JP2019191087A - Interference signal phase correction method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To correct a phase shift which is inevitably generated when measuring a physical phenomenon involving a periodic function. SOLUTION: An object to be measured is irradiated with a measurement medium from a light source, an interference signal exhibiting a periodic function is acquired, the interference signal is sampled at a plurality of sampling points, a phase shift at each sampling point is obtained, and the phase is concerned. A method for correcting the phase of an interference signal, which corrects the phase of the interference signal based on the shift. [Selection diagram] Fig. 3

Description

  The present invention relates to an interference signal phase correction method for removing a system error caused when a periodic function is digitally sampled.

  There are many measurement and analysis devices that use physical phenomena of periodic functions. For example, a scanning white interference microscope or phase shift electron beam holography. The interference phenomenon is expressed using a trigonometric function and exhibits a periodic function. The present invention is directed to a physical phenomenon having a periodic function (for example, an interference phenomenon) regardless of light or electrons. The method of intentionally shifting the phase, generally called the phase shift method, can also be applied because the sampling timing itself is similarly shifted.

  The importance of sampling timing has hitherto been noted as represented by Patent Document 1. Patent Document 1 shows a technique related to so-called preprocessing for aligning sampling timing when data is acquired.

  Also, in Patent Document 2, an interference signal is acquired using a trigger signal in order to ensure the linearity of sweeping, but this is also a technique related to preprocessing when acquiring data.

Non-Patent Document 1 describes a systematic error that is twice the signal frequency, and introduces canceling a systematic error by averaging it with a 90 ° sampling timing shifted.
Also, it is stated that some algorithms for correcting systematic errors are susceptible to random noise.

  Non-Patent Document 2 introduces an algorithm related to a systematic error twice the signal frequency and a method for removing the systematic error in the interference measurement apparatus.

  In Non-Patent Document 3, there is also a report regarding periodic noise, and it is said that a phase error is caused by vibration noise. An example in which the phase error is corrected has been reported.

JP 2013-250127 A JP 2017-9327 A

Interferogram Analysis for Optical Testing, Second Edition, D. Malacara, et.al., CRC Press, p213, 2005. Digital wave-front measuring interferometry: some systematic error sources, J. Schwider, et.al., Appl. Optics, Vol.22, 1983. Vibration in phase-shifting interferometry: P.Groot, J. Opt. Soc. Am.A, Vol.12, pp.354-365,1995

  The object of the present invention is not related to preprocessing as in Patent Document 1 and Patent Document 2, but relates to postprocessing after data acquisition. If only one point is measured, it is possible to align the sampling timing at the time of data acquisition. However, for example, in three-dimensional shape measurement using a camera, a point to be sampled is not a single point measurement, but millions of pixels are to be sampled. In the three-dimensional shape measurement, since the measurement target has an arbitrary shape, it is theoretically difficult to acquire data by aligning the sampling timing for all the pixels in each pixel. This is a problem that occurs even when the linearity of the light source at the time of wavelength sweeping or the linearity of the sweeping of a physically moving device is ensured.

FIG. 3 shows a phenomenon in which even if a sample existing on the surface or inside is flat, the sampling timing shifts when the sample is tilted. Therefore, considering the case of an arbitrary shape, the acquired data is always measured with a sampling timing shift.
In the present invention, a so-called phase correction method based on an inevitable sampling timing shift (phase) is provided at the time of data acquisition to solve a systematic error.

  As introduced in Non-Patent Document 1, even if the same algorithm is averaged with a phase shifted by 90 °, the systematic error can be removed, but with this method, the phase is shifted by 90 ° and again, Data acquisition must be performed. That is, since the data acquisition start time is not the same time, initial random noise due to the fact that the data acquisition start time is not the same time cannot be avoided. In addition, it takes twice as much time to acquire data.

  As in Non-Patent Documents 2 and 3, a conventionally known phase correction method uses ArcTan, and in order to obtain the phase −π / 2 to + π / 2, the internal term X in ArcTan (X) is It is necessary to take a value of −∞ to + ∞. As shown in FIG. 6, this is expected to make it difficult to accurately determine the phase in the vicinity of −π / 2 or + π / 2 as a result.

  Obtaining a phase from ArcTan using a component shifted by 90 ° from a single acquired data cannot ensure linearity for all the inputs X, and the sensitivity to the inputs X is different. . In addition, the input X needs to take values from −∞ to + ∞ (see FIG. 6).

