JP5169438B2 - Waveform analysis apparatus, computer-executable waveform analysis program, interferometer apparatus, pattern projection shape measurement apparatus, and waveform analysis method - Google Patents

Description

  The present invention relates to a waveform analysis device applied to an interferometer device, a pattern projection shape measurement device, and the like, a computer-executable waveform analysis program, an interferometer device, a pattern projection shape measurement device, and a waveform analysis method.

The fringe analysis processing by the Fourier transform method invented by Takeda et al. Is well known (see Non-Patent Document 1). In order to calculate a fringe phase component from one fringe image measured by an interferometer or the like, an interference fringe on which carriers are superimposed is used for the fringe analysis processing. In the fringe analysis processing, the intensity distribution of the fringe image is Fourier-transformed, a + 1st-order or −1st-order spectrum is extracted from the obtained Fourier spectrum, the spectrum is inversely Fourier-transformed, and the obtained complex amplitude distribution is a predetermined amplitude. It is applied to the arithmetic expression. By subtracting a known carrier component from the calculated phase component, the signal component included in the phase component can be made known.
Mitsuo Takeda et al. "Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry", Journal of the Optical Society of America.Vol. 72, No. 1, January 1982

  However, since the data range of the fringe image, which is actually measured data, is limited, and the data is discontinuous at the fringe edge, the ripple component analysis error is included in the phase component calculated by the fringe analysis process using the Fourier transform method. Are superimposed.

  Accordingly, the present invention provides a waveform analysis apparatus using a Fourier transform method, a computer-executable waveform analysis program, and a waveform analysis method that can reliably suppress ripple-like analysis errors caused by the finiteness of the data range. With the goal. It is another object of the present invention to provide an interferometer device and a pattern projection shape measuring device with high measurement accuracy.

  One aspect of the waveform analysis apparatus of the present invention includes a main analysis unit that calculates each component of an input waveform by performing analysis processing using a Fourier transform method on the input waveform, and each component calculated by the main analysis unit. By means of function fitting using the basic data as a basic data, a model creation means for creating a model waveform with each component known, and the model waveform created by the model creation means is subjected to the same analysis processing as the analysis means to obtain the model waveform. Test analysis means for calculating a specific component of the test waveform, and error calculation means for calculating a difference between the specific component calculated by the test analysis means and the actual specific component of the model waveform as an analysis error for the specific component of the test analysis means And correction means for correcting the specific component calculated by the analysis means based on the analysis error calculated by the error calculation means. To.

  One aspect of the computer-executable waveform analysis program of the present invention includes a main analysis procedure for calculating each component of the input waveform by performing analysis processing using a Fourier transform method on the input waveform, and the main analysis procedure. A model creation procedure for creating a model waveform in which each component is known by function fitting using each calculated component as basic data, and a model waveform created in the model creation procedure is subjected to the same analysis processing as the main analysis procedure. The test analysis procedure for calculating the specific component of the model waveform and the difference between the specific component calculated in the test analysis procedure and the actual specific component of the model waveform are analyzed for the specific component of the test analysis procedure. An error calculation procedure to be calculated as an error, and a specific component calculated in the analysis procedure based on the analysis error calculated in the error calculation procedure Characterized in that it comprises a correction procedure for correcting.

  One aspect of the interferometer apparatus of the present invention is characterized by including any aspect of the waveform analysis apparatus of the present invention.

  One aspect of the projection shape measuring apparatus of the present invention is characterized by including any aspect of the waveform analysis apparatus of the present invention.

One aspect of the waveform analysis method of the present invention includes a main analysis procedure for calculating each component of the input waveform by applying an analysis process using a Fourier transform method to the input waveform, and each of the components calculated in the main analysis procedure. By performing function fitting based on components as basic data, a model creation procedure for creating a model waveform in which each component is known, and applying the same analysis process as the main analysis procedure to the model waveform created in the model creation procedure. A test analysis procedure for calculating a specific component of the model waveform, and a difference between the specific component calculated in the test analysis procedure and an actual specific component of the model waveform is calculated as an analysis error related to the specific component of the test analysis procedure An error calculation procedure and a correction procedure for correcting the specific component calculated in the analysis procedure based on the analysis error calculated in the error calculation procedure. The features.

  According to the present invention, a waveform analysis device using a Fourier transform method, a computer-executable waveform analysis program, and a waveform analysis method that can reliably suppress ripple-like analysis errors caused by the finiteness of a data range and the like are realized. . Further, according to the present invention, an interferometer device and a pattern projection shape measuring device with high measurement accuracy are realized.

