INTERFEROMETRIC MEASUREMENT DEVICE AND INTERFEROMETRIC METHOD FOR DETERMINING THE SURFACE TOPOGRAPHY OF A MEASUREMENT OBJECT

Abstract

The invention relates to an interferometric measurement device and to an interferometric method for determining the surface topography of a measurement object (1). The essence of the invention is that the light intensities I.sup.q(z.sub.i) of at least one other detector element q of the multi-element detector (6) are also used besides the light intensities I.sup.p(z.sub.i) of this detector element to determine the value z.sup.p associated with a detector element p (6b) of the measurement device.

Claims

1. A method for determining a surface topography of a measurement object (1) by interferometry, comprising the steps of: producing illumination light and reference light by at least one light source (2) and illuminating the measurement object (1) with the illumination light, bringing together the illumination light which has been reflected by the measurement object (1) as measuring light and the reference light, and producing an interference pattern in a detection region, changing at least one of an optical path length difference or a phase difference between the measuring light and the reference light, capturing luminous intensities I.sup.p(z.sub.i) of the interference pattern on a multiplicity of detector elements p (6b) of a multielement detector (6) in the detection region for at least of the two optical path length differences or the phase differences which have been changed by different amounts z.sub.i, determining an amount z.sup.p for the change in the optical path length difference or the phase difference for the multiplicity of detector elements p (6b) of the multielement detector (6), for which amount the at least one of the optical path length difference or the phase difference between the measuring light and the reference light in each case reaches at least one of an explicitly or implicitly specified value for this detector element p (6b), and ascertaining the surface topography of the measurement object (1) from the amounts z.sup.p determined for the various elements p of the multielement detector (6), and in order to determine the value z.sub.p assigned to the detector element p (6b), using the luminous intensities I.sup.q(z.sub.i) of at least one other detector element q of the multielement detector (6) in addition to the luminous intensities I.sup.p(z.sub.i).

2. The method as claimed in claim 1, wherein information about at least one of an envelope or a phase angle of the function I.sup.p(z) that is dependent on the change z in the at least one of the optical path length difference or the phase difference between the measuring light and the reference light is ascertained in order to determine the value z.sup.p assigned to the multielement detector element p, by also using the luminous intensities I.sup.q(z.sub.i) of at least one other detector element q of the multielement detector (6) in addition to the luminous intensities I.sup.p(z.sub.i) for ascertaining this information.

3. The method as claimed in claim 1, wherein the at least one other detector element q, whose luminous intensities I.sup.q(z.sub.i) are used to determine the value z.sup.p assigned to the detector element p (6b), is chosen having specified neighborhood properties in relation to the detector element p (6b).

4. The method as claimed in claim 3, wherein the neighborhood properties are defined at least in part with a metric, wherein the metric comprises at least one of a spatial distance between the detector elements p (6b) and q or a spatial distance between points assigned thereto on at least one of the measurement object (1) or an optical surface conjugate to the multielement detector (6).

5. The method as claimed in claim 4, wherein the metric for determining the neighborhood of detector elements p (6b) and q comprises a metric in the vector space of n-dimensional luminous intensity vectors (I.sup.p(z.sub.1), I.sup.p(z.sub.2), . . . , I.sup.p(z.sub.n)) and (I.sup.q(z.sub.1), I.sup.q(z.sub.2), . . . , I.sup.q(z.sub.n)) given by the I.sup.p(z.sub.i) and I.sup.q(z.sub.i) or a metric in a vector space of the vectors that emerged therefrom by at least one of projection or transformation.

6. The method as claimed in claim 5, wherein the value z.sup.p assigned to the detector element p (6b) is ascertained using an approximation to at least some of the n-dimensional luminous intensity vectors (I.sup.p(z.sub.1), I.sup.p(z.sub.2), . . . , I.sup.p(z.sub.n)) and (I.sup.q(z.sub.1), I.sup.q(z.sub.2), . . . , I.sup.q(z.sub.n)) given by the I.sup.p(z.sub.i) and I.sup.q(z.sub.i) or the vectors that emerged therefrom by the at least one of the projection or transformation.

7. The method as claimed in claim 6, wherein the approximation comprises a fit of a differentiable submanifold M to a point distribution from points (I.sup.p(z.sub.1), I.sup.p(z.sub.2), . . . , I.sup.p(z.sub.n)) and (I.sup.q(z.sub.1), I.sup.q(z.sub.2), . . . , I.sup.q(z.sub.n)) in an n-dimensional vector space or in a vector space of the vectors that emerged therefrom by at least one of projection or transformation.

8. The method as claimed in claim 7, wherein the differentiable submanifold M is at most a three-dimensional submanifold of an associated vector space.

9. The method as claimed in claim 8, wherein the approximation to the n-dimensional luminous intensity vectors (I.sup.p(z.sub.1), I.sup.p(z.sub.2), . . . , I.sup.p(z.sub.n)) and (I.sup.q(z.sub.1), I.sup.q(z.sub.2), . . . , I.sup.q(z.sub.n)) or the vectors that emerged therefrom by the at least one of the projection or transformation is described by a one-dimensionally parameterized curve (15a) in the associated vector space.

10. The method as claimed in claim 9, wherein the approximation to the luminous intensity vectors (I.sup.p(z.sub.1), I.sup.p(z.sub.2), . . . , I.sup.p(z.sub.n)) and (I.sup.q(z.sub.1), I.sup.q(z.sub.2), . . . , I.sup.q(z.sub.n)) or the vectors that emerged therefrom by the at least one of the projection or transformation is, at least locally, a linear approximation.

11. The method as claimed in claim 10, wherein the approximation used when determining the value z.sup.p assigned to the detector element p (6b) comprises a determination of a direction vector (15) which at least locally in a neighborhood of the luminous intensity vector (I.sup.p(z.sub.1), I.sup.p(z.sub.2), . . . , I.sup.p(z.sub.n)) or a vector that emerged therefrom by the at least one of the projection or transformation approximates a principal direction of the point distribution given by way of the vectors (I.sup.p(z.sub.1), I.sup.p(z.sub.2), . . . , I.sup.p(z.sub.n)) and (I.sup.q(z.sub.1), I.sup.q(z.sub.2), . . . , I.sup.q(z.sub.n)) or the vectors that emerged therefrom by the at least one of the projection or transformation.

12. The method as claimed in claim 11, wherein the determination of the direction vector (15) comprises a principal component analysis (PCA) or parts thereof, an eigenvalue determination, a linear regression or any other optimization method for minimizing a deviation of a straight line defined by at least one of the direction vector (15) or a foot suitable therefor to point distribution given the vectors (I.sup.p(z.sub.1), I.sup.p(z.sub.2), . . . , I.sup.p(z.sub.n)) and (I.sup.q(z.sub.1), I.sup.q(z.sub.2), . . . , I.sup.q(z.sub.n)) or the vectors that emerged therefrom by the at least one of the projection or transformation.

13. The method as claimed in claim 12, wherein a tangential vector to the differentiable manifold M is determined by differentiating the latter.

14. The method as claimed in claim 13, wherein the determined direction or tangential vector is used to determine a phase-shifted signal Q.sup.p(z.sub.1), Q.sup.p(z.sub.2), . . . , Q.sup.p(z.sub.n) for the light intensities I.sup.p(z.sub.1), I.sup.p(z.sub.2), . . . , I.sup.p(z.sub.n) or to determine a corresponding associated phase-shifted signal for vectors that emerged from the I.sup.p(z.sub.1), I.sup.p(z.sub.2), . . . , I.sup.p(z.sub.n) by the at least one of the projection or transformation.

15. The method as claimed in claim 14, wherein at least two detector elements q of the multielement detector are used to determine the approximation.

16. The method as claimed in claim 15, wherein the light intensities I.sup.p(z.sub.1), I.sup.p(z.sub.2), . . . , I.sup.p(z.sub.n) together with the phase-shifted signals Q.sup.p(z.sub.1), Q.sup.p(z.sub.2), . . . , Q.sup.p(z.sub.n) are used to ascertain at least one of an envelope or a phase angle of the signal curve given by the light intensities I.sup.p(z.sub.1), I.sup.p(z.sub.2), . . . , I.sup.p(z.sub.n) or to carry out a corresponding action for vectors that emerged from the I.sup.p(z.sub.1), I.sup.p(z.sub.2), . . . , I.sup.p(z.sub.n) by the at least one of the projection or transformation and for the associated phase-shifted signals.

17. The method as claimed in claim 16, wherein the at least one of the determined phase angle or envelope is used to determine, for the element p of the multielement detector (6), the amount z.sup.p for the change in the optical path length difference or phase difference for which the optical path length difference or the phase difference between the measuring light and the reference light reaches the at least one of the explicitly or implicitly specified value.

18. The method as claimed in claim 17, wherein the amount z.sup.p for the change in the optical path length difference or phase difference for which the optical path length difference or the phase difference between the measuring light and the reference light reaches the at least one of the explicitly or implicitly specified value, as determined for the element p of the multielement detector (6), is used to obtain information about the relative spatial position of a surface point of the measurement object (1) assigned to the detector element p (6b) in order to ascertain the surface topography of the measurement object (1).

