JP6853659B2 - Determining method, optical equipment, projection optical system, exposure equipment and manufacturing method of articles - Google Patents

Description

The present invention relates to a determination method, an optical device, a projection optical system, an exposure device, and a method for manufacturing an article.

In astronomical observations using astronomical equipment such as telescopes on the ground, blurring of star images due to air fluctuations becomes a problem. Therefore, in such a telescope, by using a variable mirror with a variable surface (reflection surface) shape called an adaptive optics system, the fluctuation of air measured by the wavefront sensor is corrected and the blur of the star image is reduced. ing.

In addition, in the photolithography process of transferring a mask (reticle) pattern to a substrate when manufacturing a semiconductor device, an image of a very fine pattern is formed on the substrate, so that the influence of optical system aberrations becomes a problem. Become. Even in such a case, the imaging characteristics can be improved by using a variable optical element that deforms the lens or mirror of the optical system of the exposure apparatus, as in the case of the adaptive optics system described above.

In a variable mirror, which is a typical variable optical element, the shape of the mirror itself is controlled by deforming the mirror itself by driving a large number of actuators arranged on the mirror. As the actuator, a piezo actuator, a voice coil motor (VCM), a linear motor, a solenoid and the like are used.

In actuators that use electromagnetic force, such as VCMs and linear motors, the stator and mover are non-contact (that is, they are non-contact actuators), so the structure on the stator side may be deformed when the mirror is driven. It has the characteristic that it is not easily affected by vibration. Therefore, an actuator such as a VCM is advantageous from the viewpoint of avoiding thermal deformation and vibration of peripheral parts when controlling the shape of the mirror with high accuracy. Further, since the actuator using the electromagnetic force drives the mirror by the force, it is not essential to measure the displacement of the actuator. Therefore, in contrast to piezo actuators and ball screws, which require displacement measurement, displacement sensors can be omitted in actuators that utilize electromagnetic force, which contributes to cost reduction. In the variable mirror, in order to achieve both high-precision shape control and cost, open control drive that omits the displacement sensor is effective.

In a variable mirror using a non-contact type actuator, the thrust of each actuator for obtaining the target shape can be obtained from the linear sum of the relationship between the drive of each actuator and the deformation of the mirror. Such a relationship can be expressed by the following equations (1) to (4) using the compliance matrix.

In the equations (1) to (4), C represents the compliance matrix, X represents the displacement (target shape) of the mirror, F represents the thrust of each actuator, and n ≧ m.

The ideal value of the compliance matrix can be obtained by finite element analysis. However, in reality, the rigidity of the entire variable mirror is not in the ideal state due to errors and non-uniformity of the physical property values of each member, thrust variation of the actuator, mounting error, etc., so the compliance matrix has a value different from the ideal value. It becomes. Therefore, it is necessary to identify the compliance matrix specific to such a variable mirror using an actual variable mirror.

In the identification of the compliance matrix, for example, one row of compliance matrix is obtained by driving one actuator with a unit thrust and measuring the displacement of the mirror at that time. By performing such actuator drive and mirror displacement measurement for all actuators, the compliance matrix represented by the equation (2) can be obtained.

The displacement of the mirror is measured using, for example, a measuring instrument such as an interferometer or a multipoint displacement meter (see Patent Document 1). Patent Document 1 discloses a technique of configuring a wave surface measurement system for measuring the displacement of a mirror and creating a voltage template (compliance matrix) which is an offset for each device.

Japanese Unexamined Patent Publication No. 2007-25503

However, in the variable mirror, the compliance matrix changes due to the thrust fluctuation of the actuator due to the heat of moving the device, the change of the physical properties of each member with time, the familiarity of the assembly of each member, and the like. If the compliance matrix changes, an error will occur in driving the mirror using it, so calibration to reidentify the compliance matrix will be required.

As described above, the compliance matrix can be calibrated by providing a measuring instrument such as an interferometer or a multi-point displacement meter. However, in order to obtain the thrust of all the actuators, at least the same number of measuring instruments as the actuators are required to measure the displacement of the mirror due to the driving of the actuators. Therefore, the conventional variable mirror has problems such as an increase in cost due to mounting of a measuring instrument, a problem of arrangement of measuring instruments, and a decrease in operating rate due to measurement of displacement of the mirror. It is also difficult to calibrate only the changed compliance matrix instead of calibrating all the compliance matrices.

