dimensional space that is usually spanned in the three spatial directions shown. The plane is indeed a two-dimensional plane of n-dimensional space, but is not usually a plane in a three-dimensional vector space spanned by the axes shown. Correspondingly, the illustration of Fig. 19 should be understood as a simplified illustration for better understanding.

[0229] For further evaluation of this embodiment of the method of the present invention, we consider below only the plane of FIG. 19 with the projected points.

[0230] Figure 20 shows in sub-view a the plane 14 of Figure 19. This plane has been determined by a principal component analysis to determine the two largest eigenvalues ​​of the covariance matrix and the associated eigenvectors, as already described. Similarly, it is possible to carry out a partial principal component analysis until said values ​​are determined.

[0231] The two eigenvectors 17a, 17b span the plane in which the ellipse lies. We then project the points given by the correlogram vector onto this plane.

[0232] In Fig. 20a, for simplicity the orientation of the plane has been chosen such that the x-axis of the plane is determined by the eigenvector 17b to the largest eigenvalue, and the y-axis is determined by the eigenvector 17a to the second largest eigenvalue. The lengths of the semi-axes of the ellipse are proportional to the two eigenvalues. An affine map that transfers the ellipse to a circle can therefore be performed, for example via stretching the y-axis by the ratio of the two eigenvalues.

[0233] The result is shown in FIG. 20b. In the circle present here, the relative phase angle 18 desired for evaluation can be easily determined or read off. The phase angle 18 allows the z p value or z qj Values ​​are determined for each individual detector element and therefore for each individual measurement point.

[0234] The method described with respect to Fig. 18 can also be used in white light interferometry (WLI). Therefore, in the following, a further embodiment of the method according to the invention is presented, in which WLI is carried out according to the fourth embodiment of the invention shown in Fig. 17, the light source 2 is now not a laser but a broadband light source, for example an LED or a superluminescent diode. i The method for recording intensity values ​​for is carried out here in the same way as in the embodiment described in FIG. 1. However, here the optical path length of the measurement light is not changed. The change of the OPD is achieved by changing the optical path length of the reference light by sliding the reference surface 8a of the reference mirror 8 by means of the adjustment unit 9. Here too, 64 z iFor the values, the respective intensities for each detector element p of the multi-element detector 6 are recorded, so that for each detector element there exists a correlogram which can again be represented as points in the 64-dimensional space.

[0235] Figure 21 shows a schematic representation of the point cloud in a 64-dimensional space, as in Figure 19, where again for practical reasons only the third dimension of this space is shown. Here too an approximated elliptical progression is shown, but this progression does not form a closed ellipse. Rather, this progression is a spiral around a cylinder with an elliptical cross section. The reason that a closed ellipse is not formed is that after each revolution the maximum of the envelope moves further, whereas in the PSI method, as mentioned before, the envelope can be described as a constant function.

[0236] However, even if a closed ellipse does not exist, it is still possible, here by means of principal component analysis, to determine a two-dimensional plane in n-dimensional space in which the points approximately lie, which is shown diagrammatically by the plane 14 in FIG.

[0237] In order to better understand the illustration of FIG. 21, point (and therefore detector element) q j are selected, and these correlograms c qj is the correlogram c p , the ellipse is shifted by at most more than half a period on the detector element p. This makes it clearer that the ellipse is not closed.

[0238] In the actual application of this embodiment of the method of the invention, the correlogram c belonging to the detector element p by about ±2 periods p The correlogram c shifted relative to qj is permitted. It is sufficient that the shift in correspondence is determined by methods known from the prior art that are not as insensitive to disturbances as the method of the present invention, whereby a metric for determining the neighboring characteristics is also used. Similarly, alternative configurations can be selected with other values ​​and / or combinations with the spatial spacing metric of the detector elements.

[0239] And for each point p or q j A distance vector is calculated to the plane determined for (see distance vector 19 shown by way of example in FIG. 21). Points belonging to the correlogram shifted by one or more periods have distance vectors of different lengths to this plane. This distance takes on relatively discrete values ​​at each location belonging to the same projection point, because the ellipse rolls out of the plane and goes "up a floor" with each revolution.

[0240] The length of the interval vector thus determines how many periods the correlogram has been shifted. The length of the interval vector thus produces results equivalent to the envelope estimation in the case of conventional correlogram estimation. The phase estimation is performed as described in the previous figures.

