Optical Department

Abstract

To provide an optical system that can easily correct an image surface optically while maintaining the resolution even when the imaging is being done obliquely.SOLUTION: The optical system includes: an object optical system 100a for forming an object surface OS with a non-plane shape into an image; an image formation optical system 100b having an imaging element 50 for imaging a primary image formation surface IP formed by the object optical system 100a as a plane image; and an image surface correction mirror 30 located in the primary image formation surface IP, the image surface correction mirror having a non-plane reflection 30a. The object surface OS, the primary image formation surface IP, and the imaging element 50 are arranged in an optically conjugation position, and the primary imaging surface IP and the object surface OS are arranged to satisfy the Scheimpflug principle.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to an optical system for capturing an image of an object surface having a non-planar shape as a planar image, and an optical system for projecting a planar image displayed on an image display screen onto a projection surface having a non-planar shape. [Background technology]

[0002] In an optical system equipped with an imaging optical system and a projection optical system, an image display surface, an image forming surface, and a projection surface are arranged in an optically conjugate relationship, and an image plane correction mirror having a non-planar reflecting surface is arranged on the image forming surface, and a flat image is projected onto the non-planar projection surface without distortion by correcting the image on the image forming surface (see Patent Document 1). However, the optical system in Patent Document 1 does not adequately handle projection from an oblique angle.

[0003] There is also a projector that projects reflected light from an imaging element, such as a digital mirror device (DMD), obliquely onto a projection surface using a projection lens (see Patent Document 2). In this projector, the imaging element, projection lens, and projection surface are arranged to satisfy the Scheimpflug condition, and an imaging element adjustment mechanism changes the tilt angle and position of the imaging element so that the imaging element and projection surface satisfy the Scheimpflug condition. A shift mechanism appropriately directs light from the light source onto the imaging element according to the changed tilt angle and position of the imaging element. This allows the pattern light from the imaging element to be appropriately projected onto the projection surface from the projection lens. The projector in Patent Document 2 can change the projection range by adjusting the angle and position of the imaging element, but it projects a flat projection image onto a flat projection surface, and blurring of the projected image may occur on a non-flat projection surface. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Patent Publication No. 2021-67834 [Patent Document 2] Japanese Patent Publication No. 2020-51875 Summary of the Invention

[0005] The present invention has been made in consideration of the above-described background art, and aims to provide an optical system that can easily perform optical image plane correction while maintaining resolution even when capturing or projecting from an oblique angle.

[0006] In order to solve the above-mentioned problems, the optical system according to the present invention includes an objective optical system that forms an image of an object surface having a non-planar shape, an imaging optical system having an image sensor that captures a planar image of the primary image surface formed by the objective optical system, and an image plane correction mirror that is arranged at the primary image surface and has a non-planar reflecting surface, wherein the object surface, the primary image surface, and the image sensor are arranged at positions that are optically conjugate with each other, and the primary image surface and the object surface are arranged so as to satisfy the Scheimpflug condition. Here, "arranging the image plane correction mirror at the primary image surface" includes "arranging the image plane correction mirror in the vicinity of the primary image surface."

[0007] In the above optical system, the object plane, the primary image plane, and the image sensor are arranged in an optically conjugate relationship, so that by correcting the image at the primary image plane, an image of a non-planar object plane can be captured without distortion using a planar image sensor. That is, a planar image whose image plane has been corrected by the shape of the non-planar reflecting surface of the image sensor arranged at the primary image plane can be captured on the image sensor's imaging surface. Therefore, optical image plane correction can be easily performed by appropriately adjusting the shape of the reflecting surface of the image plane correction mirror. Furthermore, by arranging the object plane and the primary image plane in a Scheimpflug arrangement, the entire image can be focused even when captured from an oblique angle, and high-resolution images can be captured from an oblique angle with respect to a non-planar object plane without compromising the brightness of the objective optical system's lenses.

[0008] In order to solve the above-mentioned problems, the optical system of the present invention comprises an imaging optical system that forms a planar image to be displayed on an image display surface, a projection optical system that projects the primary image surface formed by the imaging optical system onto a non-planar projection surface, and an image plane correction mirror that is arranged on the primary image surface and has a non-planar reflecting surface, wherein the image display surface, the primary image surface, and the projection surface are arranged in optically conjugate positions, and the primary image surface and the projection surface are arranged so as to satisfy the Scheimpflug condition.

[0009] In the above optical system, the image display surface, the primary image plane, and the projection surface are arranged in an optically conjugate relationship, so that by correcting the image at the primary image plane, a planar image displayed on the image display surface can be projected onto a non-planar projection surface without distortion. In other words, the shape of the non-planar reflecting surface of the image plane correction mirror arranged at the primary image plane allows an image whose image plane has been corrected to be projected onto the projection surface, so that optical image plane correction can be easily performed by appropriately adjusting the shape of the reflecting surface of the image plane correction mirror. Furthermore, by arranging the primary image plane and the projection surface in a Scheimpflug arrangement, the entire image can be focused even when projected from an oblique angle, and a high-resolution image can be projected onto a non-planar projection surface from an oblique angle without compromising the brightness of the lenses in the projection optical system.