On the other hand, it is also conceivable to calibrate the compliance matrix using an external measuring instrument. In this case, the measuring instrument becomes unnecessary and the cost can be reduced. However, since the variable mirror must be installed in the external measuring instrument every time the calibration is performed, the operating rate is significantly reduced.

The present invention has been made in view of such problems of the prior art, and an exemplary object is to provide an advantageous determination method for determining a matrix showing the relationship between the thrust of an actuator and the displacement of an optical element.

In order to achieve the above object, the determination method as one aspect of the present invention is in the thrust of each of the plurality of electromagnetic actuators for deforming the optical element by applying a force and the location where each of the plurality of electromagnetic actuators is provided. It is a determination method for determining a matrix showing the relationship with the displacement of the optical element, and when the first electromagnetic actuator of one of the plurality of electromagnetic actuators is driven by a unit current, each of the plurality of electromagnetic actuators the value of the current flowing in the at least one electromagnetic actuator of the plurality of electromagnetic actuators a first step of acquiring the displacement of the optical element in the first location provided, obtained in the first step The second step of calculating the column matrix based on the value of the current flowing through each of the plurality of electromagnetic actuators and the displacement of the optical element at the first location acquired in the first step , and the first electromagnetic actuator. When the second electromagnetic actuator of one of the plurality of electromagnetic actuators different from the above is driven by a unit current, the value of the current flowing through each of the plurality of electromagnetic actuators and the displacement of the optical element at the first location. Based on the third step of acquiring the above, the value of the current flowing through each of the plurality of electromagnetic actuators acquired in the third step, and the displacement of the optical element in the first location acquired in the third step. Te, possess a fourth step of calculating a column matrix, and a column matrix calculated in the second step, based on a plurality of columns matrix containing a column matrix calculated by the fourth step, the matrix It is characterized by determining.

Further objects or other aspects of the invention will be manifested in the preferred embodiments described below with reference to the accompanying drawings.

According to the present invention, for example, it is possible to provide an advantageous determination method for determining a matrix showing the relationship between the thrust of an actuator and the displacement of an optical element.

It is the schematic which shows the structure of the optical apparatus as one aspect of this invention. It is a figure for demonstrating the process which determines the compliance matrix in this embodiment. It is the schematic which shows the structure of the exposure apparatus as one aspect of this invention.

Hereinafter, preferred embodiments of the present invention will be described with reference to the accompanying drawings. In each figure, the same member is given the same reference number, and duplicate description is omitted.

In the present embodiment, the mirror will be described as an example of the optical element, but the mirror can be replaced with another optical element such as a lens, a parallel plate glass, a prism, a Fresnel zone plate, a quinoform, a binary optics, or a hologram. Is. Further, in the present embodiment, a voice coil motor (VCM) will be described as an example of an actuator that deforms the mirror by applying a force, but the VCM can be replaced with an actuator that uses electromagnetic force such as a linear motor or a solenoid. is there. Such an actuator includes a magnet and a coil, one of which is provided on the optical element and the other of which is arranged on the base plate, and drives and deforms the optical element by passing an electric current through the coil.

FIG. 1 is a schematic view showing a configuration of an optical device 1 as one aspect of the present invention. The optical device 1 is a variable mirror device that deforms the mirror 2, specifically, deforms the reflecting surface 2a of the mirror 2 into a target shape. The optical device 1 includes a mirror 2, a base plate 3, a plurality of actuators 4, a measuring unit 5, a detecting unit 7, a main control unit 10, and a supporting unit 21.

The mirror 2 is, for example, a circular mirror. The support portion 21 is provided on the base plate 3 and supports the mirror 2 at the center of the back surface 2b of the mirror 2. The base plate 3 is attached to a housing (not shown) of the optical device 1. The optical device 1 is used in combination with, for example, a light receiving element or another optical system.

The actuator 4 is provided on the mirror 2 and applies a force to the mirror 2 to deform it. The actuator 4 is composed of a VCM including a mover 401 attached to the back surface 2b of the mirror 2 and a stator 402 attached to the base plate 3 so as to face the mover 401. In the present embodiment, the mover 401 is a magnet and the stator 402 is a coil in order to avoid vibration and weight increase due to the arrangement of additional objects such as wiring on the mirror 2 on the movable side. Although it is effective to use the mover 401 as a coil as a weight reduction for improving the vibration eigenvalue of the mirror 2, the wiring design such as wiring and cooling of the coil becomes complicated. Further, the number of actuators 4 is not limited, and may be arbitrarily set according to the shape accuracy required for the mirror 2.

