JPH11230716A - Measuring apparatus for displacement of light waves - Google Patents

Abstract

PROBLEM TO BE SOLVED: To obtain a measuring apparatus which suppresses measuring errors and by which the displacement of an object is measured with high accuracy, by computing a correction amount based on the difference between the weighted mean value in which the weight of new data in terms of time is set to be stronger than the weight of old data in terms of time from among a plurality of data regarding a first displacement amount, and the similar weighted means value regarding a second displacement amount. SOLUTION: A first displacement amount which is outputted from a signal processor 13 in a data acquisition timing time tr irrespective of whether a moving mirror 5 is in a moving state or a standstill state is expressed as ΔD (f1, tr). A second displacement amount is expressed as ΔD (f2, tr). When a first processing displacement amount ΔD and a second processing displacement amount ΔD are computed, the first processing displacement amount ΔD becomes the weighted mean value of a plurality of data on the first displacement amount, and the second processing displacement amount ΔD becomes the weighted mean value of a plurality of data on the second displacement amount. From among a plurality of data which are inputted continuously in terms of time, the weight of the new data in time is set to be stronger than the weight of the old data in time. Based on their difference, a correction amount is computed by taking into consideration the influence of a change in a refractive index by a gas in an optical path.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a light wave displacement measuring device, and more particularly to a light wave displacement measuring device for measuring a displacement of an object with high accuracy.

[0002]

2. Description of the Related Art A light wave interference measuring device as a conventional light wave displacement measuring device is disclosed, for example, in Japanese Patent Publication No. 7-81819. This apparatus uses a first optical path (reference optical path) in which a fixed mirror is arranged along a same optical path between a first laser light having a first wavelength and a second laser light having a second wavelength.
And a second optical path (measurement optical path) where the movable mirror is arranged. A first interference light is formed by the first laser light passing through the first optical path and the second optical path, and a first displacement amount ΔD1 corresponding to the displacement amount of the movable mirror is detected based on the first interference light.

Further, a second interference light is formed by the second laser light passing through the first optical path and the second optical path, and based on the second interference light, a second displacement Δ corresponding to the displacement of the movable mirror is obtained.
D2 is detected. The first interference light and the second interference light are interference fringes caused by the first laser light and the second laser light that have interfered through two different optical paths, and the brightness of the interference fringes varies depending on the displacement amount of the movable mirror. Change. Therefore, a value obtained by coefficienting a change in brightness on the light receiving element by an output of the light receiving element corresponds to the first displacement amount ΔD1 and the second displacement amount ΔD2 corresponding to the displacement amount of the movable mirror.

The displacement amount ΔD of the movable mirror is calculated by the following equation (1) using the first displacement amount ΔD1 and the second displacement amount ΔD2. ΔD = ΔD1−A (ΔD1N−ΔD2N) (1) Here, A is a constant determined by the refractive index of the gas in the optical path, and the refractive indexes of the gas with respect to the first wavelength and the second wavelength are n1 and n2, respectively. Then A = (n1-
1) / (n1 -n2). ΔD1N is a first average displacement generated by simply averaging N pieces of data relating to the first displacement D1, and ΔD2N is generated by simply averaging N pieces of data relating to the second displacement D2. This is the calculated second average displacement amount. As described above, in the related art, the use of a value (ΔD1N−ΔD2N) obtained by simply averaging N pieces of data suppresses a decrease in the measurement resolution of the correction amount for the refractive index fluctuation.

[0005]

With reference to FIG. 3, a description will be given of a measurement error generated in the above-mentioned conventional light wave interference measuring apparatus. FIG. 3 shows a correction amount ｛A (A) that takes into account the effects of the first displacement amount ΔD1, the second displacement amount ΔD2, the displacement amount ΔD, and the refractive index variation when the movable mirror moves at a constant speed in a state where there is no refractive index variation. ΔD1−ΔD2)}. The displacement amounts ΔD1 and ΔD2 in FIG.
ΔD2)｝ is shown as a straight line for convenience, but is actually a step-like value corresponding to the measurement resolution.

In FIG. 3, the displacement of the movable mirror from time t0 to time t1 is considered. First, in FIG.
Considering the event at time t1, the first average displacement ΔD1N is
N first measurements taken from time t0 to time t1
It is a simple average value of the displacement amount ΔD1 (for example, the count value of the counter). That is, the value of the first average displacement ΔD1N is
This corresponds to a value at an intermediate time t2 between the time t0 and the time t1. Further, the second average displacement ΔD2N is N second displacements ΔD2 measured from time t0 to time t1.
(For example, the count value of a counter). That is, the value of the second average displacement amount ΔD2N corresponds to a value at an intermediate time t2 between the time t0 and the time t1. Therefore, A (ΔD1N−ΔD2N) is ｛A at time t2.
([Delta] D1-[Delta] D2)}. That is, instead of A (ΔD1−ΔD2), A (ΔD1N
−ΔD2N), the displacement amounts ΔD1, ΔD2
Each interpolation value can be used, and the resolution can be increased.