[First Embodiment]
Hereinafter, a first embodiment of the present invention will be described. This embodiment is an embodiment of an interferometer apparatus.

  First, the configuration of the interferometer apparatus will be described. FIG. 1 is a schematic configuration diagram of the interferometer apparatus of the present embodiment.

  As shown in FIG. 1, the interferometer apparatus includes a laser light source 1, a beam expander 2, a polarizing beam splitter 3, a quarter wavelength plate 4, a Fizeau plate 5, a wavefront conversion lens 6, a beam diameter conversion optical system 8, A dimensional image detector 9 is provided. Although not shown, the interferometer apparatus is also provided with a computer. The measurement object 7 set in the interferometer device is an optical element such as an aspherical mirror or an aspherical lens, and is supported by a stage (not shown). The shape of the measurement target surface 7a of the measurement target 7 is basically smooth.

  Among these, the laser light source 1 emits a linearly polarized light beam L. The beam L expands its diameter by passing through the beam expander 2. The light beam L having an enlarged diameter enters the polarization beam splitter 3 and is reflected by the polarization separation surface 3 a of the polarization beam splitter 3. The polarization plane of the light beam L is selected in advance so as to be reflected by the polarization separation plane 3a. When the light beam L reflected by the polarization separation surface 3a enters the Fizeau surface 5a of the Fizeau plate 5 through the quarter-wave plate 4, the light beam LM passes through the Fizeau surface 5a and the light beam LR reflects the Fizeau surface 5a. To be separated. Hereinafter, the light beam LM is referred to as “measurement light beam LM”, and the light beam LR is referred to as “reference light beam LR”.

  Here, although the light beam L that has passed through the beam expander 2 has some intensity unevenness, the intensity distribution of the cross section thereof is basically smooth, and the intensity distribution of the cross section of the measurement light beam LM, the reference light beam LR The cross-sectional intensity distribution is also smooth.

  The measurement light beam LM becomes a null wavefront by passing through the wavefront conversion lens 6. The measurement light beam LM enters the measurement target surface 7a of the measurement target 7 substantially perpendicularly. The position of the measuring object 7 in the optical axis direction is set to a position where the difference between the wavefront of the incident spherical wave and the measuring object surface 7a is small.

  The measurement light beam LM is reflected on the measurement target surface 7 a to return the optical path, and enters the polarization beam splitter 3 through the wavefront conversion lens 6, the Fizeau plate 5, and the quarter wavelength plate 4. The measurement light beam LM rotates the polarization plane by 90 ° by reciprocating the quarter-wave plate 4, so that it passes through the polarization separation surface 3 a of the polarization beam splitter 3 and enters the beam diameter conversion optical system 8. To do. The measurement light beam LM is reduced in diameter by passing through the beam diameter conversion optical system 8 and is incident on the two-dimensional image detector 9 in this state.

  On the other hand, the reference light beam LR is incident on the polarization beam splitter 3 through the quarter-wave plate 4. The reference light beam LR is rotated 90 ° by reciprocating the quarter-wave plate 4, so that it passes through the polarization separation surface 3 a of the polarization beam splitter 3 and enters the beam diameter conversion optical system 8. To do. The reference light beam LM is reduced in diameter by passing through the beam diameter converting optical system 8 and is incident on the two-dimensional image detector 9 in that state.

  Accordingly, interference fringes are generated on the two-dimensional image detector 9 due to the measurement light beam LM and the reference light beam LR. This interference fringe pattern reflects the shape of the measurement target surface 7a.

  The two-dimensional image detector 9 captures interference fringes and acquires a fringe image. The fringe image is input to a computer (not shown). A computer (not shown) performs analysis processing on the input fringe image. Note that the analysis processing program is preinstalled in the computer.

  Here, the arrangement angle of the Fizeau plate 5 is set so that the incident angle of the light beam L with respect to the Fizeau surface 5a is a predetermined angle other than zero. In this case, there is a difference between the angle at which the measurement light beam LM is incident on the two-dimensional image detector 9 and the angle at which the reference light beam LR is incident on the two-dimensional image detector 9. For this reason, stripe-shaped carrier stripes (spatial carriers) are superimposed on the interference fringes. By superimposing the carrier fringes, the spatial frequency of necessary information becomes higher than the spatial frequency of unnecessary information, so that it is possible to apply analysis processing by the Fourier transform method.

  The inclination direction of the Fizeau plate 5 is selected so as to form an angle of 45 ° with respect to both the x axis and the y axis of the two-dimensional image detector 9. In this case, the carrier fringe has a common spatial frequency in both the x direction and the y direction.