[0010] In a specific aspect of the present invention, in the optical system, the reflecting surface of the image plane correction mirror has a shape corresponding to the shape of the object plane or the projection plane. In this case, the image plane correction can be made more accurate.

[0011] In another aspect of the present invention, the image plane correction mirror is any one of a spherical mirror, an aspherical mirror, a cylindrical mirror, a free-form mirror, and a deformable mirror.

[0012] In yet another aspect of the present invention, a tilt adjustment unit is provided that tilts the image plane correction mirror, in which case the tilt angle of the image plane correction mirror can be adjusted appropriately in accordance with the tilt angle of the object plane or the projection plane. [Brief explanation of the drawings]

[0013] [Figure 1] FIG. 1 is a conceptual diagram illustrating an imaging device including an optical system according to a first embodiment. [Figure 2] FIG. 1 is a conceptual diagram illustrating an optical system of a conventional imaging device. [Figure 3] 10 is an explanatory diagram schematically illustrating the shape of an image corrected by an image plane correction mirror. FIG. [Figure 4] FIG. 1 is a diagram showing a paraxial model of an imaging lens. [Figure 5] FIG. 1A is a diagram showing the imaging relationship in a geometric optical system, and FIG. 1B is a diagram explaining the Scheimpflug arrangement in the same optical system as FIG. [Figure 6] 10A and 10B are diagrams illustrating the angular relationship between an image plane correction mirror and a primary image plane. [Figure 7] FIG. 10 is a diagram showing the difference in best focus between the central portion and the peripheral portion. [Figure 8] 10A and 10B are diagrams illustrating calculation results of the tilt of the object plane relative to the imaging lens and the tilt of the primary image plane. [Figure 9] 10(A) to 10(C) are diagrams showing the MTF when the object plane angle is 10°. [Figure 10] 10A and 10B are diagrams showing the MTF when the object plane angle is 20°. [Figure 11] 10A and 10B are diagrams showing the MTF when the object plane angle is 5°. [Figure 12] FIG. 1A is a diagram showing a comparative example of two-dimensional image simulation, and FIG. 1B is a diagram showing an example of two-dimensional image simulation. [Figure 13] FIG. 10 is a diagram showing a comparison of relative luminance values ​​at the center of each captured image. [Figure 14] FIG. 10 is a diagram showing a comparison of relative luminance values ​​of the periphery of each captured image. [Figure 15] FIG. 10 is a conceptual diagram illustrating a projection device including an optical system according to a second embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0014] [First embodiment] An imaging device including an optical system according to a first embodiment of the present invention will be described below with reference to FIG.

[0015] 1 is a diagram illustrating the configuration of an imaging device 100. The imaging device 100 includes an imaging lens 10, a beam splitter 20, an image plane correction mirror 30, a relay lens 40, and an imaging element 50. The imaging device 100 images an object surface OS having a non-planar shape from an oblique direction with respect to the optical axis OA1 of the imaging lens 10. The non-planar shape includes shapes that are not flat.

[0016] In the imaging device 100, the imaging lens 10, the beam splitter 20, and the image plane correction mirror 30 constitute an objective optical system 100a. The image plane correction mirror 30, the beam splitter 20, the relay lens 40, and the imaging element 50 constitute an imaging optical system 100b. The optical path between the beam splitter 20 and the image plane correction mirror 30 is a common optical path for the objective optical system 100a and the imaging optical system 100b.

[0017] The imaging lens 10 is disposed on the object side and forms an image of an object plane OS having a non-planar shape. That is, the imaging lens 10 forms a primary image of the object plane OS, which is the image target, on a primary image plane IP.

[0018] The beam splitter 20 is disposed between the imaging lens 10 and the image plane correction mirror 30, and between the image plane correction mirror 30 and the relay lens 40. The beam splitter 20 transmits light that has passed through the imaging lens 10 and guides it to the image plane correction mirror 30, and reflects the light reflected by the image plane correction mirror 30 and guides it to the relay lens 40. The beam splitter 20 may be of a cube type, a plate type, or the like.

[0019] The image plane correction mirror 30 is disposed at the primary image plane IP and has a non-planar reflective surface 30a. Examples of the image plane correction mirror 30 that can be used include mirrors with non-planar reflective surfaces 30a, such as spherical mirrors, aspherical mirrors, cylindrical mirrors, free-form mirrors, and deformable mirrors. The term "primary" in "primary image plane IP" refers to the fact that an image from the object plane OS is ultimately formed on the imaging plane IS of the image sensor 50. The primary image plane IP does not necessarily have to be the first imaging plane, but may be any plane on which the image from the object plane OS is formed. Furthermore, disposing the image plane correction mirror 30 at the primary image plane IP does not mean that the image plane correction mirror 30 and the primary image plane IP are entirely coincident. It means that the actual primary image plane IP is formed at a position offset from the image plane correction mirror 30 as a corrected image FI, described later, except on a reference axis such as the optical axis OA2.

[0020] The deformable mirror has a continuous reflecting surface that is moved by, for example, an actuator, and the shape of the reflecting surface 30a can be changed to match the shape of the object surface OS. By using a deformable mirror, it is possible to accommodate object surfaces OS with complex shapes.