  The present invention is a technique for obtaining a phase shift or the like based on a sampling timing shift and correcting and correcting the amount of the phase shift to provide a systematic error solution.

  According to the interference signal phase correction method of the present invention, a measurement medium is irradiated with a measurement medium to obtain an interference signal having a periodic function, the interference signal is sampled at a plurality of sampling points, and the phase at each sampling point is obtained. A shift is obtained, and the phase of the interference signal is corrected based on the phase shift.

  According to the present invention, it becomes possible to correct an inevitable sampling timing shift that occurs during digital sampling when measuring the shape of an object to be measured, and it is possible to perform shape measurement and physical measurement that eliminate systematic errors. Become.

FIG. 1 is an overall configuration diagram of a scanning white interference microscope which is one application example of an embodiment of the present invention. FIG. 2A is a graph showing a phase shift due to a sampling timing shift. FIG. 2B is a graph showing a sampling timing shift and a phase shift due to the complex refractive index. FIG. 2C is a graph showing the phase shift due to the complex refractive index. FIG. 3 is a diagram for explaining a phenomenon in which the sampling timing of the interference signal is shifted even when a measurement object having a planar shape is measured. FIG. 4 is a graph of cos and sin. FIG. 5 is a graph of ArcCos (X) and ArcSin (X). FIG. 6 is a graph of ArcTan (X), which indicates that the phase −π / 2 to + π / 2 cannot be expressed unless X takes a value of −∞ to + ∞. FIG. 7 is a process flow diagram illustrating processing of the interference signal phase correction method according to the embodiment. FIG. 8 is an example of an interference signal obtained when there is a complex refractive index. FIG. 9 is an example of an interference signal in a state including a sampling timing shift. FIG. 10 is a schematic diagram illustrating an example of a section area that is averaged in the XY plane in order to obtain a complex refractive index.

  Hereinafter, the interference signal phase correction method according to the present invention will be described in detail with reference to FIGS. 1 to 10 based on interference measurement, taking a scanning white interference microscope as an example.

  FIG. 1 is an overall configuration diagram of a scanning white interference microscope which is one application example of an embodiment of the present invention. The scanning white interference microscope 100 includes an apparatus main body 10, a stage 20 on which a sample D (measurement object) to be measured is placed, and a computer (processor) 30 that processes the obtained data. The apparatus main body 10 includes a light source (white light source) 11, a filter 12, a beam splitter 13, a two-beam interference objective lens (objective lens) 14, a sensor (detector) 15, and a piezo actuator 16.

  Irradiated light (white light) emitted from the light source 11 as indicated by an arrow A passes through a filter (for example, a wavelength filter, a polarizing filter) 12 and then is guided to a two-beam interference objective lens 14 by a beam splitter 13 ( Arrow B). The irradiation light is a beam splitter in the two-beam interference objective lens 14, and the first irradiation light toward the measurement object (including the sample D itself and the substance therein) and the second irradiation toward the reference mirror (not shown). Are divided into two. When the optical distance from the beam splitter to the measurement object in the two-beam interference objective lens 14 arranged to face the measurement object becomes equal to the optical distance from the beam splitter to the reference mirror, the measurement signal Can be observed in the form of interference signals of the two irradiation lights, and the sensor 15 images the interference signals as interference fringes (interference patterns), and the interference signal as a periodic function is held and stored in the computer 30. Further, in the embodiment of FIG. 1, since the distance from the beam splitter 13 to a reference mirror (not shown) is fixed, by sweeping using the piezo actuator 16 (movement of arrow C), The distance is changed. The scanning white interference microscope 100 uses a light source with a short coherence length (for example, the coherence length is 1 μm or less), but in the present invention, the length of the coherence length is arbitrary. Laser or white light is possible. In white light, the position where the interference signal is obtained is the z position (height position) where the measurement object exists. The operator operates the computer 30 of the scanning white interference microscope 100 to move the two-beam interference objective lens 14 in the height direction along the arrow C, and the measurement object (including the sample D and the substance therein). Are scanned in the height direction (z direction), and the surface properties (such as irregularities) of the measurement object are observed.

