JP2013231652A - Phase measurement device, phase measurement program, and phase measurement method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To improve accuracy in phase measurement using a coherence beam.SOLUTION: A phase measurement method of calculating phases of a first coherence beam transmitting through a measurement target portion and a second coherence beam transmitting through a portion other than the measurement target portion on the basis of a plurality of imaged interference fringe images includes the steps of: selecting a straight line across a prescribed area where a refractive index and a thickness of a measuring sample are deemed to be uniform and a selection point on the straight line so that two-dimensional positions thereof in a plurality of interference fringe images different in an imaged relative phase difference are the same; determining an intensity distribution curve of an interference fringe on the straight line for each of the interference fringe images; determining an initial phase which is a phase difference from the selection point to a feature point on the intensity distribution curve; and calculating a phase of the measurement target portion on the basis of the initial phase.

Description

  The present invention relates to a phase measurement apparatus and method for measuring a physical property value of a measurement object such as a refractive index distribution by interfering a coherent beam and measuring a phase change generated in the measurement object, and a computer-executable phase Related to measurement program.

  The present invention measures the characteristics of a medium by utilizing the fact that the phase of a coherent beam is changed by passing through different media. Here, first, the principle of phase measurement will be described using an example in which light is used as a coherent beam.

Light has a wave property, and there are three factors that determine the property: amplitude, wavelength, and phase. There are various wave notations, but the simplest form uses trigonometric functions,
y = A sin [2π (t / Tz / λ)] (1)
It is expressed as follows. Here, y is a physical quantity that is to be handled now, and in the case of light, it is generally an electric field. A is the amplitude, T is the period of vibration, λ is the wavelength, t and z are the coordinates of time and wave traveling direction as variables, and the inside of the sine function is called the phase. In the case of light, the period and time of vibration in the phase are much shorter than the time scale of measurement and are therefore omitted because they are averaged and have no meaning.

When light passes through an object, if it is a translucent substance, the thicker the part is, the light is absorbed and the amplitude becomes smaller, so that a gray image can be observed. However, samples in the optical element field and biological field are almost transparent in many cases, and therefore the amplitude hardly changes, so that they cannot be observed with a normal microscope. On the other hand, the phase portion changes much more greatly than the change in amplitude. When the wavelength of light in vacuum is λ ₀ , the wavelength of light in an object with a refractive index n is
λ = λ ₀ / n (2)
It is expressed. Since the refractive index of air is approximately 1, the wavelength in air can be regarded as λ ₀ . The refractive index is about 1.33 for water and about 1.5 to 1.6 for glass and optical resin.

Now, in the refractive index of the base material of n _1, consider a sample larger objects of refractive index n ₂ of the refractive index are embedded, FIG. 1 shows a state in which this light is transmitted. Since light is a wave, mountains and valleys move alternately. In this figure, the light coming from the top of the figure is represented by horizontal or a group of lines close to it, but this is a line that virtually connects the spatially corresponding peaks (or valleys) (because it is actually a solid) Is called the wavefront. The wavefront of parallel light is represented by a plane group whose interval is the wavelength λ ₀ . When this wave enters the refractive index n ₁ portion, the wavelength becomes λ ₁ shorter than that in the air according to the above formula. Considering light A that passes through the embedded portion and light B that passes only through the base material, light A and light B travel into the base material in the same manner immediately after entering the base material, so that the interval between the wave fronts is λ ₁ . Although it changes, the wavefront shape remains flat. However, when the light reaches the buried portion, the wavelength is changed to λ ₂ and the wavelength is shortened in the portion of the thickness t of the buried portion, so that the shape of the wavefront becomes convex upward.

The number N ₂ of waves entering the distance of the thickness t of the embedded portion of the optical path A is
N ₂ = t / λ ₂ (3)
The number N ₁ of waves entering the portion of thickness t corresponding to that of optical path B is
N ₁ = t / λ ₁ (4)
Therefore, the amount of shift Δφ between the wavefronts of the optical path A and the optical path B immediately after passing through the embedded portion is expressed as Δφ = N ₂ −N ₁ in terms of the number of waves, that is, wavelength units.
_{= (1 / λ 2 - 1} / λ 1) t
= (n ₂ -n ₁ ) t / λ ₀ (5)
It is expressed. The amount of wavefront deviation is generally expressed in radians and is called phase deviation, phase change, or simply phase.

For example, when measuring the refractive index distribution in the core section of an optical fiber as an example inside a thin sample having a uniform thickness, the wavelength of the laser in equation (5) is known, the thickness t is uniform and known, Since the refractive index n ₁ is uniform and known, and the refractive index n ₂ of the embedded portion is two-dimensionally changing and unknown, the phase shift Δφ of the transmitted light is also two-dimensionally distributed, and the unit of wavelength is As
Δφ (x, y) = [n ₂ (x, y) −n ₁ ] t / λ ₀ (6)
It can be expressed as.

Phase change measurement method If the refractive index n _{1 of the} base material and the thickness t of the embedded portion are known in advance from the equation (6), the phase shift distribution Δφ (x, y) of the light transmitted through the sample is measured. By doing so, the refractive index distribution n ₂ (x, y) of the embedded portion can be obtained.

  Interferometry has long been used to inspect flat and spherical surfaces of glass products. A typical example is the Newton ring method. In this method, when a plane or spherical surface to be inspected is placed on a highly accurate reference plane and viewed from directly above, the reflected light from the reference plane interferes with the reflected light from the surface to be in contact with it, Since interference fringes corresponding to the distance between the two surfaces appear, the deviation from an ideal plane or spherical surface is visualized to determine whether or not it is good. The principle of generating interference fringes from the two reflected lights at this time is as follows.

For the sake of simplicity, it is assumed that a uniform plane wave that is not disturbed by a reference wave that is a measurement reference and an object wave that comes from the plane to be examined are slightly deviated from the plane wave depending on the location. In general, a plane wave ψ traveling in the z direction has a subscript r indicating a reference wave, where the amplitude is A, the wavelength is λ, and the wave number is k = 2π / λ.
ψ _r (x, y) = A _r (x, y) exp [ikz] (7)
It is expressed. Here, x and y are coordinates in two orthogonal directions on a plane orthogonal to the z axis. Assuming that the reference wave is constant regardless of location, the right side A _r (x, y) is also constant regardless of location.

On the other hand, the object wave is also an object wave, with the subscript o indicating that it is an object wave,
ψ _o (x, y) = A _o (x, y) exp [i [kz + φ (x, y)]] (8)
It is expressed. In the object wave, changes in amplitude and phase due to the object occur in the (x, y) plane.

When these two waves overlap in the same direction, the overlapped part is simply added according to the principle of wave superposition. Ψ _o + ψ _r (9)
It is expressed. Observing the part where two waves overlap, the measured physical quantity is intensity I (x, y), so
I (x, y) = (ψ _o + ψ _r ) ² (10)
Substituting Equations (7) and (8) into this equation represents the complex conjugate as *
I (x, y) = | ψ _o + ψ _r || ψ _o + ψ _r | ^*
= | A _o (x, y) | ² + | A _r | ² + | A _o (x, y) || A _r | exp [i [kz + φ (x, y) -kz]]
+ | A _o (x, y) || A _r | exp [i [-kz-φ (x, y) + kz]]
= | A _o (x, y) | ² + | A _r | ² +2 | A _o (x, y) || A _r | cos [φ (x, y)] (11)
It becomes. The first and second terms | A _o (x, y) | ² and | A _r | ² are the intensity distributions of the object wave and the reference wave. On the other hand, the third term is an interference term, which produces light and shade according to the change in phase applied to the object wave. When the change in intensity due to the object can be ignored as in the Newton ring, the first and second terms are constant, and only the interference fringes of the third term are observed.

