JP7753129B2 - Wavefront sensor, wavefront measuring device - Google Patents

Description

The present invention relates to a wavefront sensor capable of measuring wavefronts with large aberrations with high accuracy.

A wavefront sensor (Shack-Hartmann sensor, SHS) combines an image sensor with a microlens array, which consists of numerous microlenses arranged in a grid pattern. If the wavefront has wavefront aberration, 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 determined by detecting the center of gravity. Therefore, the accuracy of the center of gravity detection is important.

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

Patent No. 6080427

Detecting the center of gravity with sub-pixel accuracy requires a certain level of point image size. However, while the method in Patent Document 1 can reduce the influence of adjacent point images, it cannot be expected to be effective if the individual point image sizes themselves are insufficient.

In addition, for wavefronts with large aberrations, the point image size tends to be small. For large aberrations above a certain value, it is difficult to achieve both sufficiently low sensitivity and a sufficient point image size, making it difficult to detect the center of gravity with high accuracy.

The present invention provides a wavefront sensor that can detect the center of gravity with high accuracy even for wavefronts with large aberrations.

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 receiving the plurality of point images formed by the microlens array, wherein the image sensor is disposed at a position f+d away from the microlens array in the optical axis direction of the microlens array, where 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, p is 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, m is the 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, and d is the defocus from the focal position of each of the plurality of microlenses,
2.44λf/Φ<ps
|d|>(ms-2.44λf/Φ)f/Φ
The present invention is characterized in that the following condition is satisfied:

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:

A wavefront measuring device equipped with the above-mentioned wavefront sensor also constitutes another aspect of the present invention.

Other objects and features of the present invention are described in the following embodiments.

The present invention provides a wavefront sensor that can detect the center of gravity with high accuracy even for wavefronts with large aberrations.

1 is a schematic diagram of a wavefront sensor according to a first embodiment. FIG. 10 is a diagram illustrating the relationship between point image size and centroid detection accuracy. 10A and 10B are diagrams illustrating the relationship between a point image without random noise and the accuracy of center of gravity detection. 10A and 10B are diagrams illustrating the relationship between a point image with random noise and the accuracy of center of gravity detection. FIG. 10 is a schematic diagram of a wavefront sensor according to a second embodiment. FIG. 10 is a schematic diagram of a wavefront measuring instrument according to a third embodiment. FIG. 10 is a schematic diagram of a wavefront measuring instrument according to a fourth embodiment.

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 the effective light beam that contributes to image formation passes. 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.

Incoming light 103 is divided by the microlens array 101 into tiny beam elements 103a-103d, each of which can be considered to be roughly parallel light. The beam elements 103a-103d form point images 105a-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-105d depend on the gradient of each beam element 103a-103d, the gradient of each beam element 103a-103d can be determined by detecting the center of gravity of the positions of the point images 105a-105d. The wavefront aberration of the incident light 103 can be determined by adjusting the gradients of the beam elements 103a-103d. However, if the size of the point images 105a-105d is too small compared to the resolution of the image sensor 102, sufficient center of gravity detection accuracy cannot be achieved. In this embodiment, the image sensor 102 is positioned at a distance of defocus d from the focal plane 104. The accuracy of center of gravity detection is improved by detecting enlarged point images 106a-106d on the image sensor surface of the image sensor 102, which are enlarged by defocusing point images 105a-105d.

Next, a method for calculating the defocus d will be described. The point image size w ₀ on the focal plane 104 is calculated by the following equation (1) where λ is the wavelength used.

w ₀ =2.44λf/Φ...(1)
If the point image size _w0 is a point image size that provides sufficient accuracy in detecting the center of gravity, then d = 0 is sufficient, but if sufficient accuracy in the center of gravity is not obtained, then the point image size must be enlarged. Therefore, the need to enlarge 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 point image size itself. 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 that correspond to the predetermined size is p, the need to enlarge the point image size is expressed by the following conditional expression (2).

