JP2001201714A - Optical processing method and optical processor using the same - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide an optical processing method taking an optical path of an optional beam from an objective surface to an image surface through an optical system as a reference axis and efficiently and precisely calculating a paraxial amount/an aberration amount developed around the axis and an optical processor using it. SOLUTION: Three or more kinds of azimuth are introduced, and paraxial/ aberration analysis are performed for an optical system with given optical data.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an optical processing method (processing method) for performing paraxial / aberration calculation and paraxial ray tracing of an optical system, and an optical processing apparatus (processing apparatus) using the same. In particular, the paraxial axis of an optical system suitable for calculating the paraxial amount and aberration amount developed around the reference axis with the optical path of an arbitrary ray from the object plane to the image plane via the optical system as a reference axis. It is suitable for aberration amount calculation, paraxial ray tracing, and the like.

[0002] The present invention also relates to an optical processing method and an optical processing apparatus using the method, which relate to the expression of a constituent surface of an optical system, and more particularly, to a constituent surface of an optical system centered on a point where a reference axis intersects each surface. This is suitable for expressing or converting the surface shape of the image.

The present invention also relates to an optical processing method suitable for determining the shape of an optical member of an optical system and an optical processing apparatus using the same, and more particularly, to an arbitrary light beam from an object plane to an image plane via the optical system. This is suitable for determining the shape of each optical member of the optical system, in which the shape of each optical member of the optical system is determined while performing paraxial / aberration calculation using the optical path as a reference axis.

Further, according to the present invention, an optical system designed by the above-described optical processing method and optical processing apparatus, in particular, an optical path (reference axis) of a reference wavelength from an object plane to an image plane through an optical system intersects a curved surface. The present invention relates to an optical system including a curved surface (Off-Axial curved surface) that is not a plane whose surface normal does not coincide with a reference axis at a point.

[0005]

2. Description of the Related Art Conventionally, a coaxial optical system having a rotationally symmetric refraction surface or reflection surface arranged around an optical axis which is a rotational symmetry axis of each surface forms an image of an object plane on an image plane. It has been used as an optical system. The paraxial theory and aberration theory of the coaxial system (Yoshiya Matsui: “Lens Design Method”, Kyoritsu Shuppan (197)
2), "Aberration theory", Optomechatronics Association (198
9)), which are used for determining the focal length and magnification when designing a coaxial optical system and for analyzing aberrations.
The framework of the coaxial optical system is determined using such paraxial amounts, and the shape of the coaxial optical system is determined by an automatic design method or the like targeting aberration.

However, recently, HMD (head mount displ.)
In display systems such as ay), designs (mainly reflecting surfaces) using an asymmetrical aspherical surface that does not belong to the category of the conventional coaxial optical system are often found with the improvement of automatic design technology. I have.

As a method of expressing such an asymmetrical aspherical surface, a coaxial system expressed by the above equation is largely decentered and the portion used as an optical system is a portion far away from the optical axis. The method of expressing an asymmetrical aspheric surface by the eccentricity of an optical system "is general, and the paraxial theory of a coaxial system was forcibly applied to the optical system expressed in this way.

Using the above-mentioned coordinate system, such an optical system is targeted only for narrowing the spot on the image plane without having a reasonable evaluation amount such as a skeleton of an optical arrangement, a focal length and a magnification. The design has been performed by an automatic design method or a method of using only the off-axis portion of the coaxial optical system, which has well-corrected off-axis aberrations.

Therefore, we have previously proposed an off-axial optical system as shown in FIG. 11 in JP-A-9-5650. The definition of the Off-Axial optical system is as follows.

[0010] Of the rays emitted from the center of the object plane (the center of the area to be imaged and observed), the reference wavelength of the reference wavelength passing through the optical system sequentially through the designated surfaces of the optical system and passing through the center of the aperture defined in the optical system. When the ray is set as the reference ray, if the optical path of the bent reference ray is referred to as a reference axis, the surface normal whose surface normal does not coincide with the reference axis at the point where the thus defined reference axis intersects the curved surface ( Off-Axial curved surface) and an optical system that arranges optical elements along the bent reference axis.
Defined as Off-Axial optical system.

The present applicant has defined the Off-Axial optical system in this way and has proposed a new optical system concept different from the conventional decentered optical system concept. By using the expansion method around the bent reference axis, it is possible to calculate the amount of paraxiality on each surface, and it is possible to summarize the form using a Gaussian bracket having a 2 × 2 component as in the optical axis rotationally symmetric system. showed that. And this new
As shown in FIG. 12, the concept of an off-axial optical system is higher than that of a conventional coaxial rotationally symmetric optical system or an anamorphic optical system that is coaxial but has no rotational symmetry. The concept was shown.

[0012]

In the above analysis, Off-Ax
Although the new concept of ial optical system was introduced, when there are multiple Off-Axial surfaces, the paraxial amount of the entire system must be adjusted unless restrictions such as azimuth dependence remain on the paraxial amount of each surface are added. Disappears. This is because even the paraxial quantity related to the first order quantity of the lowest order determined from the meridional ray does not proceed in the same plane due to the lack of symmetry, so that the paraxial quantity of each surface depends on the azimuth This is because the characteristics act on each other to produce an effect of shifting the paraxial amount of the entire system. In addition, since the relationship between the aberrations for each azimuth was not derived, it is necessary to obtain an infinite number of aberration diagrams and an infinite number of aberration coefficients when trying to obtain the aberration for each azimuth. . The two are that there is a limit to the method based on the concept of the binary vector of the coaxial rotationally symmetric optical system, and the general Off-Axia
lIn order to handle optical systems more properly, it is necessary to prepare a new analysis system, establish a processing method based on the theory, and construct a processing device using it.
At the same time, if such a processing method is established, this method will become a more extensive general optical system of general optical systems.
It also suggests that aberration-based evaluation may be possible.

The present invention completes a system of analysis methods that enables strict and systematic paraxial / aberration analysis even in a general Off-Axial optical system having a plurality of Off-Axial surfaces. And an optical processing method based on the analysis system and an optical processing apparatus using the same.

The present invention further uses the analysis system to solve the structure dependent on azimuth and completes a system capable of expressing paraxial / aberration characteristics in all azimuths with a smaller basic amount. An object of the present invention is to provide an optical processing method and an optical processing apparatus using the same.

The present invention further extends the analysis system constructed in this way to provide a general paraxial /
It is an object of the present invention to provide an optical processing method capable of evaluating aberration and an optical processing apparatus using the same.

[0016]

According to the first aspect of the present invention, there is provided an optical processing method comprising the steps of:
It is characterized in that paraxial / aberration analysis is performed by introducing more types of azimuths.

The optical processing method according to the second aspect of the present invention is the first aspect.
The present invention is characterized in that the results of paraxial and aberration analysis performed by introducing the three or more types of azimuths are displayed on a display device or printed out on a printer.

In a third aspect of the present invention, in the first or second aspect, the optical system to which the optical data is given is a rotationally asymmetric optical system.

According to a fourth aspect of the present invention, in the first aspect of the present invention, the optical system to which the optical data is given includes a plane normal to a point where a reference axis intersects and the reference axis. It is characterized by including non-matching Off-Axial surfaces.

According to a fifth aspect of the present invention, in any one of the first to fourth aspects of the present invention, the three or more azimuths are azimuths relating to a surface having a conjugate relationship between an object plane and an image plane, and an entrance pupil plane and an exit. Azimuth related to the conjugate surface of the pupil plane,
It is characterized by including three azimuths for evaluating aberrations.

According to a sixth aspect of the present invention, in the fifth aspect of the invention, at least one of an azimuth relating to a plane having a conjugate relationship between the object plane and the image plane and an azimuth relating to a plane having a conjugate relation between the entrance pupil plane and the exit pupil plane. One azimuth is characterized in that it is described as a relative azimuth to the azimuth for evaluating the aberration.

According to a seventh aspect of the present invention, in the optical processing method, the optical system to which the optical data is given is used to convert the ray passing point quaternary vector ((1) to (4)
Expression) and paraxial / aberration analysis are performed based on an analysis method that introduces the aberration quaternary vector (Equations (5) and (7)).

The optical processing method according to the eighth aspect of the present invention is the seventh aspect of the present invention.
In the invention, the quaternary vector of the ray passage point (Equations (1) to (4)) based on the component decomposition of the ray passage point, the aberration 4
It is characterized in that paraxial / aberration analysis is performed based on an analysis method in which the original vectors (Equations (5) and (7)) are introduced, and the result is displayed on a display device or printed out on a printer.

In a ninth aspect of the present invention, in the seventh or eighth aspect, the optical system to which the optical data is given is a rotationally asymmetric optical system.

According to a tenth aspect of the present invention, in the invention of any one of the seventh, eighth and ninth aspects, the optical system to which the optical data is given includes a plane normal to a point where the reference axis intersects and the reference axis. It is characterized by including non-matching Off-Axial surfaces.

An optical processing method according to an eleventh aspect of the present invention is based on an analysis method in which a ray basic quaternary vector defined by equations (8) and (9) is introduced into an optical system to which optical data is given. And perform paraxial / aberration analysis.

A twelfth aspect of the present invention provides the optical processing method according to the eleventh aspect, wherein paraxial / aberration analysis is performed based on an analysis method in which a ray basic quaternary vector defined by the equations (8) and (9) is introduced. Is displayed on a display device or printed out on a printer.

The invention of claim 13 is the invention of claim 11 or 12
In the invention, the optical system to which the optical data is given is a rotationally asymmetric optical system.

The invention of claim 14 is the invention of claim 11 or 12
In the invention according to any one of the thirteenth and thirteenth aspects, the optical system to which the optical data is given includes an Off-Axial curved surface whose surface normal at a point where the reference axis intersects does not coincide with the reference axis.

According to a fifteenth aspect of the present invention, in the optical processing method, the optical system to which the optical data is given is used for (11) and (1).
Paraxial / aberration based on an analytical method of separating azimuth dependence by the relational expression between the ray passing point quaternary vector and the ray basic quaternary vector defined by the equation (3) or the equations (12) and (14). It is characterized by performing analysis.

An optical processing method according to a sixteenth aspect of the present invention is the optical processing method according to the fifteenth aspect, wherein the ray passing point quaternary vector defined by the formula (11), (13), or (12), (14) is used. Characteristically, paraxial / aberration analysis results are displayed on a display device or printed out to a printer based on an analysis method of separating azimuth dependence using a relational expression of a ray basic quaternary vector.

The invention of claim 17 is the invention of claim 15 or 16
In the invention, the optical system to which the optical data is given is a rotationally asymmetric optical system.

The invention of claim 18 is the invention of claim 15 or 16
Or the optical system to which the optical data is given includes an Off-Axial curved surface in which a surface normal at a point where a reference axis intersects does not coincide with the reference axis.

The optical processing method according to the nineteenth aspect of the present invention provides the optical processing method according to (22), (2),
3) On the image side using tensor analysis defined by equation
It is characterized in that paraxial / aberration analysis is performed based on an analysis method that uses aberration coefficient expansion of a quaternary vector.

An optical processing method according to a twentieth aspect of the present invention is the optical processing method according to the nineteenth aspect, wherein an aberration coefficient expansion of a quaternary vector on the image side using the tensor analysis defined by the above equations (22) and (23) is used. It is characterized in that the result of paraxial / aberration analysis based on the analysis method is displayed on a display device or printed out on a printer.

The invention of claim 21 is the invention of claim 19 or 20.
In the invention, the optical system given the optical data,
It is characterized by being a rotationally asymmetric optical system.

The invention of claim 22 is the invention of claim 19 or 20.
Or the optical system to which the optical data is given includes an Off-Axial curved surface in which a surface normal at a point where a reference axis intersects does not coincide with the reference axis.

According to the optical processing method of the twenty-third aspect, the first, second and third order coefficients of the optical system given the optical data are defined by the equations (24), (25) and (26). By converting the "aberration coefficient tensor amount" that does not depend at all on the azimuth by the conversion formula to be used, the azimuth-dependent "aberration display tensor amount" is converted into an arbitrary azimuth aberration coefficient.

According to a twenty-fourth aspect of the present invention, in the optical processing method of the twenty-third aspect, the first, second and third order coefficients are (2
4), (25), (26) By converting from the “aberration coefficient tensor amount” which does not depend at all on the azimuth to the “azimuth display tensor amount” which does not depend on the azimuth at all, the aberration of an arbitrary azimuth can be obtained. The result of the calculation of the coefficient is displayed on a display device or printed out on a printer.

The invention of claim 25 is the invention of claim 23 or 24.
In the invention, the optical system to which the optical data is given is a rotationally asymmetric optical system.

The invention of claim 26 is the invention of claim 23 or 24.
In the invention according to any one of the twenty-fifth and twenty-fifth aspects, the optical system to which the optical data is given includes an Off-Axial curved surface in which a surface normal at a point where a reference axis intersects does not coincide with the reference axis.

According to the optical processing method of the twenty-seventh aspect, the optical system given the optical data is given by
2) With respect to the aberration quaternary vector obtained by substituting equation (2), the shape and relative arrangement of each constituent surface are determined so that the vector amount is closest to the zero vector.

The optical processing method according to the twenty-eighth aspect of the present invention is the optical processing method according to the twenty-seventh aspect, wherein the vector amount of the aberration quaternary vector obtained by substituting the equation (22) into the equation (7) is the zero vector. It is characterized in that an automatic design technique is used as a means for determining the shape and relative arrangement of each constituent surface so as to be close to.

The invention of claim 29 is the invention of claim 27 or 28.
In the invention, the optical system to which the optical data is given is a rotationally asymmetric optical system.

The invention of claim 30 is the invention of claim 27 or 28.
Or the optical system to which the optical data is given includes an Off-Axial curved surface in which a surface normal at a point where a reference axis intersects does not coincide with the reference axis.

An optical processing apparatus according to a thirty-first aspect is characterized by using the optical processing method according to any one of the first to thirty aspects.

An optical system according to a thirty-second aspect of the present invention is characterized in that it is designed using the optical processing method according to any one of the first to thirty aspects.

A recording medium according to a thirty-third aspect is characterized by recording the optical processing method according to any one of the first to thirty aspects.

