KR100736229B1 - System for compensating error of laser interferometer and method thereof - Google Patents

Abstract

A system for compensating error of laser interferometer and a method thereof are provided to measure displacement similar to resolution of a corresponding interferometer without an expensive measuring circumstance. A system for compensating error of laser interferometer includes an interferometer(50) using a single path heterodyne laser(51), a measuring unit(60) to measure a displacement using the interferometer, and a correcting unit(70) to correct an error of the measurement measured by the measuring unit using double Kalman filter algorithm. The correcting unit models measurement noise due to environmental error and reduces the measurement noise to increase measuring precision. The interferometer includes a laser to output a laser beam with a first frequency(f1) and a second frequency(f2), a beam splitter(52) installed on an optical path of the laser to split the first frequency and the second frequency, a first quarter plate installed on an optical path of the first frequency, a movable mirror(54) installed in a driving unit, a second quarter plate(55) installed on an optical path of the second frequency, and a fixed mirror(56) fixed on the optical path of the second frequency.

Description

System for Compensating Error of Laser Interferometer And Method Thereof}

1 is a block diagram of a system for correcting errors in a measurement system using a conventional laser interferometer.

2 is a block diagram of an error correction system of a laser interferometer according to the present invention.

3 is a flowchart illustrating an error correction method according to the present invention.

Figure 4 is a graph showing the results of the initial correction interval and one step drive of the interferometer according to the present invention.

Figure 5 is a graph showing the results of the initial correction interval and the measurement noise removal using a Kalman filter in accordance with the present invention.

6 is a graph showing measured noise measured in a stationary state and a moving state according to the present invention.

Explanation of symbols on the main parts of the drawings

50: interferometer 60: measuring unit

70: correction unit

The present invention relates to an error correction system and method of the laser interferometer, and more particularly, to an error correction system and method of the laser interferometer for increasing the accuracy of the measurement system using the laser interferometer.

In general, the most widely used equipment for nanoscale components and nanoscale measurement technology is the Heterodyne Laser Interferometer.

In the semiconductor circuit manufacturing technology, the minimum line width of a semiconductor device is processed to 100 nm using a laser interferometer.

Theoretically, the measurement resolution using a laser interferometer is 0.6 nm for a single path heterodyne laser interferometer and a double path heterodyne laser interferometer depending on the type of heterodyne laser interferometer. ) Is 0.3 nm, and the four path heterodyne laser interferometer is 0.15 nm.

1 is a conventional measurement system for measuring the displacement of the target, an interferometer 10 using a single path heterodyne laser 11, a measurement unit 20 for measuring the amount of displacement using the interferometer 10, It is composed of a correction unit 30 for correcting the error of the measured amount measured by the measuring unit 20.

The interferometer 10 is a laser 11 for outputting the laser light of the first frequency (f ₁ ) and the second frequency (f ₂ ), the optical path of the laser 10 is installed in the first frequency (f ₁ ) A first quarter wave plate installed at an optical path of a beam splitter 12 separating the second frequency f ₂ and a first frequency f ₁ passing through the beam splitter 12; 13), a movable mirror 14 and a beam splitter 12 which are installed on the optical path of the first frequency f ₁ passing through the first quarter wave plate 13 and move with the target as a target under test. Fixed to the second quarter wave plate 15 which is installed at the optical path of the second frequency f ₂ passing through), and to the optical path of the second frequency f2 which has passed through the second quarter wave plate 15. It consists of a mirror 16.

The laser 11 is composed of a dual frequency stabilized laser head having a wavelength of 633 nm, and the moving mirror 14 is mounted on a drive device and moved.

The measuring unit 20 detects an interference signal f _2- (f ₁ ± Δf ₁ ) that has passed through the beam splitter 12 of the interferometer 10, and the photodetector 21. The receiver 22 receives the output of the signal, using the interference signal f _2- (f ₁ ± Δf ₁ ) output from the receiver 22 and the reference signal f2-f1 of the laser 11. The measurement processing part 23 which processes the displacement V _r of the moving mirror 14 is comprised.