Next, consider a case where the object wave and the reference wave overlap with each other with an angle θ. Now, for example, if the reference wave is tilted by θ about the y axis as the rotation axis, the x and z coordinates after tilting are X and Z, respectively, as shown in FIG.
X = xcosθ + zsinθ (12)
Z = -xsinθ + zcosθ (13)
If the tilt angle is small
X = x + zsinθ (14)
Z = -xsinθ + z (15)
It becomes. Therefore, the reference wave assumes that the change in amplitude due to the change in the x coordinate is sufficiently small,
ψ _r (X, y) = A _r (x, y) exp [ikZ]
= A _r (x, y) exp [i [kz-kxsinθ]] (16)
It can be expressed as.

The intensity distribution of the interference fringe image of the wave of equation (16) and the object wave of equation (8) is
I (x, y) = | ψ _o + ψ _r || ψ _o + ψ _r | ^*
= | A _o (x, y) | ² + | A _r (x, y) | ² + | A _o (x, y) || A _r (x, y) | exp [i [kz + φ (x , y) -kz + kxsinθ]]
+ | A _o (x, y) || A _r (x, y) | exp [i [-kz-φ (x, y) + kz-kxsinθ]]
= | A _o (x, y) | ² + | A _r (x, y) | ² +2 | A _o (x, y) || A _r (x, y) | cos [φ (x, y) + kxsinθ]
... (17)
It is expressed. That is, an interference fringe image having an interval corresponding to the angle at which the two beams overlap is obtained, and the phase change due to the object wave is superimposed as a local change in the interference fringe interval.

From equation (11) or equation (17), it is possible to read the phase change caused by the object wave by judging the density of the interference fringes. However, strictly speaking, since the illumination light has an intensity distribution, the amplitude distributions A _r (x, y) and A _o (x, y) of the reference wave and the object wave cannot be regarded as constant, and depending on the object The induced intensity change A _o (x, y) cannot be ignored. That is, in the third term of the equation (17), the cos (cosine) term including the phase and the amplitude distribution of the object wave and the reference wave are included in an inseparable state, so this method expects high measurement accuracy. I can't.

  Representative examples of interferometric methods devised and put to practical use to overcome this drawback are the Fourier transform method and the phase shift method. The Fourier transform method is a method in which interference fringes (referred to as carrier interference fringes) corresponding to angles formed by two beams are intentionally generated as shown in equation (17), and this image is Fourier transformed.

FIG. 3 is an example in which an interference fringe image is created by simulation for a sample to be measured which has an elliptical measurement target portion in the center and the surroundings are made of a material having a uniform refractive index or a blank space. In the region around the measurement object, φ (x, y) of φ (x, y) + kxsinθ out of cos in the third term of equation (17) is constant, so that kxsinθ in the horizontal direction (x direction) Interference fringes with constant intervals and directions are generated. As described above, this is an interference fringe due to the two beams being tilted and overlapped.

On the other hand, since this phase further changes depending on the measurement target part itself inside the measurement target part, the interval and direction of the interference fringes change depending on the thickness or refractive index. Since the phase distribution of the object wave appears as a local change in the interval and direction of the carrier interference fringes, it is distributed around the spectrum corresponding to the carrier interference fringe interval when Fourier transformed as shown in FIG. Therefore, when either the left or right spectral portion is selected and Fourier inverse transformed, the phase portion and the amplitude are separated, so that the phase of the object wave can be extracted.

  The disadvantages of the Fourier transform method are that there is a trade-off between spatial resolution and phase measurement accuracy, and that the influence of the boundary when selecting a circular region from the spectrum is inevitable in principle and adversely affects accuracy. Yes, it has not been widely used.

On the other hand, the phase shift method is a method for obtaining the phase distribution of the object wave from three or more interference fringe images in which the relative phases of the reference wave and the object wave are shifted by a known amount. In this method, if the amount of phase shift is set to a positive fraction of one wavelength, the calculation process can be made extremely simple. The principle will be explained below using this assumption. Consider obtaining the phase of a certain point (x ₀ , y ₀ ) in the interference fringe image. For simplification of description, I (x ₀ , y ₀ ) is set as I, φ (x ₀ , y ₀ ) + kx ₀ sinθ is again set as φ ′, and equation (17) is expressed as follows:
I = B + A cos (φ ') (18)
rewrite.

The amount to be measured is the intensity I of the interference fringe at a certain point (x ₀ , y ₀ ) in the interference fringe image, but the unknowns are the density B of the location, the amplitude A of the interference fringe intensity, and the phase portion φ ′. Therefore, at least three independent intensity values are required for this point measurement. Therefore, when considering four interference fringe images whose phases are shifted by ¼ wavelength, the intensity I at the point (x ₀ , y ₀ ) in each interference fringe image is
I ₁ = B + Acos (φ ') (19)
I ₂ = B + Acos (φ '+ π / 2) (20)
I ₃ = B + Acos (φ '+ π) (21)
I ₄ = B + Acos (φ '+ 3π / 2) (22)
It is expressed.

Expressions (20) to (22) can be rewritten as Expressions (23) to (25), respectively, using trigonometric addition theorems.
I ₂ = B + Asin (φ ') (23)
I ₃ = B-Acos (φ ') (24)
I ₄ = B-Asin (φ ') (25)
First, B is deleted from the equations (19) and (24),
I ₁ -I ₃ = 2Acos (φ ') (26)
Erasing B from the equations (23) and (25),
I ₂ -I ₄ = 2Asin (φ ') (27)

とすれば、

のように、位相項φ'のみを分離して求めることができる。干渉縞画像内の全ての点に
ついてこの計算を行えば、視野内の透過波の位相分布を求めることができる。この１／４波長ずつずらした４枚の干渉縞画像を用いる方法が最も計算が簡潔・容易で、４点法など
と呼ばれている。 Since the value to be obtained is the phase φ ′, A is deleted from the equations (26) and (27),

given that,

As described above, only the phase term φ ′ can be obtained separately. If this calculation is performed for all points in the interference fringe image, the phase distribution of the transmitted wave in the field of view can be obtained. The method using four interference fringe images shifted by ¼ wavelength is the simplest and easiest calculation and is called a four-point method.

If the least square method is used by increasing the number of interference fringe images, the phase can be obtained with higher accuracy. When the interference fringe image is M pieces whose phases are shifted by 1 / M wavelength, the intensity distribution of the interference fringes at the point (x ₀ , y ₀ ) of each interference fringe image is
I ₁ = B + Acos (φ ') (30)
I ₂ = B + Acos (φ '+ 2π / M) (31)
I _M = B + Acos [φ ′ + 2π (M−1) / M] (32)
It becomes.

If these are expressed by one expression,
I _m = B + Acos [φ '+ 2π (m-1) / M] (33)
It becomes. However, m = 1 to M. When the equation (33) is converted using the addition theorem,
I _m = B + A [cos (φ ′) cos [2π (m−1) / M] −sin (φ ′) sin [2π (m−1) / M]] (34)
Here, at this point (x ₀ , y ₀ ), the variable resulting from the phase shift is [2π (m−1) / M], and B, A, and φ ′ are constants. So the constant part
A ₁ = Acos (φ ') (35)
A ₂ = -Asin (φ ') (36)
Variable part
X _m = cos [2π (m-1) / M] (37)
Y _m = sin [2π (m-1) / M] (38)
If you do, equation (34) is
I _m = B + A ₁ X _m + A ₂ Y _m (39)
It can be expressed as.

