JP5854889B2 - Measuring method - Google Patents

Description

  The present invention relates to a measurement method for measuring a wavefront of light that has passed through a test optical system.

  Lateral shearing interferometers divide the wavefront of light that has passed through the test optical system (hereinafter referred to as “test wavefront”) into multiple wavefronts using a diffraction grating, etc., and interfere with each other by shifting (sheared) wavefronts in the lateral direction. Measure the interference fringes obtained. The wavefront directly measured by the lateral shearing interferometer is a difference wavefront between a detected wavefront and a shear wavefront obtained by shearing the detected wavefront in the lateral direction. In order to obtain the wavefront to be detected, a technique for recovering the wavefront to be detected from the difference wavefront is required.

  In the lateral shearing interferometer, several techniques for recovering the test wavefront from the differential wavefront have been proposed, and one of them is a recovery method (calculation method) using Fourier transform (Patent Document 1). reference). In such a recovery method, instead of integrating the difference wavefront, the difference wavefront is Fourier-transformed to obtain the frequency distribution of the difference wavefront, and then the frequency distribution of the test wavefront is calculated by multiplying the frequency distribution by a correction coefficient. . The frequency distribution of the test wavefront is inverse Fourier transformed to obtain the test wavefront. According to such a technique, it is possible to recover (measure) the wavefront to be detected up to a high frequency component close to the period of the shear amount in the lateral direction using shearing interference.

JP 2005-156403 A

  However, the recovery method using the Fourier transform can recover the wavefront to be detected up to a high frequency component. However, since the two-dimensional Fourier transform is used in the calculation process, the recovery area of the wavefront to be detected is limited to a rectangular area. There is a problem of being done. Therefore, when the wavefront to be detected has a region having an arbitrary shape, the entire region of the wavefront to be detected cannot be recovered by the recovery method using Fourier transform.

  The present invention has been made in view of such a problem of the prior art, and an object of the present invention is to provide a technique that is advantageous for measuring the entire wavefront of light that has passed through a test optical system.

In order to achieve the above object, a measurement method according to one aspect of the present invention is a measurement method for measuring a wavefront of light that has passed through a test optical system, and includes a wavefront of light that has passed through the test optical system and based on the differential wavefront partial data in the rectangular-shaped first region of the differential wavefront data representing the whole of the difference wave front of the shear wave front shifted in shear amount predetermined for a predetermined shear direction of the wavefront, the object Based on the first step of recovering the first wavefront data representing the wavefront in the rectangular second region of the entire wavefront of the light that has passed through the analyzing optical system , based on the differential wavefront data and the first wavefront data, A second step of recovering the wavefront data representing the entire wavefront of the light that has passed through the test optical system , wherein in the second step, of the entire wavefront of the light that has passed through the test optical system, 3rd area excluding 2nd area Said differential wavefront data in the fourth region of the second crimp data representing the wavefront is shifted by pre Symbol the shear amount in the shear direction in pairs with the third region in the fourth region of said first wavefront data It is obtained by combining the wavefront data at.

  Further objects and other aspects of the present invention will become apparent from the preferred embodiments described below with reference to the accompanying drawings.

  According to the present invention, for example, it is possible to provide a technique that is advantageous for measuring the entire wavefront of light that has passed through a test optical system.

It is a figure showing composition of a measuring device used in a measuring method as one side of the present invention. It is a flowchart for demonstrating the measuring method as 1 side surface of this invention. It is a figure which shows the to-be-detected wave front detected by the detection part of the measuring device shown in FIG. It is a figure explaining the process of S206-S212 shown in FIG. 2 as an example when the shear direction is the X direction. It is a figure explaining the process of S206-S212 shown in FIG. 2 as an example when the shear direction is the Y direction. It is a figure which shows distribution of the dead frequency of the to-be-detected wave surface in frequency space. It is a figure for demonstrating recovery | restoration (S218) of the to-be-detected wave surface of a X direction. It is a figure for demonstrating recovery | restoration (S218) of the to-be-detected wave surface of a X direction.

  DESCRIPTION OF EXEMPLARY EMBODIMENTS Hereinafter, preferred embodiments of the invention will be described with reference to the accompanying drawings. In addition, in each figure, the same reference number is attached | subjected about the same member and the overlapping description is abbreviate | omitted.