[0021] The image plane correction mirror 30 is provided with a tilt adjustment unit 60 that adjusts the tilt of the mirror. The image plane correction mirror 30 is driven by the tilt adjustment unit 60 to change the tilt angle and tilt direction of the image plane correction mirror 30 with respect to the optical axis OA2. By tilting the image plane correction mirror 30, the optical system can be adjusted so that its position satisfies the Scheimpflug condition, which will be described later. This allows the focus to be adjusted to match the imaging direction. The tilt adjustment of the image plane correction mirror 30 by the tilt adjustment unit 60 adjusts the overall posture of the image plane correction mirror 30. The tilt adjustment unit 60 includes, for example, a motor and an encoder, and operates under the control of a control device (not shown). Specifically, the tilt adjustment unit 60 has a two-axis rotation mechanism and can change the tilt angle of the image plane correction mirror 30 within a range of ±several tens of degrees, based on a state in which the image plane correction mirror 30 is tilted, for example, 45 degrees with respect to the optical axis OA2, thereby changing the orientation of the image plane correction mirror 30 around the optical axis OA2 by 360 degrees. In other words, the posture of the image plane correction mirror 30 can be freely changed. Note that the tilt adjustment unit 60 is not essential, and the user may tilt or rotate the image plane correction mirror 30 manually.

[0022] The relay lens 40 forms a secondary image of the object plane OS on the imaging plane IS of the imaging element 50 .

[0023] The imaging element 50 captures a primary image plane IP formed by the imaging lens 10 as a planar image FF on an imaging surface IS. The imaging element 50 is a CMOS sensor, a CCD sensor, or other semiconductor device.

[0024] In the optical systems 100a and 100b constituting the imaging device 100, the object plane OS, the primary image plane IP (image plane correction mirror 30), and the imaging plane IS (image sensor 50) are arranged so as to be optically conjugate. That is, the optical systems 100a and 100b have an image plane conjugate arrangement in which the object plane OS, the primary image plane IP, and the imaging plane IS are optically conjugate. Such an image plane conjugate arrangement makes it possible to perform image plane correction in the image plane correction mirror 30 arranged at the primary image plane IP so that an image of the object plane OS, which has a non-planar shape, can be captured as a planar image FF by the image sensor 50 without distortion.

[0025] Furthermore, the imaging device 100 is arranged so that the primary image plane IP and the object plane OS satisfy the Scheimpflug condition. This allows the peripheral portion of the captured image to be in focus even when the object plane OS is captured from an oblique angle. The Scheimpflug arrangement of the primary image plane IP and the object plane OS is achieved by adjusting the tilt of the image plane correction mirror 30 via the tilt adjustment unit 60 using a control device (not shown). The tilt adjustment can be performed in real time, for example, by adjusting the overall focus state based on the focus state using the captured image, or by projecting a laser spot onto the object and adjusting the spot spread. Furthermore, if real-time adjustment is not required, the tilt can be adjusted as needed using a pre-fixed system.

[0026] As described above, in this embodiment, the image plane is corrected by taking into consideration the conjugate arrangement of the optical components and the inclination of the image plane correction mirror 30 so as to satisfy the Scheimpflug condition.

[0027] An image of the object plane OS is transmitted by the imaging lens 10 through the beam splitter 20 and formed on a primary image plane IP. The image on the primary image plane IP is reflected by the reflecting surface 30a of the image plane correction mirror 30 toward the beam splitter 20 as light of a corrected image FI. The light of the corrected image FI reflected by the image plane correction mirror 30 is bent by the beam splitter 20 in a direction perpendicular to the optical axis OA1 of the imaging lens 10 and guided to the relay lens 40. The direction of the optical axis bent by the beam splitter 20 coincides with the direction of the optical axis OA3 of the relay lens. The corrected image FI is formed on an imaging plane IS by the relay lens 40 and captured by the image sensor 50.

[0028] The principle of the optical system of this embodiment will be described below.

[0029] (Comparison between a conventional optical system and the optical system of this embodiment) FIG. 2 is a conceptual diagram of an optical system 101a of a conventional imaging device 100s, which is composed of an imaging lens 10s and an imaging element 50s. On the object side of FIG. 2, a solid line indicates an object plane OS, and a dotted line indicates a virtual planar object plane FOS. Typically, the quality of an image captured by the optical system 101a is determined by the aberration characteristics of the imaging lens 10s. The imaging lens 10s has aberrations, and coma aberration, which particularly affects image quality in the peripheral areas, can be reduced by reducing the aperture, i.e., by increasing the F-number. This results in improved image quality. Furthermore, by reducing the aperture of the imaging lens 10s, the depth of field can be increased.

[0030] However, as shown in FIG. 2, when the object plane OS is spherical or cylindrical, the change in the circle of least confusion of the imaging lens 10s becomes very large, and even if the center C is within the depth of field, the peripheral P may be outside the depth of field. Furthermore, increasing the F-number results in a darker captured image under conditions where the brightness of the object plane OS or the light source does not change. On the other hand, decreasing the F-number can widen the depth of field, but the theoretical resolving power decreases due to the diffraction phenomenon, resulting in a decrease in resolving power. Therefore, it is difficult to widen the depth of field while maintaining brightness in a typical optical system 101a.