  In FIG. 1, a white interference microscope used as a measurement medium that irradiates a measurement target with light (including white light, laser, etc.) is taken as an example. However, the present invention includes a periodic function (trigonometric function, triangular wave) including an interference phenomenon. Any device that measures a function etc. can be applied. Other devices include, for example, a device using a phase shift electron holography using an electron beam as a measurement medium, an electromagnetic wave in a broad sense, particles or the like as a measurement medium.

  The interference signal obtained by the scanning white interference microscope 100 in FIG. 1 often includes noise due to systematic errors. Conventionally, methods for canceling such noise have been presented, but none of them has been satisfactory. This time, the inventor conducted an earnest examination on the cause of this noise.

  The interference signal obtained by the scanning white interference microscope 100 of FIG. 1 is mainly expressed using a trigonometric function. 2A to 2C are diagrams for explaining the sampling timing of the interference signal (however, the Gaussian distribution at the time of white interference is not considered), the vertical axis is the interference signal intensity (luminance, etc.), and the horizontal axis is This corresponds to a phase when a specific point at which the intensity of an interference signal in a reference state, which will be described later, reaches a maximum value is 0 degree, or a phase shift indicating a phase shift with respect to the reference state. Then, the following expression (1) corresponds to an expression expressing the graphs shown in FIGS. 2A to 2C. The function f in the equation (1) is an ordinate of the graph and expresses an interference signal obtained from a measurement target to be measured, and is defined as a measurement target function. In this example, the measurement target function is a periodic function having periodicity, specifically, a trigonometric function represented by a cos function.

In Equation (1), z is a position (coordinate) in the physical sweep direction (height direction), and the obtained interference signal is digitally sampled at a plurality of sampling points at frame rate intervals according to the frame rate of the camera. Is done. φ _st is a phase term representing a phase shift inevitably caused by a difference in sampling timing described later. The phi _c, A watered down sampling timing are the same, a phase term representing the substances phase shift caused the observed waveform by the complex refractive index with a (Sample D) (late).

In a combination assuming that a reference state having no phase term due to phase shift such as φ _st and φ _c is {Z, cos (Z)}, any state is sampled by {Z, cos (Z)} as long as it is a reference state. However, in an arbitrary shape in the three-dimensional shape measurement, it is not always possible to sample at any point in the reference state of {Z, cos (Z)}. Next, as will be described with reference to FIG.

  The imaging element of the camera (sensor 15 in FIG. 1) is filled with millions of pixels (pixels) in the XY plane. In FIG. 3, attention is paid to three pixels 31 to 33 arranged at equal intervals in the XY plane (lateral direction). Each pixel arranged at equal intervals follows the predetermined frame rate (for example, 1/60 sec, etc.) 34 in the graph (the horizontal lines at equal intervals on the vertical time axis in FIG. 3). Continue to take corresponding brightness information.

  In white interference, an interference phenomenon occurs when the optical distance from the reference surface is matched using a motor or PZT. Assuming that the measurement object 35 (including the surface of the sample D and the substance inside thereof) is truly flat, and measurement is performed using the camera in an inclined state, observation is performed at each pixel of the camera. The peak position with respect to time of the interference fringe also changes. That is, the peak position shifts along a virtual straight line 36 parallel to the measurement object 35.

  The intersection of the interference signal (interference waveform) and the horizontal line representing the frame rate is the luminance information observed at each pixel. The pixel 31 samples the peak of the interference signal, that is, the peak of the luminance at the sampling point 37. On the other hand, the other pixels 32 and 33 are sampled at sampling points 38 and 39 at positions shifted from the peaks of the interference signals. That is, even the measurement object 35 assumed to be truly flat differs in that it is sampled in the interference signal at each pixel only by tilting. Although the sampling theorem is satisfied, this sampling timing shift caused by the difference in sampling timing causes a systematic error.

Such a shift in sampling timing is represented by {Z + φ _st , cos (Z + φ _st )}. In FIG. 2A, a sampling point group 21A represented by white circles corresponds to a group of sampling points sampled in the reference state. On the other hand, the sampling point group 21B represented by a black circle corresponds to a group of sampling points sampled with a phase shift corresponding to 22.5 ° relative to the sampling point group 21A. The sampling point group 21A and the sampling point group 21B correspond to the relationship between the sampling point 37 and the sampling point 38 (or the sampling point 39) in FIG. 3, and it can be understood that a sampling timing shift occurs.