However, at time t1, ｛A (Δ
D1−ΔD2)} is the value shown in FIG. 3, and the calculated value of A (ΔD1N−ΔD2N) and {A
An error indicated by reference numeral E in FIG. 3 occurs between the true value of (ΔD1−ΔD2) Ｄ. As a result, despite the fact that the true value of the displacement amount D at the time t1 is the value shown in FIG. 3, the value of the displacement amount calculated by the operation formula (1) of the related art is the true value of the displacement amount ΔD. It will differ from the value by the error E. The measurement error E increases in proportion to the moving speed of the movable mirror, that is, the moving speed of the object to be measured (as the moving speed increases, the slopes of ΔD1 and ΔD2 become steeper), and the first displacement amount ΔD1 and the second
Number of data N used for simple averaging of displacement ΔD2
(When N becomes large, it means that the time between time t0 and time t1 becomes long, and the moving distance of the movable mirror becomes large).

The present invention has been made in view of the above-mentioned problems, and has as its object to provide a light wave displacement measuring device capable of measuring a displacement of an object with high accuracy while suppressing a measurement error. I do.

[0009]

In order to solve the above-mentioned problems, according to the present invention, a first light having a frequency f1 is propagated along a predetermined optical path, and a first light having a frequency f1 is propagated along an object to be measured disposed in the optical path. A first detection system for detecting a first displacement ΔD (f1) corresponding to the displacement, and a second light having a frequency f2 different from the frequency f1 propagated along the predetermined optical path; A second detection system for detecting a second displacement ΔD (f2) corresponding to the displacement of the object to be measured, and a difference between the first displacement ΔD (f1) and the second displacement ΔD (f2) And calculating the correction amount in consideration of the influence of the refractive index fluctuation due to the gas in the optical path, and calculating the first displacement amount Δ with the calculated correction amount.
A processing operation system for correcting D (f1) to obtain a displacement amount ΔD of the object to be measured, wherein the processing operation system temporally calculates a plurality of pieces of data relating to the first displacement amount ΔD (f1). A weighted average value in which the weight of new data is set stronger than the weight of old data in time, and the second displacement amount ΔD (f
(2) calculating the correction amount based on a difference from a weighted average value in which a temporally new data weight is set stronger than a temporally old data weight from the plurality of data relating to 2). Provide a measuring device.

As described above, in the present invention, the calculation of the weighted average value of the plurality of data regarding the first displacement amount ΔD (f1) and the weighted average value of the plurality of data regarding the second displacement amount ΔD (f2) is performed. , The weight of temporally new data is set stronger than that of temporally old data.
For this purpose, the processing operation system uses the k-th data I (k) and the weighted average value O (k-1) of the first to (k-1) th data as variables, and It is preferable to calculate the weighted average value O (k) of the data from the kth data to the kth data.

[0011]

DESCRIPTION OF THE PREFERRED EMBODIMENTS In the present invention, a first displacement ΔD (f1)
And a second displacement amount ΔD (f2), and calculates a correction amount in consideration of the influence of the refractive index fluctuation, corrects the first displacement amount ΔD (f1) with the calculated correction amount, and calculates a moving object to be measured. Displacement amount ΔD
Is the same as in the prior art. However, in the prior art, the correction amount is calculated based on the difference between the simple average value of the first displacement amount ΔD (f1) and the simple average value of the second displacement amount ΔD (f2). The correction amount is calculated based on the difference between the weighted average value of the displacement amount ΔD (f1) and the weighted average value of the second displacement amount ΔD (f2).

At this time, the first displacement ΔD (f1) and the second displacement
Among a plurality of pieces of data of the displacement amount ΔD (f2), weighting is performed so that the weight of old data in time is weak and the weight of new data in time is strong. Therefore, in FIG. 3, the correction amount A (ΔD1−Δ
The value of D2) is closer to the true value of the correction amount A (ΔD1−ΔD2) at time t1 than the value of the correction amount A (ΔD1N−ΔD2N) obtained by simple averaging in the prior art. In addition, by performing the weighted averaging process, the interpolation values of the displacement amounts ΔD1 and ΔD2 can be used, so that the resolution can be increased as in the related art. As a result, with the lightwave displacement measuring device of the present invention, the displacement amount of the object to be measured can be measured with high accuracy by increasing the accuracy of the correction amount.

Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings. FIG. 1 is a view schematically showing a configuration of a light wave displacement measuring device according to a first embodiment of the present invention. FIG.
Is equipped with a light source 1 that emits two lights having different frequencies along the same optical path. The light of frequency f1 emitted from the light source 1 and the frequency f2 (f1 ≠ f
The light of 2) is linearly polarized light having the same polarization direction, and the polarization direction is inclined by 45 ° with respect to the plane of FIG. Light having the frequencies f1 and f2 emitted from the light source 1 enters the polarization beam splitter 3. The polarizing beam splitter 3 transmits light (p-polarized light) having a polarization direction in the vertical direction in the plane of FIG. 1 and reflects light (s-polarized light) having a polarization direction in a direction perpendicular to the plane of FIG.

Therefore, the light incident on the polarization beam splitter 3 is a reference light guided to a reference optical path on which a fixed mirror 4 composed of a corner cube prism is disposed, and a movable mirror composed of a corner cube prism and attached to an object to be measured. 5 is separated into measurement light guided to the arranged measurement light path. The light of the frequency f1 and the frequency f2 reflected by the polarization beam splitter 3 is reflected by the fixed mirror 4, returns to the polarization beam splitter 3 again, and is reflected by the polarization beam splitter 3. In addition, polarizing beam splitter 3
Are reflected by the movable mirror 5, return to the polarization beam splitter 3, and pass through the polarization beam splitter 3.

