Wavefront sensor, wavefront measuring device

Abstract

To provide a wavefront sensor capable of detecting accurately, a centroid, even in a wavefront with large aberration.SOLUTION: A wavefront sensor 100 comprises: a micro lens array 101 including a plurality of micro lenses; and an imaging element 102 which receives a plurality of point images being formed by the micro lens array. The wavefront sensor is configured so that a use wavelength λ, a focal distance f of the micro lens, an effective diameter Φ of the micro lens, a pixel pitch s of the imaging element, a pixel number p of the imaging element corresponding to a prescribed size of the point image when the size of the point image is smaller than the prescribed size, a pixel number m of the imaging element corresponding to an enlarged point image on an imaging surface of the imaging element obtained by enlarging the point image by defocusing, and a defocusing d of the micro lens from the focal position, satisfy a prescribed conditional expression, and the imaging element is arranged at a position away from the micro lens array by a distance of f+d, in an optical axis direction of the micro lens array.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to a wavefront sensor capable of measuring a wavefront with large aberrations with high accuracy. [Background technology]

[0002] A wavefront sensor (Shack-Hartmann sensor, SHS) combines an image sensor with a microlens array, which consists of many microlenses arranged in a grid pattern. If there is wavefront aberration in the wavefront, the position of the point image will shift according to the gradient of the wavefront. Therefore, the wavefront aberration can be calculated from the amount of positional shift of this point image. Because point images have a finite size due to diffraction, the position of the point image is calculated by detecting the center of gravity. Therefore, the accuracy of the center of gravity detection is important.

[0003] Patent Document 1 describes a method of changing the area where center of gravity detection is performed depending on the distance between point images. This is intended to improve the accuracy of center of gravity detection by optimizing the area where center of gravity detection is performed and minimizing the influence of adjacent point images. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Patent No. 6080427 Summary of the Invention [Problem to be solved by the invention]

[0005] A certain degree of point image size is necessary to detect the center of gravity with sub-pixel accuracy. However, while the method of Patent Document 1 can reduce the influence of adjacent point images, it cannot be expected to be effective if the size of each point image itself is insufficient.

[0006] Furthermore, in the case of a wavefront with large aberration, the point image size tends to be small. When the aberration exceeds a certain value, it is difficult to achieve both sufficiently low sensitivity and a sufficient point image size, which makes it difficult to detect the center of gravity with high accuracy.

[0007] The present invention provides a wavefront sensor capable of detecting the center of gravity with high accuracy even for a wavefront with large aberration. [Means for solving the problem]

[0008] A wavefront sensor according to one aspect of the present invention includes a microlens array including a plurality of microlenses each forming a point image of an object, and an image sensor that receives the plurality of point images formed by the microlens array, wherein when a wavelength used is λ, a focal length of each of the plurality of microlenses is f, an effective diameter of each of the plurality of microlenses is Φ, a pixel pitch of the image sensor is s, a number of pixels of the image sensor corresponding to a point image of a predetermined size when the size of each of the plurality of point images is smaller than a predetermined size is p, a number of pixels of the image sensor corresponding to an enlarged point image on an image capturing surface of the image sensor obtained by enlarging each of the plurality of point images by defocusing is m, and the defocus from the focal position of each of the plurality of microlenses is d, the image sensor is spaced apart from the microlens array by a distance of f+d in the optical axis direction of the microlens array. only It is located at a distance, 2.44λf / Φ <ps |d|>(ms-2.44λf / Φ)f / Φ The present invention is characterized in that the following condition is satisfied:

[0009] a wavefront sensor according to another aspect of the present invention, the wavefront sensor comprising: a microlens array including a plurality of microlenses each forming a point image of an object; an image sensor receiving the plurality of point images formed by the microlens array; and a parallel plate, wherein: λ is a wavelength used; f is a focal length of each of the plurality of microlenses; Φ is an effective diameter of each of the plurality of microlenses; s is a pixel pitch of the image sensor; t is a thickness of the parallel plate; n is a refractive index of the parallel plate; p is a number of pixels of the image sensor corresponding to a point image of a predetermined size when the size of each of the plurality of point images is smaller than a predetermined size; and m is a number of pixels of the image sensor corresponding to an enlarged point image on an imaging surface of the image sensor obtained by enlarging each of the plurality of point images by the parallel plate; the image sensor is disposed at a position f away from the microlens array in an optical axis direction of the microlens array; and the parallel plate is disposed between the microlens array and the image sensor in the optical axis direction of the microlens array; 2.44λf / Φ <ps t>((ms-2.44λf / Φ)f / Φ) / (1-1 / n) The present invention is characterized in that the following condition is satisfied:

[0010] A wavefront measuring device including the wavefront sensor constitutes another aspect of the present invention.