[0241] This phase estimate, in combination with information obtained from the interval vectors about the shift of the correlogram envelope, allows the shift of each individual correlogram to be determined relatively accurately (and independent of disturbances such as vibrations), in this case completely, rather than just one period or a remainder of 360°, as in phase-shifting interferometry.

[0242] The procedure described allows the evaluation to be carried out for a large number of points at once, which saves considerable calculation time. From the determined correlogram shifts the topography of the measuring object is determined.

[0243] In a modification of the embodiment, the evaluation is performed for a part of the points (for example, c p In the case where only the correlograms shifted by a maximum of ±2 periods with respect to the ordinate are performed, the method is preferably carried out on several, preferably overlapping, point sets and the results obtained can be summed.

[0244] A further variation of this embodiment is based on the fact that knowledge of the interval vector as explained earlier means that the location of the envelope maximum is also known. jInstead of simply projecting onto the determined plane 14, only the envelope of the correlogram is shifted if there is knowledge of the function course of the envelope. This means that, for example, j The correlogram at point q j This is done by dividing by the function envelope of point p and multiplying by the function envelope of point q. j is mapped onto the same plane as point p. If this mapping is performed for all points, preferably iteratively, a closed ellipse as shown in the previous figure is obtained, which can also be evaluated accordingly, thereby improving the quality of the evaluation result and the topographies determined therefrom.

[0245] In practical applications, WLI and PSI are typically performed at a much smaller number of locations than phase-shifting interferometry, and therefore i Another difference is that the number of z is typically smaller than in the WLI measurement. i is the phase difference with respect to the reference state of the interferometer, while in the WLI measurement, z i is the OPD difference with respect to the reference state of the interferometer. However, phase and OPD are usually proportional, i.e., they can be scaled using the scale factor 2π / λ (radians) or 360 / λ (degrees) according to phase=360° / λ*OPD, where λ is the effective optical wavelength.

[0246] In the above example, the WLI measurements are performed at 64 locations (z1, z2, ..., z 64 ), each correlogram therefore has correspondingly 64 values ​​and the complete vector space is 64-dimensional. In contrast, for PSI measurements, three or four points may already be sufficient, so that for each detector element there are correspondingly only three or four measurements at three or four z-points z1, z2, z3 or z1, z2, z3, z4.

[0247] In a variant of the PSI method previously described, only four values ​​are used. Based on Fig. 22, the influence of disturbances on such measurements and the procedure for implementing the method of the invention, as well as its advantages, are explained below.

[0248] FIG. 22 shows in subfigure a) an ideal signal curve without interference, and in c) measured values ​​which are phase shifted by 90°. p (1)~c p (4). In subfigure b), the ideal signal curve without further disturbances is shown as a solid line, but the measured values ​​have simulated disturbances which cause a shift of z in the abscissa, so that the phase shift between the measured values ​​is not exactly 90°. The deviations from the ideal values ​​(which are not known in the real measurements in this example) are represented by the differences Δz1 to Δz4. The values ​​c p (3) The ideal value c that does not cause additional damage id p (3) is shown, and therefore this value is the value c of subfigure a). p Corresponds to (3).

[0249] In this variation of the embodiment, four z i The values ​​of c are used, each of which is phase shifted by 90° in the ideal case without any disturbances. p (i) = c(OPD) = A + B * cos(Ψ + z i In this case, the z p where the offset A and amplitude B are constant but unknown values.

[0250] In the conventional evaluation by the prior art, the desired Ψ is calculated by the c p (i), which is vulnerable to errors in the presence of disturbances. i In value, Ψ=arctan2(c p (4)-c p (2), c p (1)-c p (3) =arctan2(cos(Ψ+z4)-cos(Ψ+z2),cos(Ψ+z1)-cos(Ψ+z3)) This is carried out by.

[0251] In fact, if z2 = z1 + 90°, z3 = z1 + 180°, and z4 = z1 + 270°, then Ψ = arctan2(sin(Ψ), cos(Ψ)) = Ψ, and phase unwrapping may need to be performed.

[0252] But z i If there is a fault in, this kind of evaluation is inaccurate and it is no longer possible to make a fault-free determination of Ψ.

