JPS61177411A - Optical part having form represented by analysis function - Google Patents

Abstract

(57) [Summary] This bulletin contains application data before electronic filing, so abstract data is not recorded.

Description

[Detailed description of the invention]

[Field of Sedentary Application] The present invention generally relates to an optical device particularly suitable for use in cameras. More particularly, the present invention relates to an optical element having a preferred shape expressed by an analytic function, the element being rotated about one or more different rotational fulcrums. Thus, the photographic objective can be focused over a wide range of object distances. [Prior Art] When the distance from the position of the camera objective lens to the object changes, the home distance inevitably changes but is easily calculated, and if this is not compensated for in some way, the selection The rapid deterioration of image quality over a given field of view has been known since the earliest days of handheld cameras. Anyone who has ever warped a photographic objective knows this basic fact. In practice, camera manufacturers use a variety of convenient devices for aligning photosensitive film or plates with edges in space. The most natural device, which has been in use since the beginning, focuses by simply moving the position of a photographic objective along its optical axis. The film surface is fixed
C-ru is normal. However, there are also cameras that move film or move holders for photographic plates, as is the case with telescopes. This is especially true when the photographic equipment is thick (and cumbersome). In both cases, the distance between the objective and the film is varied so that it focuses on the glass. , this ground glass is then replaced by a device that covers a photographic emulsion or other form of light-sensitive surface. In some cameras, especially modern cameras, the focusing movement is performed by moving only part of the optical device. Generally speaking, it has been found convenient to move only one element or one component. However, if an element or component is moved from its optimal position,
As a result, the quality of the treatment is poor, so the method of using moving elements or moving parts is not a good idea. Good quality images are obtained by balancing various aberrations, but when the confectionery or parts move, these aberrations appear directly, and as the element moves, these aberrations become larger. Spherical aberration, comatic aberration, As astigmatism increases, achromatic aberration and longitudinal chromatic aberration also reappear.However, by designing the aperture deeply, over considerable object distances and magnifications,
Many practical devices are also available. For example, various types of zoom devices are now in widespread use. Other forms of focusing methods have also been introduced. changing the refractive power discretely by replacing the lens elements, reducing the weaving range (focusing range) in each lens element, and stabilizing the acid quality within each range to a reasonable level; It is also possible to do this. In this case, if the respective storage areas are lined up, some of them will overlap, and this exchangeable f
This method, in which the C position can be used over a wide range of object distances, is relatively simple if the replaceable imaging element has a small positive or negative refractive power. In this case, an element E with weak refractive power used at a certain time
It only has a slight effect on the quality of the iron, and if placed properly and given the right shape, it actually does? It can be used to improve quality. By making aspherical "small changes" 5 using mold elements, the quality of the design can be selectively improved within each region. If the NB folding lens element is projected onto the rotor or disc so that it can be easily replaced, then this rotor is
ouse ) can be said to be an s child. Quarterhouse discs have also traditionally been used for aperture control and for easy filter replacement by insertion. ' Yet another type of focusing method uses a fluid-filled collapsible cell. By changing the pressure inside the cell, it is possible to produce a weak change in refractive power, which can be used for imaging. Usually a wall thickness variation in the refractive power of a handheld camera objective.