  Next, analysis processing by a computer will be described.

  FIG. 2 is a flowchart of the analysis processing of this embodiment. Each step will be described in turn.

  Step S10: The computer inputs a fringe image. The fringe image I (x, y) is expressed by Expression (1).

式（１）においてａ（ｘ，ｙ）は光束Ｌ、測定用光束ＬＭ、参照用光束ＬＲの強度ムラに起因する第１因子（未知）であり、ｂ（ｘ，ｙ）はそれらの強度ムラに起因する第２因子（未知）であり、φ（ｘ，ｙ）は縞の位相成分（未知）である。

In Expression (1), a (x, y) is a first factor (unknown) due to the intensity unevenness of the light beam L, the measurement light beam LM, and the reference light beam LR, and b (x, y) is the intensity unevenness thereof. Is a second factor (unknown) due to, and φ (x, y) is a fringe phase component (unknown).

Incidentally, when the object of analysis processing is an interference fringe, the phase component φ (x, y) is expressed by the carrier component φ _c (x, y) (known) and the signal component φ _s (x, y) as shown in the equation (2). ) (Unknown).

ステップＳ１１：コンピュータは、縞画像Ｉ（ｘ，ｙ）に対しフーリエ変換法による本解析処理を施し、位相成分φ（ｘ，ｙ）、第１因子a（ｘ，ｙ）、第２因子ｂ（ｘ，ｙ）をそれぞれ算出する。

Step S11: The computer subjects the fringe image I (x, y) to the main analysis process by the Fourier transform method, and the phase component φ (x, y), the first factor a (x, y), and the second factor b ( x, y) are calculated respectively.

However, since these calculation results include analysis errors, the true phase component φ (x, y), the true first factor a (x, y), and the true second factor b (x, y) In the following, the phase component φ (x, y) calculated in this step is referred to as “calculated phase component φ _A (x, y)”, and the first factor a ( x, y) is referred to as “calculated first factor a _A (x, y)”, and the second factor b (x, y) calculated in this step is referred to as “calculated second factor b _A (x, y)”. Called.

FIG. 3 shows a distribution (an example) of the calculated first factor a _A (x, y) in the x direction, and FIG. 4 shows the calculated second factor b _A (x, y). This is a distribution in the x direction (an example). 3 and 4, the horizontal axis represents the distance from the optical axis in terms of the number of pixels of the two-dimensional image detector 9, and the vertical axes in FIGS. 3 and 4 represent the intensity.

As shown in FIGS. 3 and 4, ripples are generated in both the calculated first factor a _A (x, y) and the calculated second factor b _A (x, y). As described above, since the intensity distribution of the cross section of the light beam is smooth, each of the true first factor a (x, y) and the true second factor b (x, y) should show a smooth distribution. Therefore, the ripple generated in both the calculated first factor a _A (x, y) and the calculated second factor b _A (x, y) is due to the analysis error of this analysis process. Although not shown in the figure, a ripple-like analysis error also occurs in the calculated phase component φ (x, y).

  Here, the main analysis processing in this step is expressed as equations (3), (4), (5), and (6).

但し、これらの式においてＦ［Ｘ］はＸのフーリエ変換を示し、Ｆ^−１［Ｘ］はＸのフーリエ逆変換を示し、Ｒｅ［Ｘ］はＸの実部を示し、Ｉｍ［Ｘ］はＸの虚部を示し、ｆ_０は０次スペクトルを切り出すためのフィルタ処理を示し、ｆ_＋１は１次スペクトルを切り出すためのフィルタ処理を示す。

In these equations, F [X] represents the Fourier transform of X, F ⁻¹ [X] represents the inverse Fourier transform of X, Re [X] represents the real part of X, and Im [X] is An imaginary part of X is indicated, f ₀ indicates a filter process for cutting out a zeroth-order spectrum, and f ₊ 1 indicates a filter process for cutting out a first-order spectrum.

  Step S12: The computer sets the number of repetitions i to an initial value “1”. Note that the number of repetitions i is the number of repetitions of subsequent steps S14 to S17.

  Step S13: The computer sets the basic data φ ′ (x, y), a ′ (x, y), and b ′ (x, y) for polynomial fitting to initial values.

The initial value of the basic data φ ′ (x, y) is the calculated phase component φ _A (x, y) as shown in the equation (7).

また、基礎データａ’（ｘ，ｙ）の初期値は、式（８）で示すとおり算出第１因子ａ_Ａ（ｘ，ｙ）である。

Further, the initial value of the basic data a ′ (x, y) is the calculated first factor a _A (x, y) as shown in the equation (8).