The lights of the frequencies f1 and f2 reflected or transmitted by the polarization beam splitter 3 enter the dichroic mirror 6 along the same optical path. The dichroic mirror 6 transmits light of frequency f1 and reflects light of frequency f2. Therefore, the reference light having the frequency f1 and the measurement light having the frequency f1 pass through the dichroic mirror 6, and the reference light having the frequency f2 and the measurement light having the frequency f2 are reflected by the dichroic mirror 6.

The reference light having the frequency f 1 transmitted through the dichroic mirror 6 and the measurement light interfere with each other via the polarizing plate 7. In addition, the polarizing plate 7 is a reference light (s-polarized light) having a frequency f1.
And at 45 ° with respect to the polarization direction of the measurement light (p-polarized light) at the frequency f1. The interference light generated via the polarizing plate 7 is photoelectrically converted by the photoelectric conversion element 8. Every time the movable mirror 5 moves by a predetermined amount, the interference fringes repeat light and dark. Therefore, each time the movable mirror 5 moves by a predetermined amount, the photoelectric conversion element 8 outputs a first interference signal having a substantially sinusoidal waveform having a cycle corresponding to the predetermined amount. Is done. The first interference signal output from the photoelectric conversion element 8 is supplied to the first converter 9. The first converter 9 is based on the first interference signal supplied from the photoelectric conversion element 8 and corresponds to a displacement amount of the movable mirror 5 (and thus a displacement amount of the measurement target object) measured by the light of the frequency f1. 1 displacement ΔD
The signal relating to (f1) is supplied to the signal processor 13. The first displacement amount ΔD (f1) is, for example, a moving mirror 5 obtained by digitally processing a sine wave signal output from the photoelectric conversion element 8.
Is a count value obtained by counting pulses for each predetermined displacement amount. Since the displacement amount per pulse is known in advance, the displacement amount can be uniquely obtained from the count value.

On the other hand, the reference light having the frequency f2 and the measurement light having the frequency f2 reflected by the dichroic mirror 6 interfere with each other via the polarizing plate 10. Note that the polarizing plate 10 is
Similarly to the above, they are arranged at an angle of 45 ° with respect to the polarization directions of the reference light (s-polarized) at the frequency f2 and the measurement light (p-polarized) at the frequency f2. The interference light generated via the polarizing plate 10 is received by the photoelectric conversion element 11, and the photoelectric conversion signal is supplied to the second converter 12 as a second interference signal. Second
Similarly to the first interference signal, the interference signal is a substantially sinusoidal signal corresponding to the displacement of the movable mirror 5 measured with the light having the frequency f2. The second converter 12 is based on the second interference signal supplied from the photoelectric conversion element 11 and has a second displacement amount ΔD corresponding to the displacement amount of the movable mirror 5 measured by the light having the frequency f2.
The signal relating to (f2) is supplied to the signal processor 13. Similarly to the first displacement amount ΔD (f1), the second displacement amount ΔD (f2) is a count value of pulses obtained for each predetermined displacement amount of the movable mirror 5 with respect to the light having the frequency f2.

The signal processor 13 converts the first displacement ΔD (f1) supplied from the first converter 9 into the first displacement ΔD (f1).
(F1s), and the second value supplied from the second converter 12
A second processing displacement amount ΔD (f2s) is created from the displacement amount ΔD (f2), and a first displacement amount ΔD (f1) and a second displacement amount ΔD (f
2) The first processing displacement amount ΔD (f1s) and the second processing displacement amount ΔD (f2s) are supplied to the calculator 14. The first processing displacement amount ΔD (f1s) and the second processing displacement amount ΔD (f2s) will be described later. The computing unit 14 corrects the displacement amount ΔD of the movable mirror 5 based on the displacement amounts supplied from the signal processor 13 and corrects the influence of the refractive index fluctuation due to the gas in the optical path.
Is output.

Hereinafter, in the first embodiment, the first displacement Δ
D (f1) and the second displacement amount ΔD (f2) from the displacement amount Δ
A procedure for obtaining D will be described. First, regardless of whether the movable mirror 5 is in the moving state or in the stationary state, the first displacement amount output from the signal processor 13 at the data acquisition timing tr is represented by ΔD (f1, tr), and data acquisition is performed. The second displacement amount output from the signal processor 13 at the timing time tr is represented by ΔD (f2, tr). The data acquisition timing is not particularly limited, but the data may be acquired in synchronization with a fixed clock. Further, a value obtained by subdividing a plurality of first displacement amounts by weighted averaging and output from the signal processor 13 at time td (immediately before the data acquisition timing time tr) is defined as a first processing displacement amount as ΔD ( f1s, td), and a value obtained by subdividing a plurality of second displacement amounts by weighted averaging and output from the signal processor 13 at time td as a second process displacement amount
D (f2s, td).

Then, the first processing displacement amount ΔD (f1s,
td) and the second processing displacement amount ΔD (f2s, td) are expressed by the following equations (2) and (3).