  Sampling theorem is satisfied if sampling is performed at a number exceeding two points with respect to one period of 360 ° in the phase of the horizontal axis. 2A to 2C show an example in which sampling is performed at 8 points in one cycle, that is, every 45 °.

Furthermore, the actual measurement object 35 has a complex refractive index, and is observed with a phase lag or advance. FIG. 2B shows an example in which a shift due to the complex refractive index is taken into account in addition to the above-described sampling timing shift, and is expressed by {Z + φ _st , cos (Z + φ _st + φ _c )} in the mathematical expression. In this example, a sampling point group 23B exists in addition to the sampling point group 21B sampled in the reference state and the sampling point group 22B sampled with a sampling timing shifted by 22.5 °. To the sampling point group 22B, when there are more complex refractive index phi _c, a position of a point sampling point group 23B is measured is shifted in the vertical direction from the position of the sampling point group 22B, the sampling point group 21B It looks like it has shifted to the left.

Figure 2C, although the sampling timing shift is not complex refractive index phi _c shows an example of 22.5 °. Although the sampling point group 23C exhibits the same shape (same sampling point) and sampling point group 22B of the sampling timing shift 22.5 ° in FIG. 2B, that are shifted laterally by the complex refractive index phi _c in Figure 2C I understand.

  As described above, the inventor has found that the phase shift based on the sampling timing and the phase shift based on the complex refractive index of the substance cause the occurrence of systematic noise during observation. Therefore, the inventor has achieved a phase correction method for obtaining and canceling these phase shifts in accordance with the steps described below.

In the case of white interference, the trigonometric function described in FIGS. 2A to 2C is multiplied by an envelope of Exp (−x ² ) that is approximately Gaussian. The complex refractive index phi _c, the peak of the macroscopic peak positions and the sampled maximum value of the envelope will be different, the sampling timing is an important factor (see FIGS. 8 and 9 described later). Although the phases of the phase terms φ _st and φ _c are similar, they are different functions from the viewpoint of the cause of the timing shift and need to be individually examined.

The present invention derives these terms by extracting the so-called phase terms φ _st and φ _c from equation (1). Here, equation (1) is premised on normalization (divided by the maximum value that equation (1) can take, ie, size 1), and is based on a white interferometer (scanning white interference microscope). The measurement data is normalized by dividing by the envelope including Exp (−x ² ). In order to extract φ _st and φ _c to be analyzed from the right side of Equation (1), cos (z) is defined as the measurement target function of Equation (1) based on the general phase modulation and trigonometric addition theorem. The following formulas (2) and (3) are obtained. cos (z) is defined as a phase modulation function used in phase modulation.

The expression (3) is multiplied by 2 in anticipation of cos (φ _st + φ _c ) to be extracted, and then a low-pass filter (averaging) is applied to cancel the second term cos (2Z + φ _st + φ _c ), Using the remaining cos (φ _st + φ _c ) as X, the following equation (4) is obtained. This expression (4) expresses a graph in which the output value is X with the phase corresponding to the input phase (this is also the phase to be obtained later) (φ _st + φ _c ) and the output value as X, which is shown in FIG. A cos wave and a sin wave can be obtained.

Then, the equation (4), by taking the ArcCos is an inverse function, albeit at sum of phi _st and phi _c, it is possible to obtain the phase information 51 as shown in FIG. That is, the output value X derived from Expressions (2) and (3), which is the result of multiplication of the measurement target function and the phase modulation function, is replaced with an input value, and this input value X is a phase calculation function for phase calculation. The phase shift at each sampling point, that is, φ _st + φ _c can be obtained from the value given to ArcCos.

  4 and 5 show the process of applying the inverse function ArcCos from the original cos function. However, the phase can be obtained correctly in the absence of noise, but in reality, random noise is included and measured, so that a phenomenon that is apt to be influenced by random noise occurs at the boundary portion.

  For example, in FIG. 4, X (= cos 0) is 1 in the reference state of 0 ° of the cos function. However, since the random noise is actually included, the true value is 1 when standardized by the maximum value. Even though there is a lower X value. This means that, finally, in the region 52 in the vicinity of X = 1 shown in FIG. 5, the phase 0 ° is not accurately obtained and a slightly larger phase value is output.

