Imaging optical system

Abstract

The present invention provides an imaging optical system capable of acquiring wide-angle image data. [Solution] An imaging optical system configured such that, in an xyz orthogonal coordinate system, a light ray traveling in the z-axis direction within a first plane perpendicular to the x-axis, whose path is contained within the first plane, is the principal ray, and a parallel beam of light incident on the first reflecting surface is focused onto the image plane, and the path of the beam of light incident on the second reflecting surface and the path of the beam of light reflected by the third reflecting surface intersect, wherein the focal length of the entire optical system along the path of the principal ray in the first plane is fy, the combined focal length of the second and third reflecting surfaces is fy23, the focal length of the entire optical system along the path of the principal ray in a plane containing the path of the principal ray and perpendicular to the first plane is fx, and the combined focal length of the second and third reflecting surfaces is fx23. 1.05 <fy23 / fx23<1.5···(1) 1.5 <fy / fx<2.2···(2) It satisfies the condition.

Description

Technical Field

[0001] The present invention relates to an imaging optical system using a mirror.

Background Art

[0002] For purposes such as surveillance and remote sensing, there is an increasing need for high-resolution images including data from visible light to infrared rays. In some cases, an imaging optical system using a mirror instead of a lens is used to acquire an image including data from visible light to infrared rays.

[0003] Also, for purposes such as surveillance and remote sensing, it is preferable to acquire image data with as wide an angle as possible. In order to acquire wide-angle image data, it is necessary to increase the sensor size or shorten the flange focal distance (flange back). However, from the perspective of downsizing the device, it is not preferable to increase the sensor size, and the flange focal distance needs to be set to a predetermined value or more in order to install the mirror without blocking the optical path.

[0004] On the other hand, in an imaging optical system using a mirror, high-precision alignment adjustment of the mirror is required, and it is preferable that the alignment adjustment is as easy as possible.

[0005] So far, imaging optical systems using mirrors have been developed (for example, Patent Documents 1-3), but an imaging optical system using a mirror that can acquire wide-angle image data and is easy to align has not been developed. Therefore, there is a need for an imaging optical system using a mirror that can acquire wide-angle image data and is easy to align.

Prior Art Documents

Patent Documents

[0006]

Patent Document 1

Patent Document 2

[0007] The object of the present invention is to provide an imaging optical system using a reflecting mirror that is easy to align and capable of acquiring wide-angle image data. [Means for solving the problem]

[0008] The imaging optical system of the present invention is configured such that, in an xyz orthogonal coordinate system, a light ray traveling in the z-axis direction in a first plane perpendicular to the x-axis, reflected by a convex first reflecting surface, passing through an aperture, and reflected by a concave second reflecting surface and a concave third reflecting surface, the light ray whose path is included in the first plane is the principal ray, and the parallel beam incident on the first reflecting surface is focused onto the image plane, and the path of the beam incident on the second reflecting surface and the path of the beam reflected by the third reflecting surface intersect, wherein the focal length of the entire optical system along the path of the principal ray in the first plane is fy, the combined focal length of the second and third reflecting surfaces is fy23, the focal length of the entire optical system along the path of the principal ray in a plane that includes the path of the principal ray and is perpendicular to the first plane is fx, and the combined focal length of the second and third reflecting surfaces is fx23. 1.05 < fy23 / fx23 < 1.5 (1) 1.5 < fy / fx < 2.2 (2) It satisfies the condition.

[0009] According to the present invention, by making the focal length fx of the entire optical system along the path of the principal ray in a plane perpendicular to the first plane that includes the path of the principal ray smaller than the focal length fy of the entire optical system along the path of the principal ray in the first plane, an anamorphic optical system is obtained in which the angle of view in the plane perpendicular to the first plane that includes the path of the principal ray is larger than the angle of view in the first plane. Therefore, wide-angle image data is obtained in the horizontal plane, with the plane perpendicular to the first plane that includes the path of the principal ray being the horizontal plane. Since distortion of image data from an anamorphic optical system can be easily removed by software, wide-angle image data in the horizontal plane is effective for applications such as surveillance and remote sensing. Furthermore, in the above imaging optical system, the effect of changes in the horizontal position of the reflective surface on optical performance becomes significant, but this can be addressed relatively easily by adjusting the horizontal alignment of the third reflective surface, which has a large impact on optical performance.

