JP2023115855A - Wavefront sensor and wavefront measuring device - Google Patents

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

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

A wavefront sensor (Shack-Hartmann sensor, SHS) is a combination of a microlens array in which a large number of microlenses are arranged in a grid pattern and an imaging device. If the wavefront has wavefront aberration, the position of the point image shifts according to the gradient of the wavefront. Therefore, the wavefront aberration can be obtained from the positional deviation amount of the point image. Since the point image has a finite size due to diffraction, the position of the point image is obtained by centroid detection. Therefore, the accuracy of centroid detection is important.

Japanese Patent Application Laid-Open No. 2002-200002 describes a method of changing the area for detecting the center of gravity according to the interval between point images. This is to optimize the region for centroid detection and minimize the influence of adjacent point images, thereby improving centroid detection accuracy.

Japanese Patent No. 6080427

To detect the centroid with sub-pixel accuracy, a certain point image size is required. However, in the method of Patent Document 1, although the influence of adjacent point images can be reduced, the effect cannot be expected when the size of each individual point image itself is insufficient.

Also, in the case of a wavefront with large aberration, the point image size tends to be small. In the case of a large aberration of a certain value or more, it is difficult to achieve both a sufficiently low sensitivity and a sufficient point image size, and there is a problem that it is difficult to detect the center of gravity with high accuracy.

The present invention provides a wavefront sensor capable of detecting the center of gravity with high accuracy even in a wavefront with large aberration.

A wavefront sensor as 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 imaging element receiving the plurality of point images formed by the microlens array. λ is the wavelength used, f is the focal length of each of the plurality of microlenses, Φ is the effective diameter of each of the plurality of microlenses, s is the pixel pitch of the imaging device, and each of the plurality of point images When the size of is smaller than a predetermined size, the number of pixels of the image sensor corresponding to the point image of the predetermined size is p, and each of the plurality of point images is enlarged by defocusing on the imaging surface of the image sensor. When the number of pixels of the imaging device corresponding to a point image is m, and the defocus from the focal position of each of the plurality of microlenses is d, the imaging device is arranged in the optical axis direction of the microlens array as follows: is located at a distance of f + d from the microlens array,
2.44λf/Φ<ps
|d|>(ms−2.44λf/Φ)f/Φ
It is characterized by satisfying the following conditional expression.

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

A wavefront measuring device including the wavefront sensor also constitutes another aspect of the present invention.

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

According to the present invention, it is possible to provide a wavefront sensor capable of detecting the center of gravity with high accuracy even on a wavefront with large aberration.

1 is a schematic diagram of a wavefront sensor of Example 1. FIG. It is a figure which shows the relationship between point image size and centroid detection accuracy. FIG. 10 is a diagram showing the relationship between a point image without random noise and the centroid detection accuracy; FIG. 10 is a diagram showing the relationship between point images with random noise and centroid detection accuracy; FIG. 5 is a schematic diagram of a wavefront sensor of Example 2; FIG. 11 is a schematic diagram of a wavefront measuring instrument of Example 3; FIG. 11 is a schematic diagram of a wavefront measuring instrument of Example 4;

BEST MODE FOR CARRYING OUT THE INVENTION Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. In each figure, the same reference numerals are given to the same members, and overlapping descriptions are omitted.
(Example 1)
FIG. 1 is a schematic diagram of a wavefront sensor 100 in Example 1. FIG. A wavefront sensor 100 in Example 1 has a microlens array 101 including a plurality of microlenses 101a to 101d each having an effective diameter Φ and a focal length f for forming a point image of an object, and an imaging element 102 having a pixel pitch s. . The microlenses 101a to 101d are arranged in a lattice. The imaging device 102 receives a plurality of point images formed by the microlens array 101 . The wavefront sensor 100 is used to obtain the wavefront aberration from the deviation of the barycentric position of the point image formed by the microlens array 101 from the reference position. Here, the effective diameter means the diameter on the lens surface of the luminous flux passing through the lens surface of the microlens at the position farthest in the radial direction (perpendicular to the optical axis) from the optical axis. In other words, the effective diameter means the diameter of the area (effective area) of the lens surface through which the effective light flux that contributes to image formation passes. The imaging element 102 is arranged at a position separated from the microlens array 101 by a distance (f+d) which is the sum of the focal length f and the defocus d in the optical axis direction of the microlens array 101 . The defocus d is obtained 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 .