  FIG. 1 is a diagram showing a configuration of a measurement apparatus 100 used in a measurement method as one aspect of the present invention. The measuring device 100 is a measuring device that measures the wavefront of light that has passed through the optical system 3 to be tested, and in this embodiment, has the same configuration as a lateral shearing interferometer. Specifically, as shown in FIG. 1, the measuring device 100 includes a light source 1, a pinhole plate 2, a two-dimensional diffraction grating (light splitting element) 4, an order selection window 5, a detection unit 6, And a processing unit 7.

  The light emitted from the light source 1 passes through a pinhole 2A formed in the pinhole plate 2 to become a spherical wave and enters the optical system 3 to be tested. The test optical system 3 is, for example, a projection optical system of an exposure apparatus used for manufacturing a semiconductor device or a liquid crystal display device, and includes a lens, a mirror, and the like.

  The light that has passed through the test optical system 3 includes the amount of aberration of the test optical system 3 and is diffracted by the two-dimensional diffraction grating 4 in two directions (X direction and Y direction). A plurality of diffracted lights having different orders are generated. Of these diffracted lights, four diffracted lights, in the present embodiment, ± first-order diffracted lights in the X direction and the Y direction are selected by the order selection window 5 (that is, the X direction formed in the order selection window 5). Through the window 5A and the Y-direction window 5B).

  The four diffracted light beams that have passed through the order selection window 5 interfere with each other, and the interference fringes (interference light) are detected by the detection unit 6 constituted by a CCD sensor. The interference fringes detected by the detection unit 6 are sent to a processing unit 7 constituted by an information processing apparatus such as a computer. The processing unit 7 calculates (recovers) the wavefront (test wavefront) of the light that has passed through the test optical system 3 based on the interference fringes detected by the detection unit 6.

  FIG. 2 is a flowchart for explaining a measurement method using the measurement apparatus 100. In S <b> 202, the detection unit 6 detects interference fringes (representing image information) of light that has passed through the test optical system 3. In S204, the processing unit 7 calculates a differential wavefront from the interference fringes detected in S202. For the calculation of the difference wavefront, a phase shift method, a Fourier transform method, or the like can be used, but detailed description thereof is omitted here.

  S206 to S220 are steps for recovering the test wavefront from the differential wavefront calculated in S204. In this embodiment, this process is roughly divided into two processes (first process and second process). In the first step, for each of the difference wavefronts in the two directions (X direction and Y direction), the rectangular difference wavefront partial data inside the region is subjected to a rectangular transformation inside the region of the wavefront to be detected using frequency conversion. This is a step of recovering the wavefront portion data having a shape. The second step is a step of recovering the entire detected wavefront (circular region) based on the detected wavefront partial data recovered in the first step.

  As described above, in the measurement apparatus 100 of the present embodiment, the detection unit 6 detects interference fringes of four lights including the diffracted light in the X direction and the diffracted light in the Y direction. FIG. 3 is a diagram illustrating interference fringes (wavefronts) detected by the detection unit 6. In this embodiment, only the detected wavefront that has undergone ± first-order diffraction in each of the X direction and the Y direction is caused to interfere. Hereinafter, the wavefront that is + 1st-order diffracted is referred to as the test wavefront, This is called the shear wave front. Further, the shift direction of the wavefront to be detected is referred to as a shear direction, and the shift amount is referred to as a shear amount. It can be said that the shear wavefront is a wavefront obtained by shifting the wavefront to be detected by a predetermined shear amount in a predetermined shear direction.

As shown in FIG. 3, in the detection unit 6, the X test wavefront 11 whose shear direction is the X direction, the X shear wavefront 12 whose shear direction is the X direction, and the Y test wavefront 13 whose shear direction is the Y direction, A Y shear wavefront 14 whose shear direction is the Y direction is detected. Further, the shear amount (first shear amount) between the X detected wavefront 11 and the X shear wavefront 12 is S _x , and the shear amount (second second) between the Y detected wavefront 13 and the Y shear wavefront 14 shear amount) is _{S y.} The shear amount S _x and the shear amount S _y may not be equal. The reason for detecting the interference fringes composed of diffracted light in two directions, the X direction and the Y direction, is to simultaneously acquire two differential wavefronts in the X direction and the Y direction from one interference fringe. Here, the two difference wavefronts are a difference wavefront (first difference wavefront data) in which the shear direction is the X direction (first shear direction) and a difference wavefront (second difference) in which the shear direction is the Y direction (second shear direction). Wavefront data).