[0010] If fy23 / fx23 is increased too much, the aberration at the third reflective surface increases, causing a decrease in resolution, so an upper limit was set for equation (1). The lower limit of equation (1) is a requirement for an anamorphic optical system.

[0011] The imaging optical system of the first embodiment of the present invention has a focal length of fy1 of the first reflecting surface along the path of the principal ray in the first plane, a focal length of fx1 of the first reflecting surface along the path of the principal ray in a plane that includes the path of the principal ray and is perpendicular to the first plane, a distance of L1 millimeters (mm) from the first reflecting surface to the second reflecting surface along the path of the principal ray, and an equivalent F value eF. |(fx1·L1) / (fy1·eF)| < 5 mm (3) It satisfies the condition.

[0012] The equivalent f-number eF is obtained by dividing the diameter of the aperture (when the aperture shape is replaced with a circle of equal area) by the average of the XZ combined focal length and the YZ combined focal length, as will be explained later. In the case of infrared, to improve resolution, the equivalent f-number eF must be below a predetermined value. Given L1, to make the equivalent f-number below a predetermined value, the aperture must be made larger. However, making the aperture larger may obstruct the path of light rays traveling to the first reflective surface. The above inequality (3) limits the size of the aperture for a given L1, or limits the size of L1 to make the imaging optical system compact for a given equivalent f-number. Note that fx1 / fy1 corresponds to the shape of the aperture. By satisfying inequality (3), a compact imaging optical system can be obtained in which the path of light rays traveling to the first reflective surface is not obstructed by the aperture.

[0013] The imaging optical system of the second embodiment of the present invention has a focal length of fy1 of the first reflecting surface along the path of the principal ray in the first plane, and a focal length of fx1 of the first reflecting surface along the path of the principal ray in a plane that includes the path of the principal ray and is perpendicular to the first plane. |fx1 / fy1| < 0.3 (4) It satisfies the condition.

[0014] |fx1 / fy1| is related to fy23 / fx23. The upper limit in equation (4) is a requirement for obtaining an anamorphic image.

[0015] The imaging optical system of the third embodiment of the present invention has a distance L3 from the third reflective surface to the image plane along the path of the principal ray. 0.6 < fy23 / L3 < 1.1 (5) 0.5 < fx23 / L3 < 0.9 (6) It satisfies the condition.

[0016] This embodiment aims to increase the flange focal length. By increasing the flange focal length, the distance between the cover glass for protecting the sensor and the sensor can be increased, thereby relaxing the standard for foreign matter adhering to the cover glass. Since fy23 is determined by the sensor size, Equation (5) defines the magnitude of the flange focal length. Equation (6) defines the magnitude of the horizontal angle of view with respect to the defined flange focal length.

[0017] The lower limits of Equations (5) and (6) are requirements for preventing a decrease in resolution due to an increase in aberration, and the upper limits of Equations (5) and (6) are requirements for obtaining an anamorphic image. Generally, when the focal length is shortened, it becomes difficult to correct aberration.

[0018] For the imaging optical system of the fourth embodiment of the present invention, the distance from the third reflecting surface to the image surface along the path of the chief ray is taken as L3 |fx1 / L3| < 1 (7) |fy1 / L3| < 6 (8) is satisfied.

[0019] The upper limits of Equations (7) and (8) are requirements for preventing the divergence of the light beam. When L3 becomes small, there is a possibility that the path of the light beam traveling from the first reflecting surface to the second reflecting surface is obstructed.

[0020] For the imaging optical system of the fifth embodiment of the present invention, the distance from the first reflecting surface to the second reflecting surface along the path of the chief ray is taken as L1, and the distance from the first reflecting surface to the image surface along the path of the chief ray is taken as L 0.35 < L1 / L < 0.5 (9) is further satisfied.