In the above method, the phase shift of f (z, φ _st , φ _c ) with respect to cos (z), that is, with respect to phase 0 °, is calculated by multiplying cos (z). Then, correction can be made from the phase shift finally obtained by taking ArcCos, but ArcCos returns a value of 0 to 180 ° as shown in FIG. When the phase of f (z, φ _st , φ _c ) is 0 °, the returned value of ArcCos (X) is also 0 ° as shown in FIG. 5, but the region 52 where the output of ArcCos (X) is near 0 °. , The amount of change in phase with respect to the input value X is large. That is, if the input value X changes even a little due to noise, the required phase also changes greatly. In other words, it is vulnerable to noise.

  Therefore, it is considered preferable to adjust the phase position to be strong against noise. Therefore, unlike equation (2), in order to adjust to a position shifted by π / 2 which is resistant to noise, instead of cos (z), cos (z + π / 2) = − sin (z) is applied as a phase modulation function. The following formulas (5) and (6) are obtained. Further, after multiplying by 2, a low-pass filter (for example, averaging) is applied to obtain Equation (7).

The inverse function of the obtained equation (7) is ArcSin, and it is preferable to take this value. That is, a value derived from Expressions (5) and (6), which is a result of multiplication of the measurement target function and the phase modulation function, is set as an input X, and this input X is given to ArcSin which is a phase calculation function for phase calculation. The phase shift at each sampling point can be obtained from the value. As shown in FIG. 5, when the phase of f (z, φ _st , φ _c ) is 0 °, the output of ArcSin (X) is a region 53 near 0 °, which is different from the divergent system like the region 52. The amount of change in phase with respect to X is small, the output is 0 °, and the region is strong against noise.

  In the above, two examples of the phase modulation function when the measurement target function is the cos function are the cos function and the −sin function (corresponding to the pattern (3) and the pattern (8) shown in Table 1 below). . Here, the function to be measured corresponding to the equation (1) is f (z), the phase modulation function for f (z) is g (z), and the phase calculation function h (z for deriving the phase shift to be finally calculated ), The phase φ to be obtained is expressed by the following equation (8).

  There are 8 patterns of 2 × 2 × 2 as basic shapes depending on the combination of each function. These are summarized in Table 1.

  Although the pattern (1) or the pattern (4) may be used, calculating the offset of −90 ° at the time of calculation increases the calculation cost. Therefore, the combination of (5) and (8) is preferable.

  ArcTan is often used to obtain the phase, but as shown in FIG. 6, since the phase 90 ° cannot be obtained unless the input X is infinite, it is more difficult to equalize the sensitivity compared to ArcCos and ArcSin. It is expected that.

Note that the low-pass, that is, averaging in the equations (6) to (7), that is, the first term sin (φ _st + φ _c ) is a constant value, while the second term sin (2z + φ _st + φ _c ). Is a periodic function of a trigonometric function. For example, the second term is canceled by obtaining an average value of sampling data in a section of −π to + π, and thus in a section of n * 2 * π (n is a positive integer). Done (becomes 0). That is, in order to extract only the target first term, for example, an interval of n * 2 * π corresponding to the n period of the periodic function, such as a section of −π to + π corresponding to the minimum one period of the periodic function. What is necessary is just to perform the average which calculates | requires the average value of the phase shift of the sampling data in an area. That is, the final phase shift can be obtained from the average value of the phase shifts at the respective sampling points in the interval of n * 2 * π corresponding to the n period of the periodic function.

Here are two points to note.
(Note 1)
When obtaining the phase of φ _st + φ _c , in order to improve the S / N, it is generally considered to average as wide a section as possible. In the above description, the pure trigonometric function without random noise shown in FIGS. 2A to 2C is assumed. However, in the case of white light interference, the coherence length is short. An interference waveform with an envelope like a Gaussian distribution determined by Expression (9) shows a function of an interference signal in accordance with an ideal Gaussian distribution in which no random noise exists, and Expression (10) shows a function of an interference signal in consideration of practically inevitable random noise.

Here μ represents the central peak position of the envelope, having a relative relationship with the complex refractive index phi _c. σ corresponds to the coherence length depending on the characteristics of the light source.

  In order to remove the envelope in order to obtain the phase information, when the equation (10) is divided by the obtained envelope for the state including the systematic error, the equation (11) is obtained.