ΔD (f1s, td) = ΔD (f1s, tb) + α ｛ΔD (f1, td) −ΔD (f1s, tb)｝ (0 <α <1) (2) ΔD (f2s, td) = ΔD (f2s, tb) + α ｛ΔD (f2, td) −ΔD (f2s, tb)｝ (0 <α <1) (3) Here, ΔD (f1s, tb) is 1 of ΔD (f1s, td). This is the first processing displacement amount before (time tb), ΔD (f2s, t
b) is the second processing displacement amount one time (time tb) before ΔD (f2s, td).

In equation (2), the first displacement ΔD (f1s, td) at time td is equal to the first displacement ΔD (f
1, td), the first processing displacement amount ΔD (f1s, tb) at the data acquisition timing time tb immediately before the time td, and the constant α
Required from. Similarly, in equation (3), the time td
Is the second processing displacement amount ΔD (f2s, td) at time td.
Displacement amount ΔD (f2, td), second processing displacement amount Δ at time tb
D (f2s, tb) and a constant α. That is, in the equations (2) and (3), as shown in the following equation (4), the k-th input I (k) and the (k-1) -th output O (k-1) Is used as a variable to determine the k-th output O (k). O (k) = O (k−1) + α {I (k) −O (k−1)} (4)

Therefore, the above equations (2) and (3)
Is used to calculate the first processing displacement amount ΔD (f1s, td) and the second processing displacement amount ΔD (f2s, td), the first processing displacement amount ΔD (f1s, td) becomes the first displacement amount ΔD (f1 ) Is a weighted average of the plurality of data, and the second processing displacement amount ΔD
(F2s, td) is a weighted average of a plurality of data of the second displacement amount ΔD (f2). Moreover, equations (2) and (3)
In the weighted averaging using, the weight of temporally new data is set to be stronger than the temporally old data among a plurality of temporally continuous input data.

As described above, in the first embodiment, the simple average of the first displacement ΔD (f1) and the second displacement ΔD (f2)
Instead of the simple average of the first displacement amount ΔD (f1), the second processing displacement amount which is the weighted average of the first displacement amount ΔD (f1s, td) and the second displacement amount ΔD (f2) ΔD (f2s, td) is used. Therefore, the displacement amount ΔD (tr) of the measurement target object at the time tr in which the influence of the refractive index fluctuation due to the gas in the optical path is corrected is obtained by the following equation (5). ΔD (tr) = ΔD (f1, tr) −A {ΔD (f1s, td) −ΔD (f2s, td)} (5)

As described above, in the weighted averaging using the equations (2) and (3), the temporally old data is weaker and the temporally newer Becomes stronger. Therefore, in FIG. 3, the value of the correction amount A (ΔD1−ΔD2) obtained by the weighted average in the first embodiment is longer than the value of the correction amount A (ΔD1−ΔD2) obtained by the simple average in the prior art in time t1 (actual time). Correction amount A (ΔD corresponding to time tr)
1 -ΔD2). As a result, the lightwave displacement measuring device of the first embodiment can measure the displacement of the measurement object with high accuracy while suppressing the measurement error generated in proportion to the moving speed of the measurement object.

As described above, with the light wave displacement measuring device of the first embodiment, it is possible to reduce the measurement error generated in proportion to the moving speed of the object to be measured. However, in the first embodiment, a certain measurement error proportional to the moving speed of the object to be measured still occurs even in a situation where there is no change in the refractive index, so that sufficient real-time characteristics cannot be achieved. Therefore, in a first modified example of the first embodiment, in order to improve the real-time characteristics of the light wave displacement measuring device, an arithmetic expression disclosed in Japanese Patent Application Laid-Open No. 9-61110 filed by the present applicant is used. I do.

In the light wave displacement measuring device disclosed in Japanese Patent Application Laid-Open No. 9-61110, the calculated value A · ΔX (tw), the calculated value ΔM (tw), and ΔD (f3, tn) at time tn are calculated. And the displacement Δ at time tn by the following equation (6):
D '(tn). ΔD ′ (tn) = ΔD (f3, tn) {1−A · ΔX (tw) / ΔM (tw)} (6)

By the way, ΔD (f1, tw1), ΔD (f2, tw1),
ΔD (f3, tw1) and ΔD (f3, tn) are represented by the following equations (7) to (10), respectively.

ΔD (f1, tw1) = ｛1 + N (tw1) F (f1)｝ ΔD (tw1) (7) ΔD (f2, tw1) = ｛1 + N (tw1) F (f2)｝ ΔD (tw1 (8) ΔD (f3, tw1) = ｛1 + N (tw1) · F (f3)｝ ΔD (tw1) (9) ΔD (f3, tn) = ｛1 + N (tn) · F (f3)｝ ΔD (tn (10) where N (t) is the gas density at time t,
D (t) is the displacement amount at time t. Also, F (f)
Is a function that depends only on the frequency f of light without depending on the density of the gas if the composition ratio of the gas does not change.

From equations (7) and (8), A.ΔX (tw)
Is transformed as in the following equation (11).

A · ΔX (tw) = A ｛ΔD (f2, tw1) −ΔD (f1, tw1)｝ = A [｛1 + N (tw1) · F (f2)｝ ΔD (tw1) − ｛1 + N (tw1 ) · F (f1)｝ ΔD (tw1)] = A [｛F (f2) -F (f1)｝ N (tw1) · ΔD (tw1)] = F (f3) / ｛F (f2) -F ( f1)｝ × [｛F (f2) -F (f1)｝ N (tw1) ・ ΔD (tw1)] = F (f3) ・ N (tw1) ・ ΔD (tw1) (11)

Therefore, ｛1-A · in equation (11)
ΔX (tw) / ΔM (tw)｝ is transformed as in the following equation (12).