[0021] If the L1 / L value falls below the lower limit, L2 becomes relatively larger, making it impossible to realize an imaging optical system due to interference between the second and third reflective surfaces. If the L1 / L value exceeds the upper limit, the imaging optical system becomes too large. [Brief explanation of the drawing]

[0022] [Figure 1] This is a perspective view of the imaging optical system of one embodiment of the present invention. [Figure 2] This figure shows a cross-section of the imaging optical system shown in Figure 1, perpendicular to the x-axis, including the path of the principal ray of the parallel light beam that travels parallel to the z-axis and enters the imaging optical system. [Figure 3] This figure shows a cross-section of the imaging optical system shown in Figure 1, perpendicular to the x-axis, including the path of the principal ray of the parallel light beam that travels parallel to the z-axis and enters the imaging optical system. [Figure 4] This is a flowchart illustrating the design method for an imaging optical system. [Figure 5] This is a perspective view of the imaging optical system of Embodiment 1 of the present invention. [Figure 6] This figure shows a cross-section of the imaging optical system of Embodiment 1 perpendicular to the x-axis, including the path of the principal ray of the light beam traveling parallel to the z-axis and incident on the imaging optical system. [Figure 7] This figure shows the distortion caused by the imaging optical system of Example 1. [Figure 8A] This figure shows the lateral aberrations related to the meridian plane (Y-FAN) and the spherical missing image plane (X-FAN) at (X,Y)=(0,0) on the sensor surface 109. [Figure 8B] This figure shows the lateral aberrations related to the meridian plane (Y-FAN) and the spherical missing image plane (X-FAN) at (X,Y)=(0,-1.51) on the sensor surface 109. [Figure 8C] This figure shows the lateral aberrations related to the meridian plane (Y-FAN) and the spherical missing image plane (X-FAN) at (X,Y)=(0,1.51) on the sensor surface 109. [Figure 8D] This figure shows the lateral aberrations related to the meridian plane (Y-FAN) and the spherical missing image plane (X-FAN) at (X,Y)=(2.69, 0) on the sensor surface 109. [Figure 8E] This figure shows the lateral aberrations related to the meridian plane (Y-FAN) and the spherical missing image plane (X-FAN) at (X,Y)=(2.69,1.51) on the sensor surface 109. [Figure 8F] This figure shows the lateral aberrations related to the meridian plane (Y-FAN) and the spherical missing image plane (X-FAN) at (X,Y)=(2.69,-1.51) on the sensor surface 109. [Figure 9] This is a perspective view of the imaging optical system of Embodiment 2 of the present invention. [Figure 10] This figure shows a cross-section of the imaging optical system of Embodiment 2 perpendicular to the x-axis, including the path of the principal ray of the light beam traveling parallel to the z-axis and incident on the imaging optical system. [Figure 11] This figure shows the distortion caused by the imaging optical system of Example 2. [Figure 12A] This figure shows the lateral aberrations related to the meridian plane (Y-FAN) and the spherical missing image plane (X-FAN) at (X,Y)=(0,0) on the sensor surface 109. [Figure 12B] This figure shows the lateral aberrations related to the meridian plane (Y-FAN) and the spherical missing image plane (X-FAN) at (X,Y)=(0,-1.51) on the sensor surface 109. [Figure 12C] This figure shows the lateral aberrations related to the meridian plane (Y-FAN) and the spherical missing image plane (X-FAN) at (X,Y)=(0,1.51) on the sensor surface 109. [Figure 12D] This figure shows the lateral aberrations related to the meridian plane (Y-FAN) and the spherical missing image plane (X-FAN) at (X,Y)=(2.69, 0) on the sensor surface 109. [Figure 12E] This figure shows the lateral aberrations related to the meridian plane (Y-FAN) and the spherical missing image plane (X-FAN) at (X,Y)=(2.69,1.51) on the sensor surface 109. [Figure 12F] This figure shows the lateral aberrations related to the meridian plane (Y-FAN) and the spherical missing image plane (X-FAN) at (X,Y)=(2.69,-1.51) on the sensor surface 109. [Figure 13] This is a diagram to explain the magnitude of distortion. [Modes for carrying out the invention]