Incident light 103 is divided into minute light flux elements 103a to 103d by microlens array 101, and each light flux element can be regarded as roughly parallel light. Light flux elements 103a-103d form point images 105a-105d, respectively, on focal plane 104, which is separated from microlens array 101 by focal length f. Since the positions of the point images 105a to 105d depend on the gradients of the light flux elements 103a to 103d, respectively, the gradients of the light flux elements 103a to 103d can be obtained by detecting the centers of gravity of the positions of the point images 105a to 105d. By matching the gradients of the light beam elements 103a to 103d, the wavefront aberration of the incident light 103 can be obtained. However, if the size of the point images 105a to 105d is too small for the resolution of the imaging device 102, sufficient centroid detection accuracy cannot be obtained. In this embodiment, the image sensor 102 is arranged at a position separated from the focal plane 104 by a defocus d. By detecting the enlarged point images 106a to 106d on the imaging surface of the imaging element 102 obtained by enlarging the point images 105a to 105d by defocusing, the center-of-gravity detection accuracy is improved.

Next, how to obtain the defocus d will be described. The point image size _w0 on the focal plane 104 is obtained 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 centroid detection accuracy, d=0 is sufficient, but if sufficient centroid accuracy cannot be obtained, the point image size must be enlarged. Therefore, the necessity of enlarging the point image size is determined. A small point image size is sufficient for a fine image pickup device, but a large point image size is required for a rough image pickup device. Instead of the point image size itself, it is necessary to consider it in terms of the number of pixels. 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 point images of the predetermined size is p, the necessity of enlarging the point image size is expressed by the following conditional expression (2 ).

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

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

w=2.44λf/Φ+|d|Φ/f (3)
The point image is magnified by defocusing, and the value of defocus d changes depending on the size of the point image to be magnified. Necessary for enlarging the point image size, where m (≧p) is the number of pixels of the image sensor 102 corresponding to the enlarged point images 106a to 106d on the imaging surface of the image sensor 102 obtained by enlarging the point images 105a to 105d by defocusing. A defocus d is obtained by the following conditional expression (4).

|d|>(ms−2.44λf/Φ)f/Φ (4)
In FIG. 1, the imaging element 102 is arranged at a position farther than the focal plane 104 with respect to the microlens array 101 , but the imaging element 102 may be arranged at a position closer than the focal plane 104 . The sign of the defocus d is positive when the imaging device 102 is located farther than the focal plane 104 with respect to the microlens array 101, and the imaging device 102 is closer to the microlens array 101 than the focal plane 104. It is negative if it is placed at the position.

Next, the pixel number p and the pixel number m of the enlarged point images 106a to 106d are obtained. As a basis for this, the relationship between the point image size and the centroid detection accuracy will be described. The required centroid detection accuracy is sub-μm, but the pixel pitch s of the image sensor 102 is about several μm. Therefore, it is necessary to detect the center of gravity with sub-pixel accuracy, and for this purpose, the point image size must be larger than the pixel pitch (point image size>pixel pitch). 2, 3, and 4 show simulation results of centroid detection accuracy with respect to point image size. FIG. 2 shows the relationship between point image size and centroid detection accuracy. The point image size increases by 1 pix in order from (a) to (h), and (a) is 3 pix and (h) is a 10 pix point image. In addition, although the random noise is 0 for all of these, a positional shift of 1.25 pix is given. FIG. 3 plots the center-of-gravity detection results of FIG. When the point image size is less than 5 pix, the center-of-gravity detection accuracy decreases. It can be seen that a point image size of 5 pix or more is required to detect the center of gravity with sufficient accuracy. FIG. 4 plots the result of adding 10,000 kinds of random noise to the point image of FIG. 2 and similarly detecting the center of gravity. Considering noise, it can be seen that even 5 pix is slightly less accurate. Therefore, it is better to enlarge the point image to about 6 pix with a margin instead of 5 pix. That is, it is preferable that the pixel number p is 5 or more (p≧5), and the pixel number m of the enlarged point images 106a to 106d is p+1 or more (m≧p+1).