[0253] The procedure of the present invention preferably comprises the steps of: p (Here, c p =(c p (1), c p (2), c p (3), c p (4))) according to the procedures described in the specification and the preceding examples, p (Here, s p =(s p (1),s p (2),s p (3),s p (4))) and repeat the same procedure for the other detector elements q j , possibly with another appropriately selected correlogram c qj The information is used.

[0254] To do this, we first obtain the direction vector Q by using the difference formation, approximation, fitting, principal component analysis, etc. p (z i )=1 / f p *s p (1), and then use one of the methods described above to find the scaling factor f p Determine.

[0255] Particularly advantageously, in phase-shifting interferometry, for all i, (c p (i) 2 +(s p (i) 2 For the same constant value w p must occur, where c p (i) is their offset op The light intensity of the correlogram corrected by I p (z i ), i.e. c p (i)=I p (z i )-o p The offset o p For example, (a) an appropriate z i (For example, four z i ), or (b) particularly advantageously, by averaging over the scaling factor f, p At the same time, (I p (z i )-o p ) 2 +(f p *Q p (z i )) 2 f is constant p To p Determine.

[0256] In step (a), as mentioned above, p There exists a coefficient f p Only one must be determined, where (I p (z i )-o p ) 2 +(f p ) 2 *(Q p (z i )) 2 =w p is a constant value w for all i p which preferably yields m*x i +b=y i (However, x i =(Q p (z i )) 2 , y i =-(I p (z i )-o p ) 2 ) is performed by linear regression, and the slope m = (f p ) 2 From f pWe can immediately obtain the desired value for

[0257] In step (b), f p To p All (I p (z i )-o p ) 2 +(f*Q p (z i )) 2 =w p which gives rise to a further minimization problem. In this case, for example, f p ,o p and w p is the sum ((I p (z i )-o p ) 2 +(f p *Q p (z i )) 2 This minimization problem can be solved by related known mathematical methods, and f p To p The desired value for is obtained.

[0258] In both cases, the composite correlogram s p (Here, s p =(s p (1),s p (2),s p (3),s p (4))) and the original correlogram c with the offset adjusted p (z i )=I p (z i )-o p (Here, c p =(c p (1), c p (2), c p (3), c p (4))) is obtained.

[0259] Composite correlograms p Once calculated, the original correlogram cp In combination with each part z i The phase position at z is precisely determined, and therefore another z i There is no need to use Ψ(z i )=arctan2(s p (I C p (i)), However, in some cases, phase unwrapping is performed again.

[0260] For phase-shifting interferometry, different points p are used for topography determination. j Since only the difference in phase position in is important, the corresponding phase difference Ψ p2 -Ψ p1 can subsequently be determined for any value of i, i.e. Psi p2 -Ψ p1 =arctan2(s p2 (I C p2 (i))-arctan2(s p1 (I C p1 (i) Optionally, appropriate averaging values ​​for the results are determined for various or all i as well.

[0261] In the evaluation of the present invention, for example, z due to vibration i It should be noted that these disturbances have little effect on the results of the evaluation, which means that the method of the present invention usually provides much better results than the conventional methods of the prior art, even in the presence of disturbances. [Explanation of symbols]

[0262] 1. Measurement object 1a Measurement surface 1b Hot plate 1c air vortex 2 light source 3. Capacitor 4. Semi-transparent mirror 5 Imaging optical system 5a, 5b Optical lenses 5c Optical aperture 6 Multi-element detector 6a Flat sensor 6b Detector element 7 Optical Filters 8 Reference Mirror 8a Reference plane 9 Adjustment Unit 9a Piezoelectric Controller 10 Evaluation Units 11 Reference plane 12 Mirow Objective Lens 12a Front lens 12b Beam splitter 13 Cylindrical Lens 14 Planes determined by PCA 15 Directional Vector 15a curve 16a Tangent vector at p 16b Tangent vector at q1 16c Tangent vector at q2 Tangent vector in 16d q3 Tangent vector in 16e q4 17a,17b Eigenvectors 18 Relative Phase Angle 19 Interval Vector

