JPH0625644B2 - Optical micro displacement measuring device - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Industrial field of application] The present invention relates to a positioning mechanism for an XY stage such as a microscope,
The present invention relates to an optical micro-displacement measuring device used in a stepper of a semiconductor manufacturing apparatus or a positioning mechanism of a moving mirror of a Fourier spectrometer, and more particularly to an optical micro-displacement measuring device having a measurement accuracy of one wavelength or less.

[Conventional technology]

As one of the optical minute displacement measurement techniques, an image sensor that forms a sinusoidal interference fringe on the image plane using an interferometer that uses a monochromatic light source such as a He-Ne laser, and places it on the image plane There is known a technique of measuring the displacement of the movable mirror with sub-fringe accuracy based on the phase information of the output signal of the. There is also a method of obtaining a minute displacement amount by measuring the displacement amount of the center burst using a white light source.

FIG. 1 is a block diagram showing an example of a conventional optical micro displacement measuring device.

Reference numeral 1 denotes a white light source, which is a light source having a continuous spectrum in a specific wavelength range such as a small light bulb or a light emitting diode. 20 is a Michelson interferometer in which the fixed reflecting mirror 26 is tilted by a small angle θ,
Aperture that limits the light receiving solid angle for the white light source 1.
21, a beam splitter 23 for amplitude-splitting a parallel light beam to separate it into two light beams, a movable reflecting mirror 25 mounted vertically on a moving body 24 whose displacement is to be measured in one optical path, and an optical axis of an optical axis in the other optical path. It is composed of a fixed reflecting mirror 26 provided with an inclination angle θ with respect to the vertical direction, and an image forming lens 27 for forming an interference fringe localized by the both light beams in the vicinity of the fixed reflecting mirror 26.

By the way, the light beam reflected by the moving reflecting mirror 25 and the fixed reflecting mirror 26
The light flux reflected by is superposed by the beam splitter 23,
An interferogram (intensity pattern of coherent light) with the optical path difference as a variable is spatially created on the image plane, but when the light source is monochromatic light, it is a sine curve-like interference fringe pattern. When the light source includes various wavelength components as in this example, the sinusoidal interference fringes of various wavelengths are linearly superposed, and as a result, as shown in FIG. It has a center burst (peak value) with a difference of zero, and has an interference fringe pattern in which vibration is damped to the left and right.

Here, it is assumed that the moving body 25, that is, the moving reflecting mirror 25 is displaced rightward by the displacement amount d. The position of the center burst before displacement is L1, and the position of the center burst after displacement is L
2, the center burst is displaced to the right by L = L
2-L1 displacement is performed. Therefore, the displacement direction of the moving reflecting mirror 25 can be identified by measuring the displacement direction of the center burst. Between the displacement amount d of the movable reflecting mirror 25 and the displacement amount L of the center burst, since the center burst position has a zero optical path difference, the following equation is established.

d = tan θ · L (1) Here, by measuring the displacement amount L of the center burst as a mark, the displacement of the movable reflecting mirror 25 is calculated by the product of the tangent of the known tilt angle θ and the displacement amount L. It will be possible to determine the quantity d. When the tilt angle θ is finely adjusted, the measurement region of the displacement amount d of the movable reflecting mirror 25 can be changed, and the tilt angle θ is significant as a scale factor. Therefore, it is possible to measure the displacement in a wide measurement area.

An image sensor 30 having a large number of photoelectric conversion units in the transverse direction of the interferogram is provided on the image plane of the interferometer 20. The image sensor 30 sequentially scans the photoelectric conversion unit at a predetermined cycle and outputs the intensity distribution of the interferogram as a serial signal. For example, a self-scanning photodiode array or the like is used. Reference numeral 31 is a preamplifier that amplifies the output signal of the image sensor 30. An analog / digital converter 32 converts the amplified analog signal of the interferogram into a digital signal and outputs it. 40 is a signal processing unit, which processes the digitized interferogram data,
It is used to calculate the displacement of the moving reflecting mirror 25. The function of this signal processing unit 40 is shown as each block in the broken line.

First, the interferogram before displacement is the image sensor
30 has the intensity distribution shown in FIG. Now, assuming that the position of the center burst is at the i-th photoelectric conversion unit from the left, the pre-displacement peak value determination means 41 determines this i-th photoelectric conversion unit. Specifically, the intensity signal of the interferogram before displacement is temporarily stored in an address number corresponding to each order of the photoelectric conversion units of the image sensor 30,
The address number with the largest content of each address number (=
i-th) is memorized. Next, assuming that the position of the center burst after displacement is at the j-th photoelectric conversion section from the left, the switch SW1 is switched, and the peak value determination means 42 determines the j-th photoelectric conversion section. Since the determination of the photoelectric conversion unit can be performed in a time division manner, it can be realized by a single peak value determination unit. The calculation means 43 takes the difference between the i-th and the j-th difference, and based on this difference (i-j) and the pitch P of the photoelectric conversion portion of the image sensor 30 input from the outside, the displacement (i-) of the center burst. j) P is calculated, tan θ is calculated from the tilt angle θ input from the outside, and then tan
θ (i−j) P is calculated and output to the output device 44. The positive value of (i-j) represents the displacement in the right direction, and the negative value represents the displacement in the left direction, and the absolute value thereof represents the displacement amount (movement amount). However, here, the magnification of the imaging lens 27 is set to 1 for the sake of simplicity, but generally, when the magnification is k, the above calculation result may be multiplied by k.