As long as these conditions are satisfied, these values may be changed as appropriate. For example, if it is desired to have a margin in judging the size of the point image, p should be made large. For example, a point image of 5.5 pix is judged to be a large point image if p=5, so it is not defocused. If p=6, it is judged to be a small point image, so it is defocused. Become. Further, if it is desired to increase the robustness against noise, it is sufficient to increase the defocus amount by increasing m and increase the size of the point image.

Also, in this embodiment, defocus d is used as a variable, but any variable may be used as long as conditional expression (4) is satisfied. For example, the focal length f may be a variable, or may be two or more variables.

By using this method, the point image size can be controlled by the defocus d while reducing the sensitivity by shortening the focal length f of the microlenses 101a to 101d. Therefore, it is possible to realize the wavefront sensor 100 that achieves both sufficiently low sensitivity and sufficient point image size.
(Example 2)
FIG. 5 is a schematic diagram of a wavefront sensor 500 in Example 2. FIG. A wavefront sensor 500 according to the second embodiment includes a microlens array 501 including a plurality of microlenses 501a to 501d each having an effective diameter Φ and a focal length f for forming a point image of an object, an imaging element 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. An imaging device 502 receives a plurality of point images formed by the microlens array 501 . The wavefront sensor 500 is used to obtain the wavefront aberration from the deviation of the barycentric position of the point image formed by the microlens array 501 from the reference position. The imaging device 502 is arranged at a position (focal position) separated from the microlens array 501 by a focal length f in the optical axis direction of the microlens array 501 . A parallel plate 507 having a thickness of t and a refractive index of n is inserted between the microlens array 501 and the imaging device 502 in the optical axis direction of the microlens array 501 . Due to the parallel plate 507 , the apparent position of the imaging element 502 is a position 508 closer to the microlens array 501 by a distance (1−1/n) t than a position distant from the microlens array 501 by the focal length f. In the second embodiment, the same effect as in the first embodiment when the defocus d is set to d=(1−1/n)t is obtained. By detecting the enlarged point images 506a to 506d on the imaging surface of the imaging device 502 obtained by enlarging the point images 505a to 505d by the parallel plate 507, the centroid detection accuracy is improved.

The point image size of the enlarged point images 506a to 506d is determined by the thickness t and the refractive index n of the parallel plate 507. FIG. The thickness t of the parallel plate 507 necessary for enlarging the point image size is obtained by the following conditional expression (5) obtained by replacing the defocus d in the 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 imaging device 502 corresponding to the enlarged point images 506a to 506d on the imaging surface of the imaging device 502 obtained by enlarging the point images 505a to 505d by the parallel plate 507. FIG.

The necessity of enlarging the point image size can be determined by conditional expression (2) as in the first embodiment. The number of pixels p and the number of pixels m of the enlarged point images 506a to 506d are preferably p≧5 and m≧p+1 as in the first embodiment, but may be changed as appropriate as long as the conditions are satisfied.

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

Using this method, the point image size can be controlled by the parallel plate 507 while the sensitivity is lowered by shortening the focal lengths of the microlenses 501a to 501d. Therefore, it is possible to realize the wavefront sensor 500 that achieves both sufficiently low sensitivity and sufficient point image size.
(Example 3)
FIG. 6 is a schematic diagram of a wavefront measuring device 600 using the wavefront sensor 100 shown in the first embodiment. The wavefront measuring apparatus 600 includes a point light source 601, a test optical system 602 that emits the light from the point light source 601 as test light, and receives the test light to measure the wavefront aberration of the test light. A wavefront sensor 604 is provided as the wavefront sensor 100 . A light beam emitted from a point light source 601 passes through a test optical system 602 and becomes test light 603, and the test light 603 is divided into minute beam elements 603a to 603d. A wavefront sensor 604 acquires a point image of each light flux element 603a to 603d. Since these point images are enlarged by the defocus d, even if the test light 603 has relatively large aberration, it is possible to accurately detect the center of gravity.

When the position of the point image formed by each light flux element 603a to 603d is a reference position, and the position of the center of gravity of the point image formed by each light flux element 603a to 603d is _Δxn , each light flux element 603a to The gradient _θn of 603d is obtained by the following equation (6).

θ _n =tan ⁻¹ (Δx _n /(f+d)) (6)
Equation (6) is basically the same as in a general wavefront sensor, but differs by defocus d.

The wavefront aberration of the test light 603, that is, the aberration of the test optical system 602 can be obtained by matching the gradients _θn of the light flux elements 603a to 603d.