[Equation 5] {1−A · ΔX (tw) / ΔM (tw)} = {ΔD (f3, tw1) −A · ΔX (tw)} / ΔD (f3, tw1) = [｛1 + N (tw1) · F (f3)｝ ΔD (tw1) −A · ΔX (tw)] / [｛1 + N (tw1) · F (f3)｝ ΔD (tw1)] = ΔD (tw1) / [｛1 + N (tw1) · F ( f3)｝ ΔD (tw1)] = 1 / ｛1 + N (tw1) · F (f3)｝ (12)

Thus, equation (6) is transformed into the following equation (13).

ΔD ′ (tn) = ΔD (f3, tn) ｛1−A · ΔX (tw) / ΔM (tw)} = [｛1 + N (tn) · F (f3)} / ｛1 + N (tw1) F (f3)｝] × ΔD (tn) (13) Equation (13) gives the gas density N (tn) and time tw at time tn.
If the gas densities N (tw1) at 1 are equal, it indicates that the measurement error of the displacement ΔD ′ (tn) obtained by the arithmetic expression (6) is zero. That is, by setting the difference between the time tn and the time tw1 to be sufficiently small, it is possible to correct the measurement error due to the change in the refractive index in real time according to the arithmetic expression (6) regardless of the moving speed of the object to be measured. it can.

When the above equation (6) is applied to the first modification, time tn corresponds to time tr, time tw1 corresponds to time td, and ΔD ′ (tn) is the displacement ΔD (tr). And ΔD
(f3, tn) corresponds to the first displacement amount ΔD (f1, tr), and ΔX
(tw) is the difference ｛ΔD between the first processing displacement and the second processing displacement.
(F1s, td) -ΔD (f2s, td)}, ΔM (tw)
Corresponds to the first processing displacement amount ΔD (f1s, td). Therefore, in the first modification, the displacement amount ΔD (tr) in real time tr in which the influence of the refractive index fluctuation is corrected is calculated by the following equation (14).
Required by

[0032]

ΔD (tr) = ΔD (f1, tr) × [1−A ｛ΔD (f1s, td) −ΔD (f2s, td)} / ΔD (f1s, td)] (14) In the modified example, regardless of the moving speed of the object to be measured, the measurement error caused by the change in the refractive index can be corrected in real time according to the arithmetic expression (14), and the real-time characteristic of the light wave displacement measuring device is improved. be able to.

By the way, according to the arithmetic expression (14) of the first modification, when the displacement of the object to be measured is 0, the first processing displacement ΔD (f1s, td) becomes 0, and the computation result ΔD (tr) Will result in an error. Therefore, in the second modification of the first embodiment, the displacement amount ΔD (t
r).

ΔD (tr) = ΔD (f1, tr) × [1-A ｛ΔD (f1s, td) −ΔD (f2s, td) + Y｝ / ｛ΔD (f1s, td) + X｝] (15)

Hereinafter, a constant X in the case of using equation (15)
Consider the relationship between and Y. When the displacement of the object to be measured is 0, ΔD (f1s, td) = 0 and ｛ΔD (f1
s, td) −ΔD (f2s, td)｝ = 0, therefore, the arithmetic expression (15)
Is transformed as in the following equation (16). ΔD (tr) = ΔD (f1, tr) (1-AY / X) (16)

In equation (16), the displacement amount ΔD (tr) is obtained by multiplying the first displacement amount ΔD (f1, tr) by (1−AY / X). Here, referring to equation (15), ΔD (tr) is a constant X
In order not to include the offset caused by the addition of the values of Y and Y, it is necessary that the value of (1-AY / X) satisfies the relationship shown in the following equation (17). 1-AY / X = 1 / {1 + N (tr) .F (f1)} (17)

Equation (17) is modified as shown in the following equation (18).

Y = (X / A) · [1-1 / {1 + N (tr) · F (f1)}] = {X · N (tr) · F (f1)} / [A ｛1 + N (tr ) · F (f1)｝] (18) where N (tr) is the gas density at time tr,
It fluctuates over time.

Therefore, for example, the actual environmental conditions measured by appropriate sensor means according to predetermined design environmental conditions (temperature, humidity, water vapor pressure, carbon dioxide concentration, etc.) in which the apparatus is set, or when the apparatus is reset. (Temperature, humidity, water vapor pressure, carbon dioxide concentration, etc.), N (tr)
Can be set to a predetermined value N. In this case, equation (18) is modified as shown in the following equation (19). Y = X ・ NF ・ (f1) / [A {1 + NF ・ (f1)}] (19)

In the third modification of the first embodiment, the second modification
For the same purpose as the modification, the displacement amount ΔD (tr) is obtained according to the following equation (20).