2.44λf/Φ<ps...(2)
Conditional expression (2) is easy to satisfy when a wavefront with large aberration is targeted or when high robustness is desired. This is because the focal length needs to be short in order to suppress sensitivity of the center of gravity shift to the gradient of the wavefront, and as a result, the value of the left side of conditional expression (2) becomes small.

When conditional expression (2) is satisfied, the point image size w 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):

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 the image sensor 102 corresponding to enlarged point images 106a to 106d on the imaging surface of the image sensor 102, obtained by enlarging point images 105a to 105d by defocusing, is m (≧p), the defocus d required to enlarge the point image size is found by the following conditional expression (4):

|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.

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) through (h), with (a) being a 3-pixel point image and (h) being a 10-pixel point image. Furthermore, all of these have zero random noise, but a 1.25-pixel positional shift 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 of gravity detection when 10,000 random noise patterns are added to the point image of Figure 2. When noise is taken into account, it can be seen that accuracy drops slightly even at 5 pixels. 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 be 5 or more (p≧5) and the number of pixels m of the enlarged point images 106a-106d be p+1 or more (m≧p+1).

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 increase robustness against noise, you can increase m to increase the amount of defocus and make the point image size larger.

In addition, while this embodiment has been described with defocus d as a variable, any variable may be used as long as conditional expression (4) is satisfied. For example, focal length f may be used as a variable, or two or more variables may be used.

By 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 accuracy of center of gravity detection is improved by detecting enlarged point images 506a to 506d on the image sensor surface of the image sensor 502 that are obtained by enlarging the point images 505a to 505d using the parallel plate 507.

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.

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 506 a to 506 d on the image sensing surface of the image sensor 502 obtained by enlarging the point images 505 a to 505 d by the parallel plate 507 .

The need to enlarge 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, respectively, but these may be changed as appropriate as long as the conditions are met.

In addition, in this embodiment, the thickness t of the parallel plate is described as a variable, but any variable may be used as long as conditional expression (5) is satisfied. For example, the focal length f may be used as a variable, or two or more variables may be used.

By 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
6 is a schematic diagram of a wavefront measuring device 600 using the wavefront sensor 100 shown in Example 1. 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 Example 1 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.

When the position where each of the light beam elements 603 a to 603 d 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 603 a to 603 d is taken as Δx _n , the gradient θ _n of each of the light beam elements 603 a to 603 d can be found by the following equation (6):

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.

By adjusting the gradients θ _n of the light beam elements 603 a to 603 d, the wavefront aberration of the test light 603, that is, the aberration of the test optical system 602, can be obtained.

Furthermore, for simplicity, this embodiment describes only a point light source 601 and a test optical system 602, but an auxiliary optical system for aberration correction and light beam size control may also be included.

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. Therefore, it is 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 a wavefront 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.

Light emitted from point light source 701 passes through test optical system 702 to become test light 703, which is then split into tiny beam elements 703a to 703d. These point images are enlarged by the defocusing effect of the parallel plate, equivalent to a distance of (1-1/n)t, making it possible to accurately detect the center of gravity even if test light 703 has a relatively large aberration.

When 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 taken as _Δxn , the gradient _θn of each of the light beam elements 503a to 503d can be found by the following equation (7):

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.

By adjusting the gradients θ _n of the light beam elements 703 a to 703 d, the wavefront aberration of the test light 703, that is, the aberration of the test optical system 702, can be obtained.

Furthermore, for simplicity, this embodiment describes only the point light source 701 and the optical system to be tested 702, but an auxiliary optical system for aberration correction and light beam size control may also be included.

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

The above describes preferred embodiments of the present invention, but the present invention is not limited to these embodiments, and various modifications and variations are possible within the scope of the invention.

101 Microlens array 102 Image pickup element

Claims (6)

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: 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. The wavefront sensor according to claim 1, wherein the number of pixels p is 5 or more. 4. The wavefront sensor according to claim 1, wherein the number of pixels m is equal to or greater than p+1. 5. The wavefront sensor according to claim 1, wherein the point image is formed on a focal plane of the microlens array. 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;