19. The method as claimed in claim 18, wherein the method is configured to determine the surface topography of measurement objects (1) when at least one of the following interferences is present: (i) vibrations or movements which influence a length of at least one of a measuring or reference arm of an interferometer during the measurements, (ii) changes in at least one of a density or a refractive index of at least one of a media through which the light passes in the at least one of the measuring or reference arm, (iii) at least one of inaccuracies or errors when determining the amount z of the change in the at least one of the optical path length difference or the phase difference between the measuring light and the reference light by the adjustment unit (9).

20. A device for determining a surface topography of a measurement object (1) by interferometry, comprising at least one light source (2) configured for illuminating the measurement object (1) and for producing reference light, an interferometer optical unit configured for bringing together illumination light reflected by the measurement object (1) as measuring light and reference light, with an interference pattern being produced in a detection region, at least one adjustment unit (9) for changing at least one of an optical path length difference or a phase difference between the measuring light and the reference light by an amount z, a multielement detector (6) having a multiplicity of detector elements p which are configured to capture luminous intensities I.sup.p(z.sub.i) of the interference pattern on the detector elements p in a detection region for at least two optical path length differences or phase differences which have been changed by different amounts z.sub.i, an evaluation unit (10) which is connected to the multielement detector (6) and which is configured to determine, for a multiplicity of detector elements p of the multielement detector (6), an amount z.sup.p for the change in the optical path length difference or phase difference for which the optical path length difference or phase difference between the measuring light and the reference light reaches at least one of an explicitly or implicitly specified value for this detector element p (6b), and to ascertain the surface topography of the measurement object (1) therefrom, and the evaluation unit (10) is configured to also use the luminous intensities I.sup.q(z.sub.i) of at least one other detector element q of the multielement detector (6) in addition to the light intensities I.sup.p(z.sub.i) in order to determine the value z.sup.p assigned to the detector element p (6b).

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0143] Further advantageous features and configurations are explained below on the basis of exemplary embodiments and the figures. In this case:

[0144] FIG. 1 shows a first exemplary embodiment of a device according to the invention with a Michelson interferometer;

[0145] FIGS. 2A, 2B, 3A-3C, 4A-4C, 5, 6A-6C, 7A-7D, 8A, 8B, 9A-9C, 10A-10C, and 11 show illustrations for explaining exemplary embodiments of methods according to the invention to be carried out by means of the device as per FIG. 1;

[0146] FIG. 12 shows a second exemplary embodiment of a device according to the invention with a Michelson interferometer;

[0147] FIGS. 13 and 14 show illustrations for explaining exemplary embodiments of methods according to the invention to be carried out by means of the device as per FIG. 12;

[0148] FIG. 15 shows a third exemplary embodiment of a device according to the invention with a Mirau objective;

[0149] FIG. 16 shows an illustration for explaining an exemplary embodiment of a method according to the invention to be carried out by means of the device as per FIG. 15;

[0150] FIG. 17 shows a fourth exemplary embodiment of a device according to the invention with a Michelson interferometer; and

[0151] FIGS. 18, 19, 20A, 20B, 21, 22A and 22B show illustrations for explaining exemplary embodiments of methods according to the invention to be carried out by means of the device as per FIG. 17.

DETAILED DESCRIPTION

[0152] The figures show schematic illustrations that are not true to scale. In the figures, the same reference signs denote the same elements of elements with the same effect.

[0153] FIG. 1 shows a first exemplary embodiment of a device according to the invention with a Michelson interferometer. The device serves to determine the surface topography of a measurement surface la of a measurement object 1 by means of interferometry.

[0154] The device comprises a light source 2, embodied as an LED in the present case, with a broadband light spectrum, in this case in the wavelength range of 490 nm to 550 nm with a maximum at 520 nm.

[0155] Via a condenser 3, the light from the light source reaches a semi-transparent mirror 4, by means of which approximately 50% of the luminous intensity is guided as illumination light to the measurement surface 1a of the measurement object 1. The illumination light reflected by the measurement surface 1a as measuring light partly passes through the semi-transparent mirror 4 and is imaged by means of an imaging optical unit 5, embodied in the present case as a telecentric imaging optical unit, into a detection region of the device where a multielement detector 6 is arranged. In the present case, the imaging optical unit 5 comprises optical lenses 5a and 5band an optical stop 5c for the telecentric embodiment.

[0156] In the present case, the multielement detector 6 is designed as a CCD camera and has a CCD sensor, which is embodied as an area sensor 6a with 1024×1024 sensor elements, which, as a sensor array, are arranged on the crossing points of a square grid. Each sensor element represents a detector element of the multielement detector 6.

[0157] Approximately 50% of the light produced by the light source 2 passes through the semi-transparent mirror 4 as reference light and reaches a reference mirror 8 via an optical filter 7. The reference light reflected at the reference mirror 8 once again passes through the optical filter 7 and is partly deflected by the semi-transparent mirror 4 in order likewise to be imaged into the detection region by means of the imaging optical unit 5. Consequently, an interference pattern is generated in the detection region by superposition of measuring light and reference light and can be evaluated by means of the multielement detector 6. In this case, the filter 7 serves to attenuate the luminous intensity of the reference light in order to obtain approximately the same luminous intensities of measuring light and reference light in the detection region.

[0158] The distance of the device from the measurement object 1, and hence the optical path length difference OPD between the measuring light and the reference light, can be changed by means of an adjustment unit 9. In the present exemplary embodiment, the optical path length of the measuring light is consequently changed to this end.

[0159] Consequently, the luminous intensities I.sup.p(z.sub.i) of the interference pattern on the detector elements of the multielement detector 6 in the detection region can be captured for at least two optical path length differences OPD which have been changed by different amounts z.sub.i by means of the multielement detector 6.

[0160] The device consequently comprises an interferometer optical unit for bringing together the measuring light and the reference light and for producing the interference pattern in the detection region, wherein the interferometer optical unit in the present case comprises the elements of condenser 3, semi-transparent mirror 4, imaging optical unit 5, optical filter 7 and reference mirror 8.

[0161] The device furthermore comprises an evaluation unit 10, which is designed as a commercially available computer, presently in the form of a laptop, with a processor, data memory, visual display unit and a keyboard as an input unit. The evaluation unit 10 is connected to the multielement detector 6 and the adjustment unit 9 such that measuring signals from the detector elements of the multielement detector can be read by means of the evaluation unit and the optical path length difference OPD can be changed by means of control signals by way of the adjustment unit 9.

[0162] The evaluation unit is designed to determine the amount z.sup.p for the change in the optical path length difference for a multiplicity of detector elements p of the multielement detector 6, for which amount the optical path length difference between the measuring light and the reference light reaches an explicitly and/or implicitly specified value, 0 in the present case, in order to ascertain the surface topography of the measurement surface 1a of the measurement object 1 therefrom.

[0163] What is essential is that the evaluation unit is designed to also use the luminous intensities I.sup.q(z.sub.i) of at least one other detector element q of the multielement detector in addition to the luminous intensities I.sup.p(z.sub.i) in order to determine the value z.sup.p assigned to the detector element p, as explained in more detail below using an exemplary embodiment of the method according to the invention:

[0164] The first exemplary embodiment of a method according to the invention is configured as scanning white-light interferometry (WLI).

[0165] Initially, the device is displaced into a reference state by means of the adjustment unit 9. The virtual reference surface 11, which corresponds to an optical path length difference OPD=0 in the reference state, is labeled by a dash-dotted line in FIG. 1 and is perpendicular to the plane of the drawing of FIG. 1. The precise relative position of this reference surface 11 is unimportant to the measurement. Thus, the reference surface 11 can pass through the object like in the present example. However, it is likewise possible for the reference surface to be located above the object, for example. What is essential is that height information h.sup.p is ascertained for a multiplicity of measurement points p such that it is possible to calculate the relative height difference of the measurement points from one another and therefore a surface topography of the measurement surface la is obtained.

[0166] Proceeding from the above-described reference state, the adjustment unit 9 is now controlled by means of the evaluation unit 10 in such a way that the device is removed from the measurement object 1 by way of equidistantly specified steps, i.e., moved upward in the representation as per FIG. 1. This increases the optical path length of the measuring light while the optical path length of the reference light however remains unchanged such that, as a result, there is a change in the OPD. In the present case, measurement values for all detector elements p of the multielement detector 6 are captured in each case at 64 positions of the device. A measurement point p on the measurement surface la of the measurement object is assigned to each of the 1024×1024 (=1 048 576) detector elements p of the multielement detector 6 in the device illustrated in FIG. 1.

[0167] Consequently, the associated intensities I.sup.p(z.sub.1), I.sup.p(z.sub.2), . . . , I.sup.p(z.sub.n) are recorded in interferograms by means of the evaluation unit for a total of 64 OPDs that have been changed in relation to the reference state by z.sub.1, z.sub.2, (n=64), and so the associated correlogram c.sup.p=(c.sup.p(1), c.sup.p(2), . . . , c.sup.p(n)) is obtained for each measurement point p, with the measured luminous intensity of the i-th point of the correlogram being c.sup.p(i)=I.sup.p(z.sub.i) in each case.