が最小となるようなＢ、Ａ₁、およびＡ₂の値を求めればよい。係数Ｂ、Ａ₁、およびＡ₂はいずれも、大きすぎても小さすぎても誤差が大きくなることは明らかであるので、求める最小値は極小値でもある。従って、係数Ｂを変化させたときの極小値は、（４０）式をＢで偏微分して０になる条件を求めればよい。 From the equations (39), (35), and (36), it can be seen that the phase φ ′ at this point can be determined by obtaining A ₁ and A ₂ . According to the least squares method, the measured value I _m and (39) coefficients such that the sum of the squares becomes minimum difference of the right-hand side value calculated by the formula B of the beam intensity of this point, A _1, and A ₂ If a value is determined, it is the coefficient with the smallest statistical error. That is,

B but that minimizes, it may be determined a value of A _1, and A _2. The coefficients B, A ₁ , and A ₂ are all too large or too small, and it is clear that the error increases. Therefore, the minimum value to be obtained is also a minimum value. Therefore, the minimum value when the coefficient B is changed may be obtained by obtaining a condition that the equation (40) is partially differentiated by B and becomes zero.

従って、

また、係数Ａ₁を変化させたときは、

となり、

係数Ａ₂を変化させた場合も同様に、

という式が得られる。

Therefore,

When the coefficient A ₁ is changed,

And

Similarly, when the coefficient A ₂ is changed,

Is obtained.

となるが、離散的三角関数の性質により、

となるため、（４６）式の右辺３×３行列の中は対角成分以外全て０となり、この行列の値をＤとすれば、

となる。 Equations (42), (44) and (45) can be expressed as a matrix,

However, due to the nature of discrete trigonometric functions,

Therefore, in the right side 3 × 3 matrix of equation (46), all but the diagonal components are all 0, and if the value of this matrix is D,

It becomes.

係数Ａ₁は、

係数Ａ₂は

となる。 The coefficients B, A ₁ , and A ₂ are obtained by dividing the matrix obtained by replacing the column corresponding to the coefficient B of the matrix D with the left side of the equation (46) when the Kramel formula, that is, the coefficient B is obtained. be able to. As a result, the coefficient B is

The coefficient A ₁ is

The coefficient A ₂ is

It becomes.

であるから、

となる。さらに、三角関数の倍角の公式から、
X_m ² - Y_m ² = cos²[2π(m-1)/M] - sin²[2π(m-1)/M]² = cos[4π(m-1)/M]
・・・（５５）
となるため、

すなわち、

であるので、（５４）式は

となる。 The relationship between the obtained φ ′ and the coefficients B, A ₁ , and A ₂ is the same as the discussion in the equation (28).

Because

It becomes. Furthermore, from the trigonometric double angle formula,
X _m ² -Y _m ² = cos ² [2π (m-1) / M]-sin ² [2π (m-1) / M] ² = cos [4π (m-1) / M]
... (55)
So that

That is,

Therefore, the equation (54) is

It becomes.

To summarize the measurement principle of the phase shift method,
1. M interference fringe images obtained by shifting the relative phase difference between the reference wave and the object wave by 1 / M (M: a positive number of 3 or more) are obtained.
2. For each point of the interference fringe image, the distribution of the phase change of the object wave due to the sample to be measured can be obtained by calculating the equation (58).

  This is schematically shown in FIG. In this example, four interference fringe images and the optical path length of the reference wave or object wave are changed by ¼ wavelength, and then taken into the computer. That is, the first image of the interference fringe image is shifted by ¼ wavelength, but the phase shift amount of the first image is set to 0 in the development of the above formula. This is intentionally changed for explanation, and the numerator and denominator are obtained in the equation (58) depending on whether the first image is counted as the first image or the 0th image. The phase distribution is totally equivalent only by a quarter wavelength shift.

The phase distribution obtained here is
φ (x, y) + kxsinθ (59)
Since the second term includes a phase gradient component corresponding to the angle at which the two beams overlap, if the angle between the two beams is known accurately, it is corrected numerically. If not, the inclination component may be obtained from the image and corrected.

J. E. Greivenkamp and J. H. Bruning, "Phase Shifting Interferometry", Optical Shop Testing pp.501-598, 2nd ed., Edited by Daniel Malacara, John Wiley & Sons (1992) Joanna Schmit and Katherine Creath, "Extended averaging technique for derivation of error-compensating algorithms in phase-shifting interferometry", Applied Optics Vol.34, No.19 (1995) P. Carre, Metrologia, Vol.2, No.1, pp.13-23 (1966) K. Yamamoto, I. Kawajiri, T. tanji, M. Hibino, and T. Hirayama, "High precision phase-shifting electron holography", Journal of Electron Microscopy 49 (1), pp. 31-39 (2000)

In the basic phase shift method described above, it is desirable to shift the relative phase difference between the reference wave and the object wave by an integer number of one wavelength. It is not necessary in the discussions from (30) to (46) that the angle in the trigonometric function of Xm and Ym, that is, the term of phase shift amount is 2π (m−1) / M. ) To (49), it is possible to use the property that the sum of the discrete trigonometric functions becomes zero. Therefore, a method of shifting by an integral number of one wavelength is usually used. Even when the amount of phase shift is not a fraction of an integer, equation (46) can be solved as it is. In this case, the equations (37) and (38) are respectively
X _m = cos (δ _m ) (60)
Y _m = sin (δ _m ) (61)
It becomes. δ _m is the phase shift amount of the m-th interference fringe image. As described above, the phase shift amount does not necessarily have to be an integral wavelength, and it may be difficult to obtain calculation accuracy or increase the calculation amount, but there is no big problem.

  However, in this method, it is crucial that the phase shift amount of each interference fringe image is accurately understood. Interferometry is extremely sensitive and accurate, but this means that the measurement results are likely to be affected by very slight changes in conditions. For this reason, in general, in an optical system, an interferometer is mounted on a vibration isolation table to improve stability, and one of the reflecting mirrors constituting the interferometer is driven by a piezo element to accurately control the change in the optical path. Yes. Further, a highly accurate position sensor, for example, a capacitance type position sensor that is integrated into the piezoelectric element is also used. The relationship between the amount of fine movement and the amount of phase shift due to the piezo element naturally depends on the configuration of the interferometer, but it is also affected by a slight change in the positional relationship of the interferometer and the temperature during measurement. In general, calibration data is acquired prior to measurement. An analysis algorithm that minimizes the phase shift error has also been devised, and a five-point method (Non-patent Document 1), an extended average method (Non-Patent Document 2), and a Carre method (Non-patent Document). Document 3) is known.

  However, these methods are effective in reducing the influence of errors contained in the known phase shift amount, but cannot cope with the case where the phase shift amount is unknown. However, as an actual problem, for example, an unexpected phase shift is often added to some of the plurality of interference fringe images during measurement due to external sound or vibration. Further, in interferometry using an electron beam (hereinafter referred to as electron beam interferometry), a more serious problem is encountered.

  In the electron beam apparatus, the wavelength of electrons is 1 that is approximately 200,000 times the wavelength of light, so that measurement with extremely high resolution and accuracy is possible, but on the other hand, the mechanical and electrical instability factors of the apparatus are large. The time that can be observed and measured under exactly the same conditions is limited to about 1 minute. Usually, the exposure time when taking a picture with an electron microscope is about 10 seconds is determined by the balance between the stability of the apparatus, the sensitivity of the imaging apparatus, and the amount of information carried by the electron beam. In addition, the electron beam constantly oscillates slightly, but the irradiation direction of the beam easily varies due to disturbances such as an alternating magnetic field generated from an external device, for example, a surrounding device or a variation in power supply voltage.