Both the positive and negative cases are extremely small, measuring several tens of microns at a normal focal length. However, after focusing has taken place, it is imperative that the deformed flexible cell has a sufficiently clear optical surface for an image of acceptable quality. Yet another type of focusing method was published on February 21, 1967.
U.S. Patent No. 3 in the name of Nori, W. and Alvarez.
This is the method disclosed in No. 305,294. In this method, a pair of deformed plates are laterally displaced by the same size but in opposite directions. Although these plates have the same shape, they are arranged so that the changes in thickness cancel out at the zero position, and the refractive power across these two plates is zero. A polynomial is used to determine a common aspherical shape.This polynomial is a power series of two variables, and its 6-missing term is a large principal term, and the characteristics are almost determined by this term.These The coefficients of the polynomial are carefully chosen so that these plates influence the action of the refractive lens by its transmission and refraction. When these plates are moved laterally relative to each other, the overall As a young fruit, it acts as a simple biconvex element or biconcave cord, thereby changing the refractive power of continuous magnitude.Alvarez
The deformed board disclosed in the name can be used inside a narrow space.
Although this method satisfies the requirements and provides a favorable change in focal length, the resulting thin lens device does not have sufficient correction for mechanical aberrations, which poses a problem in its application to various situations. James (), Baker U.S. Patent No. 5,5
No. 83,790 discloses a laterally movable plate. This movable plate is an improvement over the plate disclosed in the Alvarez name, in that movement of the plate allows focusing while also correcting aberrations. In this case, it has one special lens element,
One surface is a plane, and one surface has a shape described by a preferred polynomial, and generally speaking, a shape defined by a preferred analytic function, so that the element By moving in one direction, the focusing effect is changed and aberrations are minimized when in one direction. The refractive action of this moving element, when it is combined with the refractive action of a fixed opposing surface of a fixed optical element located in the immediate vicinity, is reflected in the rotationally symmetrical lens element corrected by this opposing surface. [Problem to be Solved by the Invention] It has been found that focusing action can also be obtained by other forms of lateral movement.Therefore, the main object of the invention is to , with a novel lateral motion and suitable optical precision.
The object of the present invention is to disclose an embodiment that performs the same as a similar type of rotationally symmetrical refractive element with variable refractive power. A further object of the invention is to provide a preferred form in which it is possible to rotate at least two such elements relative to one another, so that the relationship can be adjusted depending on the object distance. to get,
It is to hang optical elements. A primary object of the present invention is to rotate an optical element around one or more supporting axes at different positions with respect to the optical axis, thereby providing the same optical properties as a rotationally symmetrical aspherical system having variable refractive power. two or more rotatable cables having an optical element with a preferred shape expressed by an analytic function, capable of performing an optical function, and having the same optical function as an aspherical rotationally symmetric element of variable power; It is to have a child. Other objects of the invention will be apparent in part and will become apparent in part below. Accordingly, the present invention comprises optical elements and optical devices having the structures, combinations, and arrangements of elements exemplified in the detailed description below. SUMMARY OF THE INVENTION The present invention generally relates to optical devices. A particularly suitable application for this optical device is a photographic camera. More particularly, the invention relates to optical elements having a shape described by a preferred analytic function or a preferred ° polynomial, the elements having one or more different positions relative to the optical axis in °C. A well-compensated rotational symmetry that can be used to maintain focus settings over a wide range of object distances or perform complex functions by rotating relative to a rotational fulcrum. It can perform the same function as the variable refractive power and aspherical function of the lens element. For this purpose, the optical elements themselves! The general form of the analytic function surface is It is a polymonomial equation containing two independent variables, and is written as an equation appropriately truncated by a finite term. The membrane shape Q is expressed by the following formula. where 1 is the surface number and represents the engineering coefficient % X * y + Z7 is the coordinate in the preferred non-Cartesian seat system. In such an embodiment, a pair of elements are used, one of which rotates about an axis of rotation that is parallel to the optical axis of the device, but in a central position. In each of the examples, novel elements (engineering,
Typically, the confectionery is transparent, preferably cast in a suitable optical glass material. on one side of the element there is provided a first surface of a predetermined shape, which is at least a part of a rotationally symmetrical surface (although in the case of a dense device this surface is preferably flat); and on one side of this element there is provided a second aspherical surface which is rotationally asymmetric and which can be mathematically described by a preselected polynomial having at least one non-zero term of at least fourth order. It will be done. The first and second surfaces of the element are configured such that the element can be displaced generally transversely to the optical axis when the element rotates nine revolutions about an axis of rotation different from the optical axis; When the element moves relative to the optical axis, the surface of the second element gives a continuous change in its optical properties, while the surface of the first element remains optically unchanged, causing no change in the optical properties. It doesn't even give an analogy. Embodiments As explained above, the present invention generally relates to an optical device that is particularly suitable for use in cameras. More specifically, the invention relates to an optical confectionery having a preferred shape defined by a preferred polynomial, or more generally, defined by a preferred analytic function. The design of these new devices is different from the prior art devices, which are devices that can be moved laterally. These preferred analytical function surfaces can be rotated about an axis different from the optical axis to maintain focus settings over a wide range of object distances, or to perform more elaborate functions. FIG. 1 is a schematic diagram of element 10. This device is a device having the general characteristics of the invention. The element 10 is a thin, transparent, annular part which is accommodated by a suitable mechanical device in such a way that it can rotate about an axis R, which is parallel to the optical axis OA. Along the optical axis, a region 12 is shown which is nominally circular.This circular region 12 represents the diameter of the largest aperture in a plane of the element 10. When the original passes through the confectionery 10 from the object space to the iron space, the beam of light passes through the transmission area 12.The confectionery 100 has a section 14 with a constant width in the radial direction.This section 14 can be selectively moved while maintaining optical alignment with the transmissive region 12 as the element 10 rotates about the axis of rotation RA.The peripheral portion 140 shown is one surface 16 that is planar. Therefore, when the element 10 rotates, this surface becomes the transparent region 1