[0168] In this case, the z.sub.i values are specified equidistantly, that is to say—at least according to the stipulation—the specified distance Δz between two successive z.sub.i values is constant.

[0169] Consequently a correlogram with 64 measurement values is available for each detector element p after this measurement is carried out.

[0170] FIG. 2A illustrates an example of such a correlogram of a detector element p. The specified z values are plotted along the x-axis in [μm] and the luminous intensity is plotted along the y-axis in arbitrary units, in this case advantageously normalized to the luminous intensity outside of the interference region of the correlogram, that is to say normalized to the offset of the correlogram. This also applies to the further correlograms illustrated in the figures provided nothing else is stated.

[0171] In principle, it is now possible—as explained at the outset in the description of the prior art—to determine an envelope for the correlogram as per FIG. 2A and determine the value for z.sup.p which corresponds to the maximum of the envelope (approximately at a z-position of 5 μm in the present case). For this measurement point, h.sup.p would consequently be determined as half of the determined z value, i.e., 2.5 μm.

[0172] However, if disturbances occur, for example in the form of tremors during the measurement, the measurements are not implemented exactly at the specified z values. Rather, the z values of the actual measurements are shifted to the right or left in the correlogram representation, depending on the effect of the vibrations.

[0173] FIG. 2B illustrates a disturbance-afflicted correlogram in exemplary fashion. In principle, the measurement conditions are identical to the measurement conditions as per FIG. 2A; however, disturbances were introduced herein, as described above, leading to displacements of the z.sub.i values so that these are no longer exactly equidistant.

[0174] Initially, the effect of such disturbances in the evaluation according to the prior art should be described below:

[0175] FIGS. 3A-3C illustrate an evaluation according to the prior art in the undisturbed case, that is to say with equidistant z.sub.i values:

[0176] FIG. 3A shows the undisturbed correlogram from FIG. 2A.

[0177] The synthetic correlogram s.sup.p(z) illustrated in FIG. 3B is produced by means of a Hilbert transform. As described at the outset, the envelope env.sup.p(z) as per FIG. 3C can be obtained from the original correlogram c.sup.p(z) and the synthetic correlogram s.sup.p(z) which was obtained by way of the Hilbert transform.

[0178] Determining the z value of the maximum of this envelope in the undisturbed case already facilitates, to a good approximation, a determination of the sought-after value for z.sup.p and hence twice a value of h.sup.p at this measurement point p (approximately 5 μm

[0179] Reference should additionally be made to the fact that the offset was removed from the original correlogram c.sup.p(z) during the evaluation such that the values of c.sup.p(z), as also illustrated in FIG. 3C, are now distributed around the zero value.

[0180] The correlogram as per FIG. 4A corresponds to the correlogram as per FIG. 2B with the non-equidistant z.sub.i values on account of the introduced disturbance of the measurement as a result of tremors.

[0181] If the Hilbert transform is now applied to this correlogram as per FIG. 4A, this yields the correlogram s.sup.p(z) as per FIG. 4B. On account of the disturbances, the envelope env.sup.p(z), which is plotted in FIG. 4C together with the original (FIG. 4A) correlogram c.sup.p(z) but without the offset and which was determined in the same way as previously, has a non-uniform curve. In particular, it is not possible to determine a unique maximum. Consequently, using the evaluation process as per the prior art, the sought-after value of 5 μm for z.sup.p cannot be ascertained or can only be ascertained very inaccurately in the case of such a disturbance.

[0182] The peculiarity of the method according to the invention which facilitates an evaluation with great accuracy despite the presence of such disturbances is explained with reference to the first exemplary embodiment and further embodiments of the method according to the invention on the basis of FIGS. 5, 6A-6C, 7A-7D, 8A, 8B, 9A, 9B, 10A-10C and 11 below.

[0183] FIG. 5 schematically shows a section of the area sensor 6a of the multielement detector 6. As already described, the CCD chip has 1024×1024 detector elements, wherein one detector element p with reference sign 6b is marked in exemplary fashion by way of being filled-in in black. What is essential is that in order to determine the value z.sub.p assigned to the detector element p the luminous intensities I.sup.q(z.sub.i) of at least one other detector element q of the multielement detector are also used in addition to the luminous intensities I.sup.p(z.sub.i).

[0184] To this end, the neighboring elements are considered in a square of 3×3 pixels in the present exemplary embodiment: the detector element 6b has eight neighboring elements q.sub.j, which are highlighted in FIG. 5 by a thick black edge. Now, one neighboring element is selected from these eight neighboring elements as follows:

[0185] The difference between the correlogram of the neighboring element and the correlogram of the detector element p is formed for each neighboring element. In exemplary fashion for the neighboring elements q.sub.1, q.sub.2 and q.sub.3, the correlogram of this neighboring point is represented in an upper diagram in each case and the difference between the correlogram of this neighboring point and the correlogram of the detector element p (6b) is represented in a lower diagram in each case.

[0186] A measure is assigned to each difference correlogram, which consequently represents the difference vector c.sup.qj−c.sup.p, by means of a vector norm. In the present case, the measure is determined on the basis of the standard deviation formed from the elements c.sup.qj(i)−c.sup.p(i) of the difference vector. If the correlograms of a neighboring element q.sub.j and of the detector element p only have a minor deviation according to this measure, the correlograms of these two detector elements are very similar and this, in the present case, is disadvantageous for the evaluation as per the present exemplary embodiment since signal noise possibly makes an exact subtraction very difficult. In principle, a relatively large deviation as per the above-described measure may also be disadvantageous since a linear approximation as described below is no longer admissible in that case. However, in the present measurement situation, a relatively large deviation is unlikely because only nearest neighbors are considered, in the case of which the correlograms only differ slightly as a rule.

[0187] Consequently, in the present exemplary embodiment of the method according to the invention, the neighboring element of the eight neighboring elements q.sub.j where the difference vector as per the above-described measure has the greatest value is selected. This is the detector element q.sub.3 in the example as per FIG. 5.

[0188] Consequently, to determine the value z.sup.p assigned to the multielement detector p, use is also made of the luminous intensities of the detector element q.sub.3 in the present case, as will be explained in more detail below:

[0189] FIG. 6A shows the correlograms of the detector elements p and q=q.sub.3 where disturbances have been introduced into the measurements like in the case of FIG. 2B as well. Since the neighboring detector elements p and q are assigned to spatially neighboring measurement points p and q on the measurement surface la of the measurement object 1, there are only minor differences in the correlograms.

[0190] FIG. 6B therefore illustrates an enlarged excerpt around the z value of 5 μm. FIG. 6C shows the difference correlogram c.sup.q(z)−c.sup.p(z). Accordingly, this difference correlogram can also be considered to be a 64-dimensional difference vector. In the present exemplary embodiment, the further evaluation is carried out in 64 dimensions, that is to say the measurement points of all z.sub.i values are used.

[0191] The scope of the invention also includes the use of a subset, that is to say lower-dimensional difference vector, for instance a selection of points which, e.g., are arranged approximately symmetrically around a maximum of the correlogram c.sup.p, for example ±16 points, that is to say a total of 33 points. In an alternative configuration, a symmetric selection of points is implemented around the point at which the modulation is strongest. The latter is evident as a result of the fact that the amount of the difference of two successive points is greatest there. In a further development of the exemplary embodiment, there is a sine fit to the correlograms, and the value the maximum amplitude of this fit is determined as a central value for a symmetric selection of a subset of points for the subsequent evaluation.

[0192] FIG. 7A plots the correlogram of the detector element p and the difference correlogram as per FIG. 6C. As explained previously, the difference correlogram Q.sup.p as per FIG. 6C can be considered to be a synthetic correlogram s.sup.p=f*Q.sup.p with a scaling factor of f=1.

[0193] However, to determine the correlogram envelope, there is a need for a synthetic correlogram s.sup.p which was scaled by the scaling factor f in such a way that it has the same amplitude as the original correlogram c.sup.p.

[0194] As illustrated in FIG. 7B and FIG. 7D, the determination of the correlogram envelope env.sup.p(z.sub.i) by taking the square root of (c.sup.p(z.sub.i)).sup.2+(s.sup.p(z.sub.i)).sup.2 without correct scaling of the s.sup.p(z.sub.i) would lead to a wavy result for the envelope env.sup.p(z.sub.i), which would not allow the determination of a maximum or would at least lead to a significant risk of error. In this case, FIG. 7B shows the case where, as per FIG. 7A, scaling was carried out with a factor f that was too small.

[0195] By contrast, if as per FIG. 7C scaling is carried out with a factor f that is too large, this likewise yields a wavy envelope that is not evaluable or only evaluable with a significant risk of error, as shown in FIG. 7D.