  Before explaining the process of recovering the wavefront to be detected, the difference wavefront between the wavefront to be detected and the shear wavefront will be described as an example where the shear direction is the X direction. FIG. 4A is a diagram showing the X wavefront 11 and the X shear wavefront 12 whose shear direction is the X direction among the four wavefronts shown in FIG. In FIG. 4A, a circular region 21 indicated by a solid line indicates a region of the X wavefront 11 to be detected, and a circular region 22 indicated by a dotted line indicates a region of the X shear wavefront 12. The region 23 indicates a region where the region 21 and the region 22 overlap (that is, a region where interference fringes are detected), and is a region of the differential wavefront whose shear direction is the X direction (differential wavefront data representing the entire differential wavefront). . A phase amount corresponding to the difference between the phase of the X test wavefront 11 and the phase of the X shear wavefront 12 is detected as a differential wavefront whose shear direction is the X direction.

Here, information required in the process of recovering the test wavefront from the differential wavefront will be described. When the shear direction is the X direction, the phase amount of the differential wavefront in the region 23 shown in FIG. Further, information on the regions 21 and 22 of the X test wavefront 11 and the X shear wavefront 12 is also necessary. These areas are defined in units of pixels on the CCD sensor constituting the detection unit 6. The fact that the information of the region 21 and the region 22 is known means that the information of the shear amount S _x and the region 23 of the differential wavefront is also known.

  Returning to FIG. 2, the process (first process) of recovering the rectangular test wavefront partial data inside the area of the test wavefront will be described.

  In S206, a rectangular area for recovering data representing the wavefront is set for each of the test wavefront and the differential wavefront. Specifically, a rectangular area (second area) for recovering the detected wavefront partial data (that is, data representing the wavefront in the rectangular area) with respect to the entire detected wavefront (circular area). Area). Further, a rectangular area (first area) necessary for recovering the detected wavefront partial data is set for the entire differential wavefront. In S208, the rectangular area set in the differential wavefront in S206 is expanded.

  FIG. 4B is a diagram showing a rectangular region 24 set in the region 21 of the X detected wavefront 11. The rectangular area 24 is defined in units of pixels on the CCD sensor that constitutes the detection unit 6. In the present embodiment, the width of the area 24 is N pixels, and the height of the area 24 is M pixels. In this embodiment, in order to maximize the area of the rectangular region 24, the region 24 is set so as to be inscribed in the region 21 of the X wavefront 11 to be detected. However, the present invention is not limited to this. Absent. The rectangular region 24 only needs to be set inside the region 21 of the X wavefront 11 to be detected, and is not necessarily inscribed in the region 21.

FIG. 4C is a diagram showing a rectangular region 25 set in the region 22 of the X shear wave front 12. The rectangular region 25 is set so as to be inscribed in the region 22 of the X shear wave front 12. The positions of the four sides of the region 25 with respect to the center of the region 22 of the X shear wavefront 12 and the area of the region 25 with respect to the area of the region 22 are determined by the four sides of the region 24 with respect to the center of the region 21 of the X wavefront 11 to be tested. The position is equal to the area of the region 24 with respect to the area of the region 21. The positional relationship between the rectangular region 25 set in the region 22 of the X shear wavefront 12 and the rectangular region 24 set in the region 21 of the X test wavefront 11 is as shown in FIG. The region 25 has a positional relationship that is shifted from the region 24 by the shear amount _{Sx in the} −X direction.

FIG. 4D is a diagram showing a state in which the region 21 of the X test wavefront 11 and the region 22 of the X shear wavefront 12 are superposed on the regions 24 and 25 set in the respective regions. Referring to FIG. 4D, an area where the rectangular area 24 and the rectangular area 25 overlap, that is, a rectangular area 26 having a width of N-S _x pixels and a height of M pixels. Is an area expanded in S208. The rectangular area 26 is shorter than the rectangular areas 24 and 25 by _{Sx in} the X direction. In addition, since the rectangular area 26 is within the differential wavefront area 23, the phase amount of the differential wavefront in the entire area 26 is known.

  The principle of S206 to S212 will be described. The wavefront (test wavefront) w in the rectangular region 24 set in the region 21 of the X test wavefront 11 is expressed by the following equation (1).

Since the wavefront in the rectangular region 25 set in the region 22 of the X shear wavefront 12 is a wavefront obtained by shearing the wavefront in the region 24 by the shear amount _Sx in the −X direction, the following equation is obtained from the equation (1). It is represented by (2).