The correction unit 30 is for correcting the error of the displacement amount measured by the measurement unit 20, the temperature sensor 32 for measuring the atmospheric temperature of the place where the interferometer 10 is installed, the atmospheric pressure A pressure sensor 33 to measure, a humidity sensor 34 to measure atmospheric humidity, and a correction processor 31 that corrects the amount of displacement output from the measurement processor 23 using the measured values of the respective sensors. do.

The conventional measuring system configured as described above has a phase difference between the first frequency f1 and the second frequency f2 generated according to the movement of the moving mirror 14 to measure the movement displacement of the moving mirror 14. Is detected through the light detector 21 of the measuring unit 20, and the analog signal of the light detector 21 is input to the receiver 22, the measurement processor 23 of the receiver 22 The displacement amount Vr of the moving mirror 14 is measured using the output signal f _2- (f ₁ ± Δf ₁ ) and the reference signal f ₂ -f ₁ of the laser 11.

However, the results measured by the measuring unit 20 may not be reliable due to various sources of error affecting the interferometer 20.

That is, the error causes affecting the interferometer 10 include an error caused by the laser 11 and an optical device (a quarter wave plate, a mirror, etc.) and a mechanical error which is a nonlinear error. In addition, there is a geometry error which is an alignment error between the optical device, the laser 11 and the driving device of the moving mirror 14. In addition, there are environmental errors caused by temperature, humidity, vibration, and air perturbation that produce the largest errors.

The environmental error accounts for more than 60% of the total error and is the most difficult error to correct. For this reason, we can only use precision above 100nm, well below the actual resolution (0.6nm).

The method for improving the environmental error is a method for correcting the change in the air refractive index due to environmental changes. This method establishes a system that stabilizes the experimental environment, establishes various external environmental control systems such as constant temperature, humidity, dust protection, and soundproofing, and uses the Edlen formula through temperature, humidity, and barometric pressure measurement. How to calibrate.

That is, the correction unit 30 measures the atmospheric environmental conditions using the temperature sensor 32, the pressure sensor 33, and the humidity sensor 34, and the correction processing unit 31 uses the measured results. This calibration method is expensive to stabilize the lab environment, and it is difficult to accurately measure the correlation of displacement error with temperature, barometric pressure, and humidity changes, which limits the measurement accuracy. There was this.

An object of the present invention is to provide an error correction system and method of a laser interferometer that improves measurement accuracy by applying a Kalman filter algorithm to a measurement system using a laser interferometer to improve environmental errors.

In addition, another object of the present invention is to provide a laser interferometer error correction system and method for reducing the economic loss and improve the measurement accuracy by applying a Kalman filter algorithm to the laser interferometer measurement system It is.

The present invention to achieve the above object, an interferometer for detecting the displacement of the moving target using the optical interference of the laser; A measuring unit for measuring displacement by sensing an optical output of the interferometer; And a correction unit for correcting and outputting an error of the displacement measured by the measurement unit using a Kalman filter.

The interferometer uses a laser having two frequencies.

The interferometer is a laser for outputting laser light of a first frequency and a second frequency, a beam splitter installed at an optical path of the laser to separate the first frequency and the second frequency, the second through the beam splitter A first quarter wave plate installed in an optical path of one frequency, a moving mirror installed in the same manner as the target so as to be movable in the optical path of the first frequency that has passed through the first quarter wave plate, and the beam splitter passed through the first quarter wave plate And a second quarter wave plate installed on the optical path of the second frequency, and a fixed mirror fixed to the optical path of the second frequency passing through the second quarter wave plate.

The moving mirror further comprises a drive device.

The drive device is characterized in that it further comprises a control unit for controlling the drive.

The laser is characterized by consisting of a dual frequency stabilized laser head.

The laser is characterized in that for outputting a laser light having a wavelength of 633nm.

The beam splitter is characterized in that the polarizing beam splitter.