[0031] The above concept can also be applied to cases where the object or subject has a three-dimensional shape. Because the imaging surface IS of the image sensor 50s is flat, the object or subject surface on which the focus is achieved is also flat (the planar object surface FOS shown in FIG. 2). Therefore, when the object has a three-dimensional shape, the focus is achieved on the conjugate plane of the image sensor 50s, so a high-resolution image can be obtained, but object surfaces away from the conjugate plane are outside the depth of field, resulting in a low-resolution image.

[0032] In the optical systems 100a and 100b of the imaging device 100 of this embodiment shown in FIG. 1, a primary image plane IP is formed by the imaging lens 10, and an image plane correction mirror 30 is disposed at the primary image plane IP. The primary image plane IP is disposed conjugate with the object plane OS and the imaging plane IS. Furthermore, by making the shape of the image plane correction mirror 30 non-planar, the primary image plane IP is shaped to match the shape of the object plane OS. Furthermore, by tilting the image plane correction mirror 30 in accordance with the tilt of the object plane OS, a Scheimpflug arrangement is formed, allowing for the acquisition of an image with a wide depth of field. This allows the imaging device 100 of this embodiment to capture high-resolution images of objects with non-planar shapes, even from oblique directions, without compromising the brightness of the imaging lens 10.

[0033] (Imaging from the object plane to the imaging plane) Image plane correction will be described in detail below. Fig. 3 is a diagram illustrating the shift of the primary image plane IP due to reflection. In Fig. 3, the dotted line indicates a virtual image plane IPm, which is the primary image plane where a planar image FF on the imaging plane IS is hypothetically imaged by the relay lens 40.

[0034] First, when an image of an object plane OS shown in FIG. 1 is formed on a primary image plane IP by the imaging lens 10, if an image plane correction mirror 30 is placed on the primary image plane IP, the shape of the image plane will change depending on the shape of the image plane correction mirror 30. The image plane-corrected primary image plane IP is captured by the image sensor 50 as a corrected image FI via a relay lens 40. If the image plane correction mirror 30 is, for example, a spherical mirror, the reflecting surface 30a will be shaped in the direction of the optical axis OA2, and will reflect earlier at the periphery on the optical axis OA2 than at the center, and the shape of the corrected image FI will be changed in the direction of the optical axis OA2 at the periphery relative to the center. In this embodiment, the actual primary image plane IP is formed before incidence on the image plane correction mirror 30, and a virtual image at a virtual image plane IPm is formed on the imaging plane IS as the corrected image FI by reflection from the image plane correction mirror 30.

[0035] The shape of corrected image FI reflected by image plane correction mirror 30 is shown schematically in Figure 3. If image plane correction mirror 30 is positioned so that center point C1 on optical axis OA2 is at primary image plane IP, light rays heading toward center point C1 on optical axis OA2 will form primary image IP0 or corrected image FI0 on primary image plane IP, but light rays heading toward adjacent peripheral point P1 will form primary image IP1 at a position shifted forward in the axial direction by a distance d1 from reflecting surface 30a of image plane correction mirror 30, and will be reflected by reflecting surface 30a of image plane correction mirror 30, which is positioned axially shifted from primary image IP1 by the distance d1. As a result, a virtual image positioned further axially shifted from reflecting surface 30a by the distance d1 is reflected as corrected image FI1. Similarly, a light ray traveling toward peripheral point P2 forms a primary image IP2 at a position axially shifted by a distance d2 from the reflecting surface 30a of the image plane correction mirror 30, and is reflected by the reflecting surface 30a of the image plane correction mirror 30, which is also axially shifted by a distance d2 from the primary image IP2. As a result, a virtual image at a position further axially shifted by a distance d2 from the reflecting surface 30a is reflected as a corrected image FI2. In this way, the corrected image FI (a collection of corrected images FI0, FI1, FI2, etc.) becomes a virtual image plane IPm, and its overall shape in the axial direction is changed in accordance with the shape of the reflecting surface 30a of the image plane correction mirror 30. In the illustrated example, the virtual image plane IPm is a plane perpendicular to the optical axis OA2.

[0036] As described above, in the imaging device 100 shown in FIG. 1, the primary image plane IP, the object plane OS, and the image sensor 50 are in a conjugate relationship. Therefore, when the image on the object plane OS is reflected by the image plane correction mirror 30 disposed at the primary image plane IP and the shape of the corrected image FI is changed along the optical axis OA2, and the corrected image FI is formed on the image sensor 50's image plane IS via the relay lens 40, the shape of the image formed on the image plane IS changes, resulting in a planar image FF corresponding to the virtual image plane IPm shown in FIG. 3. In other words, by controlling the reflecting surface 30a of the image plane correction mirror 30 to have a shape corresponding to the shape of the object plane OS, the image on the object plane OS is captured on the image sensor IS as a planar image FF without distortion. Therefore, it is preferable that the shape of the image plane correction mirror 30 corresponds to the shape of the object plane OS. Note that when the primary image plane IP is formed in front of the image plane correction mirror 30, the image on the object plane OS can be corrected by the imaging lens 10 and the image plane correction mirror 30.