ΔD (tr) + Z = {ΔD (f1, tr) + X} × [1-A ｛ΔD (f1s, td) −ΔD (f2s, td) + Y} / {ΔD (f1s, td) + X} (20) where A = F (f1) / {F (f1) -F (f2)}

Hereinafter, a constant X in the case of using equation (20)
And the relationship between the constant Y and the offset Z.
When the displacement of the object to be measured is 0, ΔD (f1, tr) = 0, ΔD (f1s, td) = 0, and ｛ΔD (f1s, td) −ΔD (f2
s, td)｝ = 0, therefore, the arithmetic expression (20) is given by the following expression (21)
It is transformed as follows. Z = X (1−AY / X) = X−AY (21) Further, referring to the equation (10), to make the offset Z caused by the addition of the constants X and Y constant,
It is necessary that the relationship shown in the following expression (22) be established between {ΔD (tr) + Z} and {ΔD (f1, tr) + X}. ΔD (tr) + Z = {ΔD (f1, tr) + X} / {1 + N (tr) · F (f1)} (22)

Equation (22) is transformed into the following equation (23).

ΔD (tr) + Z = {ΔD (f1, tr) + X} / {1 + N (tr) · F (f1)} = [｛1 + N (tr) · F (f1)｝ ΔD (tr) + X] / {1 + N (tr) · F (f1)} = ΔD (tr) + X / {1 + N (tr) · F (f1)} (23) Therefore, from the equation (23), the relation shown in the following equation (24) is obtained. Is obtained. Z = X / {1 + N (tr) · F (f1)} (24) Here, when N (tr) is set to a predetermined value N, the equation (24) is obtained.
Is transformed as shown in the following equation (25). Z = X / {1 + NF (f1)} (25)

As described above, in the second modification, the displacement X of the object to be measured can be obtained by using the arithmetic expression (15) by selecting the constant X and the constant Y satisfying the expression (19). In the third modified example, a constant X, a constant Y, and an offset Z satisfying Expressions (24) and (25) are selected, and the displacement amount of the measurement target object is obtained using Expression (20). it can. In each case, the possible displacement range of the object to be measured is set so that the denominator of the division in the arithmetic expressions (15) and (20) does not become 0 or a value close to 0 and no error occurs. Therefore, it is preferable to select the constant X such that {ΔD (f1s, td) + X} does not become 0 or a value close to 0.

When the object to be measured is, for example, a moving stage of an exposure apparatus, {ΔD (f1s, td) −ΔD (f2s, td)} becomes 0 or the sign changes to ± near the reset position. Therefore, it is desirable to select the constant Y such that {ΔD (f1s, td) −ΔD (f2s, td) + Y} does not become 0 or a value close to 0 with respect to the possible displacement range of the measurement object. As described above, according to the second modification and the third modification, the denominator does not become 0 or a value close to 0 in the division of the arithmetic expression with respect to the displacement range of the measurement target object.
Irrespective of the amount of displacement of the object to be measured, it is possible to stably correct a measurement error caused by a change in the refractive index in real time.

FIG. 2 is a diagram schematically showing the configuration of a light wave displacement measuring device according to a second embodiment of the present invention. In the first embodiment, the displacement is measured by the homodyne interference method. In the second embodiment, the displacement is measured by the heterodyne interference method. In the second embodiment, light of frequency f1 and light of frequency f1 'having slightly different frequencies and orthogonal polarization directions are compared with light of frequency f2 and light of frequency f2' having slightly different frequencies and orthogonal polarization directions. A light source 21 that emits light along the same optical path is provided. Here, the light having the frequency f1 and the light having the frequency f2 (f1２f2) are linearly polarized light having a polarization direction in the vertical direction in the plane of FIG. The light of frequency f1 'and the light of frequency f2'(f1'1f2') are linearly polarized light having a polarization direction perpendicular to the plane of FIG.

The light having the frequency f1 and the light having the frequency f1 'and the light having the frequency f2 and the light having the frequency f2' emitted from the light source 21.
Is transmitted through the beam splitter 22 and then enters the polarization beam splitter 23. The polarizing beam splitter 23 transmits light (p-polarized light) having a polarization direction in the vertical direction in the plane of FIG. 2 and reflects light (s-polarized light) having a polarization direction in a direction perpendicular to the plane of FIG. Therefore, the light incident on the polarization beam splitter 23 is guided to a reference optical path on which a fixed mirror 24 composed of a corner cube prism is disposed, and is guided to a measurement optical path on which a movable mirror 25 composed of a corner cube prism is disposed. It is separated from the measurement light.

The light of frequency f 1 ′ and the light of frequency f 2 ′ reflected by the polarization beam splitter 23 return to the polarization beam splitter 23 again after being reflected by the fixed mirror 24, and are reflected by the polarization beam splitter 23. The light of the frequency f1 and the light of the frequency f2 that have passed through the polarization beam splitter 23 are reflected by the movable mirror 25 and then return to the polarization beam splitter 23 again.
Through. Thus, the light of the frequency f1 'and the light of the frequency f2' emitted from the polarization beam splitter 23 via the reference optical path, and the light of the frequency f1 and the light of the frequency f2 emitted from the polarization beam splitter 23 via the measurement optical path are Along the same optical path, the dichroic mirror 26
Incident on. The dichroic mirror 26 has a frequency f
The light near the frequency 1 is transmitted, and the light near the frequency f2 is reflected. Therefore, the reference light of frequency f1 'and the frequency f
The first measurement light is transmitted through the dichroic mirror 26, and the reference light having the frequency f2 'and the measurement light having the frequency f2 are reflected by the dichroic mirror 26.