In the optical processing method according to the thirty-fourth aspect, a light beam having a certain wavelength from one or a plurality of points on an object plane to an image plane passes through an optical system to which optical data is given. It is characterized in that paraxial / aberration analysis is performed around the optical path of the light beam of the wavelength from each object plane to the image plane.

In an optical processing method according to a thirty-fifth aspect of the present invention, in the thirty-fourth aspect, a light beam having a certain wavelength is passed from one or more points on the object plane to an image plane, and the respective object planes are passed. The parallax / aberration analysis is performed on the optical path of the light beam of the wavelength from to the image plane, and the result is displayed on a display device or printed out on a printer.

The invention of claim 36 is the invention of claim 34 or 35.
In the invention, the paraxial / aberration analysis is performed by introducing three or more types of azimuths.

According to a thirty-seventh aspect of the present invention, in the thirty-sixth aspect, the three or more kinds of azimuths are azimuths relating to a surface having a conjugate relation between an object plane and an image plane, and conjugate relations between an entrance pupil plane and an exit pupil plane. It is characterized by including azimuth related to a certain surface and azimuth evaluating aberration.

According to a thirty-eighth aspect of the present invention, in the thirty-seventh aspect, at least one of an azimuth relating to a plane having a conjugate relationship between the object plane and the image plane and an azimuth relating to a plane having a conjugate relation between the entrance pupil plane and the exit pupil plane are provided. One azimuth is characterized in that it is described as a relative azimuth to the azimuth for evaluating the aberration.

In a thirty-ninth aspect of the present invention, in any one of the thirty-fourth to thirty-eighth aspects, the optical system to which the optical data is given is a rotationally asymmetric optical system.

According to a fortieth aspect of the present invention, in any one of the thirty-fourth to thirty-ninth aspects, in the optical system to which the optical data is given, the reference axis does not coincide with a surface normal at a point where the reference axis intersects. It is characterized by including Off-Axial surfaces.

The invention according to claim 41 is characterized in that, in the invention according to any one of claims 34 to 38, the optical system to which the optical data is given is a rotationally symmetric optical system.

In the optical processing method according to the present invention, a light beam having a certain wavelength from one or more points on the object plane to the image plane is passed through the optical system given the optical data. A ray passing point quaternary vector (Equations (1) to (4)) and an aberration quaternary vector (Equation (1) to (4)) based on the component decomposition of the ray passing point around the optical path of the light ray of the wavelength from each object plane to the image plane. It is characterized in that paraxial / aberration analysis is performed based on an analysis method introducing (5) and (7).

The optical processing method according to claim 43 is the optical processing method according to claim 42, wherein a light beam of a certain wavelength is passed from one or more points on the object plane to the image plane, and the respective object planes are passed. Around the optical path of the light beam of that wavelength from to the image plane, the light beam passing point quaternary vector (Equation (1) to (4)) based on the component decomposition of the light beam passing point, the aberration quaternary vector ((5), ( The method is characterized in that the result of paraxial / aberration analysis based on the analysis method introducing equation 7) is displayed on a display device or printed out on a printer.

The invention of claim 44 is the invention of claim 42 or 43.
In the invention, the optical system to which the optical data is given is a rotationally asymmetric optical system.

The invention of claim 45 is the invention of claim 42 or 43.
Alternatively, in the invention according to the forty-fourth aspect, the optical system to which the optical data is given includes an Off-Axial curved surface in which a surface normal at a point where a reference axis intersects does not coincide with the reference axis.

The invention of claim 46 is the invention of claim 42 or 43.
In the invention, the optical system to which the optical data is given is a rotationally symmetric optical system.

In the optical processing method according to the forty-seventh aspect, a light beam having a certain wavelength from one or more points on the object plane to the image plane is passed through the optical system to which the optical data is given. Paraxial / aberration analysis around the optical path of the light beam of that wavelength from each object plane to the image plane based on the analysis method that introduced the basic ray quaternary vector defined by equations (8) and (9) It is characterized by performing.

In an optical processing method according to a forty-eighth aspect of the present invention, in the forty-seventh aspect, a light beam having a certain wavelength from one or a plurality of points on the object plane to an image plane is passed, and the respective object planes are passed. The paraxial / aberration analysis was performed around the optical path of the light beam of that wavelength from to the image plane, based on the analysis method that introduced the light fundamental quaternary vector defined by the equations (8) and (9). It is displayed on a display device or printed out on a printer.

The invention of claim 49 is the invention of claim 47 or 48.
In the invention, the optical system to which the optical data is given is a rotationally asymmetric optical system.

The invention of claim 50 is the invention of claim 47 or 48.
Alternatively, in the invention according to the forty-ninth aspect, the optical system to which the optical data is given includes an Off-Axial curved surface in which a surface normal at a point where a reference axis intersects does not coincide with the reference axis.

The invention of claim 51 is the invention of claim 47 or 48.
In the invention, the optical system to which the optical data is given is a rotationally symmetric optical system.

In the optical processing method according to the invention, a light beam having a certain wavelength from one or more points on an object plane to an image plane is passed through an optical system to which optical data is given. A ray passing point quaternary vector and a ray defined by the equations (11), (13), or (12), (14) around the optical path of the ray of the wavelength from each object plane to the image plane. It is characterized in that paraxial / aberration analysis is performed based on an analysis method of separating azimuth dependence by a relational expression of a basic quaternary vector.

The optical processing method according to claim 53 is the optical processing method according to claim 52, wherein a light beam of a certain wavelength passes from one or more points on the object plane to the image plane, and the respective object planes are passed. (11), (13), or (12), (1)
4) The ray passing point quaternary vector defined by the equation and the ray basic
Characteristically, paraxial / aberration analysis results are displayed on a display device or printed out to a printer based on an analysis technique of separating azimuth dependence by a four-vector relational expression.

The invention of claim 54 is the invention of claim 52 or 53.
In the invention, the optical system to which the optical data is given is a rotationally asymmetric optical system.

The invention of claim 55 is the invention of claim 52 or 53.
Alternatively, the optical system to which the optical data is given includes an Off-Axial curved surface in which a surface normal at a point where a reference axis intersects does not coincide with the reference axis.

The invention of claim 56 is the invention of claim 52 or 53.
In the invention, the optical system to which the optical data is given is a rotationally symmetric optical system.

The optical processing method according to the fifty-seventh aspect is characterized in that a light beam having a certain wavelength from one or more points on the object plane to the image plane is passed through the optical system given the optical data. An analysis using the aberration coefficient expansion of the quaternary vector on the image side using the tensor analysis defined by the equations (22) and (23) around the optical path of the light beam of the wavelength from each object plane to the image plane. It is characterized in that paraxial / aberration analysis is performed based on a technique.

An optical processing method according to a fifty-eighth aspect of the present invention is the optical processing method according to the fifty-seventh aspect, wherein a light beam of a certain wavelength is passed from one or more points on the object surface to an image surface, and the respective object surfaces are passed. Around the optical path of the light beam of that wavelength from to the image plane, a close approximation is made based on an analysis method using the expansion of the aberration coefficient of the quaternary vector on the image side using the tensor analysis defined by the equations (22) and (23). It is characterized in that the result of the axis / aberration analysis is displayed on a display device or printed out on a printer.

The invention of claim 59 is the invention of claim 57 or 58.
In the invention, the optical system to which the optical data is given is a rotationally asymmetric optical system.

The invention of claim 60 is the invention of claim 57 or 58.
Alternatively, in the invention according to the 59th aspect, the optical system to which the optical data is given includes an Off-Axial curved surface in which a surface normal at a point where a reference axis intersects does not coincide with the reference axis.

The invention of claim 61 is the invention of claim 57 or 58.
In the invention, the optical system to which the optical data is given is a rotationally symmetric optical system.

In the optical processing method according to the invention, a light beam having a certain wavelength from one or more points on the object plane to the image plane is passed through the optical system to which the optical data is given. Around the optical path of the light beam of that wavelength from its respective object plane to the image plane, the first, second and third order coefficients are (24),
Calculate the aberration coefficient of an arbitrary azimuth by converting the “aberration coefficient tensor amount” that does not depend at all on the azimuth into the “aberration display tensor amount” that depends on the azimuth by the conversion expressions defined by the expressions (25) and (26). It is characterized by being made possible.

The optical processing method according to claim 63 is the optical processing method according to claim 62, wherein a light beam of a certain wavelength passes from one or a plurality of points on the object plane to the image plane, and the respective object planes are passed. The first, second and third order coefficients are (24), (25), (2)
6) The result that the aberration coefficient of an arbitrary azimuth can be calculated by converting the “aberration coefficient tensor amount” that does not depend at all on the azimuth by the conversion expression defined by the expression into the “aberration display tensor amount” that depends on the azimuth. Is displayed on a display device or printed out on a printer.

The invention of claim 64 is the invention of claim 62 or 63.
In the invention, the optical system to which the optical data is given is a rotationally asymmetric optical system.

The invention of claim 65 is the invention of claim 62 or 63.
Alternatively, in the invention according to the 64th aspect, the optical system to which the optical data is given includes an Off-Axial curved surface in which a surface normal at a point where a reference axis intersects does not coincide with the reference axis.

The invention of claim 66 is the invention of claim 62 or 63.
In the invention, the optical system to which the optical data is given is a rotationally symmetric optical system.

In the optical processing method according to the present invention, a light beam having a certain wavelength from a point on the object plane to the image plane is passed through the optical system to which the optical data is given, Around the optical path of the light beam of that wavelength reaching the image plane,
It is characterized in that the shape and relative arrangement of each constituent surface are determined so that the vector amount of the aberration quaternary vector obtained by substituting the expression (22) into the expression (7) is close to the zero vector.

An optical processing method according to a sixty-eighth aspect of the present invention is the optical processing method according to the sixty-seventh aspect, wherein a light beam of a certain wavelength passes from the point on the object plane to the image plane, and each of the rays passes from the object plane to the image plane. Around the optical path of the light beam having the wavelength, (2)
2) An automatic design method is used as means for determining the shape and relative arrangement of each constituent surface such that the vector amount is close to a zero vector with respect to the aberration quaternary vector obtained by substituting the expression. I have.

The invention of claim 69 is the invention of claim 67 or 68.
The present invention is characterized in that the number of points on the object plane through which a light beam of a certain wavelength passes from the point on the object plane to the image plane.

The invention of claim 70 is the invention of claim 67 or 68.
Alternatively, in the 69th invention, the optical system provided with the optical data is a rotationally asymmetric optical system.

The invention of claim 71 is the invention of claim 67 or 68.
Alternatively, in the invention according to any one of 69 or 70, the optical system to which the optical data is given includes an Off-Axial curved surface in which a surface normal of a point where a reference axis intersects does not coincide with the reference axis. I have.

The invention of claim 72 is the invention of claim 67 or 68.
Alternatively, the optical system to which the optical data is given is a rotationally symmetric optical system.

An optical processing apparatus according to a seventy-third aspect uses the optical processing method according to any one of the thirty-fourth to seventy-second aspects.

An optical system according to a seventy-fourth aspect is characterized in that it is designed using the optical processing method according to any one of the thirty-fourth to seventy-second aspects.

The recording medium according to claim 75 is the recording medium according to claim 34.
72. An optical processing method according to claim 72, wherein the optical processing method is recorded.

In the optical processing method according to the seventy-sixth aspect of the present invention, a light beam having a certain wavelength from one or more points on an object plane to an image plane is passed through an optical system to which optical data is given. When performing paraxial / aberration analysis around the optical path of a light beam of the wavelength from each object plane to the image plane, an arithmetic module for tracing rays by specifying the light beam for paraxial / aberration analysis around the optical path It is characterized by using.

An optical processing method according to a seventy-seventh aspect of the present invention is the optical processing method according to the seventy-sixth aspect, wherein the optical path of the calculation result calculated by using the calculation module is displayed on a display device, printed out on a printer, or recorded on a recording medium. Features.

The invention of claim 78 is the invention of claim 76 or 77.
The invention is characterized in that the designated light ray can be selected from a principal ray or an arbitrary light ray among rays emitted from an off-axis object point.

The invention according to claim 79 is characterized in that, in the invention according to any one of claims 76 to 78, the optical system to which the optical data is given includes a rotationally asymmetric optical system.

An eighteenth aspect of the present invention is the optical system according to any one of the seventy-sixth to seventy-ninth aspects, wherein the optical system to which the optical data is given does not coincide with the surface normal at a point where the reference axis intersects. It is characterized by including Off-Axial surfaces.

The invention of claim 81 is characterized in that, in any one of the inventions of claims 76 to 78, the optical system to which the optical data is given includes a rotationally symmetric optical system.

The optical processing method according to claim 82, wherein a light beam having a certain wavelength from one or more points on the object plane to the image plane is passed through the optical system given the optical data. When paraxial and aberration analysis is performed around the optical path of the light beam of the wavelength from each object plane to the image plane, an arithmetic module that calculates optical data along the optical path for the specified optical path is used. It is characterized by:

An optical processing method according to an 83rd aspect of the present invention is the optical processing method according to the 82nd aspect, wherein the optical path of the operation result calculated by using the operation module is displayed on a display device, printed out on a printer or recorded on a recording medium. Features.

The invention of claim 84 is the invention of claim 82 or 83.
In the invention, the optical data along the optical path for the designated optical path includes the optical path lengths (surface intervals) along the optical path, the local surface shape at the point where the ray traced optical path intersects each surface (the optical path is It is characterized in that it includes a local expression of a plane whose origin is a point that intersects the plane), angle information that regulates how the light path traced by the ray is bent, and refractive index information before and after the bend.

The invention according to claim 85 is characterized in that, in the invention according to any one of claims 82 to 84, the optical system to which the optical data is given includes a rotationally asymmetric optical system.

The invention of claim 86 is the invention according to any one of claims 82 to 85, wherein in the optical system to which the optical data is given, the plane normal at a point where the reference axis intersects does not coincide with the reference axis. It is characterized by including Off-Axial surfaces.

The invention according to claim 87 is characterized in that, in the invention according to any one of claims 82 to 84, the optical system to which the optical data is given includes a rotationally symmetric optical system.

The optical processing method according to claim 88, wherein only two or one kind of azimuth is used in the coordinate system of the aberration analysis expression of the given optical data for the given optical system. If not, an arithmetic module that detects this and converts it into a coordinate system in which three or more azimuths are introduced is used.