[0037] Since the primary image plane IP and the object plane OS are conjugate planes, a change in the direction of the optical axis OA2 of the primary image plane IP can be replaced with a change in the object plane OS, which means a change in the shape on the primary image plane IP.

[0038] FIG. 4 is a diagram showing a paraxial model of the imaging lens 10 shown in FIG. 4. In FIG. 4, the focal length of the imaging lens 10 is f, the image height at the primary imaging position is y, the height of the object plane OS is y', the distance from the focal point F to the on-axis primary imaging point Q is x, and the distance from the focal point F' to the on-axis object plane Q' is x'. When the object plane OS changes Δx' in the direction of the optical axis OA1 of the imaging lens 10, the amount of change Δx in the primary imaging plane IP can be calculated. The following equation (1) is obtained from the paraxial model shown in FIG. 4. TIFF0007779722000001.tif15160

[0039] When the object surface OS has a spherical surface, the radius of curvature r of the primary image plane IP is calculated by the following equation (2). TIFF0007779722000002.tif14160

[0040] (Scheimpflug state) Figure 5(A) shows the imaging relationship in a geometric optical system. The following relational expression (3) holds, where L is the distance from lens 1 to image 2, L' is the distance from lens 1 to object 3, y is the image height, y' is the object height, and m is the magnification of the optical system. TIFF0007779722000003.tif17160

[0041] 5(B) shows the Scheimpflug arrangement in the same optical system. In this embodiment, object 3 corresponds to object plane OS, and image 2 corresponds to primary image plane IP. If the tilt of object 3 is α, the tilt of image 2 is β, and the distance from optical axis OA to intersection point k with the extension of object 3 and image 2 is s, the following relational expressions (4) to (6) hold. TIFF0007779722000004.tif42160

[0042] From the above, it can be seen that the tangent of the tilt angle β of the image 2 is the magnification m multiplied by the tangent of the tilt angle α of the object 3.

[0043] [Example] (optical system) The optical system of this example is the same as that shown in Figure 1. Optical design software Code-V was used for the optical simulation of this example. In the simulation, ideal lenses are arranged as the imaging lens 10 and relay lens 40, and the magnification of the relay lens 40 is set to 1, and the magnification of the imaging lens 10 is set to 1 / 2. In this example, in order to accommodate an object or subject having a cylindrical surface, the image plane correction mirror 30 arranged at the primary image plane IP is a cylindrical mirror.

[0044] (mirror curvature radius) If the radius of curvature R of the object plane OS is 25 mm and the optical magnification is 1 / 2, the radius of curvature r of the primary image plane IP is 25 mm according to the above formula (2), but since the primary image plane IP is an image corresponding to the image plane correction mirror 30, the radius of curvature rm of the image plane correction mirror 30 is 50 mm.

[0045] (Scheimpflug imaging when an image plane correction mirror is placed on the primary image plane) Because the image plane correction mirror 30 is positioned at the primary image plane IP, the imaging lens 10 creates a conjugate relationship between the primary image plane IP and the object plane OS. When the object plane OS and the primary image plane IP are arranged in a Scheimpflug configuration relative to the imaging lens 10, the primary image (actual primary image) is bent by the image plane correction mirror 30. The tilt of the primary image plane IP is twice the tilt of the image plane correction mirror 30. Figure 6 shows the angular relationship between the image plane correction mirror 30 and the primary image plane IP. In Figure 6, the dotted line indicates a virtual image plane IPm that would result if a planar image FF on the imaging plane IS were imaged using the relay lens 40. The difference Δ between the MTF peak at the center of the object plane OS and the MTF peak at the periphery of the object plane OS is calculated for a width x and height y of the imaging element 50 of 4.0 mm and 4.0 mm, respectively. Figure 7 shows the relationship between the mirror angle β0 and the MTF peak difference Δ for different object plane OS angles α. The mirror angle β0 at which the peak difference Δ between the central and peripheral MTFs becomes 0 is 1 / 4 of the angle of the object plane OS. Because the image plane correction mirror 30 is located at the primary image plane IP, the mirror angle β0 is half the Scheimpflug angle (the angle of the primary image plane IP).

[0046] As described above, the angular relationship between the object plane OS and the primary image plane IP is determined from the magnification relationship in equation (6) above, and this angular relationship changes depending on the magnification m of the imaging lens 10. In other words, once the magnification m of the imaging lens 10 and the angle α of the object plane OS are determined, the angle β of the primary image plane IP is determined, and so is the angle β0 of the image plane correction mirror 30. The angle β0 of the image plane correction mirror 30 is half the angle β of the primary image plane IP, and is determined independently of the magnification m of the imaging lens 10.