  Further, the differential wavefront d in the rectangular region 26 is expressed by the following formula (3).

  As described above, in the entire rectangular region 26, the differential wavefront d expressed by the equation (3) is known. Therefore, it is possible to recover the wavefront w in the rectangular region 24 expressed by the equation (1) from the differential wavefront d.

If the frequency distribution obtained by performing two-dimensional discrete Fourier transform on the wavefront w in the rectangular region 24 is W, it is expressed by the following equation (4). In the formula (4), _{f x} and _{f y} are the coordinates in the frequency space.

  Here, in order to use the two-dimensional discrete Fourier transform, it is assumed that the wavefront w in the rectangular region 24 represented by Expression (1) is a two-dimensional periodic function of the region 24. Similarly, assuming that the wavefront in the rectangular region 25 represented by the equation (2) is also a two-dimensional periodic function of the region 25, the wavefront in the rectangular region 25 is obtained by two-dimensional discrete Fourier transform. The obtained frequency distribution is expressed by the following equation (5).

As described above, in this embodiment, in order to recover the test wavefront using the two-dimensional discrete Fourier transform, it is assumed that the test wavefront and the shear wavefront are two-dimensional periodic functions having the same period. In order to recover the wavefront in the rectangular region of the entire detected wavefront using the two-dimensional discrete Fourier transform, the difference wavefront is equivalent to one period corresponding to the rectangular region of the entire detected wavefront. Must be known in the region. In other words, the differential wavefront d expressed by the equation (3) must be known in a region having the same size as the rectangular region 24 set in the region 21 of the X test wavefront 11. However, the known region of the differential wavefront d represented by the equation (3) is a rectangular region 26, and the region 26 has a side in the X direction shorter than the region 24 by the shear amount _Sx . Therefore, it is necessary to expand the region 26 that is a known region of the differential wavefront to the same size (area) as the region 24 under the assumption that the wavefront to be detected is periodic.

The expansion (S208) of the area 26, which is a known area of the differential wavefront, will be specifically described. As one method of expanding the region 26, which is a known region of the difference wavefront, to the same size (area) as the region 24, there is a method of setting the side length in the shear direction to an integral multiple of the shear amount of each difference wavefront. is there. In the present embodiment, when the rectangular region 24 is set with respect to the region 21 of the X test wavefront 11 in S206, the width of the region 24, that is, N may be an integral multiple of the shear amount _Sx. . Although detailed description is omitted, under such conditions, the width S _x that is insufficient with respect to the size of the region 24 from the region 26 that is a known region of the differential wavefront according to the following equation (6): Can be obtained.

  Here, the differential wavefront defined by the expanded region 26 (that is, a region having the same size as the region 24) is referred to as a differential wavefront d again. FIG. 4E is a diagram showing a region 26 (region before expansion) that is a known region of the differential wavefront and a region (first region) 24 ′ in which the region 26 is expanded.

  Assuming that the frequency distribution obtained by performing the two-dimensional discrete Fourier transform on the differential wavefront d in the rectangular region 24 ′ is D, the frequency distribution D is calculated based on the linearity of the Fourier transform from the equations (4) and (5). Is represented by the following formula (7).

  When formula (7) is transformed, the following formula (8) is derived.

  In S210, the difference wavefront (first difference wavefront partial data) d expanded in S208 is two-dimensionally discrete Fourier transformed to calculate the frequency distribution (first frequency distribution) D of the difference wavefront d.

  In S212, the frequency distribution W of the wavefront to be detected is calculated from the frequency distribution D of the differential wavefront d calculated in S210 using Expression (8). Specifically, the frequency distribution D of the differential wavefront is multiplied by a correction coefficient (first correction coefficient) represented by the following equation (9). Such a correction coefficient is determined according to the shear direction and shear amount of the wavefront to be detected, as shown in Equation (9).

  In equation (9), the frequency at which the denominator becomes zero is called a dead frequency and is represented by the following equation (10).

  In Formula (10), n is an integer. With respect to the dead frequency represented by the equation (10), since the equation (9) cannot be defined, the wavefront cannot be recovered.