In the optical processing method according to the present invention, a light beam having a certain wavelength from one or more points on the object plane to the image plane is passed through the optical system to which the optical data is given. When paraxial and aberration analysis is performed around the optical path of the light beam of that wavelength from each object plane to the image plane, only two or one azimuth is used in the coordinate system of the aberration analysis expression of the given optical data. If not, an arithmetic module that detects this and converts it into a coordinate system in which three or more azimuths are introduced is used.

The invention of claim 90 is the invention of claim 88 or 89.
In the invention, the three or more types of azimuth are azimuths relating to a surface having a conjugate relationship between an object surface and an image surface, azimuths relating to a surface having a conjugate relationship between an entrance pupil surface and an exit pupil surface, and azimuth for evaluating aberrations. It is characterized by including three.

A ninth aspect of the present invention is the invention according to the ninety-fifth aspect, wherein at least one of the azimuth relating to the surface having a conjugate relation between the object plane and the image plane and the azimuth relating to the plane having a conjugate relation between the entrance pupil plane and the exit pupil plane are provided. One azimuth is characterized in that it is described as a relative azimuth to the azimuth for evaluating the aberration.

The invention of claim 92 is characterized in that, in the invention of any one of claims 88 to 91, the optical system given the optical data includes a rotationally asymmetric optical system.

[0108] According to a 93rd aspect of the present invention, in any one of the 88th to 92nd aspects, the optical system to which the optical data is given does not coincide with the surface normal at a point where the reference axis intersects. It is characterized by including Off-Axial surfaces.

The invention of claim 94 is characterized in that, in the invention of any one of claims 88 to 91, the optical system to which the optical data is given includes a rotationally symmetric optical system.

An optical processing method according to a ninety-fifth aspect of the present invention provides two components representing an emission height on the exit side of a light beam and two components representing a converted inclination on the exit side with respect to an optical system given optical data. An arithmetic module is used in which a total of four components are calculated as a function of the total of two components representing the incident height on the incident side of the light beam and two components representing the converted tilt angle on the incident side. It is characterized by:

In the optical processing method according to the nineteenth aspect of the present invention, an optical path to which an optical data is given is designated as an optical path through a light beam having a certain wavelength from one or more points on an object plane to an image plane. Regarding the path, a total of four components including two components representing the exit height on the exit side of the light ray and two components representing the converted tilt angle on the exit side constitute two components representing the incident height on the entrance side of the ray and the incident component. It is characterized in that an arithmetic module is used which is calculated as a function of the four components in total of the two components representing the converted tilt angle on the side.

The invention of claim 97 is the invention of claim 95 or 96.
The present invention is characterized in that a calculation result in the calculation module is displayed on a display device, printed out on a printer or recorded on a recording medium.

The invention of claim 98 is the invention of claim 95 or 96.
Alternatively, in the invention of Item 97, a total of four components, which are the two components representing the incident height on the incident side of the light beam and the two components representing the converted inclination on the incident side, are four components defined by Expression (8). Yes, indicating the exit height of the ray exit side
A total of four components including the two components and the two components representing the converted tilt angle on the emission side are the four components defined by the equation (9).

The invention according to claim 99 is characterized in that, in the invention according to any one of claims 95 to 98, the optical system to which the optical data is given includes a rotationally asymmetric optical system.

The invention of claim 100 is based on claims 95 to 99.
In any one of the inventions described above, the optical system to which the optical data is given includes an Off-Axial curved surface whose surface normal at a point where the reference axis intersects does not coincide with the reference axis.

The invention of claim 101 is based on claims 95 to 98.
In any one of the inventions described above, the optical system to which the optical data is given includes a rotationally symmetric optical system.

In the optical processing method according to the present invention, two components representing a passing point in an image plane on the exit side of a light beam and an exit point in an exit pupil plane with respect to an optical system given optical data. A total of four components of the two components representing the passing point is a total of four components of the two components representing the passing point in the object plane on the light incident side and the two components representing the passing point in the entrance pupil plane. It is characterized in that an arithmetic module calculated as a function of two components is used.

In the optical processing method according to the tenth aspect of the present invention, an optical system to which optical data is given is designated as an optical path through a light beam having a certain wavelength from one or more points on an object plane to an image plane. Regarding the path, a total of four components, that is, two components representing a passing point in the image plane on the exit side of the light ray and two components representing the passing point in the exit pupil plane,
An arithmetic module is used that is calculated as a function of four components, including two components representing a passing point in the object plane on the light incident side and two components representing a passing point in the entrance pupil plane. It is characterized by.

The invention according to claim 104 is characterized in that, in the invention according to claim 102 or 103, the operation result of the operation module is displayed on a display device, printed out on a printer or recorded on a recording medium.

The invention of claim 105 is the invention of claim 102, 103 or 104, wherein the two components representing the passing point in the object plane on the incident side of the light beam and the two components representing the passing point in the entrance pupil plane. The total of four components of the four components is the four components represented by the expression (1) or (3), and the two components representing the passing point in the image plane on the exit side of the light ray In addition, a total of four components of the two components representing the passing point in the exit pupil plane are the four components represented by the formula (2) or (4).

The invention of claim 106 is based on claims 102 to 1
05, a total of four components including two components representing a passing point in the image plane on the exit side of the light ray and two components representing a passing point in the exit pupil plane;
An object is obtained by using a total of four components, that is, two components representing a passing point in the object plane on the incident side of a light ray and two components representing a passing point in the entrance pupil plane, which are input information of the operation. It is characterized in that aberration information of at least one of aberration and pupil aberration is calculated.

The invention of claim 107 is characterized in that, in the invention of claim 106, the aberration information of at least one of the object aberration and the pupil aberration is calculated by using equation (5) or (7). .

The invention according to claim 108 is the invention according to claim 106 or 107, wherein the shape and relative arrangement of each constituent surface are determined such that at least one of the object aberration and the pupil aberration is almost zero. It is characterized by having.

[0124] The invention of claim 109 is based on the invention of claim 108 and has an automatic function as a function of determining the shape and relative arrangement of each constituent surface such that at least one of the object aberration and the pupil aberration is almost zero. It is characterized by the use of a design method.

The invention of claim 110 is the invention of claims 102 to 1
09, wherein the optical system to which the optical data is given includes a rotationally asymmetric optical system.

The invention of claim 111 is based on claims 102 to 1
The invention according to any one of the tenth aspects, wherein the optical system to which the optical data is given includes an Off-Axial curved surface in which a surface normal at a point where a reference axis intersects does not coincide with the reference axis.

The invention of claim 112 is based on claims 102 to 1
09, the optical system to which the optical data is given includes a rotationally symmetric optical system.

In the optical processing method according to the present invention, two components representing a passing point in an image plane on the exit side of a light beam and an exit point in an exit pupil plane with respect to an optical system given optical data. A total of four components of the two components representing the passing point,
Or, represents the passing point in the object plane on the incident side of the light ray.
A total of four components, one component and two components representing a passing point in the entrance pupil plane, is a combination of two components representing the exit height on the exit side of the light ray and two components representing the converted tilt angle on the exit side. Using an arithmetic module that is calculated as a function of four components, or two components representing the incident height on the incident side of the light beam and two components representing the converted tilt angle on the incident side. It is characterized by.

An optical processing method according to claim 114, wherein a path designated as an optical path through a light beam of a certain wavelength from one or more points on an object plane to an image plane in an optical system given optical data. , Two components representing the passing point in the image plane on the exit side of the light ray and two components representing the passing point in the exit pupil plane, for a total of four components, or in the object plane on the incident side of the ray A total of four components, the two components representing the passing point at the entrance and the two components representing the passing point in the entrance pupil plane, are the two components representing the exit height of the ray on the exit side and the converted tilt angle on the exit side. Is calculated as a function of the total of the four components, or the sum of the two components that represent the incident height on the incident side of the light ray and the two components that represent the converted inclination on the incident side. Using an arithmetic module It is characterized by having.

The invention of claim 115 is characterized in that, in the invention of claim 113 or 114, the calculation result of the calculation module is displayed on a display device, printed out on a printer or recorded on a recording medium.

The invention according to claim 116 is the invention according to claim 113 or 114 or 115, wherein two components representing a passing point in the object plane on the incident side of the light beam and 2 representing a passing point in the entrance pupil plane. The total of the four components is the four components represented by the formula (1) or the formula (3), the two components representing the passing point in the image plane on the exit side of the light beam, and the exit A total of four components of the two components representing the passing point in the pupil plane are the four components represented by the formula (2) or (4). A total of four components, which are one component and two components representing the converted inclination on the incident side, are (8)
The four components defined by the expression, the total of two components representing the emission height on the exit side of the light beam and the two components representing the converted tilt angle on the exit side, are defined by the expression (9). It is characterized by having four components.

The invention of claim 117 is based on claims 113 to 1
16. In the invention of any one of the sixteenth aspects, a total of four components including two components representing a passing point in the image plane on the exit side of the light ray and two components representing a passing point in the exit pupil plane,
Or, represents the passing point in the object plane on the incident side of the light ray.
A total of four components, one component and two components representing a passing point in the entrance pupil plane, is a combination of two components representing the exit height on the exit side of the light ray and two components representing the converted tilt angle on the exit side. When four components are calculated as a function of the four components, or two components representing the incident height on the incident side of the light ray and two components representing the converted tilt angle on the incident side, the calculation is represented by ( It is characterized in that the calculation is performed using the equations (11), (13), (12) and (14).

The invention of claim 118 is based on claims 113 to 1
In the invention of any one of the sixteenth aspects, a total of four components including the two components representing the passing point in the image plane on the exit side of the light ray and the two components representing the passing point in the exit pupil plane, When the two components representing the injection height on the injection side and the two components representing the converted inclination on the injection side are calculated as a function of four components, the calculation is performed using equations (22) and (23). Equations and (24), (25),
It is characterized by being performed using equation (26).

The invention of claim 119 is based on claims 113 to 1
The invention according to any one of the eighteenth aspects, wherein the optical system to which the optical data is given includes a rotationally asymmetric optical system.

The invention of claim 120 is based on claims 113 to 1
The invention according to any one of the nineteenth aspects, wherein the optical system to which the optical data is given includes an Off-Axial curved surface whose surface normal at a point where the reference axis intersects does not coincide with the reference axis.

The invention of claim 121 is based on claims 113 to 1
The invention according to any one of the eighteenth aspects, wherein the optical system to which the optical data is given includes a rotationally symmetric optical system.

In the optical processing method according to the present invention, a light beam having a certain wavelength from one or a plurality of points on the object plane to the image plane is passed through the optical system given the optical data. When paraxial / aberration analysis is performed around the optical path of the light beam of the wavelength from each object plane to the image plane, it is determined whether the paraxial / aberration analysis is performed for one or more optical paths. It is characterized by using an arithmetic module.

In the optical processing method according to the 123rd aspect, a light beam having a certain wavelength from one or a plurality of points on the object plane to the image plane is passed through the optical system given the optical data. When performing paraxial / aberration analysis around the optical path of the light beam of the wavelength from each object plane to the image plane, an arithmetic module for determining whether or not a common plane evaluation is required is used.

The invention of claim 124 is characterized in that, in the invention of claim 123, the judgment that the common surface evaluation is necessary is made in the case of an input that the user needs.

In the optical processing method according to the 125th aspect of the present invention, a light beam having a certain wavelength from one or more points on the object plane to the image plane is passed through the optical system given the optical data. When paraxial / aberration analysis is performed around the optical path of the light beam of the wavelength from each object plane to the image plane, when it is determined that a common plane evaluation is necessary, the inclination of the object plane and the image plane with respect to the common evaluation plane And an arithmetic module for performing defocus conversion is used.

The invention of claim 126 is the invention of claim 122
The invention according to any one of the twenty-fifth aspects, wherein a calculation result of the calculation module is displayed on a display device, printed out on a printer, or recorded on a recording medium.

The invention of claim 127 is based on claims 122 to 1.
The invention according to any one of the twenty-sixth aspects, wherein the optical system to which the optical data is given includes a rotationally asymmetric optical system.

The invention of claim 128 is based on claims 122 to 1
27. The invention according to any one of the twenty-seventh aspects, wherein the optical system to which the optical data is given includes an Off-Axial curved surface whose surface normal at a point where the reference axis intersects does not coincide with the reference axis.

The twelfth aspect of the present invention is the twelfth aspect of the present invention.
26. The invention according to any one of the twenty-sixth aspects, wherein the optical system to which the optical data is given includes a rotationally symmetric optical system.

An optical processing method according to claim 130, wherein an arithmetic module for determining whether there is one or more azimuths for performing paraxial / aberration analysis on an optical system given optical data. It is characterized by using.

In the optical processing method according to the thirty-first aspect, a light beam having a certain wavelength from one or a plurality of points on an object plane to an image plane is passed through an optical system to which optical data is given. When paraxial / aberration analysis is performed around the optical path of the light beam of the wavelength from each object plane to the image plane, it is determined whether there is one or more azimuths to perform the paraxial / aberration analysis. It is characterized by using an arithmetic module.

The optical processing method according to the invention of claim 132 is characterized in that an arithmetic module for judging whether the azimuth dependency evaluation is necessary for an optical system to which optical data is given is used.

In the optical processing method according to the invention, a light beam having a certain wavelength from one or more points on the object plane to the image plane is passed through the optical system given the optical data. When performing paraxial / aberration analysis around the optical path of the light beam of the wavelength from each object plane to the image plane, an arithmetic module that determines whether or not the azimuth dependence evaluation is necessary is used. .

The invention of claim 134 is characterized in that, in the invention of claim 132 or 133, the judgment that the azimuth dependency evaluation is necessary is made when the user inputs that the evaluation is necessary.

In the optical processing method according to the present invention, when it is determined that the azimuth dependency evaluation is required for the optical system to which the optical data is given, the aberration characteristics calculated for each azimuth are collectively displayed. It is characterized by the use of an arithmetic module that summarizes the data into a form that can be drawn on a graph.