[0047] (Confirming the effect of angle differences through optical simulation) When the tilt angle is small, tan α is considered to be approximately equal to α. Figure 8 shows the calculation results for the tilt α of the object plane OS relative to the imaging lens 10 and the tilt β of the primary image plane IP. Using equation (6), we calculated the proportionality β1 of the tangent to the magnification and the proportionality β2 of the angle to the magnification for the tilt α of the object plane OS and the tilt β of the primary image plane IP at an optical magnification of 0.5, for tilts of the object plane OS ranging from 0° to 45.00°. As shown in Figure 8, when the angle of the object plane OS is 10.00°, the difference in image plane tilt is approximately 0.8%, and as the angle of the object plane OS increases, the difference between values ​​β1 and β2 increases.

[0048] Next, we performed a simulation to examine the effect of the tilt of the primary image plane IP corresponding to a tilt of 10.00° on the object plane OS. Figure 9(A) shows the results for 4 lp / mm on the object plane OS when the angle of the primary image plane IP is 5.00°. Figure 9(B) shows the results for 4 lp / mm on the object plane OS when the angle of the primary image plane IP is 5.04°, as shown in Figure 8. These results indicate that when the tilt of the object plane OS is 10° or less, the angle can be set proportional to the magnification. Figure 9(C) shows the results for 4 lp / mm on the object plane OS when the angle of the primary image plane IP is 0.00°, i.e., when the primary image plane IP is not tilted relative to the object plane OS. As shown in Figure 9(C), when the primary image plane IP is not tilted, the image in the peripheral area is out of focus by approximately 1.5 mm relative to the center. Regarding the MTF, the contrast of the image in the peripheral area decreases by approximately 30%.

[0049] 10(A) and 10(B) show the MTF when the angle of the object plane OS is 20.00°. As shown in FIGS. 10(A) and 10(B), the difference between the peaks of the MTF is small. However, as shown in FIG. 10(B), as the angle of the object plane OS and the angle of the primary image plane IP increase, the angle of incidence deviates from the entrance pupil of the imaging lens 10. Therefore, the maximum tilt angle of the object plane OS must be smaller than the marginal ray angle.

[0050] (Optical simulation of Scheimpflug imaging for a cylindrical object surface) Figure 11(A) shows the through-focus MTF at 4 lp / mm on the object plane OS when the object plane OS is cylindrical, the radius of curvature R of the object plane OS is 25 mm, the radius of curvature rm of the reflecting surface 30a of the image plane correction mirror 30 is 50 mm, the inclination of the object plane OS is 5.00°, and the inclination of the primary image plane IP and the image plane correction mirror 30 is 0.00°. As shown in Figure 11(A), the peak at the center and the peak at the periphery are offset by approximately 0.7 mm, and the MTF is reduced by approximately 20%. This indicates that there is a difference in resolution between the center and periphery within the same plane.

[0051] Figure 11(B) shows the MTF results when the primary image plane IP is tilted by 2.50°, i.e., the image plane correction mirror 30 is tilted by 1.25°, corresponding to an object plane OS angle of 5.00°. As shown in Figure 11(B), it can be seen that the peaks coincide at the center and periphery.

[0052] Figure 12(A) shows the results of a two-dimensional image simulation implemented as a function of Code-V, where the tilt β0 of the image plane correction mirror 30 is set to 0°, while Figure 12(B) shows the results when the tilt β0 of the image plane correction mirror 30 is set to 1.25°. Because the horizontal axis area in the center of the image is on the rotation axis, it is not affected by the tilt of the object plane OS, and both images are in focus. In contrast, comparing the charts in the peripheral areas, the chart image is unsharp at the top and bottom edges, where the angle from the optimal image plane causes the focus plane to shift, at an angle of 0°. On the other hand, as shown in Figure 12(B), when the angle of the image plane correction mirror 30 is 1.25°, the simulation results show high contrast.

[0053] (Image results) The radius of curvature of the object plane OS is R (mm), the radius of curvature of the image plane correction mirror 30 is rm (mm), and under the conditions of R = 25 mm and rm = 50 mm, the imaging results were obtained when the angle of the object plane OS was 0° and the angle of the image plane correction mirror 30 was 0°. The imaging results were also obtained when the angle of the object plane OS was 10° and the angle of the image plane correction mirror 30 was 0°. The imaging results were also obtained when the angle of the object plane OS was 10° and the angle of the image plane correction mirror 30 was 2.5°. When only the object plane OS is tilted, the center of the image is in focus, but the periphery of the image is out of depth, resulting in reduced image contrast.

[0054] Fig. 13 shows a comparison of the relative luminance values ​​at the center of each captured image. As shown in Fig. 13, there is no significant difference between when the object plane OS and image plane correction mirror 30 are not tilted, when only the object plane OS is tilted, and when the tilt of the tilted object plane OS is corrected by the image plane correction mirror 30.

[0055] Fig. 14 shows a comparison of the relative luminance values ​​of the peripheral areas of the images in each captured image. As shown in Fig. 14, when the tilt of the object plane OS is not corrected by the image plane correction mirror 30, the edge where black-white-black changes is blurred.