[0011] Other objects and features of the present invention will be described in the following embodiments. [Effects of the Invention]

[0012] According to the present invention, it is possible to provide a wavefront sensor capable of detecting the center of gravity with high accuracy even for a wavefront with large aberration. [Brief explanation of the drawings]

[0013] [Figure 1] 1 is a schematic diagram of a wavefront sensor according to a first embodiment. [Figure 2] FIG. 10 is a diagram illustrating the relationship between point image size and centroid detection accuracy. [Figure 3] 10A and 10B are diagrams illustrating the relationship between a point image without random noise and the accuracy of center of gravity detection. [Figure 4] 10A and 10B are diagrams illustrating the relationship between a point image with random noise and the accuracy of center of gravity detection. [Figure 5] FIG. 10 is a schematic diagram of a wavefront sensor according to a second embodiment. [Figure 6] FIG. 10 is a schematic diagram of a wavefront measuring instrument according to a third embodiment. [Figure 7] FIG. 10 is a schematic diagram of a wavefront measuring instrument according to a fourth embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0014] DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings. In the drawings, the same reference numerals are used to designate the same components, and redundant explanations will be omitted. Example 1 FIG. 1 is a schematic diagram of a wavefront sensor 100 according to a first embodiment. The wavefront sensor 100 according to the first embodiment includes a microlens array 101 including multiple microlenses 101a to 101d, each of which has an effective diameter Φ and a focal length f and forms a point image of an object, and an image sensor 102 having a pixel pitch s. The microlenses 101a to 101d are arranged in a grid pattern. The image sensor 102 receives the multiple point images formed by the microlens array 101. The wavefront sensor 100 is used to calculate wavefront aberration from the deviation of the center of gravity of the point images formed by the microlens array 101 from a reference position. Here, the effective diameter refers to the diameter on the lens surface of a light beam that passes through a position farthest radially from the optical axis (perpendicular to the optical axis) among light beams that pass through the lens surface of the microlens. In other words, the effective diameter refers to the diameter of the area (effective area) on the lens surface through which effective light beams that contribute to image formation pass. The image sensor 102 is disposed at a distance (f+d) from the microlens array 101 in the optical axis direction of the microlens array 101, the distance being the sum of the focal length f and the defocus d. The defocus d is calculated from the effective diameter Φ of the microlenses 101a to 101d, the focal length f of the microlenses 101a to 101d, and the pixel pitch s of the image sensor 102.

[0015] The incident light 103 is divided into minute beam elements 103a to 103d by the microlens array 101, and each beam element can be considered to be approximately parallel light. The beam elements 103a to 103d form point images 105a to 105d, respectively, on a focal plane 104 that is a focal distance f away from the microlens array 101. Because the positions of the point images 105a to 105d depend on the gradients of the beam elements 103a to 103d, the gradients of the beam elements 103a to 103d can be calculated by detecting the positions of the point images 105a to 105d as their centers of gravity. The wavefront aberration of the incident light 103 can be calculated by adjusting the gradients of the beam elements 103a to 103d. However, if the size of the point images 105a to 105d is too small compared to the resolution of the image sensor 102, sufficient accuracy in detecting the center of gravity cannot be achieved. In this embodiment, the image sensor 102 is placed at a position defocused d away from the focal plane 104. The accuracy of center of gravity detection is improved by detecting enlarged point images 106a to 106d on the image sensor 102, which are obtained by enlarging the point images 105a to 105d by defocusing.

[0016] Next, a method for calculating the defocus d will be described. The point image size w0 on the focal plane 104 is calculated by the following equation (1) where λ is the wavelength used.

[0017] w0=2.44λf / Φ (1) If the point image size w0 provides sufficient accuracy in detecting the center of gravity, then d = 0 is sufficient, but if sufficient accuracy in detecting the center of gravity is not obtained, then the point image size must be enlarged. Therefore, the necessity of enlarging the point image size is determined. A fine image sensor can have a small point image size, but a coarse image sensor requires a larger point image size. It is necessary to consider the point image size in terms of the number of pixels rather than the actual point image size. When the size of the point images 105a to 105d is smaller than a predetermined size, and the number of pixels of the image sensor 102 corresponding to the predetermined size is p, the necessity of enlarging the point image size is expressed by the following conditional expression (2).