The measuring unit 5 measures the displacement of the mirror 2 at a location (first location) where at least one of the plurality of actuators 4 is provided. The measuring unit 5 detects the displacement of at least one actuator and obtains the displacement of the mirror 2 based on the displacement. In the present embodiment, the measuring unit 5 includes a displacement sensor provided in one of the plurality of actuators 4.

The detection unit 7 detects the current flowing through each of the plurality of actuators 4, specifically, the current for driving the actuator 4, and the induced electromotive force generated in the actuator 4. In the present embodiment, the detection unit 7 includes a plurality of ammeters provided for each of the plurality of actuators 4.

The main control unit 10 comprehensively controls the entire optical device 1 (each unit). In the present embodiment, the main control unit 10 includes an actuator control unit 6 and a processing unit 8. The actuator control unit 6 controls each of the plurality of actuators 4. For example, the actuator control unit 6 feeds back the value of the current detected by the detection unit 7 to precisely control (adjust) the drive current applied to the actuator 4. The processing unit 8 determines (identifies) a matrix showing the relationship between the thrust of each of the plurality of actuators 4 and the displacement of the mirror 2 at the location where each of the plurality of actuators 4 is provided, that is, a so-called compliance matrix. Further, the processing unit 8 determines the value of the current applied to each of the plurality of actuators 4 in order to deform the mirror 2 into the target shape based on the compliance matrix.

With reference to FIG. 2, a process for determining the compliance matrix in the present embodiment, which is performed by the processing unit 8, will be described. Here, as shown in FIG. 2, _n VCMs of _{VCM 1 , VCM 2} , VCM ₃ , VCM ₄ , ..., VCM n are considered as a plurality of actuators 4. _{Also, I '1, I' 2} , I '3, I' 4, ···, I 'n denotes the value of the induced electromotive current generated in each of the VCM ₁ to VCM _n.

As shown in Equation (1), the thrust of each actuator and the displacement of the mirror are required to determine the compliance matrix. However, in the present embodiment, it is not necessary to obtain the thrust of each actuator, and the compliance matrix is determined based on the value of the induced electromotive force generated in each actuator and the displacement of the mirror 2 at the location where each actuator is provided. ..

As will be described later, in the present embodiment, one of the plurality of actuators 4 is driven by a unit current. At that time, the value of the current generated in each of the plurality of actuators 4 and the displacement of the mirror 2 at the first place where at least one actuator of the plurality of actuators 4 is provided are acquired (first step). Then, the matrix is determined based on the value of the current generated in each of the acquired plurality of actuators 4 and the displacement of the mirror 2 at the first position (second step). At this time, based on the ratio of the values of the currents generated in each of the acquired plurality of actuators 4, the displacement of the mirror 2 in each of the plurality of second locations is obtained with reference to the displacement of the mirror 2 in the first location. Then, the compliance matrix is determined based on the displacement of the mirror 2 at the first location and the displacement of the mirror 2 at each of the plurality of second locations. The plurality of second locations are locations where actuators other than at least one actuator (that is, the actuator provided at the first location) of the plurality of actuators 4 are provided.

The process of determining the compliance matrix will be specifically described. By driving the VCM ₁ , a column compliance matrix of only one column shown in the following equation (5) can be obtained. By linearly adding the column compliance matrix obtained by performing this for all VCMs, a complete compliance matrix of n rows and n columns corresponding to the number of VCMs can be obtained.

In the present embodiment, first, the VCM ₁ is driven by the unit current I ₁ to deform the mirror 2, and then the supply of the unit current I _{1 to the VCM 1} is stopped. When the mirror 2 which is deformed by driving of the VCM1 returns to its original shape, each induced electromotive current I _'1 to I' _n the VCM ₁ to VCM _n occurs.

Unit current I ₁ which drives the VCM _1, the induced electromotive current I _'1 to I' _n and the mirror 2 to be measured by the measurement unit 5 displaced, how to get the column compliance matrix shown in the following equation (6) explain.