[Problems to be Solved by the Invention]

However, the above measurement technique has the following problems. That is, in the method of obtaining the displacement amount from the phase information using the monochromatic light source or the method of obtaining the displacement amount from the position of the center burst using the white light source, only one observation value can be obtained in one measurement, It is not possible to obtain displacement measurement values (observation values) for each element. Further, it is necessary to know the value of the tilt angle of the fixed reflecting mirror in advance, and the error is included in the displacement amount, which adversely affects the high precision measurement. Therefore, any of the above-mentioned conventional methods has a problem that the measurement accuracy is unreliable.

The present invention solves the above problems, and an object of the present invention is to provide an optical micro-displacement measuring device with high measurement accuracy and reliability.

[Means for solving problems]

In order to solve the above problems, the optical micro-displacement measuring device according to the present invention has the following six constituent requirements.

There is a white light source.

The "white light source" means a monochromatic light source, and may be, for example, a light source having a continuous spectrum in a specific wavelength range.

There must be a two-beam interferometer that spatially creates an interferogram having a center burst that receives the white light and has an optical path difference as a variable on the image plane.

There is an image sensor having a large number of photoelectric conversion units in the transverse direction of the interferogram.

There is a means for collecting the white light interferogram before and after displacement of the optical element that imparts the optical path difference.

There must be a means to Fourier transform those interferograms.

Using the terms of the real part and the imaginary part of the result of each Fourier transform, determine the phase for each wave number element, calculate the displacement amount for each wave number element from the difference in the phase spectrum before and after the displacement, and calculate them. There must be a calculation method that statistically processes and obtains the final displacement amount.

〔Example〕

FIG. 3 is a block diagram showing an embodiment of an optical micro displacement measuring device according to the present invention. In this embodiment, the displacement is measured with high accuracy without measuring the tilt angle θ. In FIG. 3, the same parts as those shown in FIG. 1 are designated by the same reference numerals, and the description thereof will be omitted.

First, to explain the measurement principle, assuming that the wave number of one monochromatic light included in the white light source 1 is σ ₀ , the intensity G (x) of the sinusoidal interference fringe formed on the image plane is given. Is G (x) = b (σ ₀ ) cos {2πf ₀ x + φ (σ ₀ )} + a ...
(2) where: a: DC bias component, b (σ ₀ ): monochromatic spectrum intensity of wave number σ ₀ , f ₀ : spatial frequency of interference fringes, φ
(σ ₀ ); phase term corresponding to wave number σ ₀ , x: coordinates in the scanning direction of the image sensor 30.

Further, the following equation holds between the spatial frequency f of the interference fringes and the tilt angle θ.

f ₀ = 2σ ₀ tan θ (3) Therefore, substituting (3) into the expression (2), G (x) = b (σ ₀ ) cos {4πσ ₀ tan θ · x + φ (σ ₀ )} + a ... (4) Therefore, the intensity L of the interference fringes for all the wave numbers of the white light source 1
(X), that is, the interferogram, is given by the following expression obtained by integrating the expression (4) over the entire wave number region.

If this AC term is I (x), Here, b (σ) is an even function b _e (σ) and an odd function b
Separating the components _{o (σ), b (σ} ) = b e (σ) + b o (σ) ... (7) (7) and rearranging by substituting expression (6) below, phi (sigma) = Since −φ (−σ), Where b _e (σ) is newly set to the spectrum B of the white light source 1.
If (σ) and 4πtan θ · x = X, From equation (9), B (σ) exp {jφ (σ)} is I
Since it can be seen that it is given by the inverse Fourier transform of (X), here, Then, the equation (10) is as follows: B (σ) cosφ (σ) + jB (σ) sinφ (σ) = C (σ) −jS (σ)
(11) Therefore, tan φ (σ) = − S (σ) / C (σ), that is, the phase for each wave number, that is, the phase spectrum φ (σ) is given by the following equation.

φ (σ) = tan ⁻¹ {−S (σ) / C (σ)} (12) By the way, the following equation is established between the displacement amount d and the phase term φ (σ).