[0196] In the present exemplary embodiment, the correct scaling factor f is determined by virtue of the fact that, by ascertaining the maximum of the correlogram c.sup.p, an approximate value i.sub.m is initially determined for the index i at which the envelope maximum is located. Then, to determine the scaling factor f, use is made of 21 points of the offset-free original correlogram c.sup.p, which are located symmetrically around the index i.sub.m, and of the synthetic correlogram s.sup.p=f*Q.sup.p scaled by the factor f. For these points, the standard deviation σ(f) of the 21 values of (c.sup.p(z.sub.i)).sup.2+(s.sup.p(z.sub.i)).sup.2 with i=i.sub.m−10, . . . , i=i.sub.m−9, . . . , i=i.sub.m+10 can be specified for each possible value of f. Now, the value for f at which the specified standard deviation becomes minimal is determined with the aid of a gradient method. With the aid of this value for f, the correctly scaled synthetic correlogram s.sup.p=f*Q.sup.p is now ascertained for the further evaluation.

[0197] FIG. 8A now shows the correlogram c.sup.p(z.sub.i) from FIG. 6A or FIG. 2B together with the correctly scaled synthetic correlogram s.sup.p (z.sub.i)=f*Q.sup.p (z.sub.i) determined as described above. It is possible to recognize that the amplitude of the synthetic correlogram s.sup.p(z.sub.i) scaled by this factor f corresponds to that of the original correlogram c.sup.p(z.sub.i).

[0198] FIG. 8B illustrates the envelope env.sup.p(z) which arises from the correlogram c.sup.p and the correctly scaled synthetic correlogram s.sup.p determined as described above. In this case, the envelope env.sup.p(z.sub.i) was ascertained by taking the square root of (c.sup.p(z.sub.i)).sup.2+(s.sup.p(z.sub.i)).sup.2 as described.

[0199] As a summary, FIGS. 9A-9C in partial image a show the correlogram of the detector element p which has been afflicted by disturbances in the z values. Partial image b shows the synthetic correlogram s.sup.p which was scaled with the ascertained correct factor f as described above. This synthetic correlogram was consequently determined with additional use being made of the correlogram of the detector element q.sub.3.

[0200] Partial image 9C shows the correlogram c.sup.p as per partial image a together with the envelope env.sup.p which was obtained as described above. A comparison of this envelope ascertained using the method according to the invention and the envelope from FIG. 4C, which was determined with the aid of one of the methods as per the prior art, impressively shows that a significant robustness in relation to disturbances, such as tremors for example, that lead to non-equidistant z.sub.i values was obtained.

[0201] Now, the maximum of the envelope env.sup.p as per FIG. 9C is determined in order to ascertain the z.sup.p value for the detector element p and, accordingly, the measurement point p. In the specific case, this is implemented by way of a parabolic fit to the envelope env.sup.p(z.sub.i) at the previously selected 21 points z.sub.i.

[0202] However, the measurement data allow a further increase in the accuracy when determining the z.sup.p value, as explained below on the basis of FIG. 10 in an advantageous development of the described exemplary embodiment.

[0203] FIG. 10A shows the correlogram c.sup.p and the envelope obtained by means of the synthetic correlogram as per the illustration from FIG. 9C.

[0204] FIG. 10B shows, in the direction of the abscissa z, a magnified excerpt around the previously determined maximum of the envelope env.sup.p(z). However, the coordinate axis now does not plot the intensity against the associated z value but a phase φ.sup.p(z) which is assigned to the z value. As described above, an associated point s.sup.p(i) is respectively ascertained for each correlogram point c.sup.p(i) by way of the synthetic correlogram, wherein the synthetic correlogram s.sup.p can be considered to be a correlogram that has been shifted through 90° in terms of the carrier frequency in relation to the correlogram c.sup.p. Therefore, a phase can be determined for each position z.sub.i from the two correlograms, for example by virtue of forming the extended arctan arctan2(s.sup.p(z.sub.i), c.sup.p(z.sub.i)) at the corresponding indices i for each point z.sub.i and carrying out phase unwrapping.

[0205] As described at the outset, the reference state was chosen by comparison of the optical path lengths (OPD=0) in this exemplary embodiment. The specified value for the optical path length difference is consequently 0 in this exemplary embodiment. Accordingly, the specified phase value for determining the amount z.sup.p is also 0° in the present case. As illustrated in FIG. 10b, a straight line is fitted by means of a linear regression and the z value for z.sup.p at which the phase value corresponds to the specified value (0° in the present case) is determined.

[0206] This two-stage method, in which an approximate value z.sup.p was initially obtained by determining the maximum of the envelope and the z.sub.p value with a phase of 0° was subsequently determined by means of the straight regression line, facilitates a significant improvement in the measurement accuracy or a yet again increased robustness in relation to disturbances such as tremors, for example.

[0207] FIG. 10C finally illustrates how the method according to the invention can in principle also be used to obtain the information regarding the amount Δz with which a z value z.sub.i was changed on account of the disturbance: in the ideal, disturbance-free case, the values z.sub.i in the illustration as per FIG. 10B or FIG. 10C are located on the regression straight line plotted in dotted fashion. Consequently, a value Δz.sub.i can be determined for each value z.sub.i by virtue of, for each value z.sub.i, subtracting the value z.sub.i from the z value which corresponds to the assigned phase value on the regression straight line. These correction values Δz are elucidated by horizontal arrows in FIG. 10c for the z.sub.i values with i=30, 31, . . . , 37.

[0208] Thus, the scope of the invention in principle also contains undertaking a correction of the z.sub.i values by way of the correction values Δz.sub.i obtained as per FIG. 10C and carrying out an evaluation, in particular in a manner known per se, by means of the corrected z.sub.i values.

[0209] Moreover, a more accurate correction of the z.sub.i value can be obtained by virtue of, for each z.sub.i, an averaging of the correction value being implemented for all detector elements or a selection of detector elements. This is because to a good approximation and for a fixed value of i, which corresponds to a measurement time in accordance with the present exemplary embodiment, the disturbance Δz.sub.i is the same for all measurement points and hence also for all detector elements. Therefore, a correction value Δz.sub.i is advantageously determined for a subset, preferably for all detector elements, and the correction value Δz.sub.i for carrying out a correction of all z.sub.i values is calculated by averaging the correction value over the subset of measurement points, preferably over all measurement points, in particular by way of weighted averaging.

[0210] FIG. 11 schematically illustrates that, in the present exemplary embodiment, the non-scaled synthetic correlogram Q.sup.p=s.sup.p/f can be considered to be the difference vector of the correlograms c.sup.q−c.sup.p and consequently represents a direction vector in the n-dimensional vector space, which approximates the point distribution given by the n-dimensional luminous intensity vectors (c.sup.p(1), c.sup.p(2), . . . , c.sup.p(n))=(I.sup.p(z.sub.1), I.sup.p(z.sub.2), . . . , I.sup.p(z.sub.n)) and [0211] (c.sup.q(1), c.sup.q(2), . . . , c.sup.p(n))=(I.sup.q(z.sub.1), I.sup.q(z.sub.2), . . . , I.sup.q(z.sub.n)), said point distribution however only consisting of two points in this exemplary embodiment.

[0212] For practical reasons, only three dimensions rather than the actual 64 dimensions present were selected for illustrative purposes in the illustration: only dimensions 31, 32 and 33 of the 64-dimensional vector space are shown in the illustration as per FIG. 11.

[0213] In particular, a restriction to a subset of z.sub.i values, presently 21 of the possible 64 z.sub.i values as described above in relation to FIG. 6, in the vector space corresponds to a projection onto a subspace, the dimension of which corresponds to the number of selected z.sub.i values. Consequently, an evaluation by means of the method according to the invention can also be implemented using such vectors that emerged by projection and/or transformation.

[0214] An example of such a further transformation is that the offset is initially subtracted from each correlogram by virtue of the offset being, e.g., ascertained on the basis of the correlogram points outside of the interference region or determined by averaging the correlogram values and said offset then being subtracted. Likewise, scaling or any other change due to normalization of the correlogram represents such a transformation. Rotations and other transformations can likewise be undertaken.

[0215] The measuring device as per the first exemplary embodiment and the method as per the first exemplary embodiment can also be used for measurement objects which partly reflect the measuring light at a plurality of planes:

[0216] In the case of such a measurement object with a plurality of partly reflecting surfaces for measurement by means of the device as per FIG. 1, the measurement surface 1a of the measurement object 1 on the side facing the device can be, e.g., a coated glass surface which only partly reflects the measuring light, in an alternative to the preceding description of the measurement object 1. Furthermore, in the volume of the measurement object, the measurement object has a further boundary with a metal coating at the back side (the side facing away from the device, the bottom side in FIG. 1), at which the component of the measuring light that penetrates into the measurement object is reflected within the measurement object. By means of the methods known from the prior art and by means of the method according to the invention, it is consequently possible to assign two or more values z.sup.p to one spatial point p since there is a (partial) reflection of measurement light at two or more height positions h.sup.p. If the difference of the various heights h.sup.p is greater than the coherence length of the detected measuring light and reference light, the interferences belonging to the various reflecting layers do not overlap in the correlograms, and so the partial correlograms belonging to the various layers can be separated within the measurement data and can consequently be evaluated separately, and it is possible to ascertain the various z.sup.p values separately from one another. However, the method according to the invention can also be used particularly advantageously if the various partial correlograms of the points z.sup.p overlap since the synthetic correlograms can even be determined correctly by means of the method according to the invention in this case. As a result, it is firstly possible to use the known methods to evaluate overlapping correlograms; then again, additional advantageous evaluation possibilities are provided since, for example, the common envelope and the common phase of the various partial correlograms can be determined very easily in accordance with the described procedure.