また、基礎データｂ’（ｘ，ｙ）の初期値は、式（９）で示すとおり算出第２因子ｂ_Ａ（ｘ，ｙ）である。

Further, the initial value of the basic data b ′ (x, y) is the calculated second factor b _A (x, y) as shown in the equation (9).

ステップＳ１４：コンピュータは基礎データφ’（ｘ，ｙ）、ａ’（ｘ，ｙ）、ｂ’（ｘ，ｙ）の各々に多項式フィッティングを施すことによりリップル部分を排除し、真の位相成分φ（ｘ，ｙ）に類似したモデルφ_ｍ（ｘ，ｙ）、真の第１因子ａ（ｘ，ｙ）に類似したモデルａ_ｍ（ｘ，ｙ）、真の第２因子ｂ（ｘ，ｙ）に類似したモデルｂ_ｍ（ｘ，ｙ）を作成する。フィッティングに使用される多項式は、二次元形状を表す所定の多項式であり、例えば所定次数のツェルニケ多項式である。

Step S14: The computer eliminates the ripple portion by applying polynomial fitting to each of the basic data φ ′ (x, y), a ′ (x, y), b ′ (x, y), and the true phase component φ Model φ _m (x, y) similar to (x, y), model a _m (x, y) similar to true first factor a (x, y), true second factor b (x, y) A model b _m (x, y) similar to) is created. The polynomial used for the fitting is a predetermined polynomial representing a two-dimensional shape, for example, a Zernike polynomial of a predetermined order.

Incidentally, the model φ _m (x, y) is expressed by the following equation (10) by the basic data φ ′ (x, y) and the fitting residual δφ (x, y).

また、モデルａ_ｍ（ｘ，ｙ）は、基礎データａ'（ｘ，ｙ）とフィッティング残差δａ（ｘ，ｙ）とにより以下の式（１１）で表される。

The model a _m (x, y) is expressed by the following equation (11) with the basic data a ′ (x, y) and the fitting residual δa (x, y).

また、モデルｂ_ｍ（ｘ，ｙ）は、基礎データｂ’（ｘ，ｙ）とフィッティング残差δｂ（ｘ，ｙ）とにより以下の式（１２）で表される。

The model b _m (x, y) is expressed by the following equation (12) by the basic data b ′ (x, y) and the fitting residual δb (x, y).

ステップＳ１５：コンピュータは、前のステップＳ１４で取得されたモデルφ_ｍ（ｘ，ｙ）、ａ_ｍ（ｘ，ｙ）、ｂ_ｍ（ｘ，ｙ）を以下の式（１３）に当てはめることにより、各成分が既知のモデル縞画像Ｉ_ｍ（ｘ，ｙ）を作成する。

Step S15: The computer applies the models φ _m (x, y), a _m (x, y), b _m (x, y) obtained in the previous step S14 to the following equation (13), A model fringe image I _m (x, y) in which each component is known is created.

ここで、前述したとおりモデルφ_ｍ（ｘ，ｙ）、ａ_ｍ（ｘ，ｙ）、ｂ_ｍ（ｘ，ｙ）は、真の位相成分φ（ｘ，ｙ）、真の第１因子ａ（ｘ，ｙ）、真の第２因子ｂ（ｘ，ｙ）にそれぞれ類似する。よって、モデル縞画像Ｉ_ｍ（ｘ，ｙ）に対する解析処理と、縞画像Ｉ（ｘ，ｙ）に対する解析処理とが同じアルゴリズムであるならば、両者の解析誤差は互いに類似するはずである。

Here, as described above, the models φ _m (x, y), a _m (x, y), and b _m (x, y) have the true phase component φ (x, y) and the true first factor a ( x, y) and true second factor b (x, y), respectively. Therefore, if the analysis processing for the model fringe image I _m (x, y) and the analysis processing for the fringe image I (x, y) are the same algorithm, the analysis errors of both should be similar to each other.

Step S16: The computer applies the test analysis process of the same algorithm as the main analysis process (Step S11) to the model fringe image I _m (x, y), thereby calculating the calculated phase component φ ″ (x, y), 1 factor a ″ (x, y) and calculated second factor b ″ (x, y) are acquired. When the test analysis process in this step is expressed as an equation, equations (14), (15), (16), (17 ).