Claims

1. 1. A method for interferometrically determining a surface topography of a measurement object (1), comprising: forming an illumination light and a reference light by at least one light source (2) and illuminating the measurement object (1) with the illumination light; a step of combining the illumination light reflected back as measurement light from the measurement object (1) with the reference light to form an interference pattern in a detection area; Varying an optical path length difference and / or a phase difference between the measurement light and the reference light; In the detection region, the light intensity I of the interference pattern is detected on a plurality of detection elements p (6b) of the multi-element detector (6). ｐ (z ｉ ) with different absolute values ​​z ｉ detecting at least two optical path length differences or phase differences that have been changed by The absolute value z of the change in optical path length difference or phase difference for the multiple detection elements p (6b) of the multi-element detector (6) ｐ determining the absolute value at which the optical path length difference and / or phase difference between the measurement light and the reference light, respectively, reaches a value explicitly and / or implicitly set for the detector element p (6b); The surface topography of the measurement object (1) is then measured by means of the absolute values ​​z ｐ and The value z assigned to the detector element p (6b) ｐ In order to determine the light intensity I ｐ (z ｉ ), as well as the light intensity I of at least one other detector element q of the multi-element detector (6). ｑ (z ｉ ) is also used, The light intensity I ｑ (z ｉ ) is the value z ｐ the at least one other detector element q used for the determination of is selected to have a predetermined neighborhood property with respect to the detector element p (6b); The neighboring characteristics are defined at least in part using a metric; the metric comprises the spatial spacing of the detector elements p (6b) and q and / or the spatial spacing of points assigned to them on the measurement object (1) and / or on an optical surface conjugate to the multi-element detector (6); The at least one metric for determining the neighboring characteristics of the detector elements p (6b) and q is I ｐ (z ｉ ) and I ｑ (z ｉ ) is given by ｐ (z １ ), I ｐ (z ２ ), . . . , I ｐ (z ｎ )) and (I ｑ (z １ ) ， I ｑ (z ２ ), . . . , I ｑ (z ｎ )) or a metric in the vector space of vectors resulting from projections and / or transformations therefrom.

2. 1. A method for interferometrically determining a surface topography of a measurement object (1), comprising: forming an illumination light and a reference light by at least one light source (2) and illuminating the measurement object (1) with the illumination light; a step of combining the illumination light reflected back as measurement light from the measurement object (1) with the reference light to form an interference pattern in a detection area; Varying an optical path length difference and / or a phase difference between the measurement light and the reference light; In the detection region, the light intensity I of the interference pattern is detected on a plurality of detection elements p (6b) of the multi-element detector (6). ｐ (z ｉ ) with different absolute values ​​z ｉ detecting at least two optical path length differences or phase differences that have been changed by The absolute value z of the change in optical path length difference or phase difference for the multiple detection elements p (6b) of the multi-element detector (6) ｐ determining the absolute value at which the optical path length difference and / or phase difference between the measurement light and the reference light, respectively, reaches a value explicitly and / or implicitly set for the detector element p (6b); The surface topography of the measurement object (1) is then measured by means of the absolute values ​​z ｐ and The value z assigned to the detector element p (6b) ｐ In order to determine the light intensity I ｐ (z ｉ ), as well as the light intensity I of at least one other detector element q of the multi-element detector (6). ｑ (z ｉ ) is also used, The value z assigned to the detector element p (6b) ｐ I ｐ (z ｉ ) and I ｑ (z ｉ ) is the n-dimensional light intensity vector (I ｐ (z １ ), I ｐ (z ２ ), . . . , I ｐ (z ｎ )) and (I ｑｊ (z １ ) ， I ｑｊ (z ２ ), . . . , I ｑｊ (z ｎ )) or a vector resulting from a projection and / or transformation therefrom.

3. A value z assigned to the detector element p of the multi-element detector ｐ To determine the function I, which depends on the change z of the optical path length difference and / or the phase difference between the measurement light and the reference light, ｐ (z) to the light intensity I ｐ (z ｉ ), as well as the light intensity I of at least one other detector element q of the multi-element detector (6). ｑ (z ｉ 3. The method according to claim 1 or 2, wherein the determination is also made using

4. The approximation is to define a differentiable submanifold M as a set of points (I ｐ (z １ ), I ｐ (z ２ ), . . . , I ｐ (z ｎ )) and (I ｑ (z １ ) ， I ｑ (z ２ ), . . . , I ｑ (z ｎ 3. The method of claim 2, comprising fitting a distribution of points in a vector space of vectors resulting from a projection and / or transformation to or from a distribution of points consisting of

5. The method of claim 4 , wherein the differentiable submanifold M is an at most three-dimensional submanifold of the vector space to which it belongs.