  In electron beam interference, an electron biprism is often used as an interference element, and the method of controlling the relative phase difference between the reference wave and the object wave is to control the tilt of the electron beam that illuminates the sample to be measured. And a method of shifting the electron biprism in a direction orthogonal to both the electron beam and the optical axis are known. In either method, the distance between the interference fringes is determined by the inclination of the two electron beams superimposed after being divided into two and the focal position when the sample to be measured is imaged. The positional relationship in the image plane is determined by the irradiation direction of the electron beam.

  Therefore, the interval and direction of the interference fringes and the positional relationship between the interference fringes and the sample are easily changed by adjusting the brightness of the image and focusing. Thus, in the case of electron beam interference, it is difficult to control the phase shift amount with high accuracy compared to general optical interference such as laser.

  Even in electron beam interferometry, it is necessary to obtain calibration data prior to measurement. However, even if a plurality of interference fringe images are obtained while phase shifting using the calibration data, each interference fringe is obtained for the reasons described above. The amount of phase shift of the image is much inaccurate compared to laser interference.

Conventional Correction Method In the case of electron beam interference, a countermeasure when the phase shift amount is unknown has been taken (Non-Patent Document 4). In this method, first, about 100 or more interference fringe images are acquired and converted into phase information using a Fourier transform method. Thereby, the real part and the imaginary part of the phase term of each point in the interference fringe image are obtained. The real part and the imaginary part correspond to the denominator and numerator in the right parenthesis of the equation (44), respectively.

Next, select a point in the image that is common to all interference fringe images and plot the values of the real part and imaginary part on the complex plane, or select an area and average the values of the real part and imaginary part When the values are plotted on the complex plane, they are distributed in a circle. Since the obtained real part and imaginary part naturally contain an error, they are distributed with variation on the circle. Therefore, for example, the least square method is used to determine a circle with the least error. The rotation angle obtained by plotting the position of each interference fringe image plotted on the circle from the x-axis direction of the circle is the initial phase of the interference fringe image, that is, the phase shift amount when the interference fringe image is acquired. By using the initial phase of each interference fringe image determined in this way as the phase term of X _m and Y _{m in} the equation (46), the phase distribution in the field of view can be obtained by the phase shift method.

However, this method is logical in that the initial phase of each interference fringe image is determined using the Fourier transform method, which is disadvantageous in terms of measurement accuracy, and the initial phase is used in the phase shift method to obtain a more accurate phase distribution. It is based on contradiction. In order to determine a circle with high accuracy, it is necessary to Fourier transform many interference fringe images. The error of the initial phase of each interference fringe image obtained by Fourier transform is determined by the basic phase shift method. This corresponds to an error in the amount of phase shift when acquiring. Although it is difficult to comprehensively evaluate the influence of this phase shift error on the phase measurement result of the phase shift method, as an example, in our simulation, the phase shift is ± 1.
When there is a variation of / 50 wavelength, the measured phase has a result of having an uncertainty of about ± 1/100 wavelength. As far as evaluation is made based on this result, this method requires a large number of interference fringe images and enormous calculation, but the error is reduced to about half.

  In addition, by using Fourier transform of each interference fringe image, the data of only one point or a part of the region in which the phase can be considered constant is obtained, although the phase distribution of the entire screen is obtained. Since most of the remaining data is not used, it is a method that cannot be said to be highly efficient.

In order to solve the above problems, the phase measurement device according to the present invention is:
An interference element that forms an interference fringe by superimposing a first coherent beam that has passed through the measurement target portion and a second coherent beam that has passed through other than the measurement target portion;
An optical system that images the interference fringes formed by the interference element on the imaging surface of the imaging element;
A phase control mechanism that varies a relative phase difference between the first coherent beam and the second coherent beam;
A calculation unit that calculates the phase of a coherent beam that has passed through the measurement target part, and
The calculation unit includes:
In a predetermined region where the refractive index and thickness in the sample to be measured can be considered uniform so that two-dimensional positions are common in a plurality of interference fringe images having different relative phase differences imaged by the imaging device. Select a straight line to cross and a selection point on the straight line,
For each interference fringe image, determine the intensity distribution curve of the interference fringe on the straight line, determine the initial phase that is the phase difference from the feature point of the intensity distribution curve to the selected point,
The phase of the measurement target portion is calculated based on the initial phase.

Furthermore, in the phase measurement device according to the present invention,
The coherent beam is a laser beam;
The interference element is a combination of a reflecting mirror and a semi-transmissive mirror,
The phase control mechanism mechanically finely moves at least one of a reflecting mirror or a semi-transmissive mirror.

Furthermore, in the phase measurement device according to the present invention,
The coherent beam is a laser beam;
The interference element is a Fresnel biprism,
The phase control mechanism mechanically finely moves the Fresnel biprism.

Furthermore, in the phase measurement device according to the present invention,
The coherent beam is an electron beam;
The interference element is an electron biprism,
The phase control mechanism mechanically finely moves the electron beam by-by prism.

The phase measurement program according to the present invention is
The first coherent beam that has passed through the measurement target portion and the second coherent beam that has passed through the portion other than the measurement target portion are superimposed, and the relative relationship between the first coherent beam and the second coherent beam is determined. In a phase measurement program that can be executed by a computer that calculates the phase of a coherent beam that has passed through the measurement target portion, based on a plurality of interference fringe images that are captured with a variable phase difference,
A straight line crossing a predetermined region in which the refractive index and thickness in the sample to be measured can be regarded as uniform so that two-dimensional positions are common in the plurality of interference fringe images having different relative phase differences. A process of selecting a selected point on the straight line;
For each interference fringe image, a process for determining an intensity distribution curve of the interference fringe on the straight line and determining an initial phase that is a phase difference from the selected point to a feature point of the intensity distribution curve;
And a process of calculating a phase of the measurement target portion based on the initial phase.

Moreover, the phase measurement method according to the present invention includes:
The first coherent beam that has passed through the measurement target portion and the second coherent beam that has passed through the portion other than the measurement target portion are superimposed, and the relative relationship between the first coherent beam and the second coherent beam is determined. In a phase measurement method for calculating the phase of a coherent beam that has passed through the measurement target portion, based on a plurality of interference fringe images picked up by varying a typical phase difference,
A straight line crossing a predetermined region in which the refractive index and thickness in the sample to be measured can be regarded as uniform so that two-dimensional positions are common in the plurality of interference fringe images having different relative phase differences. , Select the selected point on the straight line,
For each interference fringe image, determine the intensity distribution curve of the interference fringe on the straight line, determine the initial phase that is the phase difference from the feature point of the intensity distribution curve to the selected point,
The phase of the measurement target portion is calculated based on the initial phase.

  As described above, according to the present invention, the initial phase (the phase difference from the feature point of the intensity distribution curve to the selected point on the straight line) is determined using a predetermined region in which the refractive index and thickness in the sample to be measured can be regarded as uniform. Thus, there is no need to acquire the initial phase at the time of measurement, and no measurement error occurs when acquiring the initial phase.

  In addition, although it is conceivable to determine the initial phase by the conventional Fourier transform, when using the Fourier transform, a huge amount of calculation is required, and in order to improve accuracy, a large number of interference fringe images are required. Will be needed. On the other hand, in the present invention, since the phase difference from the feature point to the selected point of the intensity distribution curve in the predetermined area of one interference fringe image is determined as the initial phase, the number of data in the predetermined area is sufficiently large. Therefore, it is easy to obtain the accuracy of the least square method when determining the initial phase of one point. Therefore, it is possible to reduce the number of acquired interference fringe images.