但し、これらの式においてＦ［Ｘ］はＸのフーリエ変換を示し、Ｆ^−１［Ｘ］はＸのフーリエ逆変換を示し、Ｒｅ［Ｘ］はＸの実部を示し、Ｉｍ［Ｘ］はＸの虚部を示し、ｆ_０は０次スペクトルを切り出すためのフィルタ処理を示し、ｆ_＋１は１次スペクトルを切り出すためのフィルタ処理を示す。

In these equations, F [X] represents the Fourier transform of X, F ⁻¹ [X] represents the inverse Fourier transform of X, Re [X] represents the real part of X, and Im [X] is An imaginary part of X is indicated, f ₀ indicates a filter process for cutting out a zeroth-order spectrum, and f ₊ 1 indicates a filter process for cutting out a first-order spectrum.

  Step S17: The computer calculates an analysis error of the test analysis process (step S16). The analysis errors include an analysis error Δφ related to the phase component, an analysis error Δa related to the first factor, and an analysis error Δb related to the second factor.

Of these, the analysis error Δφ is calculated by subtracting the model φ _m (x, y) from the calculated phase component φ ″ (x, y) as shown in the equation (18).

また、解析誤差Δａは、式（１９）で示すとおり算出第１因子ａ”（ｘ，ｙ）からモデルａ_ｍ（ｘ，ｙ）を差し引くことにより算出される。

The analysis error Δa is calculated by subtracting the model a _m (x, y) from the calculated first factor a ″ (x, y) as shown in the equation (19).

また、解析誤差Δｂは、式（２０）で示すとおり算出第２因子ｂ”（ｘ，ｙ）からモデルｂ_ｍ（ｘ，ｙ）を差し引くことにより算出される。

Further, the analysis error Δb is calculated by subtracting the model b _m (x, y) from the calculated second factor b ″ (x, y) as shown in the equation (20).

ステップＳ１８：コンピュータは、現在の繰り返し回数ｉが最大値ｉ_ｍａｘに至ったか否かを判別し、最大値ｉ_ｍａｘに至っていなければステップＳ１９へ移行し、最大値ｉ_ｍａｘに至っていればステップＳ２１へ移行する。

Step S18: The computer current iteration number i, it is determined whether or not reached the maximum value _{i max,} the process proceeds to step S19 if not reached the maximum value _{i max,} step S21 if reached the maximum value _{i max} Migrate to

The maximum value i _max is a value set in advance by the manufacturer or user of this apparatus, and is set to a large value when high measurement accuracy is required, and when the analysis time is required to be shortened. Set to a small value.

  Step S19: The computer increments the number of repetitions i by one.

  Step S20: The computer uses the current basic data φ ′ (x, y), a ′ (x, y), b ′ (x, y) as the analysis error Δφ (x, y) calculated in the previous step S17. ), Δa (x, y), Δb (x, y).

Here, the updated basic data φ ′ (x, y) is obtained by subtracting the analysis error Δφ (x, y) from the calculated phase component φ _A (x, y) as shown in equation (21).

また、更新後の基礎データａ’（ｘ，ｙ）は、式（２２）のとおり算出第１因子ａ_Ａ（ｘ，ｙ）から解析誤差Δａ（ｘ，ｙ）を差し引いたものである。

The updated basic data a ′ (x, y) is obtained by subtracting the analysis error Δa (x, y) from the calculated first factor a _A (x, y) as shown in the equation (22).

また、更新後の基礎データｂ’（ｘ，ｙ）は、式（２３）のとおり算出第１因子ｂ_Ａ（ｘ，ｙ）から解析誤差Δｂ（ｘ，ｙ）を差し引いたものである。

Further, the updated basic data b ′ (x, y) is obtained by subtracting the analysis error Δb (x, y) from the calculated first factor b _A (x, y) as shown in Expression (23).

これらの更新によれば、基礎データφ’（ｘ，ｙ）は真の位相成分φ（ｘ，ｙ）に近づき、基礎データａ’（ｘ，ｙ）は真の第１因子ａ（ｘ，ｙ）に近づき、基礎データｂ’（ｘ，ｙ）は真の第２因子ｂ（ｘ，ｙ）に近づく。

According to these updates, the basic data φ ′ (x, y) approaches the true phase component φ (x, y), and the basic data a ′ (x, y) becomes the true first factor a (x, y). ), The basic data b ′ (x, y) approaches the true second factor b (x, y).

Thereafter, the computer returns to step S14 to re-execute model fringe image creation and test analysis processing using the updated basic data φ ′ (x, y), a ′ (x, y), b ′ (x, y). To do. That is, the computer updates the basic data φ ′ (x, y), a ′ (x, y), b ′ (x, y), and updates the model fringe image until the number of repetitions i reaches the maximum value i _max. Repeat the creation and test analysis process.