φ (σ) = 4πdσ (13) From equations (12) and (13), d is obtained as a function d (σ) of σ.

d (σ) = tan ⁻¹ {−S (σ) / C (σ)} / 4πσ ... (14) d (σ) should be logically uniquely determined for various wave numbers σ However, due to variations in the sensitivity of the photoelectric conversion unit of the image sensor 30, etc., all wave numbers σ _i (i
= 1, 2, ... N, N is the number of elements of the image sensor and may not be unique with respect to the discrete Fourier transform score). Therefore, the displacement amount d _i is calculated for each wave number element. If it is considered that the white light source 1 is composed of N wave number elements and has uniform intensity, the S / N ratio (standard deviation) is calculated by taking the arithmetic mean of the respective displacement amounts d _i. ) Is improved in proportion to N ^1/2 as compared with the case where the light source is a monochromatic light source. In addition, considering the spectral characteristics of the white light source 1, {C (σ) ² + S (σ)
It is also conceivable to obtain a power spectrum given by ² } ^1/2 and take a weighted average considering the intensity distribution of each wave number element.

The signal processing unit 50 shown in FIG.
The collecting means 51 collects the interferogram before displacement. The collecting means 51 is a kind of storage device, and the image sensor 30
The number of addresses is equal to the number of photoelectric conversion units. The frequency analyzer 53 as a Fourier transform means performs a Fourier transform on the interferogram before displacement, and the arithmetic unit 55 uses the apex of the real part and the apex of the imaginary part of the result of the Fourier transform to generate the result shown in FIG. The power spectrum (amplitude spectrum) A1 as shown in FIG. 4) and the phase spectrum P1 as shown in FIG. 4B are obtained. When the reference point is located at the center of the image sensor 30, in an ideal case, the phase spectrum P1 is 0 between the measurement areas σ _{1 and} σ ₂ .
However, the position of the reference point may be arbitrary. Next, after the displacement, the switch SW2 is switched, the collecting means 52 collects the interferogram after the displacement, the frequency analyzer 54 performs the Fourier transform on the interferogram, and the arithmetic unit 55 calculates the real part of the result of the Fourier transform. Figure 4 (A) using the terms of sum and imaginary part
The power spectrum A2 as shown in Fig. 4 and the phase spectrum P2 as shown in Fig. 4B are obtained. Since the power spectrum depends on the spectral characteristics of the white light source 1, the power spectra A1 and A2 overlap. Since the collection and Fourier transform of such interferograms can be executed in a time-division manner, they can be realized by a single collecting means and frequency analyzer. Next, the computing device 55 calculates the displacement amount for each wave number element from the difference between the phase spectra before and after the displacement, statistically processes them, and supplies the final displacement amount to the output device 56. That is, since the difference between the phase spectrum P1 before the displacement and the spectrum P2 after the displacement is the phase term φ (σ) associated with the displacement, the power is calculated using the equation (13), d = φ (σ) / 4πσ. A weighted average is calculated in consideration of the spectra A1 and A2.

According to such an apparatus, the S / N ratio is improved in proportion to the number of wavenumber elements and the square root of the number of photoelectric conversion units of the image sensor 30 under the best conditions, and the high accuracy of the order of 1/100 or less of the wavelength is obtained. Displacement measurement is possible. Since all the wave number elements emitted from the white light source 1 are used in the calculation of the displacement d, the fast Fourier transform (FET) algorithm is used in the calculation of the Fourier transform.
However, when the number of wave number elements is limited to a few, discrete Fourier transform (DFT) is performed from the viewpoint of calculation time.
Is preferred.

〔The invention's effect〕

As described above, the optical micro-displacement measuring device according to the present invention measures the displacement from the phase of each wave number element, and it is possible to obtain a highly accurate displacement amount by performing simple statistical processing. Also, since the tilt error of the fixed reflecting mirror can be eliminated, highly reliable displacement measurement is possible.

[Brief description of drawings]

FIG. 1 is a block diagram showing an example of a conventional optical micro displacement measuring device. 2 (A) and 2 (B) are waveform diagrams showing an interferogram before displacement and an interferogram after displacement in the conventional example. FIG. 3 is a block diagram showing an embodiment of an optical micro displacement measuring device according to the present invention. FIGS. 4A and 4B are graphs showing the power spectrum and phase spectrum of the interferogram in the same example. [Description of symbols] 1 …… White light source 20 …… Michelson interferometer with a fixed reflecting mirror θ …… Tilt angle of fixed reflecting mirror 26 …… Moving reflecting mirror 26 …… Fixed reflecting mirror 30 …… Image sensor 31 ...... Preamplifier 32 …… Analog / digital converter 40,50 …… Signal processing unit 41,42 …… Determination means 43,55 …… Computing means 44,56 …… Output device 51,52 …… Collection means 53,54 ...... Frequency analyzer.

Claims (1)

[Claims] 1. A white light source, a two-beam interferometer for spatially creating an interferogram having a center burst that receives the white light and has an optical path difference as a variable on an image plane, and in a transverse direction of the interferogram. An image sensor having a large number of photoelectric conversion units, a means for collecting white light interferograms before and after displacement of an optical element that imparts the optical path difference, a means for performing Fourier transform on these interferograms, and Using the terms of the real part and the imaginary part of the result of the Fourier transform, the phase is obtained for each wave number element,
An optical micro-displacement measuring device comprising: a calculating unit that calculates a displacement amount for each wave number element from a difference between phase spectra before and after displacement, and statistically processes them to obtain a final displacement amount.