[0023] Figure 1 is a perspective view of an imaging optical system according to one embodiment of the present invention. The imaging optical system comprises three mirrors, each having a reflective surface. A light beam incident on the first reflective surface 101 is reflected by the first reflective surface 101, passes through the aperture 103, and then incident on the second reflective surface 105. The light beam is reflected by the concave second reflective surface 105 and the concave third reflective surface 107, and then focused onto the sensor surface 109. In the xyz Cartesian coordinate system, the direction perpendicular to the sensor surface 109 is defined as the z-axis direction. The imaging optical system is configured such that the principal rays of parallel light beams traveling in the z-axis direction and incident on the imaging optical system are reflected by the third reflective surface 107, then travel in the z-axis direction and incident perpendicularly to the sensor surface 109. The path of the principal rays lies in a plane perpendicular to the x-axis.

[0024] Figure 2 shows a cross-section of the imaging optical system shown in Figure 1, perpendicular to the x-axis, which includes the path of the principal rays of the parallel light beam traveling parallel to the z-axis and incident on the imaging optical system.

[0025] Figure 3 shows a cross-section of the imaging optical system shown in Figure 1, perpendicular to the x-axis, including the path of the principal rays of the parallel light beams traveling parallel to the z-axis and incident on the imaging optical system. Figure 3 shows the paths of light rays parallel to the z-axis and light beams inclined with respect to the z-axis.

[0026] Figure 4 is a flowchart illustrating the design method of an imaging optical system.

[0027] In step S1010 of Figure 4, the sensor size is determined.

[0028] In step S1020 of Figure 4, the arrangement of the reflectors is determined. The arrangement of the three reflectors is determined so that the principal rays of the parallel light beam traveling in the z-axis direction and incident on the imaging optical system are reflected by the third reflecting surface 107, and then travel in the z-axis direction to reach the sensor surface 109.

[0029] In step S1030 of Figure 4, the surface shape of each reflecting mirror is determined so that the horizontal field of view is widened. The horizontal field of view is the field of view in a cross-section parallel to the x-axis that includes the path of the principal rays of the parallel light beams traveling in the z-axis direction and incident on the imaging optical system.

[0030] In step S1040 of Figure 4, it is determined whether the resolution satisfies the required specifications. Specifically, the modulation transfer function, which is a function of spatial frequency, is obtained by simulation and the resolution is evaluated. If the resolution is sufficient, the process proceeds to step S1050; otherwise, the process proceeds to step S1060.

[0031] In step S1050 of Figure 4, it is determined whether the design is suitable for mass production based on its sensitivity. Specifically, the change in resolution due to deviations from the design values ​​of the shape and arrangement of the reflective surfaces is determined by simulation and used as the sensitivity. If the sensitivity is below a predetermined value, the process ends; if the sensitivity is greater than the predetermined value, the process returns to step S1020.

[0032] In step S1060 of Figure 4, the aperture size is changed to improve resolution. When resolution is reduced due to darkness, such as in the case of infrared light, the aperture size is increased. When resolution is thought to be reduced due to a large aperture size, such as in the case of short-duration visible light or ultraviolet light, the aperture size is decreased. When the aperture size is increased, the arrangement of the reflectors needs to be readjusted.

[0033] The reflector may be formed from plastic, and the plastic may be coated with a metal to create the reflective surface. It is preferable to use a metal such as aluminum for the metal coating in order to utilize a wide range of wavelengths of light.

[0034] Examples of the present invention are described below.

[0035] Table 1 shows the arrangement of the optical system in an embodiment of the present invention. [Table 1]

[0036] In Table 1, "horizontal" refers to a cross-section parallel to the x-axis, and "vertical" refers to a cross-section perpendicular to the x-axis.

[0037] The shape of the aperture is an ellipse, with the horizontal diameter and the vertical diameter being the major axis and minor axis, respectively.