As the number of repetitions increases, the model φ _m (x, y) approaches the true phase component φ (x, y), and the model a _m (x, y) is the true first factor a (x, y). Since the model b _m (x, y) approaches the true second factor b (x, y), the analysis errors Δφ (x, y), Δa (x, y), Δb (x , Y) approaches an analysis error related to the phase component of the analysis process, an analysis error related to the first factor of the analysis process, and an analysis error related to the second factor of the analysis process.

Step S21: The computer subtracts the analysis error Δφ of the test analysis process calculated in the previous step S17 from the calculated phase component φ _A (x, y) calculated in the present analysis process, thereby calculating the calculated phase component φ _A. (X, y) is corrected (formula (24)).

これによって、算出位相成分φ_Ａ（ｘ，ｙ）に重畳されていた解析誤差（本解析処理に起因する解析誤差）は、高精度に除去される。

As a result, the analysis error (analysis error resulting from this analysis process) superimposed on the calculated phase component φ _A (x, y) is removed with high accuracy.

Thereafter, the computer subtracts the carrier component φ _c (x, y) (known) from the corrected calculated phase component φ _A ′ (x, y) to thereby obtain a signal component included in the phase component φ (x, y). φ _s (x, y) is known, and the shape of the measurement target surface 7a is known based on the signal component φ _s (x, y) and the light source wavelength.

As described above, in the analysis processing of the present embodiment, polynomial fitting is performed using the analysis results (φ _A , a _A , b _A ) of the analysis processing (step S11) as basic data, and each component has a known model fringe image (I _m ) is created (steps S13, S14, S15). Then, the test analysis using model fringe image _{I m} (step S16, S17) by analysis error ([Delta] [phi, .DELTA.a, [Delta] b) calculating the analysis result of the analysis at the analysis error (step S11) (phi _A ) Is corrected (step S21).

Therefore, in the analysis processing of the present embodiment, the analysis result (φ _A ′) can be obtained with higher accuracy than the conventional analysis processing (when the test analysis processing is not performed).

  Moreover, in the analysis processing of this embodiment, the test analysis processing errors (Δφ, Δa) are repeated by repeating the test analysis processing (steps S16, S17) while updating the basic data (φ ′, a ′, b ′). , Δb) is brought close to the analysis error of this analysis process.

Therefore, in the analysis processing of this embodiment, the analysis result (φ _A ) of this analysis processing can be corrected with high accuracy by the analysis error (Δφ) calculated in the last iteration.

FIG. 5 is a diagram showing the analysis error of the conventional analysis process, and FIG. 6 is a diagram showing the total analysis error (when i _max = 10) of the analysis process (FIG. 2) of the present embodiment. 5 and 6, the horizontal axis represents the distance from the optical axis by the number of pixels of the two-dimensional image detector 9, and the vertical axes in FIGS. 5 and 6 represent the phase by the light source wavelength λ. Is.

  As is clear from comparison between FIGS. 5 and 6, a ripple-like analysis error occurs in the conventional analysis process, whereas the ripple-like analysis error is removed in the analysis process of this embodiment. I understand that.

  As a result of the above, the interferometer device of this embodiment can measure the shape of the measurement target surface 7a with high accuracy.

  Note that the update target in step S20 of the present embodiment is all of the basic data φ ′, a ′, and b ′, but may be limited to only the basic data φ ′. However, when all of φ ′, a ′, and b ′ are set, the total analysis error of the analysis processing of the present embodiment becomes smaller.

  Further, the interferometer apparatus of the present embodiment measures the shape of the measurement target surface 7a (that is, the spatial distribution of the height), but measures the time change of the height of an arbitrary point on the measurement target surface 7a. May be.

  In that case, instead of generating carrier fringes (that is, spatial carriers), a time change waveform of a pixel value corresponding to that point may be measured while generating a time carrier, and the time change waveform may be set as an analysis target.

  If this measurement is performed for each pixel, the shape change of the measurement target surface 7a (including the shape change due to the movement of the measurement target surface 7a) can be measured. Such measurement is suitable for measuring an element having a variable surface shape, such as a micromirror array.

  In order to generate a time carrier by the interferometer device, the Fizeau plate 5 or the measurement object 7 may be displaced in the optical axis direction by a piezo element or the like. Incidentally, when no spatial carrier is generated, it is not necessary to incline the Fizeau surface 5a.

  Further, although the Fizeau interferometer is applied to the interferometer apparatus of the present embodiment, other types of interferometers such as a Twiman Green type may be applied. Incidentally, in order to generate a spatial carrier in a Twiman Green interferometer, the reference plane may be inclined, and in order to generate a time carrier, the reference plane may be moved in the optical axis direction.