The reference light having the frequency f 1 ′ and the measurement light having the frequency f 1 transmitted through the dichroic mirror 26 are
Interfere through. Note that the polarizing plate 27 includes a reference light (s-polarized light) having a frequency f1 'and a measurement light (p-polarized light) having a frequency f1.
Are arranged at an angle of 45 ° with respect to the polarization direction of The interference light generated through the polarizing plate 27 is received by the photoelectric conversion element 28, and the photoelectric conversion signal is used as the first interference signal as the first interference signal.
It is supplied to a converter 29.

On the other hand, the reference light having the frequency f 2 ′ and the measurement light having the frequency f 2 reflected by the dichroic mirror 26 interfere with each other via the polarizing plate 30. Note that, similarly to the polarizing plate 27, the polarizing plate 30 is rotated 45 degrees with respect to the polarization direction of the reference light (s-polarized light) at the frequency f2 'and the measuring light (p-polarized light) at the frequency f2.
° It is arranged at an angle. The interference light generated via the polarizing plate 30 is received by the photoelectric conversion element 31, and the photoelectric conversion signal is supplied to the second converter 32 as a second interference signal.

On the other hand, part of the light emitted from the light source 21 is reflected by the beam splitter 22 and then enters the dichroic mirror 35. Dichroic mirror 3
5 has a frequency f like the dichroic mirror 26.
The light near the frequency 1 is transmitted, and the light near the frequency f2 is reflected. Accordingly, the light having the frequency f1 'and the light having the frequency f1 pass through the dichroic mirror 35, and the light having the frequency f2' and the light having the frequency f2 are reflected by the dichroic mirror 35.

The light having the frequency f 1 ′ and the light having the frequency f 1 transmitted through the dichroic mirror 35 interfere with each other via the polarizing plate 36. The polarizing plate 36 is, like the polarizing plate 27,
It is arranged at an angle of 45 ° with respect to the polarization directions of the light of frequency f1 '(s-polarized light) and the light of frequency f1 (p-polarized light).
The interference light generated via the polarizing plate 36 is
7, and the photoelectric conversion signal is supplied to the first converter 29 as a first reference signal.

On the other hand, the light of the frequency f 2 ′ and the light of the frequency f 2 reflected by the dichroic mirror 35 are
Interfere through. Note that, similarly to the polarizing plate 30, the polarizing plate 38 is arranged at an angle of 45 ° with respect to the polarization direction of the light having the frequency f2 '(s-polarized light) and the light having the frequency f2 (p-polarized light). The interference light generated via the polarizing plate 38 is received by the photoelectric conversion element 39, and the photoelectric conversion signal is supplied to the second converter 32 as a second reference signal.

The first converter 29 measures the phase change of the first interference signal with respect to the first reference signal, and thereby detects the displacement of the movable mirror 25 (and thus the displacement of the object to be measured) measured by the light of frequency f1. ) Corresponding to the first displacement ΔD
The signal relating to (f1) is supplied to the signal processor 33. Further, the second converter 32 measures a phase change of the second interference signal with respect to the second reference signal, thereby obtaining a second change corresponding to the displacement amount of the movable mirror 25 measured by the light having the frequency f2.
A signal related to the displacement amount ΔD (f2) is supplied to the signal processor 33. Note that, like the first embodiment, the first displacement amount ΔD
(F1) and the second displacement amount ΔD (f2) are equal to the frequency f1
Is a count value of a pulse obtained for each predetermined displacement amount of the movable mirror 25 with respect to the light having the frequency f2.

The signal processor 33 converts the first displacement amount ΔD (f1) supplied from the first converter 29 into the first displacement amount ΔD (f1).
D (f1s) is created, and the second processing displacement amount ΔD (f2s) is obtained from the second displacement amount ΔD (f2) supplied from the second converter 32.
And the first displacement amount ΔD (f1) and the second displacement amount ΔD
(F2), the first processing displacement amount ΔD (f1s), and the second processing displacement amount ΔD (f2s) are supplied to the calculator 34. The arithmetic unit 34 calculates and outputs the displacement amount ΔD of the movable mirror 25 in which the influence of the refractive index fluctuation due to the gas in the optical path is corrected based on the displacement amounts supplied from the signal processor 33.

As described above, in the second embodiment, similarly to the first embodiment, the displacement amount of the movable mirror 25 is obtained by using the arithmetic expression (5), so that the displacement amount is generated in proportion to the moving speed of the object to be measured. Measurement errors can be reduced. In addition, in the second embodiment, by calculating the displacement of the movable mirror 25 using the arithmetic expression (6) of the first modified example, the measurement error due to the change in the refractive index is realized irrespective of the moving speed of the object to be measured. It can be corrected by time. Further, in the second embodiment, the displacement amount of the movable mirror 25 is obtained by using the operation expression (15) of the second modification or the operation expression (20) of the third modification, so that the displacement amount of the measurement target object is obtained. Regardless, it is possible to stably correct a measurement error caused by a change in the refractive index in real time.

In each of the above embodiments, the first displacement ΔD (f1) measured using the light of frequency f1 and the second displacement ΔD (f2) measured using the light of frequency f2. hand,
The displacement ΔD of the object to be measured is determined. However, the third displacement ΔD (f3) is further detected by using the third light having the frequency f3, and is calculated based on the difference between the first displacement ΔD (f1) and the second displacement ΔD (f2). The displacement amount ΔD of the object to be measured can be obtained by correcting the third displacement amount ΔD (f3) with the corrected amount.