In the optical processing method according to the present invention, a light beam having a certain wavelength from one or more points on the object plane to the image plane is passed through the optical system given the optical data. When paraxial / aberration analysis is performed around the optical path of light of that wavelength from each object plane to the image plane, when it is determined that azimuth dependency evaluation is necessary, the aberration characteristics calculated for each azimuth are summarized. It is characterized by the use of an operation module that organizes the data into a form that can be written in a table or graph.

The invention of claim 137 is based on claims 130 to 1
36. The invention according to any one of the thirty-sixth aspects, wherein a calculation result in the calculation module is displayed on a display device, printed out on a printer, or recorded on a recording medium.

The invention of claim 138 is based on claims 130 to 1.
37. The image forming apparatus as defined in any one of Items 37 to 37, wherein the optical system to which the optical data is given includes a rotationally asymmetric optical system.

The invention of claim 139 is based on claims 130 to 1
The invention according to any one of the thirty-eighth invention, wherein the optical system to which the optical data is given includes an Off-Axial curved surface in which a surface normal at a point where a reference axis intersects does not coincide with the reference axis.

The invention of claim 140 is based on claims 130 to 1
37. The invention according to any one of the 37th aspects, wherein the optical system to which the optical data is given includes a rotationally symmetric optical system.

An optical processing apparatus according to the invention of claim 141 is characterized in that it is used in the optical processing method according to any one of claims 76 to 140.

The optical system according to claim 142 is the invention according to claim 76.
140 is characterized by being designed using the optical processing method according to any one of claims 140 to 140.

The recording medium according to claim 143 is the recording medium according to claim 7.
The optical processing method according to any one of claims 6 to 140 is recorded.

[0159]

BEST MODE FOR CARRYING OUT THE INVENTION The present invention introduces some new concepts and definitions and codifies a new way of analyzing more general images using the newly introduced concepts. The main items are as follows. -The processing method adopts three azimuths by organizing the azimuth concept in the off-axial optical system. A processing method based on an analysis method that introduces a quaternary vector of ray passing points and a quaternary vector of aberrations based on the decomposition of components of ray passing points. -The processing method must be based on an analysis method that introduces the basic ray vector. -A processing method based on an analysis method of separating azimuth dependence using a relational expression between a ray passing point quaternary vector and a ray basic quaternary vector. -The processing method must be based on an analysis method that uses tensor analysis and expands the quaternary vector on the exit side using the quaternary vector on the incident side. -With the extension of the analysis system, it must be a general paraxial and aberration-based evaluation processing method for more general optical systems.

As described above, by adopting the processing method mentioned as the main means of the present invention, the Off-Axial optical system, which is generally considered to be complicated due to less symmetry, has an outlook. This has the effect of enabling good analysis, and can provide a processing apparatus suitable for the optical design of the off-axial optical system. In particular, such analysis methods can separate the azimuth dependence as a paraxial tracking value matrix J _ij , that is, if the system-specific quantity is first determined, all azimuth dependencies are converted by multiplying by the paraxial tracking value matrix. Off-Axia, which was considered complicated due to the lack of rotational symmetry in the past because it had the effect of being required by
l A processing apparatus suitable for the optical design of the optical system can be obtained. Furthermore, along with the extension of the analysis system, this analysis method,
It can be applied not only to the off-axial optical system in a narrow sense but also to general paraxial and aberration theory evaluation of more general optical systems, and it has comprehensive paraxial and aberration theory evaluation of more general optical systems. And a processing device suitable for the design can be obtained.

Next, an analysis theory and an analysis system relating to the optical processing method (processing method) of the present invention and the optical processing apparatus (processing apparatus) using the same will be sequentially described. 1 Concept of Azimuth in Off-Axial Optical System: Processing Method Introducing Three Azims The Off-Axial optical system has no rotational symmetry, so that the azimuth is not as simple as a coaxial system in which one azimuth is sufficient. In order to generalize the expression of the off-axial optical system, the following three types of azimuths are introduced as azimuths around the reference axis as shown in FIG.

1. Azimuth of Evaluation Since the Off-Axial optical system is rotationally asymmetric, there is a problem in which plane including the reference axis is evaluated for object aberration and pupil aberration. Azimuthξ is the azimuth of the evaluation plane including the reference axis.

2. Relative azimuth of object and image point ζ, ζ ′
The amount of aberration changes depending on the difference between the object and the azimuth of the image point. So
Here, the azimuth of the object and the image point are respectively ++ ζ≡ξ _b, Ξ +
ζ′≡ξ ′_b(Ζ, ζ 'are relative azimuths of object and image point)
Define and introduce.

3. Relative azimuths η, η 'of points on the entrance pupil plane and points on the exit pupil plane Similarly, for the azimuth 収 差 whose aberration is to be evaluated, a point on the entrance pupil plane through which light rays pass, The amount of aberration changes depending on the difference of the azimuth at a point on the pupil plane. Therefore, the azimuths of a point on the entrance pupil plane through which light rays pass and a point on the exit pupil plane are ξ + η≡ξ _r and ξ + η′≡ξ ′ _r (η and η ′ are points on the entrance pupil plane through which light rays pass, and the exit pupil, respectively). Define and introduce relative azimuths of points on the surface.

The two types of relative azimuths defined here are:
In the conventional theory of coaxial rotational symmetry, ζ corresponds to the azimuth appearing in the expression of the pupil aberration, and η corresponds to the azimuth appearing in the expression of the aberration of the object. It corresponds to.

In the following, the quantity on the incident side will be referred to as the quantity relating to the object plane and the entrance pupil plane, and the quantity relating to the exit pupil plane and the image plane will be treated as the exit side. And symbolically, there is no expression such as ζ, η on the incident side,
On the emission side, expressions such as ζ 'and η' are added. (Because the azimuth 評 価 in the above evaluation is defined as the same amount on the incidence side and the emission side, it is represented by ξ as a representative.

2 Processing method based on analysis method introducing ray passing point quaternary vector and aberration quaternary vector based on ray passing point component decomposition 2.1 Decomposition of ray passing point and introduction of ray passing point quaternary vector As described in the above, for azimuth ξ of a certain evaluation, it is considered to divide the passing points of light rays on the object plane, the entrance pupil plane, the exit pupil plane, and the image plane into components in order to obtain an aberration expression. As shown in FIGS. 2 and 3, component decomposition examples in the object plane and the entrance pupil plane are shown. The azimuth component in the evaluation (parallel component to the azimuth ξ in the evaluation) and the component in the direction perpendicular to the azimuth are evaluated. A method of dividing into components (perpendicular to the azimuth 評 価 of evaluation) is taken.

As shown in the figure, the distance between the passing point in the object plane and the origin (the passing position of the reference axis) in the object plane is B, and the passing point in the entrance pupil plane and the distance in the entrance pupil plane are B. R is the distance from the origin (passing position of the reference axis), B 'is the distance between the passing point in the image plane and the origin (passing position of the reference axis) in the image plane, and the passing point is in the exit pupil plane. Assuming that the distance from the origin (passing position of the reference axis) in the exit pupil plane is R ′, the parallel component (symbol ‖) and the vertical component (symbol ⊥) with respect to the azimuth の of the evaluation on those planes are Using the relative azimuths ζ, η, ζ ′, η ′, they can be expressed as follows, respectively.

[0169]

[Outside 1]

[0170]

[Outside 2]

[0171]

[Outside 3]

[0172]

[Outside 4]

[0173]

[Outside 5]

[0174]

[Outside 6]

[0175]

[Outside 7]

[0176]

[Outside 8]

[0177]

[Outside 9]

[0178]

[Outside 10]

6 Comprehensive paraxial / aberration theory processing method for general optical system with extension of analysis system Up to the previous section, paraxial / abaxial optical system newly constructed Off-Axial optical system
We have explained the system of aberration analysis, but this Off-Axia
The concept of the optical system also means that paraxial expansion along a similar bent optical path can be performed around an arbitrary ray such as the principal ray of various optical systems. The various optical systems can be applied not only to the off-axial optical system that has been considered until now, but also to general rays of a coaxial system (rotationally symmetric coaxial system, anamorphic system). This is because, in contrast to the conventional optical system in which the evaluation of the number of aberrations with a high angle of view off-axis light beam cannot be performed due to the absence of higher-order aberration development,
If paraxial development is performed around a general light ray represented by a chief ray, optical evaluation can be performed with low-order aberration development. The system of Off-Axial paraxial / aberration analysis around general rays such as off-axis rays will be referred to as “extended paraxial / aberration analysis” in the future. When developing the system of aberration theory as “extended paraxial / aberration analysis”, procedures and items to be added that differ from the paraxial / aberration analysis system of the Off-Axial optical system described so far are described. It is shown below.

1. For an optical system given optical data,
Selection of rays that should be paraxially expanded around them and ray tracing The idea of the off-axial optical system is that “of the rays coming out from the center of the object plane (the center of the area to be imaged or observed), the optical system is specified. When a light beam having a reference wavelength passing through the optical system in a plane-sequential manner and passing through the center of the aperture defined in the optical system is set as a reference light beam, the optical path of the bent reference light beam is referred to as a reference axis. A surface whose normal does not coincide with the reference axis at the point where the reference axis defined in
Axial curved surface), and the optical elements are arranged along the bent reference axis. "Therefore, the surface spacing is taken along the reference axis, and the surface shape is also expressed by the point where the reference axis intersects the curved surface as the origin. It is generally given by Therefore, paraxial / aberration analysis around the reference axis can be performed only by the data of the given optical system. However, in the above-mentioned “expanded paraxial / aberration analysis”, it is necessary to select a ray of a certain wavelength to be subjected to paraxial / aberration analysis, trace the ray, and determine an optical path around which paraxial expansion should be performed. There is.

2. Calculation of “optical data along the optical path” for the optical path traced by the light ray Around the optical path traced by the ray ray, the reference axis of the conventional Off-Axial optical system (referred to as “on axis”) In order to perform paraxial / aberration analysis equally, it is necessary to calculate “optical data along the optical path” similar to the data given earlier in the Off-Axial optical system around the optical path traced by the ray. is there.
“Optical data along the optical path” refers to the length of each optical path along the optical path (surface interval), the local surface shape at the point where the traced optical path intersects each surface (the surface whose origin is the point where the optical path intersects each surface) ), Angle information that regulates how the optical path traced by the ray is bent, and refractive index information before and after the bend. The given data can be used for the refractive index information before and after the bending, but the remaining information needs to be newly calculated.

Each optical path length (surface interval) along the optical path is calculated as a distance between absolute coordinates of points where the optical path intersects each surface.

The local surface shape at the point where the ray traced optical path intersects each surface (the local expression of the surface with the origin at the point where the optical path intersects each surface) is generally expressed as follows. It is convenient to take a point that intersects with the surface and express it with, for example, the following expression in which one coordinate axis x-axis is aligned with the surface normal direction there.

X (y, z) = C ₂₀ y ² + 2C ₁₁ yz + C ₀₂ z ² + D ₃₀ y ³ + 3D ₂₁ y ² z + 3D ₁₂ yz ² + D ₀₃ z ³ + E ₄₀ y ⁴ + 4E ₃₁ y ³ z + 6E ₂₂ y ² z ² + 4E ₁₃ yz ³ + E ₀₄ z ⁴ + ... (27) (where the binomial coefficient is added before the expansion coefficient of each order for convenience) This is because adding a binomial coefficient prevents a fractional coefficient from remaining in the paraxial amount and the aberration coefficient.) Generally, in order to obtain an expression in such a coordinate system, May be obtained by performing coordinate transformation of origin movement and three-dimensional rotation with respect to the original origin and coordinate axes. The analytic representation of this coordinate transformation is generally complex. Therefore, it may be an effective method to numerically obtain a local expression of a plane whose origin is a point where the optical path intersects each plane by fitting using several points on the original curved surface.

In the Off-Axial optical system, the angle information that defines the bending of the ray traced light path is defined as “the angle (Off-Ax) between the surface normal and the reference axis at the point where the reference axis intersects the curved surface.
ial angle) and an angle (twist angle) of how a plane (reference plane) including the reference axis before and after the bending point is displaced from the same plane and twisted. To obtain angle information equivalent to these at the point where the optical path intersects each surface, the direction of the normal at the point where the optical path intersects each surface, and
It can be calculated by determining the direction of the optical path after deflection using the laws such as refraction, reflection, and diffraction.

3. Inclination of object plane and image plane with respect to common evaluation plane and defocus conversion If paraxial expansion is performed around one general ray represented by the principal ray described in 1.2. Above, low-order aberration expansion can be achieved. Was to be able to perform optical evaluations. Further, a plurality of light rays for this evaluation are provided per optical system (for example,
It is also possible to take principal rays having different angles of view. In such a case, paraxial / aberration analysis may be performed independently for each paraxially developed ray, but the object plane where the ray emerges is shared, and the evaluation plane is also shared with the image plane of the principal ray at a certain angle of view. Sometimes you want to evaluate. In such a case, it is necessary to take measures to make the inclinations of the object plane and the evaluation plane uniform. In addition, when there is aberration, the positions of the image planes of the principal rays of each angle of view do not generally match each other. In such a case, the positions of the evaluation planes may be aligned by defocusing together with the common inclination. The inclination of the object plane and the image plane with respect to the common evaluation plane and the defocus conversion are performed as described above when a plurality of light rays to be evaluated are provided for one optical system (for example, principal rays having different angles of view). This is very effective because the state of the aberration can be seen with a common evaluation standard. This concludes the introduction of some new concepts and definitions and the use of them for new more general methods of analyzing images and their methods for comprehensive paraxial and aberrological evaluation of more common optical systems. . Using this method, the optical axis of an optical system that includes an off-axial surface whose surface normal does not coincide with the reference axis at the point where the reference axis of the reference wavelength from the object surface to the image surface intersects the curved surface is When designing, the shape and relative arrangement of each component surface should be determined so that the vector amount of the aberration quaternary vector obtained by substituting Expression (22) into Expression (7) is the closest to the zero vector. I just need. At this time, it is useful to use an automatic design method as a means for determining the shape and relative arrangement of each constituent surface such that the vector amount of the aberration quaternary vector is closest to the zero vector. On the other hand, for a coaxial optical system, comprehensive paraxial and aberrological evaluation that incorporates the same concept around off-axis chief rays having an angle of view is possible. It is possible.