The measuring unit measures the displacement of the target by using a photo detector for detecting an interference signal of the interferometer, a receiver for receiving the output of the photo detector, an interference signal output from the receiver and an optical signal of the laser as a reference. Characterized in that it comprises a measurement processing unit.

The correction unit may include a measurement noise model that models a noise causing a displacement measurement error of the target by the interferometer, and a correction processor that corrects the measurement result output from the measurement unit using a Kalman filter algorithm. It is done.

The correction processor may include a first Kalman filter algorithm for initial position correction of the target.

The first Kalman filter algorithm is characterized in that the offset error is removed by synchronizing the reference position of the measurement noise by the measurement noise model and the reference position to which the target is set.

The correction processing unit may include a ramp function model for a moving target and a second Kalman filter algorithm for removing measurement noise for the ramp function model.

The correction processing unit may include a constant function model for the stationary target and a third Kalman filter algorithm for removing measurement noise for the constant function model.

The present invention provides a method of correcting a displacement error of a target measured using a laser interferometer, the method comprising: (a) constructing a dynamic model of a moving target; (b) building a dynamic model of the stationary target; (c) correcting an initial position of the target; (d) checking a driving state of the target; (e) correcting the error using the model built in step (a) if the target is in a moving state, and correcting the error using the model built in step (b) if the target is in a stationary state. It also provides an error correction method of a laser interferometer comprising.

The model of step (a) is characterized in that the ramp function model.

The model of step (b) is characterized in that the constant function model.

The initial position correction for the target of step (c) is characterized by estimating the offset error from the actual reference point through the first Kalman filter for a predetermined time, and then correcting by removing the offset error estimated from the measured value.

In operation (d), the driving state of the target may be determined by using a driving command signal of a driving device for driving the target.

In the step (e), if the target is in the moving state, the error is corrected using the second Kalman filter to which the model constructed in the step (a) is applied.

In the step (e), if the target is stationary, the error is corrected using a third Kalman filter to which the model constructed in the step (a) is applied.

(Example)

Hereinafter, the error correction system and method of the laser interferometer according to the present invention will be described in detail with reference to the accompanying drawings showing a preferred embodiment of the present invention.

2 is a block diagram of an error correction system of a laser interferometer according to the present invention, FIG. 3 is a flowchart illustrating an error correction method according to the present invention, and FIG. 4 is an initial correction interval of an interferometer according to the present invention. 5 is a graph showing a result of driving according to one step, and FIG. 5 is a graph showing a result of removing an initial correction interval and measurement noise using a Kalman filter according to the present invention.

The error correction system of the laser interferometer according to the present invention, as shown in Figure 2, the interferometer 50 using a single path heterodyne laser 51, the measuring unit 60 for measuring the amount of displacement using the interferometer 50 And a correction unit 70 for correcting the error of the measured amount measured by the measurement unit 60 using a double kalman filter algorithm.

Among the error correction system of the laser interferometer according to the present invention, the interferometer 50 and the measurement unit 60 is made of the same configuration as that of the conventional measurement system of Figure 1, the correction unit 70 is due to the environmental error Model measurement noise and design Kalman filters for it to reduce measurement noise to increase measurement accuracy.

That is, the interferometer 50 is composed of a dual frequency stabilized laser head having a wavelength of 633 nm, the laser 51 for outputting the laser light of the first frequency (f ₁ ) and the second frequency (f ₂ ), the laser 50 A beam splitter 52 installed at an optical path of a beam splitter 52 separating the first frequency f ₁ and a second frequency f ₂ , and a beam of a first frequency f ₁ passing through the beam splitter 52. A first quarter wave plate 53 installed in the furnace and a moving mirror installed in the driving device so as to be movable in an optical path of a first frequency f ₁ passing through the first quarter wave plate 53. (54), a second quarter wave plate 55 installed at the optical path of the second frequency f ₂ passing through the beam splitter 52, and a second frequency passed through the second quarter wave plate 55 ( f ₂ ) and a fixed mirror 56 fixed to the optical path.