  So far, the processes of S206 to S212 have been described by taking the case where the shear direction is the X direction as an example. However, the processing of S206 to S212 is performed in the same way for the test wavefront and the differential wavefront whose shear direction is the Y direction, as shown in FIGS. 5 (a) to 5 (e). Therefore, also in the Y direction, the frequency distribution (second frequency distribution) of the differential wavefront is calculated by performing two-dimensional discrete Fourier transform on the differential wavefront (second differential wavefront partial data) expanded in S208 in S210. In S212, the frequency distribution of the wavefront to be detected is calculated by multiplying the calculated frequency distribution of the difference wavefront by the correction coefficient (second correction coefficient).

FIG. 5A is a diagram showing the Y test wavefront 13 and the Y shear wavefront 14 whose shear direction is the Y direction among the four wavefronts shown in FIG. In FIG. 5A, a circular region 31 indicated by a solid line indicates a region of the Y wavefront 13 to be detected, and a circular region 32 indicated by a dotted line indicates a region of the Y shear wavefront 14. A region 33 indicates a region where the region 31 and the region 32 overlap, and is a region of a differential wavefront in which the shear direction is the Y direction. FIG. 5B is a diagram illustrating a rectangular region 34 set in the region 31 of the Y wavefront 13 to be detected. In the present embodiment, the width of the region 34 is N pixels, and the height of the region 34 is M pixels. FIG. 5C is a diagram showing a rectangular area 35 set in the area 32 of the Y shear wave front 14. FIG. 5D is a diagram showing a state in which the region 31 of the Y test wavefront 13 and the region 32 of the Y shear wavefront 14 are overlapped with the regions 34 and 35 set in the respective regions. In FIG. 5D, an area where the rectangular area 34 and the rectangular area 35 overlap, that is, a rectangular area 36 having a width of N pixels and a height of M-S _y pixels is shown in S208. It becomes an area to be expanded. FIG. 5E is a diagram showing a region 36 (region before expansion) which is a known region of the differential wavefront and a region 34 ′ where the region 36 is expanded.

  When the shear direction is the Y direction, the expressions corresponding to the expressions (2) to (9) are essentially the same except that the shear direction is changed to the Y direction. Therefore, the description corresponding to the equations (2) to (9) is omitted, and only the equation corresponding to the equation (10) will be described. When the shear direction is the Y direction, the dead frequency is expressed by the following formula (11).

  In Formula (11), m is an integer. As for the dead frequency represented by the equation (11), the wavefront cannot be recovered as described above.

  In S214, the frequency distribution of the test wavefront obtained from the differential wavefront whose shear direction is the X direction and the frequency distribution of the test wavefront obtained from the differential wavefront whose shear direction is the Y direction are synthesized in the frequency space to obtain a synthesized frequency distribution. calculate. At this time, the wavefront recovery accuracy can be improved by synthesizing the frequency distribution while compensating for the dead frequencies.

  However, when combining the frequency distributions of multiple test wavefronts obtained from each of multiple differential wavefronts in the frequency space, the rectangular areas set in the test wavefronts in real space are matched with the multiple test wavefronts. It is necessary to let For example, when the rectangular region 34 is set in the circular region 31 of the Y test wavefront 13, the position and size of the region 34 with respect to the region 31 are set to the circular region 21 of the X test wavefront 11. The position and size of the rectangular area 24 set for the same must be matched. As described above, by matching the rectangular regions set in the test wavefront with the plurality of test wavefronts, the frequency distribution of the same region of the test wavefront can be obtained from each differential wavefront.

  A synthesized frequency distribution obtained by synthesizing in a frequency space a frequency distribution of a test wavefront obtained from a differential wavefront whose shear direction is X direction and a frequency distribution of the test wavefront obtained from a differential wavefront whose shear direction is Y direction. An example is shown in the following formula (12).

In Expression (12), W _{restore on} the left side represents a combined frequency distribution, and W _x and W _{y on} the right side represent the frequency distribution of the wavefront to be measured and the shear direction determined from the differential wavefront in which the shear direction is the X direction. The frequency distribution of the wavefront to be detected obtained from the difference wavefront in the direction is shown.

The expression on the first stage from the top of the right side of Expression (12) represents a case where both W _x and W _y are insensitive frequencies. Since this frequency is still unknown, it is set to zero in this embodiment. However, this is an example, and for example, a value interpolated based on the value of the coordinates near the dead frequency may be substituted.

The expressions in the second and third stages from the top of the right side of Expression (12) represent the case where one of W _x and W _y is a dead frequency. In such a case, a known value that is not a dead frequency out of W _x and W _y may be used.