6. The n-dimensional light intensity vector (I ｐ (z １ ), I ｐ (z ２ ), . . . , I ｐ (z ｎ )) and (I ｑ (z １ ) ， I ｑ (z ２ ), . . . , I ｑ (z ｎ 6. The method according to claim 2, 4 or 5, wherein the approximation to the vectors obtained by projection and / or transformation therefrom is represented by a one-dimensional parametric curve (15a) in the associated vector space.

7. The light intensity vector (I ｐ (z １ ), I ｐ (z ２ ), . . . , I ｐ (z ｎ )) and (I ｑ (z １ ) ， I ｑ (z ２ ), . . . , I ｑ (z ｎ 7. The method according to claim 2, wherein the approximation to the vectors obtained from them by projection and / or transformation is at least locally linear.

8. The value z assigned to the detector element p (6b) ｐ The approximation used in determining comprises the determination of a direction vector (15), which is a function of the light intensity vector (I ｐ (z １ ), I ｐ (z ２ ), . . . , I ｐ (z ｎ )) or vectors resulting from them by projection and / or transformation, at least locally around said vectors (I ｐ (z １ ), I ｐ (z ２ ), . . . , I ｐ (z ｎ )) and (I ｑ (z １ ) ， I ｑ (z ２ ), . . . , I ｑ (z ｎ 8. The method according to claim 2, wherein the main directions of the point distribution are approximated by vectors resulting from the vectors i) or from the vectors i) by projection and / or transformation.

9. The determination of the directional vector (15) may be performed by principal component analysis (PCA) or a part thereof, eigenvalue determination, linear regression, or by the determination of a vector (I ｐ (z １ ), I ｐ (z ２ ), . . . , I ｐ (z ｎ )) and (I ｑ (z １ ) ， I ｑ (z ２ ), . . . , I ｑ (z ｎ 9. The method according to claim 8, comprising other optimization methods for minimizing the deviations to or from the vectors resulting from the projection and / or transformation.

10. A method according to claim 4, 5 or any one of claims 6 to 9, which determines a tangent vector to the differentiable submanifold M by differentiating it.

11. The determined directional vector or tangent vector is expressed as the light intensity I ｐ (z １ ), I ｐ (z ２ ), . . . , I ｐ (z ｎ ) the phase-shifted signal Q ｐ (z １ ), Q ｐ (z ２ ), . . . Q ｐ (z ｎ ) or I ｐ (z １ ), I ｐ (z ２ ), . . . , I ｐ (z ｎ 11. The method according to claim 8, wherein the method is used to determine the corresponding associated phase-shifted signals for vectors resulting from a projection and / or transformation from the vectors.

12. 12. The method of claim 2 or any one of claims 4 to 11, wherein at least two detector elements q of the multi-element detector are used to determine the approximation.

13. The light intensity I ｐ (z １ ), I ｐ (z ２ ), . . . , I ｐ (z ｎ ) to the phase-shifted signal Q ｐ (z １ ), Q ｐ (z ２ ), . . . Q ｐ (z ｎ ) together with the light intensity I ｐ (z １ ), I ｐ (z ２ ), . . . , I ｐ (z ｎ ) to determine the envelope and / or phase position of the signal curve given by or corresponding to I ｐ (z １ ), I ｐ (z ２ ), . . . , I ｐ (z ｎ 13. The method according to claim 11 or 12, which is used to perform on vectors resulting from projections and / or transformations from the vectors and the associated phase-shifted signals.

14. The determined phase position and / or envelope is calculated for the element p of the multi-element detector (6) by calculating the absolute value z ｐ The method according to claim 3 or 13, which is used to determine the absolute value at which the optical path length difference or phase difference between the measurement light and the reference light reaches an explicitly and / or implicitly set value.

15. The absolute value z for the change in optical path length difference or phase difference determined for the element p of the multi-element detector (6) ｐ 15. The method according to claim 1, wherein the absolute value at which the optical path length difference or the phase difference between the measurement light and the reference light reaches an explicitly and / or implicitly set value is used to obtain information about the spatial position of a surface point of the measurement object (1) assigned to the detection element p (6b).