The moving mirror 54 is movable by the driving device and is moved together with the target which is the object to be measured (the description of the displacement and the amount of displacement in the following description is directed to the target or the moving mirror).

The measuring unit 60 detects an interference signal f _2- (f ₁ ± Δf ₁ ) that has passed through the beam splitter 52 of the interferometer 50, and the photo detector 61. The receiver 62 receives the output of the interference signal, and the interference signal f _2- (f ₁ ± Δf ₁ ) output from the receiver 62 and the reference signal f ₂ -f ₁ of the laser 51. It is comprised by the measurement processing part 63 which measures the displacement amount V _r of the said moving mirror 54 using it.

The correction unit 70 corrects a displacement error using a double kalman filter, and the correction unit 70 includes a measurement noise model in which modeling of noise affecting a measurement error is established. 72) and a correction processor 71 for correcting the measurement result output from the measurement unit 60 using the double Kalman filter algorithm.

The measurement noise model 72 is a model constructed to obtain a measurement noise parameter used in the double Kalman filter algorithm of the correction processor 71.

The displacement error correction by the double Kalman filter algorithm of the correction processor 71 is determined by how accurately the measured noise model 72 is constructed.

Therefore, in order to accurately model the measurement noise, the measurement noise model 72 is constructed as follows.

First, when the displacement of the movable mirror 54 is measured by the measuring unit 60 while the movable mirror 54 is stopped, it is possible to accurately measure the measurement noise due to environmental errors. That is, since the measurement signal measured by the measuring unit 60 in the state that the moving mirror is stopped is the result of measuring the state in which the moving mirror 54 is not moved, it is purely an environmental error excluding mechanical error and geometric error. It can be seen that the error due to.

In addition, when the target is stopped, the measurement noise measured by the measurement board is measured only by the measurement error due to environmental errors. However, when the target moves, the measurement noise affects the measurement noise not only because of environmental errors but also by geometrical errors.

Therefore, in order to minimize geometrical errors when the target moves, the alignment of the optical devices constituting the laser interferometer 50 is optimally adjusted so that only measurement noise due to environmental errors can be measured.

6 shows the measured noise measured by the target in the stationary state and the moving state.

6 illustrates a state in which the target is stopped from 0 to 200 seconds, a state in which the target is moved from 200 to 300 seconds, and a state in which the target is stopped from 300 to 400 seconds.

If the measurement noise is measured without correcting the geometric error, if the cosine error, which is a representative error of the geometric error, is described as an example, the measurement error increases or decreases in proportion to the movement displacement when the target is moved. However, as shown in FIG. 6, since the measurement was performed in the state in which the error cause except the environmental error was completely removed, it can be seen that the characteristics of the measured noise were similar in the stationary state and the moving state.

The measured noise measured as above is modeled assuming a Markov process. In addition, we calculate beta, which is the inverse of the correlation time of the discrete Markov process used as a parameter of the double Kalman filter, and variance of the white noise used as the input of the discrete Markov process. Use it as an important constant.

The Kalman filter algorithm used in the correction processing unit 71 is composed of a Kalman filter algorithm for correcting the initial position to 0 nm and a Kalman filter algorithm for removing measured noise measured from a moving or stationary target.

The double Kalman filter algorithm as described above will be described with reference to FIG. 3.

For reference, the flowchart shown in FIG. 3 does not show a separate termination condition because the double Kalman filter is automatically operated when the laser interferometer 50 is operated and stops when the laser interferometer 50 is operated.

In general, the measurement system must remove the measurement noise substantially and define the absolute position with respect to the target before estimating the actual displacement. The measurement noise is included before the actual displacement is measured. Set the location.

However, since the reference position of the target set as described above is not synchronized with the reference point of the measurement noise, if the reference position is incorrectly set, there is always an offset error, so the measured displacement even after the noise is removed by the Kalman filter. In addition to being unreliable, we have no idea how much offset error exists.

Therefore, the offset error should be removed by synchronizing the reference point of the measurement noise with the set reference position of the target.