The thrust F on the right side of the equation (6) is obtained by the following equation (7) from the current (driving current) supplied to the VCM. In the formula (7), F indicates the thrust of the VCM, K _f indicates the thrust constant of the VCM, and I indicates the drive current supplied to the VCM.

Then, the left side of the displacement X of the mirror 2 in the formula (6), the unit current _{I 1} which drives the VCM _1, the induced electromotive current I _'1 to I' _n and the mirror 2 to be measured by the measurement unit 5 displacement I will explain how to get it. When driving the VCM ₁ in unit current _{I 1,} by driving the VCM _1, mirror 2 is deformed portion where VCM ₁ is provided (driving point) as a starting point. _{By driving the VCM 1} in this way, the other VCM _i (i = 2, 3, 4, ..., N) are displaced, and the induced electromotive force I represented by the following equation (8) is applied to each of the _{VCM i.} ' _I1 (i = 2, 3, 4, ..., N) occurs. In the formula (8), i indicates the displacement point number, dX indicates the displacement speed of the mover 401 provided on the mirror 2, and R indicates the resistance value of the VCM.

With reference to equation (8), the induced electromotive currents _I'i1 to VCM _i (i = 2, 3, 4, ..., N) are displaced by the _{velocity dX i1 represented by the following equation (9).} You can see that there is.

However, the unit current I ₁ which drives the VCM _1, the displacement delay of each part by elastic damping of the mirror 2 material must be adjusted to drive at a speed degree of no problem. _{This is because the displacement X i1} of the mirror 2 at the location (second location) where each VCM is provided and the displacement speed dX _i1 of the mirror 2 are in a proportional relationship. Further, the degree of no problem is the range of the error from the proportional relationship between the _{displacement X i1} and the velocity dX _i1 that are allowed for the accuracy of the compliance matrix required in the design of the optical device 1.

While _{driving the VCM 1} with the unit current I ₁ , the measuring unit 5 measures _{the displacement X ref-1} of the mirror 2 at the location where the _{VCM n} is provided. As described above, the displacement X _i1 of the mirror 2 and the displacement speed dX _i1 of the mirror 2 are in a proportional relationship. Therefore, the displacement of the mirror 2 at the location where each VCM is provided is calculated by the following equation (10) from _{the displacement X ref-1} and the velocity dX _{i1 measured by the measuring unit 5.}

Further, when the equation (9) is applied to the equation (10), the following equation (11) is obtained.

Here, since the resistance value and the thrust constant of the VCM are values peculiar to the system, if the following equation (12) is defined, the displacement X _{i1 of the} mirror 2 can be obtained by the following equation (13).

When the measurement unit 5 for measuring the displacement of the mirror 2 there are multiple, the VCM _4, may be applied relationship comprising a displacement _{X ref} of VCM _4. In this case, the error in the proportional calculation of the displacement of the mirror 2 can be reduced by combining each displacement point of the mirror 2 with the location where the measuring unit 5 is provided so that the ratio of the induced electromotive force becomes small. ..

However, the displacement of the mirror 2 at the location where the VCM _{4 is provided is X ref} . Further, since the unit current I _{1 is passed through the VCM 1,} it is necessary to reverse the sign of the current value. Therefore, the displacement X _{11 of the VCM 1} is obtained by the following equation (14).

Further, the displacement X _{21 of the VCM 2} is obtained by the following equation (15).

From the formula (7) and the formula (11), the formula (5) can be expressed by the following formula (16).

Therefore, _Ci1 is represented by the following equation (17).

In this way, the column compliance matrix can be obtained by driving the _{VCM 1} with the unit current I _1. By linearly adding the column compliance matrix obtained by performing this for n VCMs, the compliance matrix _Cij shown in the following equation (18) can be obtained. In formula (18), j represents a VCM number.

Next, the actual operation of the optical device 1, that is, the operation of deforming the mirror 2 (reflection surface 2a) into the target shape will be described. _{First, based on the compliance matrix Cij} shown in the equation (18), _{the value I drv} of the current applied to the VCM in order to deform the mirror 2 into the target shape X _obj is obtained (determined). The equation for the displacement point X _{obj-1 of the mirror for obtaining the} current value I drv is expressed by the following equation (19). By solving the simultaneous equations for all the displacement points of the mirror 2, the value of the current applied to each of the VCMs can be obtained.