  Since the envelope value is close to zero at a position away from μ, which is the center position of the envelope, that is, at the base of the Gaussian distribution, division by zero occurs at that limit. That is, noise is expanded. Therefore, when the coherence length is finite as in the case of a white light source, it is not effective to increase the averaging interval excessively. For this reason, it is preferable that the averaging interval be standard, for example, −π to + π corresponding to one period. That is, the final phase shift is obtained from the average value of the phase shifts at the respective sampling points in the section of −π to + π corresponding to one period of the periodic function. In other words, it can be said that such a section need not be limited in the case of a laser (˜100 m) having a very large coherence length with respect to the wavelength.

(Note 2)
If the number of sampling points is large, the degree of influence is small, but if the number of sampling points is small, there is a problem that becomes prominent. When the number of sampling points to be averaged is an even number, the average value can be obtained because it is canceled in the periodic function. On the other hand, when the number of sampling points is an odd number, the canceling is not performed, and the phase is shifted by one remaining point from the average value which is a true value due to the last remaining point.

  Therefore, although the averaging interval is n * 2 * π (for example, −π to + π), it is preferable to obtain an even number of points for averaging in order to obtain the true value of the phase. For example, when the number of data is 8, the phase 90 ° is obtained correctly, but when it is 9, a phase different from the true value (for example, a phase of 60 °) is obtained due to the influence of the remaining one point. That is, the average value of the phase shifts of the even number of sampling points is obtained to obtain the final phase shift.

From the above process, the phase φ _st + φ _c can be obtained although the complex refractive index φ _c is included. FIG. 7 shows an overall processing flow diagram. By this processing, the measurement result (observation result) is corrected based on φ _st + φ _c which is the obtained phase shift information, so that the same phase is obtained at all measurement points, and the sampling timing shift is also relative to each measurement point. Therefore, systematic errors can be eliminated. FIG. 7 is a summary of the description so far, and shows a processing flow performed by the scanning white interference microscope 100 of FIG. Such processing is performed by the computer 30 executing a predetermined application, but the type of hardware, software, etc., the storage mode, etc. for performing the processing are not particularly limited.

  As shown in FIG. 7, first, the computer 30 removes an envelope (such as an envelope based on a Gaussian distribution) from the interference signal as a measurement result (step S41). Subsequently, the computer 30 normalizes the measurement target function obtained here (step S42). When the light source 11 is a white light source (white interference), normalization is performed using the temporarily obtained envelope, but in the case of a laser, normalization is performed with the maximum value.

  Next, the computer 30 multiplies the normalized measurement target function by the phase modulation function under the assumption that the center wavelength of the light source 11 is known (step S43). Here, it is preferable to carry out based on the criteria shown in Table 1.

  Next, the computer 30 performs an averaging process in a predetermined section (step S44). In the case of white light interference, it is preferable to average in the section of −π to + π. In the case of a laser, it may be averaged over an interval of n * 2 * π.

  Next, the computer 30 calculates an average value for an even number of sampling points in the averaging section (step S45). Further, the computer 30 obtains phase shift information that is a correction amount of the measurement result from the value of ArcSin that is a phase calculation function that receives a value derived from the result of multiplication (step S46). Finally, the computer 30 corrects the measurement result from the obtained phase shift information (step S47). Specifically, the phase shift information is added to the value of the measurement result to obtain the final phase. Thus, the interference signal phase correction method of the present invention is implemented.

Through the above-described processing, the scanning white interference microscope 100 can remove the systematic error. Therefore, the double period noise that is representative of systematic errors described in Non-Patent Document 1 and Non-Patent Document 2 can be deleted. However, even after this deletion, the complex refractive index φ _c is still measured. That is, the phase shift at each sampling point is composed of a phase shift φ _st based on the sampling timing shift and a phase shift φ _c based on the complex refractive index of the measurement object, and each of φ _st and φ _c is individual. Not asked for.

As a method for obtaining the here complex refractive index phi _c, the peak of the macro envelope as shown in FIGS. 8 and 9, since the interference signal is shifted horizontally, estimated to be available to determine It is expected that This is because the complex refractive index corresponds to an index indicating a response delay with respect to the input of a measurement medium such as light.

If the complex refractive index φ _c is obtained from the maximum peak closest to the macro envelope, there is a possibility that it is calculated including the phase error φ _error in the following equation (12) at the maximum.