Here, synchronizing the reference point of the target and the reference point of the measurement noise has the following meaning.

That is, the measurement noise measured from the laser interferometer 50 is irregularly measured, and the irregular measurement noise is modeled by the Markov process.

The measurement noise modeled by the Markov process is removed with a Kalman filter and the actual displacement is estimated as the average value of the Markov process.

Also, before measuring the displacement, it is set to 0um based on the position of the current target. If the reference position is set at the point having the average value of the Markov process, this is not a problem, but if it is not, the offset error by the dispersion of the maximum Markov process Occurs.

To solve this problem, we first estimate the mean of the measured noise with a Kalman filter and set that estimate to the reference position of the current target, which matches the mean of the two criteria, the measured noise (Markov process) and the reference position of the target. It is to motivate because it is.

First, the Kalman filter for estimating the displacement from the measurement noise is designed by dividing the target into a case where the target moves and when the target stops (S 10 and S 11).

Dynamic model building (S 10) for moving targets is designed as a ramp function, and the parameters of the ramp function are used as important design variables in the Kalman filter algorithm (S 14) for the ramp function.

In addition, the dynamic model building (S 11) for the stationary target is designed as a constant function, the parameters of the constant function is used as an important design variable in the Kalman filter algorithm (S 131) for the constant function.

The two Kalman filter algorithms designed as described above are switched to the moving target Kalman filter mode and the stationary target Kalman filter mode, respectively, according to the state of the target.

The Kalman filter algorithm for correcting the initial position of the target corrects the initial position using the Kalman filter as a method of synchronizing the reference points (S 12).

That is, the initial position correction estimates the offset error from the actual reference point through the Kalman filter for a predetermined time, and then sets an accurate reference point by removing the estimated offset error from the measured value.

When correction is made at the initial position of the target as described above, it is classified into a ramp function model or a constant function model according to the moving or stationary state of the target (S 13), and the Kalman filter algorithm for the ramp function is determined as the ramp function model. By correcting the displacement error (S 14), and checking whether the ramp function model (S 15) and if the ramp function model, the Kalman filter algorithm for the ramp function is continuously applied to correct the position error.

However, if it is determined that the constant function model after the initial position correction (S 13), the Kalman filter algorithm for the constant function is applied to correct the displacement error (S 131), and whether or not the constant function model (S 132) In the functional model, the Kalman filter algorithm for the constant function is continuously applied to correct the position error.

At this time, the information for the conversion of each function model uses a drive command signal transmitted to the drive device for driving the target.

That is, the controller (not shown) detects the driving command signal transmitted to the driving device at each mode switching, and corrects the displacement error by applying a Kalman filter algorithm corresponding to each mode.

Examples of the correction made in the above process are shown in FIGS. 4 and 5.

4 illustrates a driving experiment of a target measured using the interferometer 50. The initial position correction section, the ramp section, and the constant section show the position variation result for each time zone.

5 shows a Kalman filter for initial position correction for 0 to 200 seconds (see A of FIG. 5), the target is moved to 0 nm to 10 um for 200 to 300 seconds, and the target is held at 10 um for 300 to 400 seconds. A graph showing the Kalman filter estimation result (see B of FIG. 5) for a state.

In FIG. 5, the signal indicated by the dotted line (blue) represents the actual measured measurement error, and the signal indicated by the solid line (red) represents the estimation error of the Kalman filter for each section.

The experimental results shown in FIG. 5 show that a large amount of measurement error can be reduced as a result of applying the Kalman filter algorithm to the actually measured measurement error.

The present invention made as described above has the effect of enabling the displacement measurement to the accuracy of approaching the resolution of the interferometer without using a costly improvement of the measurement environment when measuring the displacement of the object using a laser interferometer using the Kalman filter algorithm To provide.

The present invention as described above provides an effect that enables the development of new technology related to nanomechatronics, nano-scale high-precision system.