[0217] FIG. 12 schematically illustrates a second exemplary embodiment of a device according to the invention.

[0218] This construction is also based on the principle of the Michelson interferometer. To avoid repetition, only the essential differences between the second exemplary embodiment illustrated in FIG. 12 and the first exemplary embodiment illustrated in FIG. 1 are discussed below:

[0219] In the present case, the measurement object 1 should be measured at a given elevated temperature, and so it is arranged on a hot plate 1b. By way of example, this is relevant if a curvature of the measurement surface la on account of the action of heat should be examined in the case of electronic components.

[0220] What is problematic in this case is that air turbulence 1c arises between the measurement surface 1a and the device in the beam path of the measuring light on account of the heating by the hot plate 1b. Such air turbulence leads to density changes and, accordingly, to an inhomogeneous refractive index. Variations in the refractive index of the air on account of the density variation caused by the heating can already lead to significant measurement errors. This is even the case if no additional disturbances, for example as a result of tremors, are present.

[0221] The arrangement of the optical components of the device is identical to that in the device as per the first exemplary embodiment shown in FIG. 1.

[0222] In the present case, the evaluation unit 10 is connected to the multielement detector 6 as described above. The multielement detector 6, which is embodied here as a CMOS camera, is connected to the adjustment unit 9 by way of a trigger line. This should schematically elucidate that equidistant z.sub.i values are specified in the adjustment unit in the case of the second exemplary embodiment and the adjustment unit 9 transmits a trigger signal to the multielement detector 6 every time a specified z.sub.i value is reached so that a camera image is recorded.

[0223] The reference surface 11 which reproduces the reference state OPD=0 is illustrated above the measurement object 1. In this exemplary embodiment, the reference surface 11 is therefore located above the measurement object such that negative height values h.sup.p arise for measurement points p on the measurement surface 1a of the measurement object 1.

[0224] The evaluation unit 10 is embodied to carry out an evaluation as per a second exemplary embodiment of the method according to the invention. This substantially corresponds to the first exemplary embodiment, and so likewise only the essential differences are discussed below in order to avoid repetition:

[0225] FIG. 13 in turn schematically illustrates the area sensor 6a of the multielement detector 6. A comparison between FIGS. 13 and 5 shows that a larger number of detector elements are used in this second exemplary embodiment of the method according to the invention.

[0226] A detector element p with the reference sign 6a is also labeled by being filled-in in black in the illustration as per FIG. 13. The considered neighboring detector elements are labeled by thick black edges: in the present case, the 48 neighboring elements q.sub.j of the detector element p (6a), located within a square of 7×7 detector elements, are used for the evaluation. In this case, too, desired neighborhood properties are defined in order to assess the suitability of a neighboring element for the evaluation. As a measure for assessing the neighborhood properties, the length norm of the difference vector c.sup.q−c.sup.p is formed for the detector element q as a metric. Consequently, a value is available for each of the 48 neighboring elements, illustrated in exemplary fashion in FIG. 13 for five neighboring elements q by way of a corresponding difference correlogram c.sup.q−c.sup.p and by way of the numerical value which arises from the length norm metric for this difference correlogram. In the present case, the selection is made such that the ten neighboring elements which have the most similar correlograms are selected from the 48 neighboring elements. Consequently, values corresponding to the length norm metric of the difference vector are calculated for all 48 neighboring elements and the ten neighboring elements with the ten smallest values are determined. This is expedient in the present measurement situation since the assumption can be made that a difference in the correlograms will be decisively caused by the air turbulence and consequently neighboring elements with only small differences in respect of the length norm metric of the difference vector will have similar measurement conditions.

[0227] In the exemplary illustration as per FIG. 13, the detector elements with the length norm of the difference vector of 1.2153 and 0.8715 are not in the group of detector elements with the ten lowest values. By contrast, the detector elements with the values of 0.4293, 0.3916 and 0.3444 are contained in this group and are used accordingly for the evaluation (together with seven further detector elements not illustrated in detail).

[0228] Consequently, the second exemplary embodiment differs from the first exemplary embodiment by virtue of, in particular, using more neighboring detector elements q.sub.j (ten in the present case) for determining the value z.sup.p assigned to the detector element p by virtue of also using the luminous intensities I.sup.qj(z.sub.i) of the 10 neighboring elements q.sub.1, . . . , q.sub.10, determined as described above, in addition to the luminous intensities I.sup.p(z.sub.i).

[0229] In alternative embodiments of the second exemplary embodiment, it is not a fixed number of detector elements, for example in the spatial vicinity of the detector element p, that is chosen but instead all detector elements that have certain specified neighborhood properties are selected from a certain preselection of detector elements. By way of example, it may be advantageous to select all those detector elements q.sub.j for which the correlogram c.sup.qj deviates from the correlogram c.sup.p of the detector element p by a suitable measure, for example such that the standard deviation of the values c.sup.qj(i)−c.sup.p(i) ascertained from the difference vectors corresponds to approximately twice the quantization and camera noise. In this case, an upper and lower bound is advantageously defined for the values ascertained using the corresponding metric, on the basis of which the detector elements to be used are selected. This takes account of the fact that the correlograms c.sup.qj and c.sup.p(i) should firstly not be too different because otherwise a linear approximation causes difficulties but that they should not be too similar either because otherwise the difference correlogram can be very small and can be disturbed or even dominated by possible noise.

[0230] FIG. 14 schematically illustrates how the value z.sup.p assigned to the detector element p is determined on the basis of the plurality of neighboring elements q.sub.j:

[0231] For reasons of presentability, there is a projection on a three-dimensional subspace for the illustration by virtue of only dimensions 31, 32 and 33 of the 64-dimensional vector space being illustrated in FIG. 14, in a manner analogous to FIG. 11. As described above, ten neighboring elements were selected in this exemplary embodiment, and so ten correlogram vectors c.sup.q for the neighboring elements q are present accordingly in the 64-dimensional vector space in addition to the correlogram vector c.sup.p belonging to the detector element p, said correlogram vectors c.sup.q only being represented by their endpoints, labeled as points, for reasons of simplicity.

[0232] In contrast to the illustration as per FIG. 11 and the formation of a difference vector described in this respect, the direction vector in the 64-dimensional space is not determined directly in this case by ascertaining a difference vector between two correlograms c.sup.q and c.sup.p. Instead, the direction vector 15 is determined; it belongs to that straight line which approximates the point cloud given by the endpoints (likewise denoted q.sub.j and p here for reasons of simplicity) of the correlogram vectors c.sup.qj and c.sup.p to the best possible extent, and moreover extends through the endpoint p of the correlogram vector c.sup.p, likewise denoted by p. This direction vector can be determined with the aid of a straight-line fit and subsequent ascertainment of the direction vector present therefrom in the 64-dimensional vector space.

[0233] In an alternative exemplary embodiment, a principal component analysis (PCA) is carried out on the point cloud given by the vector endpoints q.sub.j and p in the 64-dimensional vector space, wherein the eigenvector belonging to the largest eigenvalue of the covariance matrix likewise is the sought-after direction vector. Since the largest eigenvalue of the covariance matrix and the associated eigenvector are determined first in many PCA algorithms, it is particularly advantageously possible to terminate the principal component analysis once the corresponding eigenvector is present, and so the complete principal component analysis can be dispensed with in the specific exemplary embodiment and only a partial principal component has to be carried out.

[0234] Once again, the direction vector found corresponds to the non-scaled synthetic correlogram Q.sup.p(z.sub.i)=s.sup.p/f, as described in the first exemplary embodiment, and is therefore also denoted as s.sup.p/f in FIG. 14.

[0235] Consequently, according to this second exemplary embodiment, a non-scaled synthetic correlogram Q.sup.p=s.sup.p/f is determined on the basis of a plurality of detector elements q. The further evaluation is carried out as described in relation to the first exemplary embodiment: the scaling factor f for scaling the synthetic correlogram is once again determined using one of the described procedures. Subsequently, the envelope is determined from the correlogram c.sup.p and the associated, correctly scaled synthetic correlogram s.sup.p and the z value of the maximum of this envelope is determined as the value for the sought-after z.sup.p. If necessary, it is also possible once again to carry out a phase evaluation in addition to the envelope evaluation and all results emerging therefrom can be used as described or in accordance with the known options.

[0236] FIG. 15 shows a third exemplary embodiment of a device according to the invention:

[0237] In this exemplary embodiment the interference pattern is produced by means of a Mirau interferometer: illumination light which reaches a semi-transparent mirror 4 via a condenser lens 3 is produced by means of the light source 2. Consequently, the illumination light is partly reflected downward in the illustration as per FIG. 15 and is incident there on a Mirau objective, which is constructed in a manner known per se. In particular, the Mirau objective 12 comprises a front lens 12a with a central reference mirror, and a beam splitter 12b.