  Furthermore, the conventional method is easily affected by the external environment such as the brightness of the interference fringe image changing while acquiring a large number of images, and it is difficult to obtain sufficient accuracy. However, in the method of the present invention, since the number of interference fringe images is much smaller in the first place, it is possible to reduce the acquisition time of interference fringe images and suppress the influence due to fluctuations in the external environment. In addition, since the initial phase is determined from the feature point to the selected point of the intensity distribution curve in the predetermined area, even if the brightness changes for each interference fringe image, the accuracy of the initial phase determination may be affected. Absent. In addition, when there is an amplitude distribution in a predetermined region due to illumination unevenness, it affects the determination of the intensity distribution curve, but the influence is constant for each interference fringe image, so the influence on the initial phase is very small.

Diagram for explaining light traveling in media with different refractive indices The figure which shows the coordinate system for explaining the interference of the object wave and the reference wave The figure which shows the interference fringe image of the sample to be measured including the part to be measured Schematic diagram showing the measurement principle of the phase shift method Schematic diagram showing carrier interference fringes after Fourier transform Schematic diagram for explaining a phase measurement method according to an embodiment of the present invention Schematic diagram for explaining a phase measurement method according to an embodiment of the present invention Schematic diagram showing a phase measurement device (amplitude division division type) according to an embodiment of the present invention The schematic diagram which shows the phase measuring device (wavefront division | segmentation system) which concerns on embodiment of this invention The figure which shows the main flow which concerns on embodiment of this invention The flowchart which shows the imaging process which concerns on embodiment of this invention The flowchart which shows the initial phase determination process which concerns on embodiment of this invention The flowchart which shows the redetermination process which concerns on embodiment of this invention The flowchart which shows the phase change calculation process by the sample which concerns on embodiment of this invention The flowchart which shows the beam inclination correction process which concerns on embodiment of this invention.

  In the present invention, it is assumed that a sample to be measured having a predetermined region in which the phase of the object wave is constant for one period of interference fringes in the field of view is used. FIG. 6 is a diagram showing an interference fringe image when such a sample to be measured is measured. In this case, in the interference fringe image, an elliptical interference fringe due to the measurement target portion is formed in the center. In the present embodiment, the space around the measurement target portion is a base material having a uniform space or refractive index. In this base material, the portion surrounded by the lower right square is a portion (predetermined region) where the phase of the object wave can be regarded as constant. In the present embodiment, in the interference fringe image, the region other than the measurement target portion is set to a predetermined region where the refractive index and the thickness can be regarded as uniform. When the physical property value of itself can be regarded as uniform, a predetermined region may be set in the measurement target portion.

Such a predetermined region is selected so that the positions of the plurality of interference fringe images are the same, and the initial phase of each interference fringe image is determined. In the lower right of FIG. 6, this predetermined area is extracted and enlarged. In the figure, a point (x ₀ , y ₀ ) indicated by a circle is a selection point selected in common in a predetermined area of each interference fringe image, and the initial position of each interference fringe image at the position of this selection point. Determine the phase.

For this purpose, first, a straight line L passing through the selected point is arbitrarily selected, and the brightness of the image is plotted along the straight line L. The straight line L does not necessarily have to be on a single straight line, and may be a plurality of parallel straight line groups in a predetermined region or a straight line L obtained by averaging them. If a straight line is taken along the x-axis for simplicity, the brightness on the straight line passing through the point (x ₀ , y ₀ ) when a phase shift of δm is given to the m-th interference fringe image is (17) Given by the formula,
I _m (x, y ₀ ) = | Ao (x, y ₀ ) | ² + | Ar (x, y ₀ ) | ²
+2 | Ao (x, y ₀ ) || Ar (x, y ₀ ) | cos [φ (x, y ₀ ) + kxsinθ + δ _m ] (62)
It becomes. Incidentally, the relationship between the beam wavelength λ and the tilt angle θ and the resulting interference fringe spacing d is
dsinθ = λ (63)
Kxsinθ can also be written as 2πx / d.

Since the phase distribution φ (x, y) due to the sample to be measured is constant within this predetermined region, the value is set to φ ₀ and the intensity distribution of the beam on this straight line is simplified according to equation (18). As
Im (x, y ₀ ) = B (x, y ₀ ) + A (x, y ₀ ) cos [φ ₀ + 2πx / d + δ _m ] (64)
It can be expressed as. B (x, y ₀ ) and A (x, y ₀ ) are ideally constant amounts, but in practice there are intensity distributions due to the beam source, signal noise of the image sensor, etc. The resulting curve is a sinusoidal curve with some variation. Therefore, by determining the interference fringe distribution curve based on the change of the intensity Im (x, y ₀ ) with respect to the position x on the horizontal axis using, for example, the method of least squares, B (x, y ₀ ), A ( x, y ₀ ), d and φ ₀ + δm can be determined. In the present embodiment, the interference fringe distribution curve is fitted using a cos (cosine) curve.

The parameters thus obtained are used in equation (62) to select the selected point (x ₀ ,
y ₀ ) corresponds to the feature point of the interference fringe distribution curve (in this embodiment, the point of zero phase of the cosine (cosine) curve (corresponding to the peak of the curve)), and corresponds to the position in radians measured from there. In other words, by obtaining δ ₁ shown in the figure, the initial phase of the m-th interference fringe image can be determined. In general, the initial phase thus obtained has an absolute value different from the initial phase given when the interference fringe image is actually acquired. However, since the phase is an angle measured from the reference location, and the reference itself is an amount that can be used anywhere, if the initial phase of each interference fringe image is measured from a reference common to all interference fringe images. There is no problem. That is, since the important amount is the amount of phase shift between the interference fringe images, the initial phase determined by this method may be used as the initial phase in the measurement target portion.

When one optical path of the two beams of the interferometer is changed, the interference fringes also move in the beam traveling direction, but when observed in a plane perpendicular to the beam traveling direction, the interference fringes are lateral to the sample image. Move to. This is, for example, the phase portion inside cos in the second term on the right side of equation (62), where φ ₀ is originally a phase delay in the z direction that is the beam traveling direction, and δ _m is also a phase advance / delay in the z direction. However, in this equation, since it is included in a form that is not related to x and y, it corresponds to being completely equivalent even if it is regarded as an advance / delay in the x direction. FIG. 7 shows how the initial phases are obtained from a plurality of interference fringe images.

As described above, the interference fringes are shifted to the right as the selected point (x ₀ , y ₀ ) is focused on. Therefore, the phase of this point changes as δ ₁ , δ ₂ ,... As shown in FIG. This method of determining the phase of one point is a modification of the principle of the phase shift method, but is logically equivalent.

The initial phase [delta] ₁ of the first sheet of the interference fringe image is arbitrariness, [delta] ₂ with respect to the [delta] ₁ makes sense on measurement of whether [delta] ₃ · · · is shifted much, between the initial phase value Is the difference. Therefore, if the region and one point in the region are selected in common for all interference fringe images, and if the physical property value inside the sample is a uniform region, the position itself in the interference fringe image itself Is completely arbitrary.

  When the phase measurement method according to the present embodiment is compared with the phase shift method using the initial phase determined by the conventional Fourier transform method, there are the following advantages and disadvantages.

  First, the disadvantage is that a predetermined region having uniform physical properties such as refractive index and thickness is required. In general, however, this is not a significant drawback. For example, when measuring an optical element in the optical field, an optical fiber, an optical waveguide, or the like forms a high refractive index portion in a uniform base material, and the function is realized by light passing through this portion. In the case of a single optical element, the surrounding area is a space. In either case, the refractive index of the base material or space around the measurement target part is often uniform. A uniform part may not be selected in the case of a film, but for example, it is possible to select a peripheral part, or to provide a region through which a space is transmitted in a visual field by making a hole in a part. Also, in the case of electron beam interference using an electron beam as a coherent beam, there are rather many samples with free space around them, such as extremely small particle samples and thin film samples. There is often no problem in choosing a uniform location.