The expression on the fourth stage from the top of the right side of Expression (12) represents a case where both W _x and W _y are frequencies that are not dead frequencies. In such a case, an average value of W _x and W _y may be used to reduce the measurement error. However, if there is no measurement error at all, W _x and W _y should be the same value, so either one of W _x and W _y may be used.

FIG. 6 is a diagram showing the distribution of the dead frequency of the wavefront to be detected in the frequency space. FIG. 6A shows the dead frequency (formula (10)) in the frequency distribution of the wavefront to be detected, which is obtained from the differential wavefront whose shear direction is the X direction. FIG. 6B shows the dead frequency (formula (11)) in the frequency distribution of the wavefront to be detected, which is obtained from the differential wavefront whose shear direction is the Y direction. FIG. 6C shows the dead frequency in the combined frequency distribution. An unknown frequency component in the combined frequency distribution W _restore is that the dead frequency in W _{x and} the dead frequency in W _y overlap. In other words, the unknown frequency component in the combined frequency distribution W _restore is the intersection of the vertical line representing the dead frequency in W _x and the horizontal line representing the dead frequency in W _y , as shown in FIG. Exists as discrete points.

In S216, the composite frequency distribution W _restore calculated in S214 is subjected to two-dimensional discrete inverse Fourier transform to calculate the wavefront (first wavefront data) in the rectangular region set in the test wavefront in S206.

  In the present embodiment, when the wavefront in the rectangular region set in the test wavefront is recovered, the rectangular region set in the differential wavefront is expanded (S208), but the differential wavefront is set. Expansion of the rectangular area is not always necessary. For example, when the test wavefront is actually a periodic function and the differential wavefront for one cycle can be directly obtained, the expansion of the rectangular region set in the differential wavefront can be omitted.

  Further, in the present embodiment, the case where the test wavefront is recovered from two differential wavefronts has been described, but the present invention is also applied to the case where the test wavefront is recovered from one differential wavefront having a shear direction in a certain direction. be able to. When recovering the test wavefront from one differential wavefront, the process of S206 to S212 is performed on one differential wavefront, and the process of S214, that is, the test wavefront obtained from a plurality of differential wavefronts with different shear directions. The process of synthesizing the frequency distribution is omitted. However, when recovering the test wavefront from one differential wavefront, the dead frequency is higher than when recovering the test wavefront from a plurality of differential wavefronts with different shear directions. Recovery accuracy decreases.

  Further, in the present embodiment, the case where the test wavefront is recovered from two differential wavefronts has been described, but the present invention is the case where the test wavefront is recovered from a plurality of differential wavefronts in which at least one of the shear direction and the shear amount is different. It can also be applied to. For example, the shear direction may be a 45-degree direction, and the number of differential wavefronts may be three or more. Even in such a case, the processes of S206 to S212 are performed on the plurality of differential wavefronts, and in S214, all the frequency distributions of the test wavefronts obtained from each of the plurality of differential wavefronts are combined to produce one combined frequency. Find the distribution.

  A step (second step) for recovering the entire wavefront to be detected based on the wavefront in the rectangular region set on the wavefront to be detected will be described. In S218, the test wavefront in the X direction is recovered. FIG. 7 is a diagram for explaining the recovery (S218) of the wavefront to be detected in the X direction.

Referring to FIG. 7A, the wavefront in the rectangular region 24 set in the region 21 of the X test wavefront 11 has been recovered in S216, and thus is known when performing the processing of S218. . Further, the rectangular region 23, that is, the differential wavefront d whose shear direction is the X direction is also known. Accordingly, in S218, the wavefront (second wavefront data) in the region 21 outside the region 24, that is, the region excluding the rectangular region 24 (third region) in the region 21 of the X test wavefront 11 is recovered. . FIG. 7B is a diagram for explaining the recovery of the wavefront in the region on the right outer side with respect to the rectangular region 24 in the region 21 of the X detected wavefront 11. In FIG. 7B, a region 51 indicated by a lattice is defined as a region overlapping with the region 23 so that the region having the same width as _Sx and the same height as the rectangular region 24 touches the right side inside the region 24. This is the area. Here, when Expression (3) is modified, the following Expression (13) is derived.

Since the wavefront and the difference wavefront d in the region 51 are known, using the equation (13) for the wavefront and the difference wavefront d in the region 51, a region obtained by shifting the region 51 by the shear amount S _{x in the} + X direction, that is, , The wavefront in region 52 is obtained. As described above, the wavefront (second wavefront data) in the region 52 is obtained by combining the difference wavefront data in the region (fourth region) 51 corresponding to the region 52 and the wavefront data in the region 51.