In this embodiment, only the point light source 601 and the test optical system 602 are shown for the sake of simplification, but an auxiliary optical system for aberration correction and light beam size control may be provided.

Using this method, the point image size can be controlled by the defocus d while reducing the sensitivity by shortening the focal lengths of the microlenses 101a to 101d. Therefore, it is possible to realize the wavefront measuring apparatus 600 that achieves both sufficiently low sensitivity and a sufficient point image size and is capable of accurately measuring a wavefront with large aberration.
(Example 4)
FIG. 7 is a schematic diagram of a wavefront measuring device using the wavefront sensor shown in the second embodiment. The wavefront measuring apparatus 700 includes a point light source 701, a test optical system 702 that emits the light from the point light source 601 as test light, and receives the test light to measure the wavefront aberration of the test light. A wavefront sensor 704 is provided as the wavefront sensor 500 .

A light beam emitted from a point light source 701 passes through a test optical system 702 and becomes test light 703, and the test light 703 is divided into minute beam elements 703a to 703d. These point images are magnified by the defocus effect equivalent to the distance (1-1/n)t by the parallel plate, so even if the test light 703 has relatively large aberration, the center of gravity can be detected with high accuracy. is.

When the position of the point image formed by each of the light flux elements 703a to 703d is set as a reference position and the position of the center of gravity of the point image formed by each of the light flux elements 703a to 703d is _Δxn , each of the light flux elements 503a to 703d The gradient θ _n of 503d is obtained by the following equation (7).

θ _n =tan ⁻¹ (Δx _n /(f−(1−1/n)t)) (7)
Equation (7) is basically the same as in a general wavefront sensor, but differs by the defocus (1-1/n)t due to the parallel plate.

The wavefront aberration of the test light 703, that is, the aberration of the test optical system 702 can be obtained by matching the gradients _θn of the light flux elements 703a to 703d.

In this embodiment, only the point light source 701 and the test optical system 702 are described for the sake of simplification, but an auxiliary optical system for aberration correction and light beam size control may be provided.

Using this method, the point image size can be controlled by the parallel plate 507 while the sensitivity is lowered by shortening the focal lengths of the microlenses 501a to 501d. Therefore, it is possible to realize the wavefront measuring apparatus 700 that achieves both sufficiently low sensitivity and a sufficient point image size and is capable of accurately measuring a wavefront with large aberration.

Although 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.

101 microlens array 102 imaging device

Claims (6)

a microlens array including a plurality of microlenses each forming a point image of an object; and an imaging element receiving the plurality of point images formed by the microlens array,
λ is the wavelength used, f is the focal length of each of the plurality of microlenses, Φ is the effective diameter of each of the plurality of microlenses, s is the pixel pitch of the imaging device, and the size of each of the plurality of point images is p is the number of pixels of the image sensor corresponding to the point image of the predetermined size when smaller than a predetermined size; When the number of pixels of the corresponding imaging device is m and the defocus from the focal position of each of the plurality of microlenses is d,
The imaging element is arranged 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 imaging element receiving the plurality of point images formed by the microlens array; and a parallel plate,
λ is the wavelength used, f is the focal length of each of the plurality of microlenses, Φ is the effective diameter of each of the plurality of microlenses, s is the pixel pitch of the imaging device, t is the thickness of the parallel plate, and the parallel n is the refractive index of the flat plate, p is the number of pixels of the imaging element corresponding to the point image of the predetermined size when the size of each of the plurality of point images is smaller than a predetermined size, and When the number of pixels of the imaging device corresponding to the enlarged point image on the imaging surface of the imaging device magnified by the parallel plate is m,
The imaging device is arranged at a position f away from the microlens array in the optical axis direction of the microlens array,
The parallel flat plate is arranged between the microlens array and the imaging element 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 p of pixels is 5 or more. The wavefront sensor according to any one of claims 1 to 3, wherein the number of pixels m is p+1 or more. The wavefront sensor according to any one of claims 1 to 4, wherein the point image is formed on the focal plane of the microlens array. a light source;
a test optical system that emits light from the light source as test light;
A wavefront measuring apparatus comprising the wavefront sensor according to any one of claims 1 to 5, which receives the test light and measures the wavefront aberration of the test light.