Next, an embodiment of a specific optical processing apparatus of the present invention based on the above theory and analysis system will be described. FIG.
1 is a block diagram of an optical processing device according to one embodiment of the present invention. In the figure, reference numeral 11 denotes a CPU for controlling the entire apparatus, and 13
Stores programs executed by CPU11
A ROM and a main memory including a RAM used as a working area for this execution, a keyboard 14 for inputting character information, control information, etc., a mouse 15 as a pointing device, a keyboard 16 and a mouse 15 This is a key interface for performing signal connection with this device.

Reference numeral 17 denotes a network interface for connecting the apparatus with a network 18 such as a local area network (LAN) or the Internet, and 19 denotes a ROM, SRAM, RS23, or the like.
Input / output device with 2C interface
O ”). Various external devices can be connected to the I / O 19. Reference numerals 20 and 21 denote a hard disk device and a floppy disk device as external storage devices, and reference numeral 22 denotes a disk interface for performing signal connection between the hard disk device 20 and the floppy disk device 21 and the present device. Reference numeral 23 denotes a printer constituted by an ink jet printer, a laser beam printer or the like, and reference numeral 24 denotes a printer interface for performing signal connection between the printer 23 and the apparatus. Reference numeral 25 denotes a display device, and reference numeral 26 denotes a display interface for performing signal connection between the display device 25 and the present device. Reference numeral 12 denotes a system bus including a data bus, a control bus, and an address bus for connecting signals between the above devices.

In this embodiment, the CPU 11 reads out and executes the processing procedure from a recording medium on which software of the procedure of the processing method is recorded. The recording medium is a ROM section of the main memory 13 or a CDROM as an external recording medium.
Etc. Further, the reading of the processing procedure may be performed via a network or the like. The values obtained by the respective processes are stored in the RAM section of the main memory 13, respectively.

Next, a processing algorithm of one embodiment relating to the processing method and the processing apparatus according to the present invention will be described with reference to FIG. Since this processing method and processing apparatus are related to the off-axial optical system,
The ff-Axial optical system data is read. Next, since this processing method and processing apparatus can exhibit effectiveness for a coordinate system introducing three azimuths for aberration evaluation, it is checked whether the coordinate system has three azimuths introduced. If not, conversion to a coordinate system introducing three azimuths is performed. Next, a paraxial ray on the incident side is set based on the object plane and the entrance pupil plane information. This is based on the object plane, entrance pupil plane information,
This corresponds to the setting of the incident side ray basic quaternary vector by the equation (8). Next, paraxial tracking is performed using the Off-Axial optical system data, and at the same time, “aberration coefficient tensor amount” for each surface and “aberration coefficient tensor amount” for the entire system are calculated. These “aberration coefficient tensor amounts” are amounts expressed using azimuth-independent amounts such as the surface shape of each surface, the angle between the reference axis and the surface normal, the surface interval, and the refractive index of the medium. The calculation of the “aberration coefficient tensor amount” is based on the expression (23) using the expression (23).
This corresponds to the calculation of the emission-side ray basic quaternary vector defined by the equation. By the way, in the analysis system presented in the present invention, all the quantities calculated so far are
It is calculated irrespective of the azimuth の of the evaluation relating to the aberration evaluation. However, these calculated quantities contain information that can represent the aberration in azimuth の for all evaluations. Regarding the situation, the flow of the algorithm for calculating the azimuth in all evaluations using the amounts calculated so far is continued below. For this purpose, one azimuth to be evaluated for aberration is first designated. If the azimuth ξ is specified, the incident-side ray passing quaternary vector is calculated using the definition formulas (1) and (3). This means that the incident-side paraxial trace value matrix J of equation (13), which appears in the relational equation of equation (11) that links the incident side ray passing point quaternary vector and the ray basic quaternary vector, is calculated. I have. Since the paraxial tracking value has already been determined on the injection side, the injection-side paraxial tracking value matrix of equation (14) is obtained.
J 'is also calculated. Then, if this injection-side paraxial tracking value matrix J 'is obtained, then (24), (25),
(26) By the conversion formula of “aberration coefficient tensor amount” and “aberration display tensor amount” which shows the first to third order in the equation,
The “aberration display tensor amount” for each surface and the “aberration display tensor amount” for the entire system are calculated. At the same time (2),
The exit side ray passing point quaternary vector defined in (4) is also calculated by equation (12). This calculation result is obtained by adding the aberrations of each order to the exit-side ray passing point 4 obtained by Expression (22).
This is consistent with the result of the original vector. If the exit side ray passing point quaternary vector is calculated as described above, then the aberration quaternary vector defined by the equations (5) and (7) is calculated. Since the first and second components of this aberration quaternary vector represent the object aberration, and the third and fourth components represent the pupil aberration, the aberration in the azimuth of the evaluation given above is obtained as a function of the object height and the pupil diameter. Becomes The above is the calculation of the aberration in the azimuth of one evaluation given.
If there is another azimuth to be evaluated, it is only necessary to start over from the designation of the azimuth to be evaluated as shown in FIG. When calculation of the required azimuth aberration is completed, the calculated aberration information is displayed on each surface and on the image surface, and written on a recording medium. According to the algorithm of this embodiment, the flow is such that the branching to the next azimuth is performed prior to the display of the aberration information on the image plane and the display of the aberration information on the image plane, and the writing to the recording medium. The order may be reversed.
When there are a plurality of azimuths evaluated last, the display of the difference in aberration (azimuth dependency) due to the difference in azimuth and writing to the recording medium are performed. The above is an example of the processing algorithm in the present invention.

The software containing such a processing algorithm is usually recorded on a recording medium such as a disk or a tape. The processing device performs the processing using the software as necessary.

FIG. 9 shows another example of the processing algorithm in the present invention. In the algorithm of this processing, the basic flow is the same as in FIG. However, before the designation of the azimuth of the evaluation, an item for optimizing the “aberration coefficient tensor amount” throughout the entire system is added. If the result of the optimization is not within the target, and the user wants to continue the optimization, the optical system data of the off-axial system is changed, and the optimization loop of the “aberration coefficient tensor amount” is repeated. 8 is different from the case of FIG. The reason why the optimization loop may be at this position is that the azimuth dependency of aberration can be analyzed separately by the analysis system shown in the present invention. This is because even if the aberration coefficient evaluation is not performed, the aberration can be optimized for all azimuths only by optimizing a finite number of “aberration coefficient tensors” independent of the azimuth. As described above, “optimization of aberrations for all azimuths can be performed only by optimizing a finite number of“ aberration coefficient tensors ”independent of azimuths”
This is the greatest feature of the present invention.

The software containing such a processing algorithm is recorded on a recording medium such as a disk or a tape. The processing device uses the software as necessary.

FIG. 10 shows still another example of the processing algorithm according to the present invention. In the algorithm of this processing,
The basic flow is the same as in FIG. However, in this example, the paraxial / aberration analysis system of the newly constructed Off-Axial optical system is applied around a similarly bent optical path of an arbitrary ray such as the principal ray of various optical systems. . Various optical systems are not limited to off-axial optical systems that we have considered so far, but also apply to coaxial systems (rotationally symmetric coaxial systems, anamorphic systems) as described above. It is. Therefore, at the very beginning, after reading the optical system data, “selection and ray tracing of a light beam to be paraxially expanded around the optical system given the optical data” and “light tracing light path” Of “Calculation of optical data along optical path” is added. The specific methods and meanings of these items have been described in detail in the section on "Processing for Comprehensive Paraxial and Aberration Theoretic Evaluation of More General Optical Systems with the Expansion of the Analysis System". In this way, the parallax expansion and paraxial / aberration analysis methods can be used along a similar bent optical path around any ray such as the principal ray of various optical systems. can do.

In FIG. 10, before the item "display / write of aberration information on each surface and image surface", if necessary, "tilt of object surface and image surface with respect to common evaluation surface and defocus conversion" Is added. This is to standardize the object plane from which light rays are emitted, and also to evaluate the evaluation plane with the image plane of the principal ray at a certain angle of view.
This is because a measure for adjusting the inclination of the evaluation surface is required. In addition, if there is aberration, the position of the image plane is generally not the same between the principal rays at each angle of view, so in addition to the common use of the inclination, defocus and align the positions of the evaluation plane. It is necessary to do something. But in this way,
If the inclination of the object plane and the image plane with respect to the common evaluation plane and the defocus conversion are performed, a plurality of light rays to be evaluated per optical system (for example, chief rays having different plural angles of view)
Even in the case of (1), the situation of the aberration can be seen with a common evaluation standard, which is very effective.

Incidentally, software containing such a processing algorithm is usually recorded on a recording medium such as a disk or a tape. The processing device performs the processing using the software as necessary.

FIGS. 8, 9 and 10 show examples of the processing algorithms. Finally, the operation modules of the key portions in the processing algorithms will be summarized in the following paragraphs. These play a major role in the processing method and processing apparatus of the present invention. (A1) For an optical system given optical data, pass a light beam of a certain wavelength from one or more points on the object surface to the image surface, and the wavelength of the light from each object surface to the image surface. When performing paraxial / aberration analysis around the optical path of
A ray tracing module that designates light rays for paraxial and aberration analysis around the optical path. (A2) For an optical system given optical data, an image plane is obtained from one or more points on the object plane. To perform paraxial / aberration analysis around the optical path of the light beam of that wavelength from the object plane to the image plane
An arithmetic module that calculates “optical data along the optical path” for the specified optical path. (A3) For the optical system given the optical data, there are two types of coordinate systems in the aberration analysis expression of the given optical data. Or 1
If only one type of azimuth is used, an arithmetic module that detects it and converts it into a coordinate system that incorporates three or more types of azimuth. A total of four components, ie, two components representing the exit height on the exit side and two components representing the converted inclination on the exit side, form two components representing the incident height on the incident side of the light beam and the converted inclination on the entrance side. An operation module calculated as a function of the four components in total of the two components represented. (A5) For an optical system given optical data, two components representing a passing point in the image plane on the exit side of the light ray And two components representing the passing point in the exit pupil plane, the total of four components represent the passing point in the object plane on the light incident side.
An arithmetic module calculated as a function of four components by combining one component and two components representing a passing point in the entrance pupil plane. (A6) Representing a passing point in the exit-side image plane of the calculated light ray. A total of four components including two components and two components representing a passing point in the exit pupil plane, and two components representing a passing point in the object plane on the incident side of the light ray which is input information of the operation and An arithmetic module for calculating the aberration information of at least one of the object aberration and the pupil aberration using the total of two components representing the passing point in the entrance pupil plane and the four components (A7) The calculated object aberration and pupil An arithmetic module that determines the shape and relative arrangement of each component surface so that at least one of the aberrations is almost zero. (A8) For an optical system given optical data, the image plane on the light exit side Two representing the waypoints within A total of four components, ie, a component and two components representing a passing point in the exit pupil plane, or two components representing a passing point in the object plane on the light incident side and a passing point in the entrance pupil plane 2 for
The total of four components is a total of four components, ie, two components representing the exit height on the exit side of the light beam and two components representing the converted tilt angle on the exit side, or the incident height on the entrance side of the ray. (A9) An arithmetic module that is calculated as a function of four components in total of two components representing the height and two components representing the converted tilt angle on the incident side. When passing a light beam of a certain wavelength from one or more points to the image plane and performing paraxial / aberration analysis around the optical path of the light beam of that wavelength from the respective object plane to the image plane,
An arithmetic module that determines whether there is one or more optical paths for paraxial and aberration analysis. (A10) For an optical system given optical data, one or more points on the object plane Pass a light beam of a certain wavelength to the image plane, and determine whether a common plane evaluation is necessary when performing paraxial / aberration analysis around the optical path of the light beam of that wavelength from the respective object planes to the image plane. Arithmetic module (A11) Passes a light beam of a certain wavelength from one or more points on the object plane to the image plane through the optical system to which the optical data is given, from each of the object planes to the image plane. When performing paraxial / aberration analysis around the optical path of a light ray of that wavelength, when it is determined that common plane evaluation is necessary, an arithmetic module (A12) that performs object plane and image plane tilt and defocus conversion with respect to the common evaluation plane Given optical data An arithmetic module that determines whether the optical system has one or more azimuths for paraxial and aberration analysis. (A13) For an optical system given optical data, azimuth dependency evaluation is performed. Arithmetic module to determine whether it is necessary (A14) When it is determined that azimuth dependence evaluation is necessary for an optical system given optical data, aberration characteristics calculated for each azimuth are summarized in a table or graph. Arithmetic module that summarizes in a form that can be written Among them, (A1) is an arithmetic that determines the specified optical path when paraxial and aberration analysis is performed around a specified arbitrary ray such as an off-axis chief ray. The optical path of the calculation result is displayed on a display device, printed out on a printer, or recorded on a recording medium.

(A2) is the length of each optical path (surface interval) along the optical path, which is necessary for paraxial / aberration analysis around a designated arbitrary ray such as an off-axis principal ray, and the ray traced ray. Is the local surface shape at the point where each surface intersects (local expression of the surface with the origin at the point where the optical path intersects each surface), the angle information that regulates how the light path traced by the ray is bent, and the refractive index before and after the bend It calculates and calculates "optical data along the optical path" such as information. These calculation results are also displayed on a display device or printed out on a printer or recorded on a recording medium as necessary.

(A3) is a graph showing a azimuth expression which is not suitable for the paraxial / aberration analysis system of the present invention when given optical data has a conjugate relationship between the object plane and the image plane which is suitable for the analysis system. Is converted into an azimuth system including three azimuths, namely, an azimuth relating to a surface having a conjugate relationship between the entrance pupil plane and the exit pupil plane, and an azimuth for evaluating aberration.

(A4) can be expressed in terms newly defined in the present theoretical system, and the four components of the exit-side ray basic quaternary vector of equation (9) can be expressed as the four components of the incident-side ray basic quaternary vector of equation (8) This corresponds to calculation as a function of components. Although it is desirable to use a vector analysis technique, the function of the module is expressed as described above because it may be specifically written for each component.

(A5) can be expressed by words newly defined in the theoretical system, and the four components of the exit-side ray passing point quaternary vector of the equation (2) or (4) are expressed by the equation (1) or (3). This corresponds to the calculation as a function of the four components of the quaternary vector of the incident side ray passing point. As for this, it is desirable to use a vector analysis technique, but since it is also possible to specifically write down each component, the function of the module is expressed as described above.