As described above, the sampling timing shift occurs even when the measurement object is a uniform and flat material. On the other hand, the complex refractive index of the material due, complex refractive index phi _c is estimated to vary from no greater inclined. Utilizing this characteristic, each of the specific regions in the XY plane perpendicular to the direction of irradiating light to the same material (measurement point having the same complex refractive index) as shown in FIG. A phase shift φ _st + φ _c is obtained at the sampling point. Then, the average value of the phase shift at each sampling point, by determining the manner described above, it is possible to calculate the complex refractive index phi _c.

In particular, the sampling phase shift is canceled by averaging the acquired phase shift φ _st + φ _c in the section area A of n * 2 * π (n is a positive integer) corresponding to an integral multiple of one period of the periodic function. Be ringed. On the other hand, the average value remains as a baseline upon averaging is extracted as the complex refractive index phi _c.

  FIG. 10 shows an example of 2π (n = 1), 4π (n = 2), and 6π (n = 3) as an example of the section region A of n * 2 * π. Since the portion overflowing from n * 2 * π causes a deviation from the true value, n is preferably larger. This is because the ratio of the overflowing portion to the whole is reduced and the influence is reduced. Further, as described above, the number of data in the averaging interval n * 2 * π of the XY plane for canceling the sampling timing deviation is preferably an even number. In addition, it is preferable to perform this method only in the area | region (section area A) where it is estimated that a material, ie, a complex refractive index, does not change a lot.

  In addition, this invention is not limited to embodiment mentioned above, A deformation | transformation, improvement, etc. are possible suitably. In addition, the material, shape, dimension, numerical value, form, number, arrangement location, and the like of each component in the above-described embodiment are arbitrary and are not limited as long as the present invention can be achieved.

  According to the present invention, it is possible to correct a sampling timing that occurs when sampling a physical phenomenon having a periodic function, and it is possible to perform measurement while removing a systematic error.

10 Device body 11 Light source (white light source)
12 filters (including wavelength filters)
13 Beam splitter 14 Two-beam interference objective lens (objective lens)
15 Sensor 16 Piezo actuator 20 Stage 30 Computer 100 Scanning white interference microscope D Sample (including measurement object)

Claims (10)

Irradiate the measurement object to the measurement object, acquire an interference signal having a periodic function,
Sampling at a plurality of sampling points for the interference signal,
Obtain a phase shift at each sampling point, and perform phase correction of the interference signal based on the phase shift.
Interference signal phase correction method. A method for correcting a phase of an interference signal according to claim 1,
Multiply the target function of the trigonometric function, which is the periodic function of the interference signal, by the phase modulation function for phase modulation,
A phase shift at each sampling point is obtained from the value of ArcSin, which is a phase calculation function, with a value derived from the result of multiplication as an input.
Interference signal phase correction method. The phase correction method for interference signals according to claim 1 or 2,
A final phase shift is obtained from an average value of the phase shifts of the respective sampling points in an interval of n * 2 * π (n is a positive integer) corresponding to n periods of the periodic function.
Interference signal phase correction method. A method for correcting a phase of an interference signal according to claim 1,
The measurement medium is light having an arbitrary coherence length irradiated from a light source.
Interference signal phase correction method. The method for correcting a phase of an interference signal according to claim 4,
When the coherence length is finite, a final phase shift is obtained from the average value of the phase shifts at the respective sampling points in a section of −π to + π corresponding to one period of the periodic function.
Interference signal phase correction method. An interference signal phase correction method according to any one of claims 1 to 5,
Find the average phase shift of an even number of sampling points to find the final phase shift.
Interference signal phase correction method. The phase correction method for an interference signal according to any one of claims 1 to 6,
Obtaining a phase shift based on a sampling timing shift constituting a phase shift at each sampling point and a phase shift based on the complex refractive index of the measurement object in an XY plane perpendicular to the direction in which the measurement medium is irradiated;
Interference signal phase correction method. The phase correction method for interference signals according to claim 7,
By obtaining the average value of the phase shift of each sampling point in the specific area in the XY plane, the complex refractive index of the specific area is obtained.
Interference signal phase correction method. The phase correction method for interference signals according to claim 8,
The specific area is a section area of n * 2 * π (n is a positive integer) corresponding to an area that is an integral multiple of one period of the periodic function.
Interference signal phase correction method. A method for correcting a phase of an interference signal according to claim 9,
Obtaining a complex refractive index of the specific region from an average value of phase shifts of an even number of sampling points in the specific region;
Interference signal phase correction method.