[0018] 2.44λf / Φ <ps ···(2) Conditional expression (2) is easy to satisfy when dealing with wavefronts with large aberrations or when high robustness is desired. This is because the focal length must be short to suppress sensitivity to center of gravity shifts relative to wavefront gradient, and as a result, the value of the left side of conditional expression (2) becomes small.

[0019] When conditional expression (2) is satisfied, the size w of a point image at a position defocused from the focal plane 104 and at a distance f+d from the microlens array 101 is calculated by the following expression (3).

[0020] w=2.44λf / Φ+|d|Φ / f ···(3) The point image is enlarged by defocusing, and the value of defocus d changes depending on the size of the point image to be enlarged. If the number of pixels of image sensor 102 corresponding to enlarged point images 106a-106d on the imaging surface of image sensor 102, obtained by enlarging point images 105a-105d by defocusing, is m (≧p), the defocus d required to enlarge the point image size is found by the following conditional expression (4):

[0021] |d|>(ms-2.44λf / Φ)f / Φ ···(4) 1, the image sensor 102 is disposed at a position farther from the focal plane 104 than the microlens array 101, but the image sensor 102 may be disposed at a position closer to the focal plane 104. The sign of the defocus d is positive when the image sensor 102 is disposed at a position farther from the focal plane 104 than the microlens array 101, and negative when the image sensor 102 is disposed at a position closer to the microlens array 101 than the focal plane 104.

[0022] Next, we calculate the number of pixels p and the number of pixels m of the enlarged point images 106a-106d. As a basis for this calculation, we explain the relationship between point image size and centroid detection accuracy. The required centroid detection accuracy is sub-micron, but the pixel pitch s of the image sensor 102 is on the order of a few microns. Therefore, centroid detection with sub-pixel accuracy is required, which requires that the point image size be larger than the pixel pitch (point image size > pixel pitch). Figures 2, 3, and 4 show simulation results of centroid detection accuracy versus point image size. Figure 2 shows the relationship between point image size and centroid detection accuracy. The point image size increases by 1 pixel in the order (a) to (h), with (a) being a 3-pixel point image and (h) being a 10-pixel point image. Furthermore, for all of these, random noise is 0, but a positional shift of 1.25 pixels is added. Figure 3 plots the centroid detection results of Figure 2. When the point image size is less than 5 pixels, centroid detection accuracy decreases. It can be seen that a point image size of 5 pixels or more is required to detect the center of gravity with sufficient accuracy. Figure 4 plots the results of similar center detection when 10,000 random noise patterns are added to the point image of Figure 2. It can be seen that accuracy drops slightly even at 5 pixels when noise is taken into account. For this reason, it is better to enlarge the point image to around 6 pixels rather than 5 pixels, to provide some leeway. In other words, it is preferable that the number of pixels p is 5 or more (p≧5) and the number of pixels m of the enlarged point images 106a to 106d is p+1 or more (m≧p+1).

[0023] As long as these conditions are met, these values ​​may be changed as appropriate. For example, if you want more leeway in determining the size of a point image, you can increase p. For example, if a 5.5 pix point image is determined to be a large point image when p = 5, it will not be defocused, but if p = 6, it will be determined to be a small point image and defocused. Also, if you want to improve robustness against noise, you can increase m to increase the amount of defocus and make the point image size larger.

[0024] In addition, although the present embodiment has been described with the defocus d as a variable, any variable may be used as long as it satisfies conditional expression (4). For example, the focal length f may be used as a variable, or two or more variables may be used.