(A6) can be expressed in terms newly defined in this theoretical system by using the quaternary vector at the exit-side ray passing point obtained at (A5) and the quaternary vector at the incident-side ray passing point. This is an operation for obtaining the object aberration and the pupil aberration as in the expression (5) or (7). These can be obtained at the same time using the vector analysis method, but for some users,
As a derivation, when the result of the pupil aberration is unnecessary, and only the pupil aberration is required on the contrary, the expression of the module is expressed as described above.

(A7) is a design operation module for minimizing the aberration obtained in (A6), and specifically includes an automatic design module and the like. Although such a method is generally used for aberration control of a coaxial optical system, it is very difficult to use a similar method because a theoretical system has been disclosed in the present invention for a bent optical path. It is valid.

(A8) can be expressed in terms newly defined in the present theoretical system, namely, the four components of the exit side ray passing point quaternary vector in equation (2) or (4) or the equation (1) or (3) in equation (3). The four components of the incident side ray passing point quaternary vector are represented by the four components of the exit side ray basic quaternary vector of equation (9) and the incident side ray basic 4 of equation (8).
This corresponds to calculation as a function of the four components of the original vector. As for this, it is desirable to use a vector analysis technique, but since it is also possible to specifically write down each component, the function of the module is expressed as described above. The ray passing point quaternary vector and ray basic 4
In the theoretical system of the present invention, the relation between the element vectors is generally expressed by equation (11), equation (13) or equation (12),
Equation (22), equation (23) and equation (2) are performed on the exit side by performing aberration expansion for each order.
4), (25), and (26).

(A9) is a module for checking the number of optical paths for paraxial / aberration analysis when paraxial / aberration analysis is performed around a designated arbitrary ray such as an off-axis principal ray. In some cases, it is used to determine whether the common aspect evaluation of (A10) is necessary. If it is determined in the module (A10) that the common plane evaluation is necessary, the inclination of the object plane and the image plane with respect to the common evaluation plane and the defocus conversion are performed using the module (A11).

(A12) is an arithmetic module for determining whether there is one or more azimuths for performing paraxial / aberration analysis on an optical system given optical data,
The result is used to determine whether the azimuth dependency evaluation of (A13) is necessary. Then, in the calculation module for determining whether the azimuth dependency evaluation of (A13) is necessary, when it is determined that the azimuth dependency evaluation is necessary, the aberration characteristics calculated for each azimuth by the module of (A14) are summarized in a table or the like. An operation is performed to put the data into a form that can be drawn on a graph.

Incidentally, of these modules, (A1), (A
2), (A9), (A10), and (A11) pass a light beam of a certain wavelength from one or more points on the object plane to the image plane with respect to the optical system given the optical data, When paraxial / aberration analysis is performed around a specified arbitrary ray such as an off-axis principal ray, in which paraxial / aberration analysis is performed around the optical path of the light beam of the wavelength from the object plane to the image plane. It is used only for On the other hand, the remaining (A3), (A4), (A5), (A6), (A7), (A8),
(A12), (A13), (A14) are also given when the optical data of the optical path bent from the beginning as in the off-axial optical system,
For an optical system given optical data, 1
An off-axis chief ray that passes a light beam of a certain wavelength from one or more points to the image plane, and performs paraxial / aberration analysis around the optical path of the light beam of that wavelength from the object plane to the image plane. It is also used for paraxial / aberration analysis around a designated arbitrary ray.

The above modules (A1) to (A14) are usually recorded as software on a recording medium such as a disk or tape. The processing device uses the software as necessary.

In addition, a light beam having a certain wavelength from one or a plurality of points on the object plane to the image plane is passed through the optical system to which the optical data is given, and each of the light beams travels from the object plane to the image plane. When paraxial / aberration analysis is performed around a specified arbitrary ray such as an off-axis principal ray that performs paraxial / aberration analysis around the optical path of the light beam of that wavelength, the optical system given optical data Off-Ax optical path to analyze even if is a coaxial optical system
Since the optical system is bent like the ial optical system, the optical system provided with the optical data that can be processed in all the modules includes a rotationally symmetric optical system.

The results of the operations performed in all of these operation modules are displayed on a display device, printed out on a printer, or recorded on a recording medium as necessary.

As described above, Of of the embodiment of the present invention
The f-Axial optical system is generally an optical system formed by arranging a deflection surface such as a refraction surface or a reflection surface along a bent reference axis, and is an extended concept of a conventional coaxial rotationally symmetric optical system. In the embodiment of the present invention, for such an Off-Axial optical system which is generally considered to be complicated in analysis due to low symmetry, two kinds of 4
Source vector (ray passing point vector, ray basic vector)
Is newly defined and introduced, and a tensor analysis method is newly introduced into the quaternary vector to obtain (22), (2)
3) An analysis system characterized by a clear and easy-to-view expression can be created as summarized by the equation. By adopting a processing method based on the analysis system, paraxial and aberration analysis of an optical system with a good view can be performed. effective. Furthermore, such an analysis system and method allow the aberration coefficient and the basic optical characteristics to be expressed in a tensor format, so that the mutual relationship and conversion are easily formulated and easily understood.

In particular, with respect to the azimuth dependency, in which the amount of aberration differs for each azimuth, which was conventionally regarded as complicated due to lack of rotational symmetry, the azimuth dependency is 4 × by using such an analysis system and method. Gaussian bracket G of 4
_{ij and the} like, a system-specific amount “aberration coefficient tensor amount”, a paraxial tracing value matrix J _ij, and a normalized incident side ray passing point quaternary vector p can be separated. In other words, if the relationship of the separation of the azimuth dependence is understood, on the contrary, the actual aberration at an arbitrary azimuth is an amount unique to the system as a system represented by a 4 × 4 Gaussian bracket G _ij or the like. As shown in equations (24), (25), and (26), a paraxial trace value matrix J _ij including the azimuth of the evaluation, and a normalized incident side ray passing point quaternary vector including the relative azimuth There is a very effective effect that it can be obtained by conversion using p.
In particular, G _ij , which appears in the analysis system as a representation of the eigenvalue tensor of the lowest order of the system, is 2 deg.
It can be considered as an extension of the Gaussian bracket given by a × 2 matrix to a 4 × 4 matrix, and is effective as a representation of the basic characteristics of the Off-Axial optical system such as the amount of paraxial axis. There is a concept, and when used in combination with the paraxial tracking value matrix J _ij appearing in the above azimuth separation, there is an effect that the paraxial characteristics and the like of the Off-Axial optical system can be studied over all azimuths.

If the analysis system and method according to the embodiment of the present invention are used, the azimuth dependence of the aberration is represented by a 4 × 4 Gaussian bracket G _ij or the like. The fact that the parallax tracing value matrix J _ij and the normalized incident-side ray passing point quaternary vector p can be separated means that even in the optimization of the optical system, a “finite number of aberration coefficients independent of azimuth” Tensor amount "
Optimizing aberrations for all azimuths can be achieved simply by optimizing ”.

Further, using the concept of the off-axial optical system, paraxial expansion along a similar bent optical path can be performed around an arbitrary ray such as a principal ray of various optical systems.
For the optical system given the optical data, select the rays that should undergo paraxial expansion around them and trace the rays, and calculate the "optical data along the optical path" for the ray traced paths. If performed, paraxial / aberration analysis can be performed around an arbitrary ray such as an off-axis ray of various optical systems. In addition, the aberration analysis has an effect that more aberration states can be understood by low-order aberration analysis as compared with the conventional off-axis treatment.

Further, a plurality of rays for this evaluation are provided per one optical system (for example, chief rays having a plurality of different angles of view).
Since it is also possible to take, if necessary, "tilt of object plane and image plane with respect to common evaluation plane and defocus conversion"
Is carried out, there is also an important effect that even if there are a plurality of light beams to be evaluated per optical system, it is possible to see the state of aberration with a common evaluation standard.

[0216]

According to the present invention, a paraxial / aberration analysis can be strictly and systematically performed even in a general off-axial optical system having a plurality of off-axial surfaces. The system can be completed, and an optical processing method based on the analysis system and an optical processing apparatus using the same can be achieved.

In addition, according to the present invention, a system that can express paraxial / aberration characteristics in all azimuths with a smaller basic amount by solving the azimuth-dependent structure using the analysis system is completed. An optical processing method based on the system and an optical processing apparatus using the system, and furthermore, an analysis system constructed in this way is further expanded to provide an optical system capable of comprehensive paraxial and aberration theory evaluation of a general optical system. A processing method and an optical processing device using the same can be achieved.

[Brief description of the drawings]

FIG. 1 is a diagram illustrating three azimuths according to an embodiment of the present invention.

FIG. 2 is a view for explaining passing points of light rays in an object plane according to one embodiment of the present invention.

FIG. 3 is a view for explaining light passing points in the entrance pupil plane according to one embodiment of the present invention;

FIG. 4 is a diagram illustrating the decomposition of aberration on an image plane according to an embodiment of the present invention.

FIG. 5 is a diagram illustrating components of a ray basic quaternary vector before deflection according to an embodiment of the present invention.

FIG. 6 is a diagram illustrating components of a ray basic quaternary vector after deflection according to an embodiment of the present invention.

FIG. 7 is an example of a block diagram of a processing apparatus according to an embodiment of the present invention.

FIG. 8 shows an example of a processing algorithm according to an embodiment of the present invention.

FIG. 9 is another example of a processing algorithm according to an embodiment of the present invention.

FIG. 10 shows still another example of the processing algorithm according to one embodiment of the present invention.

FIG. 11 is a diagram illustrating a bent reference axis and an off-axial optical system.

FIG. 12 (Aberration theory of coaxial rotationally symmetric optical system) and Off-Axial
Diagram showing the relationship of the optical system (aberration theory)

[Explanation of symbols]

 11 CPU 12 System bus 13 Main memory 14 Keyboard 15 Mouse 16 Key interface 17 Network interface 18 Network 19 I / O interface 20 Hard disk drive 21 Floppy disk drive 22 Disk interface 23 Printer 24 Printer interface 25 Display 26 Display interface

Claims (143)