[0238] The measuring light emerging from the Mirau objective in the direction of the measurement object 1 is at least partly reflected by the measurement surface la of the measurement object and enters the beam path of the Mirau objective 12 again. At the same time, reference light is split from the illumination light by the beam splitter 12b of the Mirau objective and steered in the direction of the central reference mirror. There, this reference light is reflected and cast back to the beam splitter 12b. Some of the reference light is reflected again at the beam splitter 12b such that it is superposed on measuring light reflected by the measurement object, at least partly passed together with said measuring light through the semi-transparent mirror 4 and imaged by means of a tube lens 13 on the multielement detector 6 constructed as a CMOS camera in the present case. As an area sensor 6a, the multielement detector 6 accordingly comprises a CMOS image sensor, presently an array of 512×512 detectors, that is to say a total of 262 144 detectors.

[0239] In this exemplary embodiment, the adjustment unit 9 is designed as a piezo adjuster with a piezo controller 9a. By means of the piezo controller 9a, the adjustment unit 9 which is designed as a piezo adjuster can be controlled in such a way that the Mirau objective can be moved toward the measurement object 1 and can be moved away from the latter in accordance with the double-head arrow illustrated in FIG. 15.

[0240] By contrast, the remainder of the device is not moved by the adjustment unit 9.

[0241] In this case, too, the device comprises an evaluation unit 10 designed as a laptop, which is connected to the multielement detector 6. In a manner analogous to FIG. 12 and the second exemplary embodiment, the adjustment unit 9, the piezo controller 9a in the present case, is connected to the multielement detector 6 via a trigger line in this third exemplary embodiment.

[0242] Consequently, the interferometer optical unit in the present case comprises the condenser lens 3, the beam splitter 4, the Mirau objective 12 and the tube lens 13.

[0243] In the present case, the measurement object 1 is a MEMS element, which has an easily movable, pressure-sensitive membrane as a measurement surface 1a.

[0244] In principle, the measurement procedure is implemented in a manner analogous to the measurement procedure of the second exemplary embodiment described in FIG. 12: the Mirau objective is displaced continuously at an approximately constant speed by means of piezo controller 9a and adjustment unit 9. A trigger signal is provided via the trigger line to the multielement detector 6 at equidistant time intervals for the purposes of recording a camera image. Storage and evaluation of the camera images is implemented by means of the evaluation unit 10, like in the exemplary embodiments described previously.

[0245] The evaluation is implemented in accordance with a third exemplary embodiment of a method according to the invention, which has a similar configuration to the second exemplary embodiment described above in relation to FIG. 14.

[0246] However, a great number of detector elements q are used in the third exemplary embodiment to determine the value z.sup.p assigned to the detector element p:

[0247] In the present case, the detector elements q.sub.j are selected by virtue of using all 48 neighboring elements of the detector element p, located in a 7×7 field, for the evaluation. For reasons of presentability, FIG. 16 once again merely shows a view of dimensions 31, 32 and 33 of the n-dimensional vector space of the correlogram vectors. As is evident from FIG. 16, the point cloud represented by the correlograms of detector elements q.sub.1 to q.sub.48 can be approximated better using a curve than a straight line. In this third exemplary embodiment, a curve 15a, an ellipse segment in the present case or a parabolic piece in an alternative embodiment, is fitted to the point cloud. Consequently, there is an approximation by fitting a low dimensional differentiable submanifold to the point distribution, a one-dimensional differentiable submanifold in the present case. In the present case, the approximation is implemented by virtue of determining a mean square and optimizing the free parameters of the curve using one of the conventional mathematical methods such that the mean square is minimized.

[0248] As evident from FIG. 16, the non-scaled synthetic correlogram Q.sup.p=s.sup.p/f.sup.p can be determined as a tangential vector 16a to the curve at the point p after the curve 15a for the correlogram c.sup.p has been determined.

[0249] The further evaluation is now carried out as described above, by virtue of initially determining the scaling factor f.sup.p for the synthetic correlogram at the point p and by virtue of determining the value z.sup.p on the basis of the correlogram c.sup.p and the correctly scaled synthetic correlogram s.sup.p.

[0250] However, what is advantageous in this third exemplary embodiment is that the determined curve can be used not only to determine the tangential vector 16a at the point p but also to determine tangential vectors at the points q.sub.j (see tangential vector 16b for point qi and tangential vector 16c for point q.sub.2 in exemplary fashion). A one-time determination of the curve consequently allows the determination of not only the value z.sup.p for the point p but also the corresponding values z.sup.q for all or at least a multiplicity of points q.sub.j (j=1, . . . , 48).

[0251] FIG. 17 illustrates a fourth exemplary embodiment of a device according to the invention. The latter largely corresponds to the first exemplary embodiment as per FIG. 1. However, the adjustment unit 9 is arranged at the reference mirror 8 in the fourth exemplary embodiment in order to move said reference mirror toward the light source or away from the latter, in the direction of the double-headed arrow. Consequently, the light path of the reference light is influenced by means of the adjustment unit 9. By contrast, the position of the device relative to the measurement object 1 and, in particular, to the measurement surface 1a remains constant, that is to say the optical path length of the measuring light also remains unchanged.

[0252] However, apart from this, the functionality is the same as that of the first exemplary embodiment. In particular, the method described in relation to the first exemplary embodiment can also be carried out using the device as per FIG. 17.

[0253] A fourth exemplary embodiment of the method according to the invention is presented below on the basis of the fourth exemplary embodiment of a device according to the invention illustrated in FIG. 17:

[0254] To this end, the device as per FIG. 17 is constructed in one modification to carry out a PSI measurement. In this case, the light source 2 is designed as a monochromatic laser with a wavelength of 520 nm.

[0255] In this exemplary embodiment, the phase difference z.sub.i between the measuring light and the reference light is varied by means of the adjustment unit 9.

[0256] Consequently, the luminous intensities I.sup.p(z.sub.i) are recorded depending on the respective amount z.sub.i of the phase difference, which has been changed in relation to the reference state of the interferometer, and said luminous intensities once again yield the correlograms c.sup.p=(c.sup.p(1), c.sup.p(2), . . . , c.sup.p(n))=(I.sup.p(z.sub.1), I.sup.p(z.sub.2), . . . , I.sup.p(z.sub.n)), wherein the z.sub.i are phase differences, for example measured in degrees or radians.

[0257] In the specific exemplary embodiment present, the measurements are carried out at 6 different values for z.sub.i. The correlogram vectors c.sup.p are consequently given as vectors in the six-dimensional vector space and the same observations can be made as in the preceding exemplary embodiments, only the values of z.sub.i are given here not as OPD differences but as phase differences.

[0258] In this fourth exemplary embodiment of a method according to the invention present all detector elements are now used for evaluation purposes. This is illustrated schematically in FIG. 18 in a reduction to dimensions 3, 4 and 4: as is evident in FIG. 18, the point cloud yields an ellipse in n-dimensional space, in 6-dimensional space in the present case, only three dimensions of which are illustrated here. As mentioned at the outset, in respect of the correlograms phase-shifting interferometry can be considered to be a special case of white-light interferometry, in which a constant envelope env(OPD)=const is present.

[0259] As presented in more detail above, the point cloud can be described as a closed ellipse in the case of PSI. Below, the case of white-light interferometry is also treated in FIG. 21.

[0260] A disturbance which influences the z.sub.i values, i.e., which leads to non-equidistant z.sub.i in particular, changes the relative position in space of the ellipse sketched out in FIG. 18 but the ellipse shape is maintained. An evaluation that is based on parameters of the ellipse shape is consequently not influenced or only hardly influenced by the above-described disturbances of the z.sub.i values.

[0261] According to the fourth exemplary embodiment of the method according to the invention, an ellipse 15a is fitted to the point cloud illustrated in FIG. 18. To this end, the ellipse is parameterized in the n-dimensional space, in 6-dimensional space in the present case, with the aid of n+5 free parameters, 11 free parameters in the present case, specifically using n parameters for defining the normal vector of the plane in which the ellipse is located, including the distance of this plane from the coordinate origin, 2 parameters for defining the displacement of the ellipse in the plane relative to the point of incidence of the normal vector on this plane, and 3 parameters to define the length and rotation of the principal axes of the ellipse. Now, a distance from the ellipse parameterized thus can be provided as a function of these parameters for each correlogram vector c.sup.p and c.sup.q, wherein the sum of the mean squares over all correlogram vectors c.sup.p and c.sup.q is minimized using a mathematical minimization method known to this end and, as a result, the corresponding parameters that define the ellipse are obtained. The synthetic (non-scaled) correlogram Q.sup.p=s.sup.p/f.sup.p is determined for a point c.sup.p of the detector element p by virtue of determining the tangential vector 16a to the ellipse at the point p, which is now easily possible as a result of the ellipse being present in parameterized form as a one-dimensional differentiable manifold and the tangential vector being able to be determined by differentiation. Subsequently, as described above, the scaling factor f.sup.p is determined and the associated z.sup.p value is determined from the correlogram c.sup.p and the associated synthetic correlogram s.sup.p. As is immediately evident from FIG. 18, the determination of the ellipse facilitates the evaluation not only in respect of the detector element p but also in respect of all other detector elements, for example the illustrated detector elements q.sub.2, q.sub.2, q.sub.3 and q.sub.4 with assigned correlograms c.sup.q1, c.sup.q2, c.sup.q3 and c.sup.q4, wherein the respectively associated tangential vectors 16b, 16c, 16d, 16e are likewise illustrated. With the aid of these tangential vectors Q.sup.qj=s.sup.qj/f.sup.qj, it is consequently immediately also possible, as described above, to determine the associated scaling factors f.sup.qj, the associated correctly scaled synthetic correlograms s.sup.qj and the associated values z.sup.qj, as a result of which it is possible to save very much computational outlay in relation to respective individual determination of the values z.sup.p and z.sup.qj.