16. The surface topograph of the measurement object (1) is (i) vibrations or movements that affect the length of the measurement arm and / or reference arm of the interferometer during measurement; (ii) a change in density and / or refractive index of at least one medium through which the light passes, in the measurement arm and / or the reference arm; and (iii) inaccuracies and / or errors by the adjustment unit (9) in determining the absolute value z of the change in the optical path length difference and / or phase difference between the measurement light and the reference light, The method according to any one of claims 1 to 15, further comprising determining in the presence of at least one of the following:

17. 1. An apparatus for interferometrically determining the surface topography of a measurement object (1), comprising: At least one light source (2) for illuminating the measurement object (1) and forming a reference light; an interference optical system for combining the illumination light reflected back as measurement light from the measurement object (1) with the reference light, the interference optical system forming an interference pattern in a detection area; at least one adjustment unit (9) for changing the optical path length difference and / or the phase difference between the measurement light and the reference light by an absolute value z; A multi-element detector (6) comprising a plurality of detector elements p, each having a different absolute value z ｉ For at least two optical path length differences or phase differences changed by ｐ (z ｉ a multi-element detector configured to detect the light component p of the light component on the detection element p of the detection region; An evaluation unit (10) connected to the multi-element detector (6) for detecting a change in optical path length difference or phase difference for a plurality of detector elements p of the multi-element detector (6) is provided, the evaluation unit (10) being configured to calculate an absolute value z ｐ an evaluation unit configured to determine the absolute value at which an optical path length difference or a phase difference between the measurement light and the reference light reaches a value explicitly and / or implicitly set for said detector element p (6b) and to determine therefrom said surface topography of the measurement object (1), The evaluation unit (10) determines the value z assigned to the detector element p (6b). ｐ In order to determine the light intensity I ｐ (z ｉ ), as well as the light intensity I of at least one other detector element q of the multi-element detector (6). ｑ (z ｉ ) is also used, The light intensity I ｑ (z ｉ ) is the value z ｐ the at least one other detector element q used for the determination of is selected to have a predetermined neighborhood property with respect to the detector element p (6b); The neighboring characteristics are defined at least in part using a metric; the metric comprises the spatial spacing of the detector elements p (6b) and q and / or the spatial spacing of points assigned to them on the measurement object (1) and / or on an optical surface conjugate to the multi-element detector (6); The at least one metric for determining the neighboring characteristics of the detector elements p (6b) and q is I ｐ (z ｉ ) and I ｑ (z ｉ ) is given by ｐ (z １ ), I ｐ (z ２ ), . . . , I ｐ (z ｎ )) and (I ｑ (z １ ) ， I ｑ (z ２ ), . . . , I ｑ (z ｎ ))) or a metric in the vector space of vectors resulting from projection and / or transformation therefrom.

18. 1. An apparatus for interferometrically determining the surface topography of a measurement object (1), comprising: At least one light source (2) for illuminating the measurement object (1) and forming a reference light; an interference optical system for combining the illumination light reflected back as measurement light from the measurement object (1) with the reference light, the interference optical system forming an interference pattern in a detection area; at least one adjustment unit (9) for changing the optical path length difference and / or the phase difference between the measurement light and the reference light by an absolute value z; A multi-element detector (6) comprising a plurality of detector elements p, each having a different absolute value z ｉ For at least two optical path length differences or phase differences changed by ｐ (z ｉ a multi-element detector configured to detect the light component p of the light component on the detection element p of the detection region; An evaluation unit (10) connected to the multi-element detector (6) for detecting a change in optical path length difference or phase difference for a plurality of detector elements p of the multi-element detector (6) is provided, the evaluation unit (10) being configured to calculate an absolute value z ｐ an evaluation unit configured to determine the absolute value at which an optical path length difference or a phase difference between the measurement light and the reference light reaches a value explicitly and / or implicitly set for said detector element p (6b) and to determine therefrom said surface topography of the measurement object (1), The evaluation unit (10) determines the value z assigned to the detector element p (6b). ｐ In order to determine the light intensity I ｐ (z ｉ ), as well as the light intensity I of at least one other detector element q of the multi-element detector (6). ｑ (z ｉ ) is also used, The value z assigned to the detector element p (6b) ｐ I ｐ (z ｉ ) and I ｑ (z ｉ ) is the n-dimensional light intensity vector (I ｐ (z １ ), I ｐ (z ２ ), . . . , I ｐ (z ｎ )) and (I ｑｊ (z １ ) ， I ｑｊ (z ２ ), . . . , I ｑｊ (z ｎ )) or a vector resulting from a projection and / or transformation therefrom.

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