[0025] Using this method, the sensitivity can be reduced by shortening the focal length f of the microlenses 101a to 101d, while the point image size can be controlled by the defocus d. This makes it possible to realize a wavefront sensor 100 that achieves both sufficiently low sensitivity and a sufficient point image size. Example 2 FIG. 5 is a schematic diagram of a wavefront sensor 500 according to a second embodiment. The wavefront sensor 500 according to the second embodiment includes a microlens array 501 including a plurality of microlenses 501a to 501d, each of which has an effective diameter Φ and a focal length f and forms a point image of an object; an image sensor 502 having a pixel pitch s; and a parallel plate 507 having a thickness t and a refractive index n. The microlenses 501a to 501d are arranged in a lattice pattern. The image sensor 502 receives the plurality of point images formed by the microlens array 501. The wavefront sensor 500 is used to calculate wavefront aberration from the deviation of the center of gravity of the point images formed by the microlens array 501 from a reference position. The image sensor 502 is disposed at a position (focal position) that is a focal length f away from the microlens array 501 in the optical axis direction of the microlens array 501. A parallel plate 507 having a thickness t and a refractive index n is inserted between the microlens array 501 and the image sensor 502 in the optical axis direction of the microlens array 501. The parallel plate 507 causes the apparent position of the image sensor 502 to be a position 508 that is closer to the microlens array 501 by a distance (1-1 / n)t than a position that is a focal length f away from the microlens array 501. In the second embodiment, the same effect as when the defocus d is set to d=(1-1 / n)t in the first embodiment can be obtained. The parallel plate 507 enlarges the point images 505a to 505d, and the enlarged point images 506a to 506d are detected on the image sensor surface of the image sensor 502, thereby improving the accuracy of center of gravity detection.

[0026] The point image size of the enlarged point images 506a to 506d is determined by the thickness t and refractive index n of the parallel plate 507. The thickness t of the parallel plate 507 required to enlarge the point image size is determined by the following conditional expression (5), which is obtained by replacing the defocus d in conditional expression (4) with (1-1 / n)t.

[0027] t>((ms-2.44λf / Φ)f / Φ) / (1-1 / n) ···(5) Here, λ is the wavelength used, and m is the number of pixels of the image sensor 502 corresponding to the enlarged point images 506a to 506d on the imaging surface of the image sensor 502 obtained by enlarging the point images 505a to 505d by the parallel plate 507.

[0028] The necessity of enlarging the point image size can be determined by conditional expression (2), as in Example 1. As in Example 1, it is preferable that the number of pixels p and the number of pixels m of the enlarged point images 506a to 506d satisfy p≧5 and m≧p+1, but these may be changed as appropriate as long as the conditions are met.

[0029] In addition, although the present embodiment has been described with the thickness t of the parallel plate as a variable, any variable may be used as long as it satisfies conditional expression (5). For example, the focal length f may be used as a variable, or two or more variables may be used.

[0030] Using this method, the sensitivity can be reduced by shortening the focal lengths of the microlenses 501a to 501d, while the point image size can be controlled by the parallel plate 507. This makes it possible to realize a wavefront sensor 500 that achieves both sufficiently low sensitivity and a sufficient point image size. Example 3 FIG. 6 is a schematic diagram of a wavefront measuring device 600 using the wavefront sensor 100 described in the first embodiment. The wavefront measuring device 600 includes a point light source 601, a test optical system 602 that emits light from the point light source 601 as test light, and a wavefront sensor 604 serving as the wavefront sensor 100 in the first embodiment that receives the test light and measures the wavefront aberration of the test light. The light beam emitted from the point light source 601 passes through the test optical system 602 to become test light 603, which is split into minute beam elements 603a to 603d. The wavefront sensor 604 acquires point images of the beam elements 603a to 603d. Because these point images are enlarged by defocus d, it is possible to accurately detect the center of gravity even if the test light 603 has a relatively large aberration.

[0031] The position where each of the light beam elements 603a to 603d forms a point image when there is no aberration is taken as the reference position, and the position of the center of gravity of the point image formed by each of the light beam elements 603a to 603d is defined as Δx n When the gradient θ of each of the light beam elements 603a to 603d is n is calculated using the following equation (6).

[0032] θ n =tan -1 (Δx n / (f+d)) ···(6) Equation (6) is basically the same as that in a general wavefront sensor, but differs by the amount of defocus d.

[0033] The gradient θ of each of the light beam elements 603a to 603d n By combining these, the wavefront aberration of the test light 603, that is, the aberration of the test optical system 602, can be obtained.

[0034] In this embodiment, for the sake of simplicity, only the point light source 601 and the optical system to be tested 602 are shown, but an auxiliary optical system for aberration correction and light beam size control may also be included.

[0035] Using this method, the sensitivity can be reduced by shortening the focal lengths of the microlenses 101a to 101d, while the point image size can be controlled by the defocus d. This makes it possible to realize a wavefront measuring device 600 that achieves both sufficiently low sensitivity and a sufficient point image size, and is capable of measuring wavefronts with large aberrations with high accuracy. Example 4 7 is a schematic diagram of a wavefront measuring device using the wavefront sensor shown in Example 2. The wavefront measuring device 700 includes a point light source 701, a test optical system 702 that emits light from the point light source 601 as test light, and a wavefront sensor 704 serving as the wavefront sensor 500 in Example 2 that receives the test light and measures the wavefront aberration of the test light.