[0055]

As described above, according to the present invention,
The weighted average value of the first displacement amount ΔD (f1) and the second displacement amount ΔD
The correction amount is calculated based on the difference from the weighted average value of (f2). At this time, the first displacement ΔD (f1) and the second displacement Δ
Out of the plurality of data of D (f2), the weight of the temporally old data is weak and the temporally new data is strongly weighted. Therefore, the value of the correction amount obtained by the weighted averaging in the present invention is closer to the true value of the correction amount in real time than the value of the correction amount obtained by the simple averaging in the related art. As a result, the light wave displacement measuring device of the present invention can measure the displacement of the object to be measured with high accuracy while suppressing the measurement error by increasing the accuracy of the correction amount.

[Brief description of the drawings]

FIG. 1 is a diagram schematically showing a configuration of a light wave displacement measuring device according to a first embodiment of the present invention.

FIG. 2 is a diagram schematically showing a configuration of a lightwave displacement measuring device according to a second embodiment of the present invention.

FIG. 3 is a diagram for explaining a measurement error occurring in a conventional light wave interference measurement device disclosed in Japanese Patent Publication No. 7-81819.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1, 21 Light source 22 Beam splitter 3, 23 Polarization beam splitter 4, 24 Fixed mirror 5, 25 Moving mirror 6, 26 Dichroic mirror 7, 10 Polarizer 8, 11, Photoelectric conversion element 9, 29 First converter 12, 32 First 2 converter 13, 33 Signal processor 14, 34 Operation unit

Claims (3)

[Claims] 1. A first light having a frequency f1 is propagated along a predetermined optical path, and a first displacement ΔD (f1) corresponding to a displacement of an object to be measured disposed in the optical path is detected. And a second light having a frequency f2 different from the frequency f1 is propagated along the predetermined optical path, and a second displacement ΔD (f2 ), And considering the influence of refractive index fluctuation due to gas in the optical path based on the difference between the first displacement ΔD (f1) and the second displacement ΔD (f2). And a processing operation system for correcting the first displacement amount ΔD (f1) with the calculated correction amount to obtain a displacement amount ΔD of the object to be measured. From the plurality of data relating to the first displacement amount ΔD (f1), Weighted average value in which the weight of new data is set strongly, and weighted average value in which the weight of data that is temporally newer than the data that is temporally older is set stronger from the plurality of data related to the second displacement amount ΔD (f2). And calculating the correction amount based on a difference between the light wave displacement amount and the light wave displacement amount. 2. The processing operation system according to claim 1, wherein a time td of a plurality of data regarding the first displacement ΔD (f1)
Is the first processing displacement amount corresponding to the weighted average value in Δ
D (f1s, td), the second processing displacement corresponding to the weighted average value at time td of the plurality of data relating to the second displacement ΔD (f2) is ΔD (f2s, td), and the The first displacement corresponding to the first displacement is ΔD (f1, tr), and the displacement of the measurement object at the time tr is Δ
D (tr), and if the composition ratio of the gas in the optical path is unchanged, a predetermined function that depends only on the frequency f of light is F (f),
The displacement amount ΔD accompanying the addition of the predetermined constant X and the constant Y
When the offset of (tr) is Z, ΔD (tr) + Z = {ΔD (f1, tr) + X} × [1-
A ｛ΔD (f1s, td) −ΔD (f2s, td) + Y｝ / ｛ΔD (f1s, t
d) + X}] where A = F (f1) / {F (f1) -F (f2)}, wherein the displacement amount ΔD (tr) is obtained according to an arithmetic expression represented by the following expression. 2. The light wave displacement measuring device according to 1. 3. A first light having a frequency f1, a second light having a frequency f2 substantially different from the frequency f1, and a third light having a frequency f1 ′ slightly different from the frequency f1. And a light source for supplying a fourth light having a frequency f2 ′ slightly different from the frequency f2, and among the light supplied from the light source, the first light and the second light And a separating unit for guiding the third light and the fourth light to a reference light path via a fixed mirror, and a first light via the measurement light path. A first displacement amount ΔD corresponding to a displacement amount of the object to be measured to which the movable mirror is attached, based on interference light between the moving object and the third light via the reference optical path.
a first detection system for detecting (f1), and a displacement amount of the measurement target object based on an interference light between the second light via the measurement optical path and the fourth light via the reference optical path. And a second detection system for detecting a second displacement amount ΔD (f2) corresponding to the first and second displacement amounts ΔD (f1) and ΔD (f2) based on a difference between the first displacement amount ΔD (f1) and the second displacement amount ΔD (f2). Calculation for calculating a correction amount in consideration of the influence of the refractive index variation due to the gas, and correcting the first displacement amount ΔD (f1) with the calculated correction amount to obtain the displacement amount ΔD of the object to be measured. The processing operation system, wherein the weighted average value of the plurality of data items related to the first displacement amount ΔD (f1) and the second displacement amount ΔD (f
A light wave displacement amount measuring device, wherein the correction amount is calculated based on a difference from a weighted average value of a plurality of data items relating to (2).