[0038] L1, L2, and L3 are the distances from the first reflective surface 101 to the second reflective surface 105, from the second reflective surface 105 to the third reflective surface 107, and from the third reflective surface 107 to the sensor surface (image plane) 109, respectively, along the path of the principal ray shown in Figure 2. L is the sum of L1, L2, and L3.

[0039] The "optical layout dimensions" are the dimensions of the optically effective area of ​​each surface from the reflective surface of the first mirror to the image plane, and the area required for light rays to pass through the aperture and be focused at each point on the image plane.

[0040] The shape of each reflective surface can be expressed by the following formula.

number

[0041] Z is defined such that the region in front of the case planes of the first reflective surface 101 and the third reflective surface 107 is negative, and the region in front of the case plane of the second reflective surface 105 is positive.

[0042] Example 1 Figure 5 is a perspective view of the imaging optical system of Embodiment 1 of the present invention.

[0043] Figure 6 shows a cross-section of the imaging optical system of Embodiment 1 perpendicular to the x-axis, including the path of the principal ray of the light beam traveling parallel to the z-axis and incident on the imaging optical system.

[0044] Table 2 shows the position and inclination of each surface of the imaging optical system in Example 1. [Table 2]

[0045] In Table 2 and the following tables, the coordinates of the center of each face are the coordinates with the origin at the center O of the field of view in Figure 2, and the rotation angle is the clockwise angle with respect to the y-axis of a line perpendicular to the central axis of the face in a yz cross section perpendicular to the x-axis.

[0046] Table 3 shows the numerical data for equation (1) for surfaces 2, 4, and 5 of the imaging optical system in Example 1. Unless otherwise specified, the unit of length in Table 3 and the following tables is millimeters. From the definition of Z in equation (1), the first reflective surface 101 (surface 2) is convex, and the second reflective surface 105 (surface 4) and the third reflective surface 107 (surface 5) are concave. Each surface is not axially symmetric. [Table 3]

[0047] Table 4 shows the Seidel aberration coefficients for each surface. [Table 4]

[0048] Seidel aberration can be expressed as a function of the polar coordinates (ρ',φ') of the exit pupil plane and the distance h' from the optical axis on the image plane, as follows: Spherical aberration

number

number

number

number

number

[0049] Figure 7 shows the distortion caused by the imaging optical system of Example 1. The horizontal axis in Figure 7 represents the field of view in the horizontal direction (x-axis direction), and the vertical axis represents the field of view in the vertical direction (y-axis direction). The solid line represents the reference grid, and the dashed line represents the image of the reference grid.

[0050] Figures 8A-8F show the lateral aberrations of the meridian plane (Y-FAN) and spherical missing image plane (X-FAN) at six points on the sensor surface 109. The six points on the sensor surface 109 are the center of the sensor surface, the two vertices of the rectangle, and the midpoint of two sides. The horizontal and vertical axes in Figures 8A-8F and the following diagrams showing lateral aberrations are explained below. The horizontal axis shows the relative position of the light rays of the light beam that image at each point as they pass through the aperture plane. The position of the principal ray is 0, and the outermost position of the aperture diameter corresponds to the maximum and minimum values ​​of the horizontal axis, respectively. The vertical axis shows the amount of deviation from the position on the image plane through which the light rays that have passed through the above relative positions pass, compared to the position on the image plane through which the principal ray passes. The maximum scale of the vertical axis is 50 μm, which is shown as 0.05 mm in the figures.

[0051] Figure 8A shows the lateral aberrations of the meridian plane (Y-FAN) and the spherical missing image plane (X-FAN) at (X,Y)=(0,0) on the sensor surface 109. The units of coordinates on the sensor surface are millimeters.

[0052] Figure 8B shows the lateral aberrations related to the meridian plane (Y-FAN) and the spherical missing image plane (X-FAN) at (X,Y)=(0,-1.51) on the sensor surface 109.

[0053] Figure 8C shows the lateral aberrations related to the meridian plane (Y-FAN) and the spherical missing image plane (X-FAN) at (X,Y)=(0,1.51) on the sensor surface 109.