[0262] In a modification of the fourth exemplary embodiment a principal component analysis is carried out first and the plane in which the ellipse is located is determined as a result. For the points to be evaluated, for example c.sup.p, there is a projection of the point into this plane, in order to minimize, inter alia, noise or disturbances, that is to say there is a displacement of the point c.sup.p perpendicular to the plane such that the point is located within the plane. After all points have been projected into the plane determined in advance, the ellipse is determined subsequently. Greater accuracy is obtained as a result thereof.

[0263] FIG. 19 schematically illustrates—once again for the representation by projection into a three-dimensional subspace of the six-dimensional vector space given by the luminous intensities measured at z.sub.3, z.sub.4 and z.sub.5—the point cloud obtained by determining the plane 14 by means of PCA and projecting the individual points into this plane. It should be noted in this case that the shown plane regularly is not a plane in the three-dimensional space spanned by the three illustrated spatial directions. Although the plane is, by all means, a two-dimensional plane in n-dimensional space, it is, however, as a rule, not a plane located in the three-dimensional vector space spanned by the illustrated axes. Accordingly, the representation as per FIG. 19 should be considered to be simplified elucidation for a better understanding.

[0264] For the further evaluation as per this exemplary embodiment of the method according to the invention, all that is considered below is the plane with the projected points shown in FIG. 19:

[0265] In partial image a, FIG. 20 shows the plane 14 as per FIG. 19. As described, the latter was determined by principal component analysis for determining the two largest eigenvalues and associated eigenvectors of the covariance matrix. A partial principal component analysis is likewise possible, the latter being carried out until the specified values are determined.

[0266] The two eigenvectors 17a, 17b span the plan in which the ellipse is located. Now, the points given by the correlogram vectors are projected into this plane.

[0267] In FIG. 20A, the alignment of the plane is chosen for the sake of simplicity such that the x-axis of the plane is determined by the eigenvector 17b for the largest eigenvalue and the y-axis is determined by the eigenvector 17a for the second largest eigenvalue. The length of the semi axes of the ellipse is proportional to the two eigenvalues. Therefore, it is possible to carry out an affine mapping which converts the ellipse into a circle, for example by stretching the y-axis using the ratio of the two eigenvalues.

[0268] The result is illustrated in FIG. 20B. In the circle now present here, it is possible to determine or read the relative phase angles 18, which are sought after for the evaluation, in a simple manner. By means of the phase angles 18, it is possible to ascertain the z.sup.p values or z.sup.qj values for the individual detector elements and hence the individual measurement points in a manner known per se.

[0269] The process explained in relation to FIG. 18 can likewise be used for white-light interferometry (WLI). Therefore, a further exemplary embodiment of a method according to the invention is presented below, in which WLI is carried out by means of the fourth exemplary embodiment of a device according to the invention as illustrated in FIG. 17, with the light source 2 being a broadband light source, for example an LED or super luminescent diode, instead of a laser in this case. The method for recording the intensity values for different z.sub.i is implemented in this case in a manner analogous to the exemplary embodiment as described in relation to FIG. 1. However, it is not the optical path length of the measuring light that changes in the present case. The change in the OPD is obtained by virtue of the optical path length of the reference light being changed by shifting the reference surface 8a of the reference mirror 8 by means of the adjustment unit 9. In the present case, too, intensities for each detector element p of the multidetector element 6 are respectively recorded for 64 z.sub.i values such that a correlogram, which once again can be represented as a point in the 64-dimensional space, is available for each detector element.

[0270] FIG. 21 shows the schematic representation of the point cloud in the 64-dimensional space in a manner analogous to FIG. 19, with once again only three dimensions of this space being illustrated here for practical reasons. Here, too, an approximate elliptical profile is exhibited but the latter no longer forms a closed ellipse. Rather, the curve is more like a helix around a cylinder with an elliptical cross-sectional area. The fact that no closed ellipse is formed here is due to the maximum of the envelope having moved on after one revolution in each case, whereas the envelope, as described previously, can be described as a constant function in the case of the PSI process.

[0271] Nevertheless, even if no closed ellipse is present, it is possible to again determine, by principal component analysis in the present case, a two-dimensional plane in the n-dimensional space in which the points are approximately located, as illustrated schematically by the plane 14 in FIG. 21.

[0272] For an improved elucidation, points (and hence detector elements) whose correlograms c.sup.qj are displaced by at most slightly more than half a period in relation to the correlogram c.sup.p on the detector element p were selected for the illustration in FIG. 21. As a result, this makes the fact that the ellipse is not closed most clearly visible.

[0273] In the real application of this exemplary embodiment of the method according to the invention, correlograms c.sup.qj with approximately ±2 periods shift in relation to the correlogram c.sup.p belonging to the detector element p are admitted in the present case, wherein it is sufficient to determine the corresponding shift using one of the known methods according to the prior art, which are not as insensitive to disturbances as the method according to the invention, with, as a result, a metric likewise being used to determine neighborhood properties Likewise, in alternative configurations, it is possible to select points by other values and/or in combination with a spatial distance metric of the detector elements.

[0274] Now, the distance vector to the determined plane is ascertained for each point p or q.sub.j (see exemplary labeled distance vectors 19 in FIG. 21). Points that belong to a correlogram that has been shifted by one or more periods have distance vectors of different lengths relative to this plane. At the respective locations belonging to the same projected point, these distances adopt relatively discrete values since the ellipse winds out of the plane and comes up “one floor higher” after each revolution.

[0275] Therefore, the number of periods through which the correlogram has been shifted can be ascertained by the length of the distance vectors. The length of the distance vector consequently yields a comparable result to the envelope evaluation in the case of the convention correlogram evaluation. The phase evaluation is implemented as described in the preceding figures.

[0276] The combination of this phase evaluation with the information obtained from the distance vector in relation to the shift of the correlogram envelope allows a relatively precise determination (independent of disturbances such as vibrations) of the shift of the individual correlograms, without the shift only being given modulo one period or 360° as in the case of the phase shifting interferometry; instead, the shift is given in full in the present case.

[0277] Using the described procedure it is possible to carry out the evaluation for very many points at once, saving a lot of calculation time. The topography of the measurement object is determined from the determined correlogram shifts.

[0278] If, in a modification of the exemplary embodiment, the evaluation is only undertaken for some of the points (e.g., for correlograms shifted by no more than ±2 periods in relation to c.sup.p as described), the method is preferably carried out for a plurality of preferably overlapping point sets such that the ascertained results can be merged.

[0279] A further modification of the exemplary embodiment is based on the fact that knowledge of the above-described distance vector means that the relative position of the envelope maximum is also known. Instead of, as described above, simply projecting the point into the determined plane 14, it is only the envelope of the correlogram that is shifted if the functional curve of the envelope is known, for example by virtue of the correlogram at the point q.sub.j being divided by the functional envelope at the point q.sub.j and being multiplied by the functional envelope at the point p such that, as a result thereof, the point q.sub.j is mapped into the same plane as the point p. If this mapping is carried out, preferably iteratively, for all points, a closed ellipse is obtained again, like in the previous figures, and this can also be evaluated accordingly. This can increase the quality of the evaluation results and the topography determined therefrom.

[0280] In the practical application, WLI and PSI also typically differ in the fact that the measurements are only carried out at significantly fewer locations in the case of phase-shifting interferometry, and so the number of the z.sub.i is typically smaller than in the case of WLI measurements. In the case of PSI measurements, the z.sub.i phase differences are in relation to the reference state of the interferometer, in contrast to WLI measurements where the z.sub.i are OPD differences in relation to the reference state of the interferometer. However, as a rule, phase and OPD are proportional, that is to say they can be converted with the aid of a conversion factor 2π/λ (in radians) or 360°/λ (in degrees) as per phase=360°/λ*OPD, where λ is the effective light wavelength.

[0281] In the above-described exemplary embodiments, the WLI measurements were performed at 64 locations (z.sub.1, z.sub.2, z.sub.64) such that each correlogram accordingly has 64 values and the complete vector space is 64 dimensional. By contrast, already 3 or 4 locations may be sufficient in the case of PSI measurements, and so, accordingly, only three or four measurement values are available at the three or four z points z.sub.1, z.sub.2, z.sub.3 or z.sub.1, z.sub.2, z.sub.3, z.sub.4 for each detector element.