For formula (19), referring to equation (16), it can be seen _{that a 1} term is erased. This is because the resistance value and thrust constant of the VCM are included in the compliance matrix, and in the actual operation of the optical device 1, the mirror 2 can be deformed into the target shape only by the current (value) applied to the VCM. It shows that.

In the present embodiment, in the determination of the compliance matrix, the induced electromotive force generated in the VCM by driving the VCM is measured as a current value, but it can be similarly implemented by measuring the induced electromotive force as a voltage value. is there.

Further, the process of determining the compliance matrix in the present embodiment can be applied to both the case of determining the initial compliance matrix and the case of calibrating the compliance matrix. When calibrating the compliance matrix, the operation of the optical device 1 is temporarily stopped, and the above-described processing for determining the compliance matrix is performed. At this time, if the optical device 1 vibrates, an error is included in the compliance matrix. Therefore, take some time until the vibration is sufficiently settled, or enable the function of suppressing (blocking) the vibration input to the optical device 1. It is good to keep it. Further, the compliance matrix may be calibrated periodically or after confirming whether or not the mirror 2 is deformed to the target shape. Whether or not the mirror 2 is deformed to the target shape may be confirmed based on, for example, whether or not the displacement of the mirror 2 at the location where the measuring unit 5 is provided is the target displacement.

The exposure apparatus EX will be described with reference to FIG. The exposure apparatus EX is a lithography apparatus that exposes the substrate S. The exposure apparatus EX includes an illumination optical system IL, a projection optical system PO, a mask stage MS that holds and moves the mask M, and a substrate stage SS that holds and moves the substrate S. Further, the exposure device EX includes a CPU, a memory, and the like, and has a control unit CN that controls the entire exposure device EX.

The light from the light source (not shown) forms, for example, an arc-shaped illumination region long in the Y-axis direction on the mask through a slit (not shown) included in the illumination optical system IL. The illumination optical system IL illuminates the mask M. The mask M is held by the mask stage MS, and the substrate S is held by the substrate stage SS. The mask M and the substrate S are arranged at positions substantially conjugate with each other (positions of the object plane and the image plane of the projection optical system PO) via the projection optical system PO. The projection optical system PO projects an object onto an image plane. In the present embodiment, the projection optical system PO has a predetermined projection magnification (for example, 1/2 times) and projects the pattern formed on the mask M onto the substrate S. Then, the mask stage MS and the substrate stage SS are scanned in a direction parallel to the object surface of the projection optical system PO (for example, the X direction in FIG. 3) at a speed ratio corresponding to the projection magnification of the projection optical system PO. As a result, the pattern formed on the mask M can be transferred to the substrate S.

The projection optical system PO includes, for example, a plane mirror PM, a concave mirror CM, and a convex mirror VM, as shown in FIG. The light emitted from the illumination optical system IL and passing through the mask M is reflected by the first surface PMa of the flat mirror PM and incident on the first surface CMa of the concave mirror CM. The light reflected by the first surface CMa of the concave mirror CM is reflected by the convex mirror VM and is incident on the second surface CMb of the concave mirror CM. The light reflected by the second surface CMb of the concave mirror CM is reflected by the second surface PMb of the flat mirror PM and is imaged on the substrate. In the projection optical system PO, the convex mirror VM becomes an optical pupil.

In the exposure apparatus EX, the above-mentioned optical apparatus 1 is used as, for example, a variable mirror apparatus that deforms the reflective surface of the concave mirror CM into an arbitrary shape (that is, the concave mirror CM is a mirror 2). As described above, the optical device 1 is advantageous for determining the initial compliance matrix and calibrating the compliance matrix. Therefore, the concave mirror CM is deformed into a target shape regardless of changes over time. be able to. Here, the control unit CN in the exposure apparatus EX may be configured to include the main control unit 10 in the optical apparatus 1 described above.

The method for manufacturing an article according to an embodiment of the present invention is suitable for producing an article such as a microdevice such as a semiconductor device or an element having a fine structure, for example. The method for manufacturing an article of the present embodiment includes a step of forming a latent image pattern on a photosensitive agent (resist) supplied to a substrate using an exposure apparatus EX (a step of exposing the substrate), and a step of forming a latent image pattern in such a step. It includes a step of developing the formed substrate. In addition, such manufacturing methods include other well-known steps such as oxidation, film formation, vapor deposition, doping, flattening, etching, resist stripping, dicing, bonding, packaging and the like. The method for producing an article of the present embodiment is advantageous in at least one of the performance, quality, productivity and production cost of the article as compared with the conventional method.