[0054] Figure 8D shows the lateral aberrations related to the meridian plane (Y-FAN) and the spherical missing image plane (X-FAN) at (X,Y)=(2.69, 0) on the sensor surface 109.

[0055] Figure 8E shows the lateral aberrations related to the meridian plane (Y-FAN) and the spherical missing image plane (X-FAN) at (X,Y)=(2.69,1.51) on the sensor surface 109.

[0056] Figure 8F shows the lateral aberrations related to the meridian plane (Y-FAN) and the spherical missing image plane (X-FAN) at (X,Y)=(2.69,-1.51) on the sensor surface 109.

[0057] Example 2 Figure 9 is a perspective view of the imaging optical system of Embodiment 2 of the present invention.

[0058] Figure 10 shows a cross-section of the imaging optical system of Embodiment 2 perpendicular to the x-axis, including the path of the principal ray of the light beam traveling parallel to the z-axis and incident on the imaging optical system.

[0059] Table 5 shows the position and inclination of each plane of the imaging optical system in Example 2. [Table 5]

[0060] Table 6 shows the numerical data for equation (1) for surfaces 2, 4, and 5 of the imaging optical system in Example 2. From the definition of Z in equation (1), the first reflective surface 101 (surface 2) is convex, and the second reflective surface 105 (surface 4) and the third reflective surface 107 (surface 5) are concave. Each surface is not axially symmetric. [Table 6]

[0061] Table 7 shows the Seidel aberration coefficients for each surface. [Table 7]

[0062] Figure 11 shows the distortion caused by the imaging optical system of Example 2. The horizontal axis in Figure 11 represents the field of view in the horizontal direction (x-axis direction), and the vertical axis represents the field of view in the vertical direction (y-axis direction). The solid line represents the reference grid, and the dashed line represents the image of the reference grid.

[0063] Figures 12A-12F show the lateral aberrations related to the meridian plane (Y-FAN) and spherical missing image plane (X-FAN) at six points on the sensor surface 109.

[0064] Figure 12A shows the lateral aberrations of the meridian plane (Y-FAN) and the spherical missing image plane (X-FAN) at (X,Y)=(0,0) on the sensor surface 109. The units of coordinates on the sensor surface are millimeters.

[0065] Figure 12B shows the lateral aberrations related to the meridian plane (Y-FAN) and the spherical missing image plane (X-FAN) at (X,Y)=(0,-1.51) on the sensor surface 109.

[0066] Figure 12C shows the lateral aberrations related to the meridian plane (Y-FAN) and the spherical missing image plane (X-FAN) at (X,Y)=(0,1.51) on the sensor surface 109.

[0067] Figure 12D shows the lateral aberrations related to the meridian plane (Y-FAN) and the spherical missing image plane (X-FAN) at (X,Y)=(2.69, 0) on the sensor surface 109.

[0068] Figure 12E shows the lateral aberrations related to the meridian plane (Y-FAN) and the spherical missing image plane (X-FAN) at (X,Y)=(2.69,1.51) on the sensor surface 109.

[0069] Figure 12F shows the lateral aberrations related to the meridian plane (Y-FAN) and the spherical missing image plane (X-FAN) at (X,Y)=(2.69,-1.51) on the sensor surface 109.

[0070] Summary of Examples Table 8 shows the arrangement and optical performance of the optical system in the embodiment of the present invention. Table 8 includes the contents of Table 1. [Table 8]

[0071] In Table 8, "horizontal" refers to a cross-section parallel to the x-axis, and "vertical" refers to a cross-section perpendicular to the x-axis. Figure 3 shows the angle of view of the "vertical" section, denoted by θ.

[0072] The shape of the aperture is an ellipse, with the horizontal diameter and the vertical diameter being the major axis and minor axis, respectively.

[0073] Figure 13 is a diagram illustrating the magnitude of distortion. Assume that the image of point R in the reference coordinate system in the field of view is formed at the image point on the sensor surface. Let r be the distance from the center O of the field of view to R. In the table, "Rad" and "Tan" represent Rad / r and Tan / r, respectively. The "Rad" and "Tan" values ​​in the table indicate the values ​​for the maximum distortion in Figures 7 and 11. The locations where the maximum distortion occurs in Figures 7 and 11 are indicated by circles.