FIG. 7C is a diagram for explaining the recovery of the wavefront in the left outer region with respect to the rectangular region 24 in the region 21 of the X test wavefront 11. In FIG. 7C, a region 55 indicated by a lattice is a region in which a region having the width of _Sx and the same height as the rectangular region 24 is defined so as to contact the left side inside the region 24. On the other hand, a region 54 indicated by a horizontal line is a region defined by a region overlapping with the region 23 so as to be in contact with the left side of the region 24 with a width of _Sx and the same height as the rectangular region 24. Here, when Expression (3) is modified, the following Expression (14) is derived.

  Since the wavefront in the region 55 and the differential wavefront d in the region 54 are known, using the equation (14) for the wavefront in the region 55 and the differential wavefront d in the region 54, the wavefront in the region 54 is obtained.

  In S220, the wavefront to be detected in the Y direction is recovered. In S218, the wavefront in the region 57 indicated by the horizontal line in the region 21 of the X detected wavefront 11 shown in FIG. Therefore, in S220, the wavefront in the region 57 can be recovered by performing the same process as the process of recovering the test wavefront in the X direction (S218) in the Y direction.

  Thus, in S218 and S220, the wavefront in the region 21 (the whole) of the X detected wavefront 11 can be recovered by recovering the detected wavefront in the X direction and the detected wavefront in the Y direction.

Here, with reference to FIG. 8, the case where it is necessary to repeat the process of S218 and S220 is demonstrated. Referring to FIG. 8A, the rectangular region 61 is a region where the wavefront is recovered in S216 (that is, the rectangular region 24 set in the region 21 of the X test wavefront 11). However, in FIG. 8A, it is assumed that the width is set narrower than the rectangular region 24 shown in FIG. As a result, in FIG. 7A, the width L _{x of} the region where the wavefront is recovered in S218 is equal to or less than the shear amount _Sx , whereas in FIG. 8A, the width Lx of the region where the wavefront is recovered in S218. The width is longer than the shear amount _Sx .

When Expression (13) is used for the wavefront in the region 61 shown in FIG. 8B and the known differential wavefront d (rectangular region 23), the region 62 is shifted by the shear amount _{Sx in the} + X direction. That is, the wavefront in the region 63 is obtained. As a result, the known area of the wavefront to be detected is expanded from the area 61 shown in FIG. 8B to the area 64 shown in FIG. 8C. Next, when the same processing is repeated for the region 65 shown in FIG. 8D, the wavefront in the region 66 indicated by the horizontal line is obtained, and the wavefront can be recovered to the right end of the region 21 of the X test wavefront 11. it can. Like the X direction when recovering the wavefront of Y-direction, when the width of the Y direction of a region to recover the wavefront is longer than the shear amount S _y in S220, Y measured wavefront by repeating the above processes Can recover the whole.

  The relationship between the 1st process and the 2nd process in this embodiment is explained. The second step is a step of recovering the wavefront to be detected by adding the differential wavefronts whose shear direction is the X direction or the Y direction to each shear direction at intervals of the shear amount. At this time, if the first wave is omitted and only the second wave is recovered, information (wavefront) other than the direction of adding is not recovered. For example, when the differential wavefront whose shear direction is the X direction is added to the X direction using the equation (13), the information in the Y direction is not recovered.

  Therefore, in this embodiment, in the first step, the wavefront in the rectangular region set in the region of the wavefront to be detected is recovered. Since the wavefront recovered in the first step is composed of the differential wavefront whose shear direction is the X direction and the differential wavefront whose shear direction is the Y direction, information on the test wavefront in the X direction and the test wavefront in the Y direction are combined. And information. In the second step, the starting point of addition is set inside the wavefront (rectangular region) recovered in the first step. Thereby, even if the differential wavefront whose shear direction is the X direction is added to the X direction, the test wavefront can be recovered while maintaining the information of the Y direction that is not the addition direction.

  According to this embodiment, the detected wavefront in the entire region having an arbitrary shape can be recovered, and the detected wavefront can be recovered to a high frequency component. For example, when the fitting or least square method is adopted when recovering the test wavefront, it is necessary to set the number of fitting terms to a higher order in order to recover the test wavefront to a high frequency component. In the least square method, it is necessary to obtain an inverse matrix by LU decomposition or SVD. On the other hand, in this embodiment, Fourier transform (and inverse Fourier transform) is adopted when recovering the test wavefront, and the test wavefront can be recovered in a short time by using the FFT algorithm.