[0056] When imaging a cylindrical object surface OS from an oblique angle, a cylindrical image plane correction mirror 30 is placed at the primary image plane IP to image the object surface OS, and a Scheimpflug arrangement of the primary image plane IP allows for high-resolution images to be captured obliquely relative to the object surface OS. Simulations and experiments were performed using a Scheimpflug arrangement for a cylindrical surface. However, the idea behind correcting the primary image plane IP with an image plane correction mirror 30 corresponding to the shape of the object surface OS is to convert the conjugate plane to a plane away from the best-focus plane on the object surface OS, which is the conjugate plane of the image sensor 50. This approach can also be applied to three-dimensional free-form objects. For three-dimensional free-form objects, calculating the plane tilt that minimizes the amount of sag can minimize mirror deformation by tilting the image plane correction mirror 30 at the primary image plane IP, as shown in the Scheimpflug verification.

[0057] In the embodiment, the imaging magnification is set to 0.5. However, if the magnification is low, the tilt of the image plane correction mirror 30 needs to be large relative to the tilt of the object plane OS. However, if the primary image plane IP is tilted at an angle that exceeds the NA of the imaging lens 10, the amount of light incident on the imaging lens 10 will decrease. For this reason, the imaging lens 10 needs to have as small an F-number as possible. Conversely, if the imaging magnification is large, the distance between the imaging lens 10 and the object plane OS will increase, and it is thought that the sensitivity of the tilt of the image plane correction mirror 30 to the tilt of the object plane OS will increase.

[0058] In the optical system of the embodiment described above, the object plane OS, the primary image plane IP, and the image sensor 50 are arranged in an optically conjugate relationship. Therefore, by correcting the image at the primary image plane IP, the image at the non-planar object plane OS can be captured without distortion by the planar image sensor 50. That is, a planar image FF, whose image plane has been corrected by the shape of the non-planar reflecting surface 30a of the image plane correction mirror 30 arranged at the primary image plane IP, can be captured at the image sensor 50's image plane IS. Therefore, optical image plane correction can be easily performed by appropriately adjusting the shape of the reflecting surface 30a of the image plane correction mirror 30. Furthermore, by arranging the object plane OS and the primary image plane IP in a Scheimpflug arrangement, the entire image can be focused even when captured from an oblique angle. This allows high-resolution images to be captured from an oblique angle relative to the non-planar object plane OS without compromising the brightness of the imaging lens 10 of the objective optical system 100a.

[0059] By configuring the shape of the image plane correction mirror 30 disposed at the primary image plane IP to correspond to the object plane OS, and further configuring the primary image plane IP and the object plane OS in a Scheimpflug arrangement with respect to the imaging lens 10, it is possible to capture a high-resolution image even when imaging from an oblique angle with respect to the object plane OS, which has a non-planar shape and requires depth, while maintaining the imaging lens 10 at a small F-number. Furthermore, while a typical optical system 101a such as that shown in FIG. 2 requires tilting the image sensor 50s, the present optical systems 100a and 100b can easily form a Scheimpflug arrangement simply by tilting the image plane correction mirror 30 disposed at the primary image plane IP. Furthermore, the present optical systems can flexibly accommodate changes in the tilt of the object plane OS.

[0060] Second Embodiment The optical system according to the second embodiment will be described below. The optical system according to the second embodiment is a modification of the optical system according to the first embodiment, and matters not specifically described are the same as those of the optical system according to the first embodiment.

[0061] 15 is a conceptual diagram of a projection device 200 including an optical system according to the second embodiment. The projection device 200 includes an image display 170, a relay lens 140, a beam splitter 120, an image plane correction mirror 130, and a projection lens 110. The projection device 200 projects a planar image FF projected from the image display 170 onto a projection surface OSp having a non-planar shape from an oblique direction relative to the optical axis OA1 of the projection lens 110.

[0062] In the projection device 200, the image display 170, specifically the image display unit 150 described below, the relay lens 140, the beam splitter 120, and the image plane correction mirror 130 constitute an imaging optical system 200b. The image plane correction mirror 130, the beam splitter 120, and the projection lens 110 constitute a projection optical system 200a. The optical path between the beam splitter 120 and the image plane correction mirror 130 is a common optical path for the projection optical system 200a and the imaging optical system 200b.

[0063] The image display 170 has a function of displaying the planar image FF on the image display surface ISp of the image display unit 150. The image display unit 150 may, for example, display an image using an image display element, or may be a mask illumination mechanism that constitutes a part of an exposure apparatus and that includes a mask pattern and an illumination device that illuminates the mask pattern.

[0064] The relay lens 140 forms a secondary image of the planar image FF on a primary image plane IPp.

[0065] The beam splitter 120 is disposed between the relay lens 140 and the image plane correction mirror 130, and between the image plane correction mirror 130 and the projection lens 110. The beam splitter 120 reflects the light that has passed through the relay lens 140 and guides it to the image plane correction mirror 30, and transmits the light reflected by the image plane correction mirror 30 and guides it to the projection lens 110.

[0066] The image plane correction mirror 130 is disposed at the primary image plane IP and has a non-planar reflecting surface 130a.

[0067] The image plane correction mirror 130 is provided with a tilt adjustment unit 160 that adjusts the tilt of the mirror. The tilt adjustment unit 160 makes it possible to adjust the focus in accordance with the projection direction.