On the other hand, first, it is possible to reduce the number of interference fringe images required first. In a conventional method for determining an initial phase by Fourier transform, first, a phase distribution is obtained from each interference fringe image, and an initial phase of each interference fringe image is obtained from an average value of one point or a region having the same phase. That is, the phase is obtained by a method that requires a huge amount of calculation called Fourier transform, but most of the phase is not used. Further, since the phase of each interference fringe image is determined from limited information, a large number of interference fringe images are required to determine the phase distribution circle on which the phase is plotted with high accuracy.

  On the other hand, in this method, since the phase difference from the feature point of the intensity distribution curve of the predetermined region of one interference fringe image to the selected point is determined as the initial phase, the number of data in the predetermined region is sufficiently large. Therefore, it is easy to obtain the accuracy of the least square method when determining the initial phase of one point. This means that the number of interference fringe images can be reduced.

  Furthermore, in the conventional method, if the brightness of the interference fringe image changes while acquiring a large number of images, the brightness is the radius of the circle plotted on the complex plane, resulting in data dispersion and accuracy. It's hard to be done. In particular, in the case of electron beam interference, it is difficult to maintain an interference fringe image having a constant brightness and interval for several minutes or more. However, in the method of the present invention, the number of interference fringe images is much smaller in the first place, and since the initial phase is determined from the feature point of the intensity distribution curve in the predetermined region to the selected point, the brightness of each interference fringe image is determined. However, even if the amplitude of the intensity distribution curve changes, the accuracy of the initial phase determination is not affected. In addition, if there is an amplitude distribution within a predetermined area due to illumination unevenness, it affects the determination of the intensity distribution curve, but the influence is constant for each interference fringe image, so the influence on the initial phase is very small. .

  Furthermore, in the method according to the present invention, it is not necessary to acquire the initial phase of each interference fringe image from the measurement device at the time of measurement. The initial phase can be acquired from the control state of the means for changing the phase in the measurement device at the time of capturing the interference fringe image, but in the present invention, it is not necessary to acquire the initial phase. Measurement error does not occur during phase acquisition.

  Since the present invention has a feature in a processing method for an acquired interference fringe image, it can be applied to various phase measurement apparatuses that acquire an interference fringe image. FIG. 8 shows an embodiment using a Maha-Zehnder interferometer.

  The coherent beam emitted from the coherent beam source 1 is divided into two paths by the first beam splitter 31, and one of the beams interferes with the sample S to be measured through the first reflecting mirror 32 to the second beam splitter 34. It reaches. On the other hand, the other beam passes through the second reflecting mirror 33 and reaches the second beam splitter 34. In general, the former is called an object wave, and the latter is called a reference wave. The object wave is a first coherent beam that has passed through the measurement sample S including the measurement target portion, and the reference wave is a second coherent beam that the measurement sample S has passed through other than the measurement target portion. It is equivalent. In the second beam splitter 34, part of the object wave is reflected and partly transmitted, and part of the reference wave is reflected and partly transmitted. In the figure, only the object wave transmitted through the second beam splitter 34 and the reference wave reflected by the second beam splitter 34 are depicted.

  The imaging lens 4 functions to form a transmission image of the sample S to be measured on the imaging surface of the imaging device 5. Therefore, on the imaging surface of the imaging device 5, the object wave whose phase has changed due to the sample S to be measured interferes with the reference wave, and an interference fringe image composed of interference fringe groups whose intervals and directions have changed in accordance with the phase change. Is formed. This type of interferometer is called the “amplitude division” method because it splits the coherent beam into two in terms of intensity.

When the present invention is applied to this type of interferometer, as shown in FIG. 8, the second reflecting mirror 33 (which may be the first reflecting mirror 32) is controlled by a fine movement unit 6 (in the present invention). "Phase control mechanism"). The first interference fringe image is captured from the imaging device 5 into a computer (not shown) (“calculation unit” in the present invention), and then the fine movement unit 6 is controlled to slightly change the optical path length of the reference wave. The interference fringe image is captured. In the second interference fringe image, there is no change in the object wave, but the reference wave has a phase state when it interferes with the object wave, that is, the position in the traveling direction of the peak / valley of the wave due to the change in the optical path length. Since it is changing, the bright and dark positions of the interference fringes are different from those of the first interference fringe image. Similarly, if three or more interference fringe images are captured one after another, the initial phase of each interference fringe image can be determined by the method described in the principle section. Phase distribution, that is, the phase distribution of the irradiation beam changed depending on the measurement target portion in the sample S to be measured.

  Here, the coherent beam may be an electromagnetic wave such as a laser or an X-ray, or a so-called particle beam such as an electron beam. For the beam splitters 31 and 34, a semi-transparent mirror is exclusively used in the case of light, but a diffraction grating, a crystal, or the like is used for electron beams and X-rays, and the divisions do not have to be orthogonal to each other. Depending on the interference condition, the second beam splitter 34 may be omitted.

  FIG. 9 shows a phase measurement apparatus according to another embodiment of the present invention. In this embodiment, the coherent beam is divided into two parts in a region, which is called a “wavefront division” method. The coherent beam emitted from the coherent beam source 1 is focused once by the first lens 81 or forms a beam that diverges from the virtual focal point, and the second lens 82 having a front focal point at the focal position has a diameter. Is converted into a large beam. The sample S to be measured is placed on one side of the path of the coherent beam, and the coherent beam (object wave) transmitted through the sample to be measured S forms an image on the imaging surface of the imaging device 5 by the imaging lens 4.

  A beam splitter 3 mounted on the fine movement unit 6 is placed between the imaging lens 4 and the imaging device 5. The beam splitter 3 uses a triangular prism-shaped glass prism (called a Fresnel biprism) having a cross section as shown in the figure for an optical interferometer, and an electron biprism that performs the same function in electron beam interference. A so-called interference element is used. The object wave (light shown in gray) that has passed through the measurement sample S passes through the left side of the beam splitter 3 and is deflected to the optical axis side by the law of refraction.

  On the other hand, the reference wave passing through the side without the sample S to be measured passes through the right side of the beam splitter 3 and is deflected to the optical axis side according to the law of refraction. As a result, the object wave and the reference wave are overlapped with a certain angle, and an image is formed of interference fringes having an interval and a direction according to the phase distribution in the object wave. In this phase measuring apparatus, when the beam splitter 3 is finely moved in the horizontal direction in the figure by the fine movement unit 6, the optical path lengths of the object wave and the reference wave are changed. For example, when finely moving to the right in the figure, the phase is delayed because the reference wave passes through the thicker part of the biprism, and the phase advances because the object wave passes through the thinner part of the biprism.

  On the other hand, since the prism angle is constant, the deflection angle of the beam forming the image is also constant and the image of the sample S to be measured does not move. That is, the image of the sample to be measured does not change, but the positions of the peaks and valleys of the object wave and the reference wave have changed, so the light and dark positions of the interference fringes also change. Therefore, every time the beam splitter 3 is finely moved, an interference fringe image is taken into a computer (not shown) (“calculation unit” in the present invention) via the imaging device 5, thereby repeating a plurality of interference conditions. An interference fringe image can be obtained. In this way, the initial phase of each interference fringe image can be determined by the method described in the section of the principle, and the phase distribution of the irradiation beam changed depending on the measurement target portion in the sample S to be measured can be obtained.