[Claims] 1. An optical processing method comprising: performing paraxial / aberration analysis by introducing three or more types of azimuths into an optical system given optical data. 2. The optical processing method according to claim 1, wherein a result of paraxial / aberration analysis performed by introducing the three or more kinds of azimuths is displayed on a display device or printed out on a printer. 3. The optical system to which the optical data is given,
The optical processing method according to claim 1, wherein the optical processing method is a rotationally asymmetric optical system. 4. An optical system to which the optical data is given,
The surface normal of the point where the reference axis intersects and the reference axis does not match
The optical processing method according to claim 1, wherein the optical processing method includes an f-Axial curved surface. 5. The three or more kinds of azimuths include an object surface
Azimuth, pupil plane,
The optical processing method according to any one of claims 1 to 4, further comprising three azimuths relating to a plane having a conjugate relationship with the exit pupil plane, and azimuths for evaluating aberrations. 6. The azimuth associated with a surface having a conjugate relationship between an object plane and an image plane and the azimuth associated with a surface having a conjugate relationship between an entrance pupil plane and an exit pupil plane are azimuths for evaluating aberrations. The optical processing method according to claim 5, wherein the optical processing method is described by relative azimuth with respect to the optical axis. 7. An optical system to which optical data is given, a ray passing point quaternary vector (Equations (1) to (4)) and an aberration quaternary vector ((5)) based on the component decomposition of the ray passing point. , (7)), an paraxial / aberration analysis is performed based on an analysis method introducing (7). 8. An analysis method that introduces a ray passing point quaternary vector (Equations (1) to (4)) and an aberration quaternary vector (Equations (5) and (7)) based on the component decomposition of the ray passing point. 8. The optical processing method according to claim 7, wherein a result of performing paraxial / aberration analysis based on the result is displayed on a display device or printed out on a printer. 9. The optical system to which the optical data is given,
The optical processing method according to claim 7, wherein the optical processing method is a rotationally asymmetric optical system. 10. The optical system to which the optical data is given includes an Off-Axial curved surface in which the surface normal at a point where a reference axis intersects does not coincide with the reference axis. The optical processing method according to claim 8 or 9. 11. Performing paraxial / aberration analysis on an optical system given optical data based on an analysis method that introduces a ray basic quaternary vector defined by equations (8) and (9). An optical processing method characterized by the above-mentioned. 12. Based on an analysis method that introduces a ray basic quaternary vector defined by equations (8) and (9), paraxial
The result of performing the aberration analysis is displayed on a display device or printed out on a printer.
The optical processing method described in 1. 13. The optical system to which the optical data is given is a rotationally asymmetric optical system.
The optical processing method according to claim 1 or 12. 14. The optical system to which the optical data is given includes an Off-Axial curved surface in which a surface normal at a point where a reference axis intersects does not coincide with the reference axis. The optical processing method according to claim 12 or 13. 15. An optical system to which optical data is given is given by the following expression (11), (13), or (12), (1).
4) The ray passing point quaternary vector defined by the equation and the ray basic
An optical processing method characterized by performing paraxial / aberration analysis based on an analysis technique of separating azimuth dependence by a relational expression of a quaternary vector. 16. Separation of azimuth dependence by a relational expression between a ray passing point quaternary vector and a ray basic quaternary vector defined by the above equation (11), (13), or (12), (14). 16. The optical processing method according to claim 15, wherein a result of performing paraxial / aberration analysis based on an analysis method of performing the analysis is displayed on a display device or printed out on a printer. 17. The optical system to which the optical data is given is a rotationally asymmetric optical system.
An optical processing method according to claim 5 or 16. 18. The optical system to which the optical data has been given includes an Off-Axial curved surface whose surface normal to a point where a reference axis intersects does not coincide with the reference axis. An optical processing method according to claim 16 or claim 17. 19. An optical system to which optical data is given is based on an analysis method using expansion of aberration coefficients of a quaternary vector on the image side using tensor analysis defined by equations (22) and (23). An optical processing method characterized in that paraxial / aberration analysis is carried out by using the method. 20. A paraxial / aberration analysis result based on an analysis method using the expansion of aberration coefficients of a quaternary vector on the image side using the tensor analysis defined by the equations (22) and (23). 20. The optical processing method according to claim 19, wherein the image is displayed on a display device or printed out on a printer. 21. The optical system to which said optical data is given is a rotationally asymmetric optical system.
The optical processing method according to claim 9 or 20. 22. The optical system to which the optical data is given includes an Off-Axial curved surface whose surface normal to a point where a reference axis intersects does not coincide with the reference axis. The optical processing method according to claim 20 or 21. 23. First, second, and third order coefficients of the optical system given optical data are (24), (25), (2)
6) The arbitrary azimuth aberration coefficient can be calculated by converting the "aberration coefficient tensor amount" which does not depend at all on the azimuth by the conversion formula defined by the expression into the "aberration display tensor amount" which depends on the azimuth. An optical processing method characterized by the above-mentioned. 24. The first-order, second-order, and third-order coefficients are (24),
Calculate the aberration coefficient of an arbitrary azimuth by converting the “aberration coefficient tensor amount” that does not depend at all on the azimuth into the “aberration display tensor amount” that depends on the azimuth by the conversion expressions defined by the expressions (25) and (26). The optical processing method according to claim 23, wherein the enabled result is displayed on a display device or printed out on a printer. 25. The optical system to which the optical data is given is a rotationally asymmetric optical system.
The optical processing method according to claim 3 or 24. 26. The optical system to which the optical data is given includes an Off-Axial curved surface in which a surface normal at a point where a reference axis intersects does not coincide with the reference axis. The optical processing method according to claim 24 or 25. 27. For an optical system to which optical data is given, an aberration quaternary vector obtained by substituting equation (22) into equation (7) is such that the vector amount is closest to a zero vector. An optical processing method comprising: determining a shape and a relative arrangement of each constituent surface. 28. With respect to the quaternary aberration vector obtained by substituting equation (22) into equation (7), the shape and relative arrangement of each constituent surface are determined so that the vector amount is closest to zero vector. 28. The optical processing method according to claim 27, wherein an automatic design technique is used as the means for performing the processing. 29. The optical system to which the optical data is given is a rotationally asymmetric optical system.
An optical processing method according to claim 7 or claim 28. 30. The optical system to which the optical data is given includes an Off-Axial curved surface whose surface normal to a point where a reference axis intersects does not coincide with the reference axis. The optical processing method according to claim 28 or 29. 31. Any one of claims 1 to 30
An optical processing apparatus characterized by using the optical processing method described in the above item. 32. Any one of claims 1 to 30
An optical system characterized by being designed using the optical processing method described in the item. 33. Any one of claims 1 to 30
A computer-readable recording medium on which the optical processing method according to claim is recorded. 34. A light beam having a certain wavelength from one or a plurality of points on an object plane to an image plane passes through an optical system given optical data, and each of the light beams passes from the object plane to the image plane. An optical processing method comprising performing paraxial / aberration analysis around an optical path of a light beam having the wavelength. 35. Passing light of a wavelength from one or more points on the object plane to the image plane, and near the optical path of the light beam of the wavelength from the respective object plane to the image plane. 35. The optical processing method according to claim 34, wherein the result of the axis / aberration analysis is displayed on a display device or printed out on a printer. 36. The paraxial / aberration analysis is performed by introducing three or more kinds of azimuths.
The optical processing method according to claim 4 or 35. 37. The three or more types of azimuths are azimuths relating to a plane having a conjugate relationship between an object plane and an image plane, azimuths relating to a plane having a conjugate relation between an entrance pupil plane and an exit pupil plane, and azimuths for evaluating aberrations. 37. The optical processing method according to claim 36, comprising: 38. At least one of the azimuth of the azimuth relating to the plane having a conjugate relationship between the object plane and the image plane and the azimuth relating to the plane having a conjugate relation of the entrance pupil plane and the exit pupil plane is as follows:
38. The optical processing method according to claim 37, wherein the optical processing method is described in terms of relative azimuth to azimuth for evaluating aberration. 39. The optical system to which the optical data is given is a rotationally asymmetric optical system.
The optical processing method according to any one of claims 4 to 38. 40. The optical system to which the optical data is given includes an Off-Axial curved surface in which a surface normal at a point where a reference axis intersects does not coincide with the reference axis. 40. The optical processing method according to any one of items 39. 41. The optical system to which the optical data is given is a rotationally symmetric optical system.
The optical processing method according to any one of claims 38 to 38. 42. A light beam having a certain wavelength from one or more points on an object plane to an image plane passes through an optical system to which optical data is given, and each of the light beams passes from the object plane to the image plane. A ray passing point quaternary vector (Equations (1) to (4)) and an aberration quaternary vector (Equations (5) and (7)) based on the component decomposition of the ray passing point around the optical path of the light beam of the wavelength. An optical processing method characterized in that paraxial / aberration analysis is performed based on an analysis method that incorporates the above. 43. Passing a light beam of a wavelength from one or more points on the object plane to the image plane, and around the optical path of the light beam of that wavelength from the respective object plane to the image plane, Based on an analysis method that introduces a ray passing point quaternary vector (Equations (1) to (4)) and an aberration quaternary vector (Equations (5) and (7)) based on the component decomposition of the ray passing point, 43. The optical processing method according to claim 42, wherein a result of performing the aberration analysis is displayed on a display device or printed out on a printer. 44. The optical system to which the optical data is given is a rotationally asymmetric optical system.
44. The optical processing method according to claim 43. 45. The optical system to which the optical data is given includes an Off-Axial curved surface whose surface normal to a point where a reference axis intersects does not coincide with the reference axis. The optical processing method according to claim 43 or 44. 46. The optical system to which the optical data is given is a rotationally symmetric optical system.
44. The optical processing method according to claim 43. 47. A light beam having a certain wavelength from one or more points on an object plane to an image plane is passed through an optical system given optical data, and each of the light beams passes from the object plane to the image plane. (8), (9) around the optical path of the light beam of that wavelength
An optical processing method characterized by performing paraxial / aberration analysis based on an analysis method that introduces a ray basic quaternary vector defined by an equation. 48. Passing a light beam of a wavelength from one or more points on the object plane to the image plane, and around the optical path of the light beam of that wavelength from the respective object plane to the image plane, Characteristically, parallax / aberration analysis is performed on a display device or printed out to a printer based on an analysis method that introduces a ray basic quaternary vector defined by equations (8) and (9). The optical processing method according to claim 47. 49. The optical system to which the optical data is given is a rotationally asymmetric optical system.
49. The optical processing method according to claim 7 or 48. 50. The optical system to which the optical data is given includes an Off-Axial curved surface in which a surface normal at a point where a reference axis intersects does not coincide with the reference axis. 50. The optical processing method according to claim 48 or 49. 51. The optical system to which the optical data is given is a rotationally symmetric optical system.
49. The optical processing method according to claim 48. 52. A light beam having a certain wavelength from one or a plurality of points on an object plane to an image plane passes through an optical system given optical data, and each of the light beams passes from the object plane to the image plane. (11), (1)
Paraxial / aberration based on an analytical method of separating azimuth dependence by the relational expression between the ray passing point quaternary vector and the ray basic quaternary vector defined by the equation (3) or the equations (12) and (14). An optical processing method characterized by performing analysis. 53. Passing a light beam of a wavelength from one or more points on the object plane to an image plane, and around the optical path of the light beam of the wavelength from each of the object planes to the image plane, (11), (13), or (12), (1
4) The ray passing point quaternary vector defined by the equation and the ray basic
53. The result of performing paraxial / aberration analysis based on an analysis method of separating azimuth dependence by a four-vector vector relational expression is displayed on a display device or printed out on a printer. Optical processing method. 54. The optical system to which the optical data is given is a rotationally asymmetric optical system.
54. The optical processing method according to claim 53. 55. The optical system to which the optical data is given includes an Off-Axial curved surface whose surface normal to a point where a reference axis intersects does not coincide with the reference axis. The optical processing method according to claim 53 or 54. 56. The optical system to which the optical data is given is a rotationally symmetric optical system.
54. The optical processing method according to claim 53. 57. A light beam having a certain wavelength from one or a plurality of points on an object plane to an image plane passes through an optical system given optical data, and each of the light beams passes from the object plane to the image plane. (22), (2)
3) On the image side using tensor analysis defined by equation
An optical processing method characterized by performing paraxial / aberration analysis based on an analysis method using expansion of aberration coefficients of a quaternary vector. 58. Passing a light beam of a certain wavelength from one or more points on the object plane to the image plane, and around the optical path of the light beam of that wavelength from the respective object plane to the image plane, Display the result of paraxial / aberration analysis on a display device based on an analysis method using aberration coefficient expansion of a quaternary vector on the image side using tensor analysis defined by equations (22) and (23), or display the result on a printer. 58. The optical processing method according to claim 57, wherein the image is printed out. 59. The optical system to which the optical data is given is a rotationally asymmetric optical system.
An optical processing method according to claim 7 or claim 58. 60. The optical system to which the optical data is given includes an Off-Axial curved surface in which the surface normal of a point where a reference axis intersects does not coincide with the reference axis. The optical processing method according to claim 58 or 59. 61. The optical system to which the optical data is given is a rotationally symmetric optical system.
Or the optical processing method according to claim 58. 62. A light beam having a certain wavelength from one or more points on an object plane to an image plane passes through an optical system to which optical data is given, and each of the light beams passes from the object plane to the image plane. Around the optical path of the light beam of the wavelength, the first-, second-, and third-order coefficients do not depend on the azimuth at all according to the conversion equations defined by the equations (24), (25), and (26). "Azimuth-dependent" aberration display tensor amount "
An optical processing method characterized in that an arbitrary azimuth aberration coefficient can be calculated by converting the azimuth into an azimuth. 63. Pass light of a wavelength from one or more points on the object plane to the image plane, and around the optical path of that wavelength light from each of the object planes to the image plane. The first, second and third order coefficients are (24), (25), (2
6) The result that the aberration coefficient of an arbitrary azimuth can be calculated by converting the “aberration coefficient tensor amount” which does not depend at all on the azimuth into the “aberration display tensor amount” which depends on the azimuth by the conversion formula defined by the expression. The optical processing method according to claim 62, wherein is displayed on a display device or printed out on a printer. 64. The optical system to which the optical data is given is a rotationally asymmetric optical system.
64. The optical processing method according to claim 63. 65. The optical system to which the optical data is given includes an Off-Axial curved surface whose surface normal to a point where a reference axis intersects does not coincide with the reference axis. 63. The optical processing method according to claim 63 or 64. 66. The optical system to which the optical data is given is a rotationally symmetric optical system.
Or the optical processing method according to claim 63. 67. A light beam having a certain wavelength from a point on an object plane to an image plane is passed through an optical system to which optical data is given, and a light beam of that wavelength from each object plane to the image plane is transmitted. Around the optical path, determine the shape and relative arrangement of each constituent surface such that the vector amount is close to a zero vector with respect to the aberration quaternary vector obtained by substituting the expression (22) into the expression (7). An optical processing method characterized by the above-mentioned. 68. A light beam of a certain wavelength passes from a point on the object plane to the image plane, and around the optical path of the light beam of that wavelength from each of the object plane to the image plane, 22)
An automatic design method is used as means for determining the shape and relative arrangement of each component surface such that the vector amount is close to a zero vector with respect to the aberration quaternary vector obtained by substituting the expression. 70. The optical processing method according to item 67. 69. The optical system according to claim 67, wherein the number of points on the object plane through which a light beam of a certain wavelength passes from the point on the object plane to the image plane. Processing method. 70. The optical system to which the optical data is given is a rotationally asymmetric optical system.
The optical processing method according to claim 7 or claim 68 or claim 69. 71. The optical system to which the optical data is given includes an Off-Axial curved surface whose surface normal to a point where a reference axis intersects does not coincide with the reference axis. The optical processing method according to claim 68 or claim 69 or claim 70. 72. The optical system to which the optical data is given is a rotationally symmetric optical system.