[0282] Only 4 values are used in a modification of the above-described PSI method. Below, FIG. 22 is used to elucidate the influence of disturbances in the case of such a method and a procedure in the implementation of the method according to the invention, and the advantage thereof:

[0283] In partial image a), FIG. 22 shows an ideal, undisturbed signal curve as a solid line with four measurement values c.sup.p(1) to c.sup.p(4), which are phase-shifted by 90° in each case. In partial image b), the ideal, undisturbed signal curve is once again illustrated as a solid line, but the measurement values have simulated disturbances which lead to a displacement in the abscissa direction z such that the phase shift between the measurement values is no longer exactly 90°. The deviations from the ideal values (which are not known in the real measurement operation of the present exemplary embodiment) are elucidated by the differences Δz.sub.1 to Δz.sub.4. For the value c.sup.p(3), the ideal, undisturbed value c.sub.id.sup.p(3) has additionally been labeled, the latter consequently corresponding to the value c.sup.p(3) in partial image a).

[0284] Consequently, four values of z.sub.i are used in this modification of the exemplary embodiment, which values are each phase-shifted through 90° in the ideal, disturbance-free case. Then, the following applies:

[00012]$c^p\left(i\right)=c\left(OPD\right)=A+B^{\star }\cos \left(\psi +z_i\right)$

[0285] In this case, it is the value Ψ which is sought after and which corresponds to the sought-after z.sup.p, where the offset A and the amplitude B are constants with unknown values.

[0286] In the conventional evaluation according to the prior art, the sought-after Ψ is determined from the c.sup.p(i) of the associated correlogram, which is susceptible to errors in the case of disturbances. By way of example, in the case of four z.sub.i values shifted through 90°, this is implemented by:

[00013]$\begin{array}{cc}\begin{array}{c}\psi =\arctan 2c^p\left(4\right)-c^p\left(2\right),c^p\left(1\right),c^p\left(3\right))\\ =\mathrm{arc}\tan 2\left(\cos \left(\psi +z_4\right)-\cos \left(\psi +z_2\right),\cos \left(\psi +z_1\right)-\cos \left(\psi +z_3\right)\right)\end{array}& \left(4\right)\end{array}$

[0287] If in fact z.sub.2=z.sub.1+90°, z.sub.3=z.sub.1+180°, z.sub.4=z.sub.1+270°, then

[00014]$\psi =\arctan 2\left(\sin \left(\psi \right),\cos \left(\psi \right)\right)=\psi ,$

[0288] where phase unwrapping optionally needs to be carried out.

[0289] However, if the z.sub.i are afflicted by disturbances such an evaluation becomes incorrect and no longer allows an undisturbed determination of Ψ.

[0290] The procedure according to the invention preferably determines the associated synthetic correlogram s.sup.p (in this case s.sup.p=(s.sup.p(1), s.sup.p(2), s.sup.p(3), s.sup.p(4))) for the correlogram c.sup.p (in this case c.sup.p=(c.sup.p(1), c.sup.p(2), c.sup.p(3), c.sup.p(4))) in accordance with the procedures described in the description and the preceding exemplary embodiments, wherein, as previously, the information from other, optionally suitably chosen correlograms c.sup.qj of other detector elements q.sub.j is used.

[0291] To this end, the direction vector Q.sup.p(z.sub.i)=1/f.sup.p*s.sup.p(i) is initially ascertained by subtraction, approximation, fit, principal component analysis, etc., as described above, and then the scaling factor f.sup.p is determined with the aid of one of the described methods.

[0292] What is particularly advantageous for phase-shifting interferometry is that for all i in this case (c.sup.p(i)).sup.2+(s.sup.p(i)).sup.2 must yield the same constant value w.sup.p, wherein the c.sup.p(i) in this case are the luminous intensities I.sup.p(z.sub.i) of the correlograms which have been corrected for the offset o.sup.p, that is to say c.sup.p(i)=I.sup.p(z.sub.i)−o.sup.p. By way of example, the offset o.sup.p can be determined (a) by averaging the I.sup.p(z.sub.i) for suitable z.sub.i (e.g., for four z.sub.i shifted through 90°) or else (b), particularly advantageously, by virtue of ascertaining the offset o.sup.p at the same time as the ascertainment of the scaling factor f, by virtue of determining f.sup.p and o.sup.p such that

[00015]${\left(I^p\left(z_i\right)-o^p\right)}^2+{\left(f^p\star Q^p\left(z_i\right)\right)}^2$

is constant.

[0293] In the procedure (a) o.sup.p is already available as described, and all that still needs to be done is to determine the factor f.sup.p for which (I.sup.p(z.sub.i)−o.sup.p).sup.2+(f.sup.p).sup.2*(Q.sup.p(z.sub.i)).sup.2=w.sup.p yields the constant value w.sup.p for all i; this preferably being implemented by means of a linear regression of the type

[00016]$m*x_i+b=y_i,$

[0294] with x.sub.i=(Q.sup.p(z.sub.i)).sup.2, y.sub.i=−(I.sup.p(z.sub.i)−o.sup.p).sup.2, wherein the sought-after value for f.sup.p can be gathered immediately from the gradient m=(f.sup.p).sup.2.

[0295] In the procedure (b), f.sup.p and o.sup.p must be determined in such a way that the following always holds true:

[00017]${\left(I^p\left(z_i\right)-o^p\right)}^2+{\left(f*Q^p\left(z_i\right)\right)}^2=w^p,$

[0296] which once again leads to a minimization problem—in this case, it is necessary to determine e.g. f.sup.p, o.sup.p and w.sup.p in such a way that the sum

[00018]${\left({\left(I^p\left(z_i\right)-o^p\right)}^2+{\left(f^p\star Q^p\left(z_i\right)\right)}^2-w^p\right)}^2$

[0297] becomes minimal. This minimization problem can be solved by the relevant known mathematical methods and yields the sought-after values for f.sup.p and o.sup.p.

[0298] In any case, the synthetic correlogram s.sup.p (in this case s.sup.p=(s.sup.p(1), s.sup.p(2), s.sup.p(3), s.sup.p(4))) and the original diagram without the offset c.sup.p(z.sub.i)=I.sup.p(z.sub.i)−o.sup.p (in this case c.sup.p=(c.sup.p(1), c.sup.p(2), c.sup.p(3), c.sup.p(4))) are obtained.

[0299] As soon as the synthetic correlogram s.sup.p has been ascertained, it is possible to correctly determine the phase angle at each location z.sub.i therefrom in combination with the offset-corrected original diagram c.sup.p, without having to use the other z.sub.i to this end:

[00019]$\psi \left(z_i\right)=\mathrm{arc}\tan 2\left(s^p\left(i\right),c^p\left(i\right)\right),$

[0300] with phase unwrapping being optionally carried out again.

[0301] Since only the differences of the phase angles at different points p.sub.j are relevant for the purposes of determining the topography in the case of phase-shifting interferometry, the corresponding phase differences Ψ.sup.p2−Ψ.sup.p1 can subsequently be determined for any desired value for i, that is to say:

[00020]${\psi }^{p2}-{\psi }^{p1}=\arctan 2\left(s^{p2}\left(i\right),c^{p2}\left(i\right)\right)-\arctan 2\left(s^{p1}\left(i\right),c^{p1}\left(i\right)\right),$

[0302] wherein optionally a value which is suitably averaged for the final result is determined for different or all i.

[0303] It should be observed that disturbances of the z.sub.i, for example as a result of vibrations, once again have hardly any influence on the results of the evaluation in the case of the evaluation according to the invention, as a result of which the method according to the invention, as a rule, supplies significantly better results than the conventional methods according to the prior art if disturbances are present.

LIST OF REFERENCE SIGNS 1 Measurement object

[0304] 1a Measurement surface

[0305] 1b Hot plate

[0306] 1c Air turbulence

[0307] 2 Light source

[0308] 3 Condenser

[0309] 4 Semi-transparent mirror

[0310] 5 Imaging optical unit

[0311] 5a, 5b Optical lenses

[0312] 5c Optical stop

[0313] 6 Multielement detector

[0314] 6a Area sensor

[0315] 6b Detector element

[0316] 7 Optical filter

[0317] 8 Reference mirror

[0318] 8a Reference surface

[0319] 9 Adjustment unit

[0320] 9a Piezo controller

[0321] 10 Evaluation unit

[0322] 11 Reference surface

[0323] 12 Mirau objective

[0324] 12a Front lens

[0325] 12b Beam splitter

[0326] 13 Tube lens

[0327] 14 PCA-determined plane

[0328] 15 Direction vector

[0329] 15a Curve

[0330] 16a Tangential vector at p

[0331] 16b Tangential vector at q.sub.1

[0332] 16c Tangential vector at q.sub.2

[0333] 16d Tangential vector at q.sub.3

[0334] 16e Tangential vector at q.sub.4

[0335] 17a, 17b Eigenvectors

[0336] 18 Relative phase angle

[0337] 19 Distance vectors