[0074] The "design wavelengths" are 0.588 micrometers and 8.000 micrometers. The imaging optical system of the present invention is designed to be usable in visible and infrared light by using an appropriate sensor.

[0075] "Fno. (F-number)" is calculated by taking the angle between the optical axis and the light ray that starts from the center of the object, passes through the edge of the aperture, and reaches the image plane, where θ is the angle between the ray and the optical axis, and n is the refractive index of the medium. FNo = 1 / (2·n·sinθ) It is defined as follows. More specifically, Fno. is the mean square of the values ​​of the above formula for the four light rays passing through the horizontal and vertical ends of the aperture opening. n is 1.

[0076] The "Equivalent F-number" is a value obtained by dividing the diameter of a circle with the same area as the aperture by the average of the XZ and YZ combined focal lengths. If the aperture opening is an ellipse with major axis 2a and minor axis 2b, then the radius r of the circle with the same area as the above ellipse is π·r. 2 It can be found from =π·a·b.

[0077] "fy" includes the path of the principal rays of the parallel light beam traveling parallel to the z-axis and incident on the imaging optical system, and represents the focal length of the entire optical system, which is a combination of the first, second, and third reflecting surfaces in a plane perpendicular to the x-axis (the first plane), i.e., the distance from the principal point to the focal point.

[0078] "fx" includes the path of the principal rays of the parallel light beam traveling parallel to the z-axis and incident on the imaging optical system, and is the focal length of the entire optical system, i.e., the distance from the principal point to the focal point, which is the distance from the principal point to the focal point, and includes the path of the principal rays of the parallel light beam that travels parallel to the z-axis and is incident on the imaging optical system, and is the distance from the principal point to the focal point.

[0079] "fy23" includes the path of the principal rays of the parallel light beam traveling parallel to the z-axis and incident on the imaging optical system, and is the focal length when the second and third reflecting surfaces are combined in a plane perpendicular to the x-axis (the first plane), i.e., the distance from the principal point to the focal point.

[0080] "fx23" includes the path of the principal rays of the parallel light beam traveling parallel to the z-axis and incident on the imaging optical system, and is the focal length when the second and third reflecting surfaces in a plane perpendicular to the first plane described above are combined, i.e., the distance from the position of the principal point to the focal point.

[0081] fy1 includes the path of the principal rays of the parallel light beam that travels parallel to the z-axis and enters the imaging optical system, and is the focal length of the first reflecting surface in the first plane described above, i.e., the distance from the position of the principal point to the focal point.

[0082] fx1 includes the path of the principal rays of the parallel light beam traveling parallel to the z-axis and incident on the imaging optical system, and is the focal length of the first reflecting surface in a plane perpendicular to the first plane described above, i.e., the distance from the position of the principal point to the focal point.

[0083] The "maximum wavefront aberration" is determined by the following procedure: For each of the six points on the sensor surface mentioned above, the maximum and minimum values ​​of the deviation between the principal ray and the light ray passing through any point on the elliptical outer edge of the aperture are determined, the difference between the two (PV value) is calculated, and the maximum value of the (PV value) for the six points mentioned above is defined as the "maximum wavefront aberration." The "maximum wavefront aberration" in Table 8 is for far-infrared rays (wavelength of 8 micrometers). In this case, the size of one pixel of the sensor is 17 micrometers. According to Table 8, the maximum wavefront aberration of the imaging optical systems in Examples 1 and 2 is less than or equal to the size of one pixel of the sensor.

[0084] "Peripheral illumination ratio" is the ratio of the light intensity of the lowest light intensity among the light rays that pass through the aperture and are focused on the image plane, to the light intensity of the light rays at the center of the field of view that pass through the aperture and are focused on the image plane.