[Second Embodiment]
Hereinafter, a second embodiment of the present invention will be described. The present embodiment is an embodiment of a pattern projection shape measuring apparatus.

  FIG. 7 is a schematic configuration diagram of the pattern projection shape measuring apparatus of the present embodiment. As shown in FIG. 7, the pattern projection shape measurement apparatus includes a stage 12 that supports the measurement object 11, a projection unit 13, and an imaging unit 14. The pattern projection shape measuring apparatus also includes a computer (not shown). The surface 11a of the measurement object 11 is a measurement object surface.

  The projection unit 13 includes a light source 21, an illumination optical system 22, a pattern formation unit 23, and a projection optical system 24, and illuminates the measurement target surface 11a on the stage 12 from an oblique direction.

  Among these, the pattern forming unit 23 modulates the intensity of the light beam directed toward the measurement target surface 11a in a sine wave shape at a predetermined spatial frequency in the spatial direction. As a result, a stripe-shaped carrier stripe is projected onto the measurement target surface 11a. The carrier stripe is distorted according to the shape of the measurement target surface 11a.

  The imaging unit 14 includes an imaging optical system 25 and an imaging element 26, and images a stripe appearing on the measurement target surface 11a from the front. The fringe image (the fringe image) acquired by the imaging unit 14 through imaging is input to a computer (not shown).

  The computer calculates the fringe phase component by performing an analysis process on the inputted fringe image. This analysis process is the same as the analysis process of the above-described embodiment. Then, the computer makes the signal component included in the phase component known based on the calculated phase component and carrier component (known), and makes the shape of the measurement target surface 11a known based on the signal component and the light source wavelength. Note that the analysis processing program is preinstalled in the computer.

  Therefore, the pattern projection shape measuring apparatus of the present embodiment can measure the shape of the measurement target surface 11a with high accuracy.

  Note that the pattern projection shape measurement apparatus of the present embodiment analyzes the waveform modulated in the spatial direction and measures the shape (space distribution of the height) of the measurement target surface 11a. The shape of the measurement target surface 11a may be measured after the direction is also modulated.

  Incidentally, in order to generate both a spatial carrier and a time carrier in the pattern projection shape measuring apparatus, the projection position of the carrier fringes by the projection unit 13 may be scanned in the pitch direction of the fringes.

[Others]
In one aspect of the waveform analysis apparatus of the present invention, the model creation unit, the test analysis unit, and the error calculation unit are updated while updating a specific component of the basic data based on the analysis error calculated by the error calculation unit. The apparatus may further include a repeating unit that repeatedly operates, and the correction unit may perform the correction based on the analysis error calculated by the error calculation unit in the last round of the repetition.

  Further, the test analysis means calculates each component of the model waveform, and the error calculation means calculates the difference between each component calculated by the test analysis means and each actual component of the model waveform in the test analysis. It may be calculated as an analysis error regarding each component of the means, and the repetition means may update each component of the basic data based on the analysis error of each component calculated by the error calculation means.

  The input waveform is a waveform modulated in the spatial direction, for example.

  The input waveform is a waveform modulated in the time direction, for example.

  Further, one aspect of the computer-executable waveform analysis program of the present invention is to update the specific component of the basic data based on the analysis error calculated by the error calculation procedure, while the model creation procedure, the test analysis procedure, The method may further include an iterative procedure for repeatedly executing the error calculating procedure, and the correcting procedure may perform the correction based on the analysis error calculated by the error calculating procedure in the last round of the repetition.

  In the test analysis procedure, each component of the model waveform is calculated. In the error calculation procedure, a difference between each component calculated in the test analysis procedure and each actual component of the model waveform is calculated. It may be calculated as an analysis error regarding each component of the analysis procedure, and in the repetition procedure, each component of the basic data may be updated based on the analysis error of each component calculated in the error calculation procedure.

  The input waveform is a waveform modulated in the spatial direction, for example.

  The input waveform is a waveform modulated in the time direction, for example.