70. The optical processing method according to claim 68 or 69. 73. An optical processing apparatus using the optical processing method according to any one of claims 34 to 72. 74. An optical system which is designed using the optical processing method according to claim 34. 75. A computer-readable recording medium on which the optical processing method according to claim 34 is recorded. 76. A light beam having a certain wavelength from one or more points on an object plane to an image plane is passed through an optical system given optical data, and each of the light beams passes from the object plane to the image plane. When performing paraxial / aberration analysis around the optical path of a light beam having the same wavelength, an arithmetic module that designates a ray to be subjected to paraxial / aberration analysis around the optical path and uses ray tracing is used. Optical processing method. 77. The optical processing method according to claim 76, wherein an optical path of a calculation result calculated using the calculation module is displayed on a display device, printed out on a printer, or recorded on a recording medium. 78. The method according to claim 76, wherein the designated ray can be selected from a principal ray or an arbitrary ray among rays emitted from an off-axis object point. The optical processing method described in the above. 79. The optical processing method according to claim 76, wherein the optical system provided with the optical data includes a rotationally asymmetric optical system. 80. The optical system to which the optical data is given includes an Off-Axial curved surface whose surface normal at a point where a reference axis intersects does not coincide with the reference axis. 80. The optical processing method according to any one of the items 79. 81. The optical processing method according to claim 76, wherein the optical system to which the optical data is given includes a rotationally symmetric optical system. 82. An optical system to which optical data is given passes a light beam of a certain wavelength from one or more points on the object plane to the image plane, and from each object plane to the image plane. An optical processing method, comprising: using an arithmetic module for calculating optical data along an optical path of a designated optical path when performing paraxial / aberration analysis around the optical path of a light beam having the wavelength. 83. The optical processing method according to claim 82, wherein an optical path of a calculation result calculated using the calculation module is displayed on a display device, printed out on a printer, or recorded on a recording medium. 84. The optical data along the optical path for the designated optical path includes each optical path length (surface interval) along the optical path, and the local surface shape at the point where the ray traced optical path intersects each surface (the optical path is A local expression formula of a plane having a point of intersection with each plane as an origin), angle information defining how to bend the ray traced optical path, and refractive index information before and after the bend are included. The optical processing method according to claim 82 or 83. 85. The optical processing method according to claim 82, wherein the optical system provided with the optical data includes a rotationally asymmetric optical system. 86. The optical system to which the optical data is given includes an Off-Axial curved surface whose surface normal at a point where a reference axis intersects does not coincide with the reference axis. 85. The optical processing method according to any one of the items 85. 87. The optical processing method according to claim 82, wherein the optical system provided with the optical data includes a rotationally symmetric optical system. 88. For a given optical system given optical data, a coordinate system of aberration analysis expression of the given optical data is used.
An optical processing method characterized in that when only two or one type of azimuth is used, an arithmetic module for detecting the azimuth and converting it into a coordinate system incorporating three or more types of azimuth is used. 89. A light beam having a certain wavelength from one or more points on an object plane to an image plane is passed through an optical system given optical data, and each of the light beams passes from the object plane to the image plane. When performing paraxial / aberration analysis around the optical path of a light beam of that wavelength, if only two or one type of azimuth is used in the coordinate system of the aberration analysis expression of the given optical data, it is used. An optical processing method using an arithmetic module for detecting and converting to a coordinate system in which three or more azimuths are introduced. 90. The three or more types of azimuths are azimuths relating to a plane having a conjugate relationship between an object plane and an image plane, azimuths relating to a plane having a conjugate relation between an entrance pupil plane and an exit pupil plane, and azimuths for evaluating aberrations. 90. The optical processing method according to claim 88 or claim 89, comprising: 91. An azimuth relating to a plane having a conjugate relationship between the object plane and the image plane and an azimuth relating to a plane having a conjugate relation between the entrance pupil plane and the exit pupil plane are at least one azimuth:
The optical processing method according to claim 90, wherein the optical processing method is described in terms of relative azimuth to azimuth for evaluating aberration. 92. The optical processing method according to claim 88, wherein the optical system provided with the optical data includes a rotationally asymmetric optical system. 93. The optical system to which the optical data is given includes an Off-Axial curved surface whose surface normal at a point where a reference axis intersects does not coincide with the reference axis. 92. The optical processing method according to any one of items 92. 94. The optical processing method according to claim 88, wherein the optical system provided with the optical data includes a rotationally symmetric optical system. 95. For an optical system to which optical data is given, a total of four components, that is, two components representing the exit height on the exit side of the light beam and two components representing the converted tilt angle on the exit side, The sum of two components representing the incident height on the incident side of the lens and two components representing the converted inclination on the incident side is 4
An optical processing method using an operation module calculated as a function of two components. 96. Emission of a light beam on the exit side with respect to a path designated as an optical path through a light beam of a certain wavelength from one or more points on an object plane to an image plane to an optical system given optical data. A total of four components including two components representing the height and two components representing the converted inclination on the exit side are two components representing the incident height on the incident side of the light beam and two components representing the converted inclination on the incident side. 4 in total
An optical processing method using an operation module calculated as a function of two components. 97. The optical processing method according to claim 95, wherein the operation result of the operation module is displayed on a display device, printed out on a printer or recorded on a recording medium. 98. An incident height on the incident side of the light beam
The total of the four components including the two components and the two components representing the converted tilt angle on the incident side are the four components defined by the equation (8), and the two components representing the exit height on the exit side of the light beam and the exit component The optical processing according to claim 95, wherein the total four components of the two components representing the converted tilt angles on the side are the four components defined by the expression (9). Method. 99. The optical processing method according to claim 95, wherein the optical system provided with the optical data includes a rotationally asymmetric optical system. 100. The optical system to which the optical data is given includes an Off-Axial curved surface in which a surface normal at a point where a reference axis intersects does not coincide with the reference axis. 99. The optical processing method according to any one of items 99. 101. The optical processing method according to claim 95, wherein the optical system to which the optical data is given includes a rotationally symmetric optical system. 102. A combination of two components representing a passing point in an image plane on the exit side of a light ray and two components representing a passing point in an exit pupil plane with respect to an optical system given optical data. Are calculated as a function of the total of the two components representing the passing point in the object plane on the incident side of the light ray and the two components representing the passing point in the entrance pupil plane. An optical processing method using an arithmetic module. 103. An image on an exit side of a light beam with respect to a path designated as an optical path through a light beam of a certain wavelength from one or more points on an object plane to an image plane in an optical system given optical data. The two components representing the passing point in the plane and the two components representing the passing point in the exit pupil plane, the combined four components are the two components representing the passing point in the object plane on the light incident side. And an arithmetic module that calculates a function of four components in total of two components representing a passing point in the entrance pupil plane. 104. The optical processing method according to claim 102, wherein the operation result of the operation module is displayed on a display device, printed out on a printer or recorded on a recording medium. 105. A total of four components including two components representing a passing point in the object plane on the incident side of the light ray and two components representing a passing point in the entrance pupil plane is a total of four components. The four components represented by the formulas (1) and (3), two components representing a passing point in the image plane on the light exit side and two components representing a passing point in the exit pupil plane. 104. The optical processing method according to claim 102, wherein the total of the four components is the four components represented by the formula (2) or the formula (4). 106. A total of four components including two components representing a passing point in the image plane on the exit side of the light ray and two components representing a passing point in the exit pupil plane, and input information for calculation Two components representing the passing point in the object plane on the incident side of the ray, and 2 representing the passing point in the entrance pupil plane
106. The aberration information of at least one of the object aberration and the pupil aberration is calculated using the four components in addition to the four components.
The optical processing method described in the paragraph. 107. The optical processing method according to claim 106, wherein the aberration information of at least one of the object aberration and the pupil aberration is calculated using Expression (5) or Expression (7). 108. The apparatus according to claim 106, further comprising a function of determining the shape and relative arrangement of each constituent surface such that at least one of the object aberration and the pupil aberration is almost zero. 107. The optical processing method according to 107. An automatic design method is used as a function of determining the shape and relative arrangement of each constituent surface such that at least one of the aberration of the object and the aberration of the pupil is almost zero. The optical processing method according to claim 108, wherein 110. The optical processing method according to claim 102, wherein the optical system to which the optical data is given includes a rotationally asymmetric optical system. 111. An optical system to which the optical data is given includes an Off-Axial curved surface in which a surface normal at a point where a reference axis intersects does not coincide with the reference axis. 110. The optical processing method according to any one of items 110. The optical processing method according to any one of claims 102 to 109, wherein the optical system to which the optical data is given includes a rotationally symmetric optical system. 113. Combination of two components representing a passing point in an image plane on the exit side of a light ray and two components representing a passing point in an exit pupil plane for an optical system given optical data. The four components, or two components representing the passing point in the object plane on the entrance side of the ray and the two components representing the passing point in the entrance pupil plane, are combined into four components on the exit side of the ray. A total of four components, ie, two components representing the exit height of the light beam and two components representing the converted tilt angle on the exit side, or two components representing the incident height on the incident side of the light ray and the converted tilt angle on the incident side. An optical processing method, comprising using an operation module that is calculated as a function of four components by combining two components. 114. A path designated as the optical path through a light beam of a certain wavelength from one or more points on the object plane to the image plane to the optical system given the optical data.
A total of four components, that is, two components representing a passing point in the image plane on the exit side of the light ray and two components representing a passing point in the exit pupil plane, or a component in the object plane on the incident side of the light ray A total of four components, the two components representing the passing point and the two components representing the passing point in the entrance pupil plane, represent two components representing the exit height on the exit side of the light beam and the converted tilt angle on the exit side. 4 components in total, or 2 components
An optical processing method characterized in that an arithmetic module is used which is calculated as a function of four components by combining two components representing an incident height on the incident side of a light beam and two components representing a converted inclination on the incident side. . 115. The optical processing method according to claim 113 or claim 114, wherein a calculation result of said calculation module is displayed on a display device, printed out on a printer or recorded on a recording medium. 116. A total of four components, that is, two components representing a passing point in the object plane on the incident side of the light ray and two components representing a passing point in the entrance pupil plane, are: The sum of the four components represented by the formulas (1) and (3), the two components representing the passing points in the image plane on the exit side of the light beam, and the two components representing the passing points in the exit pupil plane The four components are the four components represented by the formulas (2) and (4). On the other hand, the two components representing the incident height on the incident side of the light beam and the two components representing the converted inclination on the incident side are combined. The four components are the four components defined by the equation (8), and the total of the four components including the two components representing the exit height on the exit side of the light beam and the two components representing the converted inclination on the exit side is: (9) There are four components defined by equation (9). 13 or claim 114 or optical processing method according to claim 115. 117. A total of four components, that is, two components representing a passing point in the image plane on the exit side of the light ray and two components representing a passing point in the exit pupil plane, or the incident side of the ray. Of the two components representing the pass point in the object pupil plane and the two components representing the pass point in the entrance pupil plane.
The four components are a total of four components, ie, two components representing the exit height on the exit side of the light beam and two components representing the converted inclination on the exit side, or two components representing the incident height on the entrance side of the ray. And two components representing the converted tilt angle on the incident side are calculated as a function of four components,
The calculation is performed by the equation (11), the equation (13) or the equation (1).
The optical processing method according to any one of claims 113 to 116, wherein the optical processing method is performed using the equations (2) and (14). 118. A total of four components, which are two components representing a passing point in the image plane on the exit side of the light ray and two components representing a passing point in the exit pupil plane, constitute the component on the exit side of the ray. When the two components representing the injection height and the two components representing the conversion angle of the injection side are calculated as a function of four components, the calculation is performed using the formula (22), (2)
113. The method according to claim 113, wherein the calculation is performed using the expression 3) and the expressions (24), (25), and (26).
17. The optical processing method according to any one of items 16. 119. The optical processing method according to claim 113, wherein the optical system provided with the optical data includes a rotationally asymmetric optical system. 120. An optical system to which the optical data is given includes an Off-Axial curved surface whose surface normal at a point where a reference axis intersects does not coincide with the reference axis. 119. The optical processing method according to any one of [119]. 121. The optical processing method according to claim 113, wherein the optical system to which the optical data is given includes a rotationally symmetric optical system. 122. An optical system given optical data passes a light beam of a certain wavelength from one or more points on an object plane to an image plane, and passes light rays from each object plane to the image plane. When paraxial / aberration analysis is performed around the optical path of a light beam having the same wavelength, an arithmetic module that determines whether there is one or more optical paths for performing the paraxial / aberration analysis is used. Optical processing method. 123. A light beam having a certain wavelength from one or more points on an object plane to an image plane is passed through an optical system to which optical data is given, and each of the light beams passes from the object plane to the image plane. An optical processing method, comprising: using an arithmetic module for determining whether a common plane evaluation is required when performing paraxial / aberration analysis around an optical path of a light beam having the same wavelength. 124. The judgment that the common plane evaluation is necessary is as follows:
124. The optical processing method according to claim 123, wherein the method is performed in the case of an input that the user needs. 125. An optical system given optical data passes a light beam of a certain wavelength from one or a plurality of points on an object plane to an image plane, and passes light rays from each object plane to the image plane. When performing paraxial / aberration analysis around the optical path of a light beam of that wavelength, when it is determined that common plane evaluation is necessary, an arithmetic module that performs object plane and image plane tilt and defocus conversion with respect to the common evaluation plane An optical processing method characterized by being used. 126. The optical processing according to any one of claims 122 to 125, wherein a calculation result of said calculation module is displayed on a display device, printed out on a printer or recorded on a recording medium. Method. The optical processing method according to any one of claims 122 to 126, wherein the optical system to which the optical data is given includes a rotationally asymmetric optical system. 128. An optical system to which the optical data is given includes an Off-Axial curved surface whose surface normal at a point where a reference axis intersects does not coincide with the reference axis. 127. The optical processing method according to any one of the items 127. The optical processing method according to any one of claims 122 to 126, wherein the optical system provided with the optical data includes a rotationally symmetric optical system. 130. An arithmetic module for determining whether there is one or more azimuths for performing paraxial / aberration analysis on an optical system given optical data. Optical processing method. 131. A light beam having a certain wavelength from one or more points on an object plane to an image plane is passed through an optical system to which optical data is given, and each of the light beams passes from the object plane to the image plane. When performing paraxial / aberration analysis around the optical path of a light beam of that wavelength, an arithmetic module that determines whether there is one or more azimuths to perform the paraxial / aberration analysis is used. Optical processing method. 132. An optical processing method using an arithmetic module for determining whether or not azimuth dependency evaluation is necessary for an optical system to which optical data has been given. 133. A light beam having a certain wavelength from one or more points on an object plane to an image plane passes through an optical system to which optical data is given, and each of the light beams passes from the object plane to the image plane. An optical processing method characterized by using an arithmetic module for judging whether or not azimuth dependency evaluation is required when performing paraxial / aberration analysis around an optical path of a light beam having the wavelength. 134. The optical processing method according to claim 132 or 133, wherein the determination that the azimuth dependency evaluation is necessary is performed when the user inputs that the evaluation is necessary. 135. An arithmetic module for summarizing aberration characteristics calculated for each azimuth into a form that can be written in a table or a graph when it is determined that azimuth dependency evaluation is necessary for an optical system to which optical data is given. An optical processing method characterized by using: 136. A light beam having a certain wavelength from one or more points on an object plane to an image plane passes through an optical system to which optical data is given, and each of the light beams passes from the object plane to the image plane. When paraxial / aberration analysis is performed around the optical path of a light beam of that wavelength, when it is judged that azimuth dependence evaluation is necessary, the aberration characteristics calculated for each azimuth are summarized in a table or graph. An optical processing method using an arithmetic module. 137. The optical processing according to any one of claims 130 to 136, wherein the calculation result of the calculation module is displayed on a display device, printed out on a printer or recorded on a recording medium. Method. 138. The optical processing method according to claim 130, wherein the optical system to which the optical data is given includes a rotationally asymmetric optical system. 139. The optical system to which the optical data is given includes an Off-Axial curved surface in which a surface normal at a point where a reference axis intersects does not coincide with the reference axis. 138. The optical processing method according to any one of 138. 140. The optical processing method according to claim 130, wherein the optical system provided with the optical data includes a rotationally symmetric optical system. 141. An optical processing apparatus used in the optical processing method according to any one of claims 76 to 140. 142. An optical system designed using the optical processing method according to any one of claims 76 to 140. 143. A computer-readable recording medium on which the optical processing method according to any one of claims 76 to 140 is recorded.