  In the first step, a plurality of rectangular regions can be set for the region of the wavefront to be detected. In the first step, the wavefront is recovered by synthesizing a plurality of differential wavefronts, so that the wavefront region recovered in the first step is made wider than the wavefront region recovered in the second step. Accuracy can be improved. Thus, in the present embodiment, as described above, one rectangular region is set so as to be inscribed in the region of the wavefront to be detected, but a plurality of rectangular regions may be set. In particular, if it is not possible to cover the entire area of the wavefront to be detected by setting only one rectangular area, it is effective to set a plurality of rectangular areas for the area of the wavefront to be detected. It becomes.

  In addition, the measurement method of the embodiment can be applied to the manufacture of articles such as machine parts. A method for manufacturing such an article includes a step of measuring a wavefront of light that has passed through a test optical system or a test surface by the measurement method described above, and a test optical system or a test surface based on a measurement result in the step. Is processed (polished or the like) so as to have a predetermined performance. Such a method for manufacturing an article is advantageous in at least one of the performance, quality, productivity, and production cost of the article as compared with the conventional method.

  As mentioned above, although preferable embodiment of this invention was described, it cannot be overemphasized that this invention is not limited to these embodiment, A various deformation | transformation and change are possible within the range of the summary.

Claims (5)

A measurement method for measuring the wavefront of light that has passed through a test optical system,
A rectangular first wavefront difference data representing a whole wavefront difference between a wavefront of light passing through the optical system to be measured and a shear wavefront obtained by shifting the wavefront by a predetermined shear amount in a predetermined shear direction. A first step of recovering first wavefront data representing a wavefront in a rectangular second region out of the entire wavefront of light passing through the test optical system , based on differential wavefront partial data in the region;
A second step of recovering wavefront data representing the entire wavefront of light that has passed through the optical system under test based on the differential wavefront data and the first wavefront data;
In the second step, the second wavefront data representing the wavefront in the third region excluding the second region of the entire wavefront of the light which has passed through the target optical system, before SL and against the third region measurement method characterized by determining by combining said differential wavefront data in the fourth region that is shifted by the shear amount in the shear direction, the wave front data in the fourth region of the first wavefront data. The first step includes
Calculating the frequency distribution of the differential wavefront partial data by Fourier transforming the differential wavefront partial data;
Multiplying the frequency distribution of the differential wavefront partial data by a correction coefficient determined according to the shear direction and the shear amount to calculate the frequency distribution of the first wavefront data;
Calculating the first wavefront data by performing an inverse Fourier transform on the frequency distribution of the first wavefront data;
The measurement method according to claim 1, comprising: The differential wavefront data represents a differential wavefront between a wavefront of light passing through the test optical system and a shear wavefront obtained by shifting the wavefront of light passed through the test optical system by a first shear amount in a first shear direction. The first differential wavefront data, the wavefront of light passing through the test optical system, and the wavefront of light passing through the test optical system are shifted by a second shear amount in a second shear direction different from the first shear direction. Second differential wavefront data representing the differential wavefront from the shear wavefront,
The first step includes
The first differential wavefront portion is obtained by Fourier transforming each of the first differential wavefront portion data in the rectangular region of the first differential wavefront data and the second differential wavefront portion data in the rectangular region of the second differential wavefront data. Calculating a first frequency distribution of data and a second frequency distribution of the second differential wavefront partial data;
The first correction coefficient determined according to the first shear direction and the first shear amount is multiplied by the first frequency distribution, and the second correction coefficient determined according to the second shear direction and the second shear amount is Multiplying the second frequency distribution;
Combining a first frequency distribution multiplied by the first correction coefficient and a second frequency distribution multiplied by the second correction coefficient to calculate a combined frequency distribution;
Calculating the first wavefront data by performing inverse Fourier transform on the synthesized frequency distribution;
The measurement method according to claim 1, comprising:   The measurement method according to claim 1, wherein the first region has a side along the shear direction, and the length of the side is an integral multiple of the shear amount.   2. The measurement according to claim 1, wherein in the second step, the second wavefront data is obtained by repeatedly combining differential wavefront data with respect to wavefront data in the fourth region and wavefront data in the fourth region. Method.

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