[0068] The projection lens 110 is disposed on the projection side and forms a projection image on a projection surface OSp having a non-planar shape.

[0069] In the optical systems 200a and 200b that make up the projection device 200, the image display surface ISp, the primary image plane IP (image plane correction mirror 130), and the projection plane OSp are arranged so as to be optically conjugate. By arranging the image planes conjugate in this manner, it becomes possible to perform image plane correction in the image plane correction mirror 130 arranged at the primary image plane IP so that the planar image FF is projected onto the projection plane OSp without distortion.

[0070] Furthermore, projection device 200 is arranged so that primary image plane IP and projection plane OSp satisfy the Scheimpflug condition, which allows the peripheral part of the projected image to be in focus even when projected onto projection plane OSp from an oblique angle.

[0071] The planar image FF displayed on the image display unit 150 is guided by the relay lens 140 to the beam splitter 120, where it is bent by the beam splitter 120 in a direction perpendicular to the optical axis OA3 of the relay lens 140 and focused on a primary image plane IPp. The corrected image FI focused on the primary image plane IPp, i.e., on the reflecting surface 130a of the image plane correction mirror 130, passes through the beam splitter 120 and is projected onto a projection plane OSp by the projection lens 110.

[0072] In the second embodiment, image plane correction by the image plane correction mirror 130 uses an optical path that is the opposite of that in the first embodiment, and the planar image FF displayed on the image display unit 150 passes through the relay lens 140 and is reflected by the image plane correction mirror 130, and then is imaged on the primary image plane IPp. In other words, the primary image plane IPp corresponds to the corrected image FI, and the real image is projected onto the projection plane OSp.

[0073] In the optical system of the second embodiment described above, the image display surface ISp, the primary image plane IPp, and the projection surface OSp are arranged in an optically conjugate relationship. Therefore, by correcting the image at the primary image plane IPp, the planar image FF displayed on the image display surface ISp can be projected without distortion onto the non-planar projection surface OSp. That is, an image whose image plane has been corrected by the shape of the non-planar reflecting surface 130a of the image plane correction mirror 130 arranged at the primary image plane IPp can be projected onto the projection surface OSp. Therefore, optical image plane correction can be easily performed by appropriately adjusting the shape of the reflecting surface 130a of the image plane correction mirror 130. Furthermore, by using a Scheimpflug arrangement between the primary image plane IPp and the projection surface OSp, the entire image can be focused even when projected from an oblique angle. This allows a high-resolution image to be projected onto the non-planar projection surface OSp from an oblique angle without compromising the brightness of the projection lens 110 of the projection optical system 200a.

[0074] Although the optical system has been described above based on the embodiments, the optical system according to the present invention is not limited to the above-described embodiments or examples, and various modifications are possible.

[0075] In the first embodiment, the primary image plane IP is configured to be imaged before it is incident on the image plane correction mirror 30, but it may also be configured to be imaged after it is incident on the image plane correction mirror 30. Note that the second embodiment has the opposite configuration to the first embodiment. [Explanation of symbols]

[0076] 10...imaging lens, 20...beam splitter, 30...image plane correction mirror, 30a...reflecting surface, 40...relay lens, 50...imaging element, 60...tilt adjustment unit, 100...imaging device, 100a...objective optical system, 100b...imaging optical system, 110...projection lens, 120...beam splitter, 130...image plane correction mirror, 130a...reflecting surface, 140...relay lens, 150...image display unit, ISp...image display surface, 160...tilt adjustment unit, 170...image display, 200...projection device, 200a...projection optical system, 200b...imaging optical system, FI...corrected image, IP,IPp...primary image plane, IS...imaging surface, FF...planar image, OA,OA1,OA2,OA3...optical axis, OS...object plane, OSp...projection plane

Claims

1. an objective optical system that forms an image of an object surface having a non-planar shape; an imaging optical system having an image pickup element that picks up an image of a primary image plane formed by the objective optical system as a planar image; an image plane correction mirror disposed on the primary image plane and having a non-planar reflecting surface; a tilt adjustment unit having a two-axis rotation mechanism and tilting the image plane correction mirror; Equipped with the object plane, the primary image plane, and the image sensor are arranged at optically conjugate positions; An optical system in which the primary image plane and the object plane are arranged so as to satisfy the Scheimpflug condition.

2. an imaging optical system that forms a planar image to be displayed on the image display surface; a projection optical system that projects a primary image plane formed by the imaging optical system onto a non-planar projection surface; an image plane correction mirror disposed on the primary image plane and having a non-planar reflecting surface; a tilt adjustment unit having a two-axis rotation mechanism and tilting the image plane correction mirror; Equipped with the image display surface, the primary image formation surface, and the projection surface are arranged at optically conjugate positions; An optical system in which the primary image plane and the projection plane are arranged so as to satisfy the Scheimpflug condition.

3. 3. The optical system according to claim 1, wherein the reflecting surface of the image plane correction mirror has a shape corresponding to the shape of the object plane or the projection plane.

4. 4. The optical system according to claim 1, wherein the image plane correction mirror is one of a spherical mirror, an aspherical mirror, a cylindrical mirror, a free-form surface mirror, and a deformable mirror.

Images