[0085] Table 9 shows the numerical data for each term of equations (1)-(9) that represent the ratio between focal lengths, the ratio between focal length and interplane distance, the ratio between interplane distances, etc., for the imaging optical system of each embodiment. Equations (1)-(9) are as follows: 1.05 < fy23 / fx23 < 1.5 (1) 1.5 < fy / fx < 2.2 (2) |(fx1·L1) / (fy1·eF)| < 5 mm (3) |fx1 / fy1| < 0.3 (4) 0.6 < fy23 / L3 < 1.1 (5) 0.5 < fx23 / L3 < 0.9 (6) |fx1 / L3| < 1 (7) |fy1 / L3| < 6 (8) 0.35 < L1 / L < 0.5 (9) [Table 9]

[0086] According to Table 9, Examples 1 and 2 satisfy formulas (1)-(9).

[0087] To obtain wider-angle image data, it is preferable that fy23 / fx23 is greater than 1.2. In Examples 1 and 2, fy23 / fx23 is greater than 1.2. Also, it is preferable that fx23 is less than 20 millimeters. In Examples 1 and 2, fx23 is less than 20 millimeters.

[0088] Table 8 shows that in Examples 1 and 2, the ratio of the horizontal field of view to the vertical field of view is greater than 3.0.

[0089] To reduce the difficulty of manufacturing this reflective optical system, it is desirable that the center of each reflective surface is located within 10% of the center of the principal ray, as a constraint on the position of the intersection point between the principal ray and the center of each reflective surface.

Claims

1. In an xyz Cartesian coordinate system, a light ray propagates in the z-axis direction within a first plane perpendicular to the x-axis, is reflected by a first convex reflecting surface, passes through an aperture, and is reflected by a second concave reflecting surface and a third concave reflecting surface, and the path of this light ray is included in the first plane. The imaging optical system is configured such that the parallel beam of light incident on the first reflecting surface is the principal ray, and the path of the beam of light incident on the second reflecting surface intersects with the path of the beam of light reflected by the third reflecting surface, wherein the focal length of the entire optical system along the path of the principal ray in the first plane is fy, the combined focal length of the second and third reflecting surfaces is fy23, the focal length of the entire optical system along the path of the principal ray in a plane that includes the path of the principal ray and is perpendicular to the first plane is fx, and the combined focal length of the second and third reflecting surfaces is fx23. 1.05 < fy23 / fx23 < 1.5 (1) 1.5 < fy / fx < 2.2 (2) An imaging optical system that satisfies the requirements.

2. Let fy1 be the focal length of the first reflecting surface along the path of the principal ray in the first plane, fx1 be the focal length of the first reflecting surface along the path of the principal ray in a plane perpendicular to the first plane that includes the path of the principal ray, L1 be the distance from the first reflecting surface to the second reflecting surface along the path of the principal ray in millimeters (mm), and eF be the equivalent F value. |(fx1・L1) / (fy1・eF)| < 5 mm (3) The imaging optical system according to claim 1 that satisfies the requirements.

3. Let fy1 be the focal length of the first reflecting surface along the path of the principal ray in the first plane, and fx1 be the focal length of the first reflecting surface along the path of the principal ray in a plane that includes the path of the principal ray and is perpendicular to the first plane. |fx1 / fy1| < 0.3 (4) The imaging optical system according to claim 1 that satisfies the requirements.

4. Let L3 be the distance from the third reflective surface to the image plane along the path of the principal ray. 0.6 < fy23 / L3 < 1.1 (5) 0.5 < fx23 / L3 < 0.9 (6) The imaging optical system according to claim 1 that satisfies the requirements.

5. Let L3 be the distance from the third reflective surface to the image plane along the path of the principal ray. |fx1 / L3| < 1 (7) |fy1 / L3| < 6 (8) The imaging optical system according to claim 3, which satisfies the requirements.

6. Let L1 be the distance from the first reflective surface to the second reflective surface along the path of the principal ray, and L be the distance from the first reflective surface to the image plane along the path of the principal ray. 0.35 < L1 / L < 0.5 (9) The imaging optical system according to claim 1, further satisfying the condition.

Images