  In this figure, for the sake of explanation, the magnifying lens may be inserted between the beam splitter 3 and the imaging device 5 when the imaging lens 4 is composed of a plurality of lenses. is there. It is also possible to realize this interferometer format with X-rays and electron beams.

The specific example of the phase measurement device according to the present invention has been described above using the two embodiments. The interference fringe image captured by the imaging device 5 of such a phase measurement device is captured by a computer (computer). For each interference fringe image, the initial phase is determined by determining the intensity distribution curve as described with reference to FIGS. The initial phase determined for each interference fringe image is used to calculate the phase of the measurement target portion in each interference fringe image. Note that such arithmetic processing is executed by a program stored in a computer (computer), but a program for calculating the phase of the measurement target portion ("phase measurement program" in the present invention), or A storage medium that stores a program for calculating the phase of the measurement target portion also falls within the scope of the present invention.

  Now, processing executed by the phase measurement device (phase measurement program) according to the embodiment of the present invention will be described. FIG. 10 is a diagram showing a main flow. The main flow of this embodiment is described as a series of processes from imaging of an interference fringe image to calculating a target physical quantity such as the thickness or refractive index of the sample to be measured, but these are independently performed as individual processes. It may be done. Specifically, it may be executed by a plurality of programs in charge of each process.

  This main flow includes an imaging process (S100) for acquiring an interference fringe image using the phase measurement device as described in FIGS. 8 and 9, an initial phase determination process (S200) for determining an initial phase, and an acquired interference fringe. Phase change calculation process (S300) for calculating the phase change in the image (sample), phase continuation process (S400), beam tilt correction process (S500) for correcting the tilt of the interfered beam, sample thickness or refraction The target physical quantity calculation process (S600) for obtaining the target quantity such as the rate is included. These processes will be described in order.

  FIG. 11 is a flowchart showing the imaging process according to the embodiment of the present invention. The imaging process is a process of acquiring an interference fringe image using a beam that has passed through the sample imaged by the imaging device 5 in FIGS. 8 and 9 and a beam that has not passed through the sample. When the optical conditions in the phase measuring device are significantly changed, the interference fringe image on the operation of the phase control mechanism (“fine movement part 6” in FIG. 8 and FIG. 9 corresponds to this) is executed before the execution of the imaging process. It is preferable to investigate the approximate relationship of the amount of fine movement of the interference fringes. Specifically, the relationship between the operation amount of the phase control mechanism required for the interference fringe to move by one interval, for example, the voltage and current applied to the phase control mechanism, is roughly grasped.

In the phase measurement apparatus measuring conditions are in place, to perform imaging of M pieces of interference fringe image P _m to m = 1~M (S102). In each interference fringe image, the interference condition, that is, the initial phase is changed by the phase control mechanism (S103). In the case of FIGS. 8 and 9, the interference condition for each imaging is changed by vibrating the optical element by the fine movement unit 6. The acquisition of the interference fringe image is repeatedly executed until the number of picked-up images m = M. The number of images M needs to be three or more with different operation amounts of the phase control mechanism, but it is not necessary to know the numerical operation amount of the phase control mechanism for each acquired interference fringe image. The numerical operation amount of the phase control mechanism between the interference fringe images does not need to be equal. However, for more accurate measurement, it is advantageous that the number of interference fringe images is large at approximately equal intervals.

  FIG. 12 is a flowchart showing the initial phase determination process according to the embodiment of the present invention. In the initial phase determination process, first, a predetermined region in which the phase change can be regarded as uniform is determined in the interference fringe image (S201). In a sample to be measured such as an optical fiber, a region filled with the same material, such as a clad or a core portion, can be selected as a predetermined region. Or it is good also considering the area | region where a measurement object part does not exist in an interference fringe image as this predetermined area | region. The predetermined region is selected so that the coordinates coincide in any interference fringe image among the plurality of acquired interference fringe images. That is, the predetermined area is always at the same position in the sample to be measured.

  A wider predetermined area is advantageous in terms of accuracy, but has the disadvantage of increasing the amount of calculation. Most simply, the initial phase can be determined by selecting a predetermined region within a range of about 1 pixel in the vertical direction and about 1 wavelength of the horizontal interference fringes. The predetermined area may be a rectangular area having a plurality of pixels vertically and horizontally, but generally the phase is shifted in the vertical direction (interference fringes are not necessarily parallel to the left and right sides of the rectangular area), so the calculation process is a little complicated. It becomes.

In S203 to S206, for each interference fringe image P _m, the line passing through a predetermined point in a given area determined in S201 (selection point), fitting using the intensity distribution curve (sine curve or cosine curve) (S205 ) Is executed. When a sine curve is used, B _m , A _m , λ _m , and φ _m are determined by fitting to equation (65) (equation (66) in the case of a cosine curve).
y = B _m + A _m sin (2πx / λ _m + φ _m ) (65)
y = B _m + A _m cos (2πx / λ _m + φ _m ) (66)
Where B _m is the brightness of the interference fringe base, A _m is the amplitude of the interference fringe, λ _m is the wavelength of the interference fringe period, φ _m is the initial phase of the interference fringe, and x is a straight line passing through the selected point. Is the position.

A selection point that is a predetermined point in the predetermined region can be selected at an arbitrary position as long as it is a common position in each interference fringe image. For example, it can be the left or right end point in the selection area, or can be the midpoint in the selection area. Alternatively, it may be x where the second term becomes zero in the equation y = B ₁ + A ₁ sin (2πx / λ ₁ + φ ₁ ) of the fitting curve performed on the first interference fringe image.

In addition, the initial phase φ _m in the present embodiment is a phase from a position where the phase of the sine curve (or cosine curve) at the selected point is zero (“feature point” in the present invention). The feature point in the intensity distribution curve can be arbitrarily selected as long as it has a predetermined phase position (such as a peak at a mountain or a valley) in the intensity distribution curve.

B _m , A _m , λ _m , and φ _m are calculated for each interference fringe image P _{1 to} P _m by repeatedly executing the processing of S 203 to S 206 for all the interference fringe images P _{1 to} P _m . Calculated B _m ,
When variation in A _m and λ _m is small between the interference fringe images (S209: Yes), the initial phase φ _m for each interference fringe image calculated in S206 is used for each interference fringe image. (S210). On the other hand, when the calculated B _m , A _m , and λ _m vary greatly between the interference fringe images (S209: No), the re-determination process S220 is executed, and the plausible B _m , A _m , and λ _m are determined. Calculated.

In fitting to an intensity distribution curve such as a sine curve, a predetermined region where the refractive index and thickness are considered to be uniform is selected. Therefore, B _m , A _m , and λ _m in the intensity distribution curve are common and only φ _m is different. Is expected. However, when B _m , A _m , and λ _m fluctuate due to fluctuations in the intensity of the light source (coherent beam source 1) and disturbance factors such as vibration, that is, variations occur in B _m , A _m , and λ _m. End up. In such a case, the re-determination process S220 averages B _m , A _m , and λ _m of the intensity distribution curve of each interference fringe image, so that the likely B _AV , A _AV , and λ _{AV are obtained.}
Seeking. As averaging, a simple averaging or a method using a least square method can be employed.

In this redetermination process, first, B _m , A _m , and λ _m of each interference fringe image calculated in S206 are averaged to obtain average values B _AV , A _AV , and λ _AV (S221). In S223, using the obtained average values B _AV , A _AV , and λ _AV , an initial phase φ _m satisfying the expression (67) is calculated for each interference fringe image. That is, the waveform having B _m , A _m , and λ _m is moved and adopted as the initial phase φ _{m at the} position that best fits the interference fringes.
y = B _AV + A _AV sin (2πx / λ _AV + φ _m ) (67)
The initial phase φ _m calculated in S220 is determined to be used for each interference fringe image in the initial phase determination process of FIG. 12 (S210).