The present invention supplies a program that realizes one or more functions of the above-described embodiment to a system or device via a network or storage medium, and one or more processors in the computer of the system or device reads and executes the program. It can also be realized by the processing to be performed. It can also be realized by a circuit (for example, ASIC) that realizes one or more functions.

Although the preferred embodiments of the present invention have been described above, it goes without saying that the present invention is not limited to these embodiments, and various modifications and modifications can be made within the scope of the gist thereof.

1: Optical device 2: Mirror 4: Actuator 5: Measuring unit 7: Detection unit 8: Processing unit 10: Main control unit

Claims (16)

It is a determination method for determining a matrix showing the relationship between the thrust of each of a plurality of electromagnetic actuators that deform by applying a force to an optical element and the displacement of the optical element at a location where each of the plurality of electromagnetic actuators is provided. ,
When driving one of the first electromagnetic actuator of the plurality of electromagnetic actuators in the unit current, the value of the current flowing through each of the plurality of electromagnetic actuators, at least one of the electromagnetic actuator of the plurality of electromagnetic actuators The first step of acquiring the displacement of the optical element at the first place provided with
The column matrix is calculated based on the value of the current flowing through each of the plurality of electromagnetic actuators acquired in the first step and the displacement of the optical element in the first location acquired in the first step. 2 steps and
When the second electromagnetic actuator of one of the plurality of electromagnetic actuators different from the first electromagnetic actuator is driven by a unit current, the value of the current flowing through each of the plurality of electromagnetic actuators and the value of the current flowing in each of the plurality of electromagnetic actuators and the first location. The third step of acquiring the displacement of the optical element and
The column matrix is calculated based on the value of the current flowing through each of the plurality of electromagnetic actuators acquired in the third step and the displacement of the optical element in the first location acquired in the third step. 4 steps and
Have a,
A determination method characterized in that the matrix is determined based on a plurality of column matrices including the column matrix calculated in the second step and the column matrix calculated in the fourth step. The determination method according to claim 1, wherein the matrix is determined by linearly adding the plurality of column matrices. The plurality of column matrices are calculated by driving all of the plurality of electromagnetic actuators one by one with a unit current.
The determination method according to claim 1 or 2, wherein the matrix is determined based on the plurality of column matrices. In the second step,
Based on the ratio of the values of the currents flowing through each of the plurality of electromagnetic actuators acquired in the first step, and based on the displacement of the optical element in the first location acquired in the first step, the plurality. The displacement of the optical element at each of the plurality of second locations provided with the electromagnetic actuators other than the electromagnetic actuator provided at the first location among the electromagnetic actuators of the above is obtained.
The column matrix is calculated based on the displacement of the optical element at the first location acquired in the first step and the displacement of the optical element at each of the plurality of second locations obtained in the second step. And
In the fourth step,
Based on the ratio of the values of the currents flowing through each of the plurality of electromagnetic actuators acquired in the third step, and based on the displacement of the optical element in the first location acquired in the third step, the plurality of The displacement of the optical element at each of the second points of
The column matrix is calculated based on the displacement of the optical element at the first location acquired in the third step and the displacement of the optical element at each of the plurality of second locations obtained in the fourth step. The determination method according to any one of claims 1 to 3, wherein the determination method is performed. In the second step,
Based on the product of the displacement of the optical element at the first location acquired in the first step and the ratio of the values of the currents flowing through each of the plurality of electromagnetic actuators acquired in the first step, the said. Obtaining the displacement of the optical element at each of the plurality of second locations,
In the fourth step,
Based on the product of the displacement of the optical element at the first location acquired in the third step and the ratio of the values of the currents flowing through each of the plurality of electromagnetic actuators acquired in the third step, the said. The determination method according to claim 4, wherein the displacement of the optical element at each of the plurality of second locations is obtained. Multiple electromagnetic actuators that apply force to the optical elements to deform them,
A detector that detects the current flowing through each of the plurality of electromagnetic actuators,
A measuring unit for measuring the displacement of the optical element in the first location to at least one electromagnetic actuator is provided among the plurality of electromagnetic actuators,