It is a schematic block diagram of the interferometer apparatus of 1st Embodiment. It is a flowchart of an analysis process. Calculating first factor _a A (x, y) is the x-direction distribution of (for example). Calculating a second factor _b A (x, y) is the x-direction distribution of (for example). It is a figure which shows the analysis error of the conventional analysis process. It is a figure which shows the total analysis error (in the case of _imax = 10) of the analysis process (FIG. 2) of this embodiment. It is a schematic block diagram of the pattern projection shape measuring apparatus of 2nd Embodiment.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 ... Laser light source, 2 ... Beam expander, 3 ... Polarizing beam splitter, 4 ... 1/4 wavelength plate, 5 ... Fizeau plate, 6 ... Wavefront conversion lens, 8 * ..Beam diameter conversion optical system, 9 ... Two-dimensional image detector

Claims (13)

This analysis means for calculating each component of the input waveform by performing analysis processing using the Fourier transform method on the input waveform;
Model creation means for creating a model waveform in which each component is known by function fitting using each component calculated by the present analysis means as basic data;
Test analysis means for calculating a specific component of the model waveform by performing the same analysis processing as the main analysis means on the model waveform created by the model creation means;
An error calculation means for calculating a difference between the specific component calculated by the test analysis means and the actual specific component of the model waveform as an analysis error related to the specific component of the test analysis means;
A waveform analysis apparatus comprising: correction means for correcting the specific component calculated by the analysis means based on the analysis error calculated by the error calculation means. The waveform analysis apparatus according to claim 1,
Recurring means for repeatedly operating the model creating means, the test analyzing means, and the error calculating means while updating a specific component of the basic data based on the analysis error calculated by the error calculating means,
The waveform analyzer according to claim 1, wherein the correction unit performs the correction based on the analysis error calculated by the error calculation unit in the last round of the repetition. The waveform analysis apparatus according to claim 2,
The test analysis means calculates each component of the model waveform,
The error calculation means calculates the difference between each component calculated by the test analysis means and each actual component of the model waveform as an analysis error for each component of the test analysis means,
The waveform analysis apparatus characterized in that the repeating means updates each component of the basic data based on an analysis error of each component calculated by the error calculating means. In the waveform analysis apparatus according to any one of claims 1 to 3,
The input waveform is
A waveform analyzer characterized by being a waveform modulated in a spatial direction. In the waveform analysis apparatus according to any one of claims 1 to 4,
The input waveform is
A waveform analyzer characterized by a waveform modulated in the time direction. This analysis procedure for calculating each component of the input waveform by performing analysis processing using the Fourier transform method on the input waveform,
A model creation procedure for creating a model waveform in which each component is known by function fitting using each component calculated in the analysis procedure as basic data;
A test analysis procedure for calculating a specific component of the model waveform by performing the same analysis process as the main analysis procedure on the model waveform created in the model creation procedure;
An error calculation procedure for calculating a difference between the specific component calculated in the test analysis procedure and an actual specific component of the model waveform as an analysis error related to the specific component in the test analysis procedure;
A computer-executable waveform analysis program comprising: a correction procedure for correcting the specific component calculated in the analysis procedure based on the analysis error calculated in the error calculation procedure. The computer-executable waveform analysis program according to claim 6,
While updating the specific component of the basic data based on the analysis error calculated in the error calculation procedure, further includes a repetition procedure for repeatedly executing the model creation procedure, the test analysis procedure, the error calculation procedure,
The computer-executable waveform analysis program characterized in that the correction procedure performs the correction based on the analysis error calculated in the error calculation procedure in the last round of the repetition. The computer-executable waveform analysis program according to claim 6,
In the test analysis procedure, each component of the model waveform is calculated,
In the error calculation procedure, the difference between each component calculated in the test analysis procedure and each actual component of the model waveform is calculated as an analysis error for each component in the test analysis procedure,
In the repetition procedure, each component of the basic data is updated based on an analysis error of each component calculated in the error calculation procedure. A computer-executable waveform analysis program. In the computer-executable waveform analysis program according to any one of claims 6 to 8,
The input waveform is
A computer-executable waveform analysis program characterized by being a waveform modulated in a spatial direction. In the computer-executable waveform analysis program according to any one of claims 6 to 9,
The input waveform is
A computer-executable waveform analysis program characterized in that the waveform is modulated in the time direction.   An interferometer apparatus comprising the waveform analysis apparatus according to any one of claims 1 to 5.   A pattern projection shape measuring apparatus comprising the waveform analysis apparatus according to claim 1. This analysis procedure for calculating each component of the input waveform by performing analysis processing using the Fourier transform method on the input waveform,
A model creation procedure for creating a model waveform in which each component is known by function fitting using each component calculated in the analysis procedure as basic data;
A test analysis procedure for calculating a specific component of the model waveform by performing the same analysis process as the main analysis procedure on the model waveform created in the model creation procedure;
An error calculation procedure for calculating a difference between the specific component calculated in the test analysis procedure and an actual specific component of the model waveform as an analysis error related to the specific component in the test analysis procedure;
A correction procedure for correcting the specific component calculated in the analysis procedure based on the analysis error calculated in the error calculation procedure.

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