Claims (21)

Heterodyne laser interferometer for detecting the displacement of the target using the optical interference of the laser; A measuring unit for measuring displacement by sensing an optical output of the interferometer; And And a correction unit for correcting and outputting a displacement error generated in the displacement measured by the measurement unit due to an environmental error affecting the interferometer, The interferometer is a laser for outputting laser light of a first frequency and a second frequency, a beam splitter installed at an optical path of the laser to separate the first frequency and the second frequency, the second through the beam splitter A first quarter wave plate installed in an optical path of one frequency, a moving mirror installed in the same manner as the target so as to be movable in the optical path of the first frequency that has passed through the first quarter wave plate, and the beam splitter passed through the first quarter wave plate And a second quarter wave plate installed on the optical path of the second frequency, and a fixed mirror fixed to the optical path of the second frequency passing through the second quarter wave plate. The error correction system of claim 1, wherein the interferometer uses a laser having two frequencies. delete The error correction system of claim 1, wherein the moving mirror further comprises a driving device. 5. The error correction system of claim 4, wherein the driving device further comprises a control unit for controlling driving. 3. The error correction system of claim 2, wherein the laser is a dual frequency stabilized laser head. 7. The error correction system of claim 6, wherein the laser outputs laser light having a wavelength of 633 nm. The error correction system of claim 1, wherein the beam splitter is a polarizing beam splitter. The apparatus of claim 1, wherein the measuring unit comprises: a photo detector detecting an interference signal passing through the beam splitter of the interferometer, a receiver receiving an output of the photo detector, an interference signal output from the receiver, and the laser of the interferometer And a measurement processor configured to measure and output the displacement of the target by using an output reference signal. The correction unit of claim 1, wherein the correction unit corrects the measurement result output from the measurement unit by using a measurement noise model modeling a noise causing a displacement measurement error of the target by the interferometer, and a Kalman filter algorithm. Error correction system of the laser interferometer comprising a processing unit. The error correction system of claim 10, wherein the correction processor comprises a first Kalman filter algorithm for initial position correction of the target. 12. The error correction system of claim 11, wherein the first Kalman filter algorithm removes an offset error by synchronizing a reference position of measurement noise by the measurement noise model with a reference position where the target is set. 11. The error correction system of claim 10, wherein the correction processor comprises a ramp function model for a moving target and a second Kalman filter algorithm for removing measurement noise for the ramp function model. . 11. The error correction system of claim 10, wherein the correction processing unit comprises a constant function model for a stationary target and a third Kalman filter algorithm for removing measurement noise for the constant function model. In the method for correcting the displacement error generated in the displacement of the target measured by using the interferometer due to the environmental error affecting the heterodyne laser interferometer, (a) constructing a dynamic model of the moving target for modeling noise causing a displacement measurement error of the moving target by the interferometer; (b) constructing a dynamic model of the stationary target modeling noise that causes displacement measurement error of the stationary target by the interferometer; (c) correcting an initial position of a target to measure displacement using the interferometer; (d) checking a driving state of the target whose initial position is corrected; (e) correcting the displacement error by applying the model constructed in step (a) or step (b) to the Kalman filter algorithm according to the moving or stationary state of the target whose driving state is confirmed; Error correction method of the laser interferometer comprising a. The method of claim 15, wherein the model of step (a) is a ramp function model. The method of claim 15, wherein the model of step (b) is a constant function model. The method of claim 15, wherein the initial position correction for the target of the step (c) is performed by estimating the offset error from the actual reference point through the first Kalman filter algorithm for a predetermined time, and then correcting the offset error estimated from the measured value. Error correction method of the laser interferometer, characterized in that the. 16. The method of claim 15, wherein the step (d) of checking the driving state of the target uses a drive command signal of a driving device for driving the target. 17. The method of claim 16, wherein in the step (e), the displacement error is corrected by using a second Kalman filter algorithm for the ramp function model when the target is in a moving state. 18. The method of claim 17, wherein if the target is stationary in the step (e), the displacement error is corrected by using a third Kalman filter algorithm for the constant function model.

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