[0036] A light ray emitted from a point light source 701 passes through a test optical system 702 to become test light 703, which is then split into minute beam elements 703a to 703d. These point images are enlarged by the defocusing effect of the parallel plate, which corresponds to a distance (1-1 / n)t, so that the center of gravity can be detected with high accuracy even if the test light 703 has a relatively large aberration.

[0037] The position where each of the light beam elements 703a to 703d forms a point image when there is no aberration is taken as the reference position, and the position of the center of gravity of the point image formed by each of the light beam elements 703a to 703d is defined as Δx n When the gradient θ of each of the light beam elements 503a to 503d is n is calculated using the following equation (7).

[0038] θ n =tan -1 (Δx n / (f-(1-1 / n)t)) (7) Equation (7) is basically the same as that in a general wavefront sensor, but differs by the amount of defocus (1-1 / n)t caused by the parallel plate.

[0039] The gradient θ of each of the light beam elements 703a to 703d n By combining these, the wavefront aberration of the test light 703, that is, the aberration of the test optical system 702, can be obtained.

[0040] In this embodiment, for the sake of simplicity, only the point light source 701 and the optical system to be tested 702 are shown, but an auxiliary optical system for aberration correction and light beam size control may also be included.

[0041] Using this method, the sensitivity can be reduced by shortening the focal lengths of the microlenses 501a to 501d, while the point image size can be controlled by the parallel plate 507. This makes it possible to realize a wavefront measuring device 700 that achieves both sufficiently low sensitivity and a sufficient point image size, and is capable of measuring wavefronts with large aberrations with high accuracy.

[0042] Although the preferred embodiments of the present invention have been described above, the present invention is not limited to these embodiments, and various modifications and changes are possible within the scope of the gist of the present invention. [Explanation of symbols]

[0043] 101 Microlens Array 102 Image sensor

Claims

1. a microlens array including a plurality of microlenses each forming a point image of an object; and an image pickup element receiving the plurality of point images formed by the microlens array; When a wavelength used is λ, a focal length of each of the plurality of microlenses is f, an effective diameter of each of the plurality of microlenses is Φ, a pixel pitch of the image sensor is s, the number of pixels of the image sensor corresponding to a point image of a predetermined size when the size of each of the plurality of point images is smaller than a predetermined size is p, the number of pixels of the image sensor corresponding to an enlarged point image on the imaging surface of the image sensor obtained by enlarging each of the plurality of point images by defocusing is m, and the defocus from the focal position of each of the plurality of microlenses is d, the imaging element is disposed at a position f+d away from the microlens array in the optical axis direction of the microlens array, 2.44λf / Φ<ps |d|>(ms-2.44λf / Φ)f / Φ A wavefront sensor characterized by satisfying the following conditional expression:

2. a microlens array including a plurality of microlenses each forming a point image of an object; an image pickup element receiving the plurality of point images formed by the microlens array; and a parallel plate; When a wavelength used is λ, a focal length of each of the plurality of microlenses is f, an effective diameter of each of the plurality of microlenses is Φ, a pixel pitch of the image sensor is s, a thickness of the parallel plate is t, a refractive index of the parallel plate is n, when the size of each of the plurality of point images is smaller than a predetermined size, the number of pixels of the image sensor corresponding to the predetermined size point image is p, and the number of pixels of the image sensor corresponding to the enlarged point image on the imaging surface of the image sensor obtained by enlarging each of the plurality of point images by the parallel plate is m, the imaging element is disposed at a position spaced a distance f from the microlens array in the optical axis direction of the microlens array, the parallel plate is disposed between the microlens array and the image sensor in the optical axis direction of the microlens array, 2.44λf / Φ<ps t>((ms-2.44λf / Φ)f / Φ) / (1-1 / n) A wavefront sensor characterized by satisfying the following conditional expression:

3. 3. The wavefront sensor according to claim 1, wherein the number of pixels p is 5 or more.

4. 4. The wavefront sensor according to claim 1, wherein the number of pixels m is equal to or greater than p+1.

5. 5. The wavefront sensor according to claim 1, wherein the point image is formed on a focal plane of the microlens array.

6. A wavefront sensor according to any one of claims 1 to 5; A light source and a test optical system that emits light from the light source as test light, a wavefront sensor for receiving the test light and measuring the wavefront aberration of the test light;

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