Anda processor for determining a matrix showing the relationship between the displacement of the optical element at a point each of the respective thrust with the plurality of electromagnetic actuators of the plurality of electromagnetic actuators are provided,
The processing unit
When the first electromagnetic actuator of one of the plurality of electromagnetic actuators is driven by a unit current, the value of the current flowing through each of the plurality of electromagnetic actuators detected by the detection unit and the first electromagnetic actuator A column matrix calculated based on the displacement of the optical element at the first location measured by the measuring unit when driven by a unit current, and
When the second electromagnetic actuator of one of the plurality of electromagnetic actuators different from the first electromagnetic actuator is driven by a unit current, the value of the current flowing through each of the plurality of electromagnetic actuators detected by the detection unit. And a row matrix calculated based on the displacement of the optical element at the first location measured by the measuring unit when the second electromagnetic actuator is driven by a unit current, and a plurality of row matrices including An optical device, characterized in that the matrix is determined based on the matrix. The optical device according to claim 6, wherein the processing unit determines the matrix by linearly adding the plurality of column matrices. The plurality of column matrices are calculated by driving all of the plurality of electromagnetic actuators one by one with a unit current.
The optical device according to claim 6 or 7, wherein the processing unit determines the matrix based on the plurality of column matrices. The processing unit
When driving the first electromagnetic actuator unit current, based on the ratio of the value of the current flowing through each of the plurality of electromagnetic actuators, based on the displacement of the optical element in the first location, wherein the plurality of electromagnetic The displacement of the optical element at each of the plurality of second locations where the electromagnetic actuator is provided, excluding the electromagnetic actuator provided at the first location of the actuator, is obtained.
The column matrix is calculated based on the displacement of the optical element at the first location and the displacement of the optical element at each of the plurality of second locations when the first electromagnetic actuator is driven by a unit current. ,
When the second electromagnetic actuator is driven by a unit current, the plurality of second electromagnetic actuators are based on the ratio of the values of the currents flowing through each of the plurality of electromagnetic actuators and the displacement of the optical element at the first location as a reference. Find the displacement of the optical element at each of the two locations.
The column matrix is calculated based on the displacement of the optical element at the first location and the displacement of the optical element at each of the plurality of second locations when the second electromagnetic actuator is driven by a unit current. The optical device according to any one of claims 6 to 8. The processing unit
The displacement of the optical element at the first location when the first electromagnetic actuator is driven by a unit current, and the value of the current flowing through each of the plurality of electromagnetic actuators when the first electromagnetic actuator is driven by a unit current. Based on the product with the ratio of, the displacement of the optical element at each of the plurality of second locations is obtained.
The displacement of the optical element at the first location when the second electromagnetic actuator is driven by a unit current, and the value of the current flowing through each of the plurality of electromagnetic actuators when the second electromagnetic actuator is driven by a unit current. The optical device according to claim 9, wherein the displacement of the optical element at each of the plurality of second locations is obtained based on the product of the ratio of the two. Any of claims 6 to 10, wherein the processing unit determines the value of a current applied to each of the plurality of electromagnetic actuators in order to deform the optical element into a target shape based on the matrix. The optical device according to item 1. The optical device according to any one of claims 6 to 11 , wherein the detection unit includes a plurality of ammeters provided in each of the plurality of electromagnetic actuators. Of claims 6 to 12 , the measuring unit detects the displacement of the electromagnetic actuator provided at the first location and obtains the displacement of the optical element at the first location based on the displacement. The optical device according to any one item. A projection optical system that projects an object onto an image plane.
Optical elements and
The optical device according to any one of claims 6 to 13 for deforming the optical element, and the optical device.
A projection optical system characterized by having. An exposure device that exposes a substrate
Illumination optics that illuminate the mask and
The projection optical system according to claim 14 , wherein a pattern of a mask illuminated by the illumination optical system is projected onto the substrate.
An exposure device characterized by having. A step of exposing the photosensitizer supplied to the substrate using the exposure apparatus according to claim 15.
A step of developing the substrate exposed in the step of the exposure,
Have a,
A method for producing an article, which comprises producing an article from a substrate developed in the developing step.

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