FIG. 14 is a flowchart showing phase change calculation processing by a sample according to the embodiment of the present invention.
In this process, the phase value for each pixel constituting each interference fringe image is calculated using the initial phase φ _m for each interference fringe image determined in the initial phase determination process of FIG. S303). Specifically, by applying the initial phase φ _m corresponding to each interference fringe image P _m (the subscript m is common) instead of (2πm / M) in the equations (46) to (48), the interference fringes are obtained. A phase value at each pixel in the image is calculated.

  The phase value in the interference fringe image calculated in S300 may cause a phase jump between adjacent pixels. In S400, a phase continuation process for correcting the interference fringe phase values so as to be continuous is executed. The pixels distributed in the horizontal direction and the vertical direction in each interference fringe image are distributed in a state where the phase values are discretized from −π to + π. However, when a phase jump as described above occurs, there is discontinuity between adjacent phase values. Therefore, in the phase continuation process (S400), for example, in the horizontal direction, sequentially compared with the next value in the horizontal direction of the screen, and when the difference is a certain amount or more, it is determined that the phase jump is 2π. If you are flying down, add 2π. If you are flying up, add 2π to make it continuous. Similarly, the vertical direction is continuous as compared with the lower value. If the interference fringes in the interference fringe image are substantially parallel to the vertical direction of the screen (specifically, the interference fringes do not cross the left and right edges of the screen), the vertical direction need not be continuous. Similarly, when the interference fringes are substantially parallel to the horizontal direction of the screen, the horizontal direction is not required to be continuous.

  In this embodiment, a beam tilt correction process (S500) is performed to correct the beam tilt from a further continuous phase distribution. Since the calculated phase value at each pixel includes a phase component due to the inclination of the two beams, the inclination is removed. In the data actually obtained, the phase component of the measurement target region of the sample is superimposed on the slope of the phase inclined in the vertical and horizontal directions of the screen. Therefore, in this beam inclination correction process, the phase component due to the inclination of the two beams (object wave and reference wave) to be used is removed. As a method for this correction, when the inclination can be calculated accurately from the experimental conditions, it may be used. However, in general, the vertical and horizontal inclinations are obtained from the measurement result and corrected. Specifically, in S501 and S502, beam tilts in the x and y directions are calculated, respectively, and the tilt correction of the phase change by the sample is executed using these (S503).

The phase calculation according to the embodiment of the present invention, that is, the calculation of the phase distribution in the measurement target portion has been described above. By using the phase distribution of the measurement target portion calculated in this way, the physical quantity (target physical quantity) of the phase measurement target portion can be obtained. In the target physical quantity calculation process (S600) for calculating the target physical quantity, the inclination-corrected phase distribution is converted into a physical quantity to be obtained. When the thickness of the used sample can be regarded as constant or substantially constant, the refractive index distribution in the measurement target portion can be calculated as the target physical quantity. In this case, from the phase value in each pixel, the thickness of the sample, and the refractive index of the reference portion, the equation (6) can be obtained using the equation (68) expressed in radians.
φ (x, y) = 2π (n (x, y)-n ₀ ) t / λ ₀ ... (
68)
On the other hand, when the refractive index of the used sample can be regarded as uniform or substantially uniform, the thickness distribution in the measurement target portion can be obtained using equation (69) obtained by modifying equation (68).
φ (x, y) = 2π (t (x, y)-t ₀ ) n / λ ₀ ... (
69)

As described above, the target physical quantity calculation processing (S60) from the imaging processing (S100) according to the embodiment of the present invention.
In the present invention (phase measurement device, phase measurement method, or phase measurement program), the initial phase determination process (S200) and the sample-based phase change calculation process (S300) (redetermination process) during these processes are described. It is necessary to execute at least.

  Note that the present invention is not limited to these embodiments, and embodiments configured by appropriately combining the configurations of the respective embodiments also fall within the scope of the present invention.

DESCRIPTION OF SYMBOLS 1 ... Coherent beam source, 3 ... Beam splitter, 31 ... 1st beam splitter, 32 ... 1st reflective mirror, 33 ... 2nd reflective mirror, 34 ... 2nd beam splitter, 4 ... Imaging lens, DESCRIPTION OF SYMBOLS 5 ... Image sensor, 6 ... Fine movement part, 81 ... 1st lens, 82 ... 2nd lens, S ... Sample to be measured

Claims (6)

An interference element that forms an interference fringe by superimposing a first coherent beam that has passed through the measurement target portion and a second coherent beam that has passed through other than the measurement target portion;
An optical system that images the interference fringes formed by the interference element on the imaging surface of the imaging element;
A phase control mechanism that varies a relative phase difference between the first coherent beam and the second coherent beam;
A calculation unit that calculates the phase of a coherent beam that has passed through the measurement target part, and
The calculation unit includes:
In a predetermined region where the refractive index and thickness in the sample to be measured can be considered uniform so that two-dimensional positions are common in a plurality of interference fringe images having different relative phase differences imaged by the imaging device. Select a straight line to cross and a selection point on the straight line,
For each interference fringe image, determine the intensity distribution curve of the interference fringe on the straight line, determine the initial phase that is the phase difference from the feature point of the intensity distribution curve to the selected point,
A phase measurement device that calculates the phase of the measurement target portion based on the initial phase. The coherent beam is a laser beam;
The interference element is a combination of a reflecting mirror and a semi-transmissive mirror,
The phase measurement device according to claim 1, wherein the phase control mechanism mechanically finely moves at least one of a reflection mirror or a semi-transmission mirror. The coherent beam is a laser beam;
The interference element is a Fresnel biprism,
The phase measurement device according to claim 1, wherein the phase control mechanism mechanically finely moves the Fresnel biprism. The coherent beam is an electron beam;
The interference element is an electron biprism,
The phase measurement device according to claim 1, wherein the phase control mechanism mechanically finely moves the electron beam by-by prism. The first coherent beam that has passed through the measurement target portion and the second coherent beam that has passed through the portion other than the measurement target portion are superimposed, and the relative relationship between the first coherent beam and the second coherent beam is determined. In a phase measurement program that can be executed by a computer that calculates the phase of a coherent beam that has passed through the measurement target portion, based on a plurality of interference fringe images that are captured with a variable phase difference,
A straight line crossing a predetermined region in which the refractive index and thickness in the sample to be measured can be regarded as uniform so that two-dimensional positions are common in the plurality of interference fringe images having different relative phase differences. A process of selecting a selected point on the straight line;
For each interference fringe image, a process for determining an intensity distribution curve of the interference fringe on the straight line and determining an initial phase that is a phase difference from a feature point of the intensity distribution curve to the selected point;
And a process of calculating a phase of the measurement target portion based on the initial phase. The first coherent beam that has passed through the measurement target portion and the second coherent beam that has passed through the portion other than the measurement target portion are superimposed, and the relative relationship between the first coherent beam and the second coherent beam is determined. In a phase measurement method for calculating the phase of a coherent beam that has passed through the measurement target portion, based on a plurality of interference fringe images picked up by varying a typical phase difference,
A straight line crossing a predetermined region in which the refractive index and thickness in the sample to be measured can be regarded as uniform so that two-dimensional positions are common in the plurality of interference fringe images having different relative phase differences. , Select the selected point on the straight line,
For each interference fringe image, determine the intensity distribution curve of the interference fringe on the straight line, determine the initial phase that is the phase difference from the feature point of the intensity distribution curve to the selected point,
A phase measurement method, wherein the phase of the measurement target portion is calculated based on the initial phase.

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