It always has the same optical effect over 2K. surface 16
The opposite surface 18 is in the foreground of the paper and is shown exaggerated. Surface 18 has a shape dictated by a preferred analytical function. This analytic function is specified by the present invention so that when the cord 10 rotates about the axis of rotation RA, the effective optical effect is changed by the surface 18. The essence of the invention is the shape of surface 18, or a similar surface. As will be explained later, by appropriately selecting the shape of the surface defined by an analytic function such as 18 (hereinafter referred to as the analytic function surface), By arranging similar elements, it is possible to produce the same effect as a rotationally symmetrical refractive element or an aspherical element with various refractive powers t. When used, one or more of them can be used with a fixed position, or some or all can be rotated around the same or different axes, in the same or opposite directions. For example, FIG. 2 shows a pair of such elements 20, 2.
2, in which the elements 20° 22 rotate in opposite directions around a rotation axis RA that is different from the optical axis OA. These elements can also be incorporated into more sophisticated devices, as shown in the examples below. In order to clearly understand the properties of analytic function surfaces according to the present invention and specific examples having these analytic function surfaces, it is necessary to first explain various coordinate systems. These coordinate systems define analytic function surfaces. It is a convenient coordinate system to describe the design in general, and it is a convenient coordinate system to calculate and specify the shape of these surfaces. FIG. 6 shows various coordinate systems that are convenient for defining, specifying, and analyzing the analytic function surface of the optical element of the present invention. The first coordinate system, which is the most convenient in manufacturing, is a cylindrical coordinate system in the cross section for the mathematical treatment of the analysis surface. In this coordinate system, the origin of coordinates in the X-7 plane is a rotation fulcrum located at a close position, that is, the intersection of the X-7 plane and the rotation axis RA. The rotational axis RA passes through this rotational fulcrum and is parallel to the optical axis OA. The arrangement in the reference cross-section is therefore in polar coordinate form, and the form of the analytic function can in principle be defined using conventional polar coordinates. That is, the coordinates of one point P on the analysis surface within the cross section are given by the coordinates r and 7 eyes (F). The preferred shape within the six-dimensional space in polar coordinates is completely determined by giving the depth of 21 in the optical axis direction, that is, the deviation from this cross section, as the PA number of polar coordinates in the cross section. In addition to using the polar position 4s, at least two other coordinate systems are used. The first of such coordinate systems is the x-y-z coordinate system commonly used in optical design. In this coordinate system, the optical axis OA is included in two axes,
The Y-Z+ plane is taken as the meridian plane, and x@ is skewed (Skθ
The axis of W) is perpendicular to these two axes. - When the celebrant faces the front from behind the objective device, the value of the 2nd coordinate is positive in the direction toward the #1 celebrant, and y
The value of the coordinate is positive in the upward direction in the meridian plane, and the value of the X coordinate is positive in the right-hand direction. On the contrary, if the observer looks from the front to the back of the objective, the value of the y coordinate is positive in the upward direction and the value of the O1x coordinate is positive in the left direction,
The value of the second position is positive in the direction away from the observer. For an arbitrarily given surface, it is convenient to select the coordinate origin bivertex, that is, the intersection of this surface and the optical axis. In general, auxiliary Cartesian coordinates can be used. Regarding the X-7-z coordinate system, the eight points of this coordinate system are on the optical axis OA, and the optical axis OA and the reference horizontal W
It is at the intersection with the r(xy) plane. In some cases, the origin of each of the two coordinate systems is moved in one direction by translation in one direction. This new non-Cartesian coordinate system is roughly related to the -7-Z coordinate system, but includes its own extensions to polar angles and radii. Therefore, one shift is calculated by subtracting the radial distance from the lower rotational fulcrum to the coordinate origin (0,0,0) from the radial distance 217) from the lower rotational fulcrum in Figure 6. The value of y is defined as follows. Positive y values correspond to above the coordinate origin. The length of the arc measured along the seven axes of the concentric arc centered on the rotation fulcrum becomes the newly defined value of ma. Positive values correspond to the left direction along the arc. 2 is either the same as 2 or differs by a constant translational distance in degrees Celsius along the Z axis. Of course, it is possible to subtract the "curve" coordinates defined above on the auxiliary Cartesian coordinate thread and adopt it as the fourth coordinate system. This F! ! l! My system is probably useful for mathematical analysis. The noble family between the polar seat and this fourth Cartesian coordinate system may hold a certain mathematical pole. However, the transmission l#R in an annular reconnaissance area whose rotational fulcrum is a rotating surface
As long as it lies well outside the region 12, this mathematical pole will not confer any advantage on the analyticity of the function within the transmission region used. In fact, one of the pair of optical water molecules of the present invention
For two adjacent fixed elements, the effective aperture will normally remain circular, as for ordinary rotationally symmetric surfaces. For a rotating cord transmission area, the circular aperture extends over an annular area or a sector-shaped annular area, thus providing adequate light transmission even as the element rotates over its entire range as described above. If the opposing surfaces of a pair of adjacent cords have a shape specified by an analytical function and the pair of elements rotates, each has a transparent region in the form of a sector-shaped annular region.
It is necessary to introduce a circular aperture, for example circle 19 in Fig. 2, fixed near (see figure) and to one element. when one of the surfaces rotated relative to each other about a staggered pivot point or, if two staggered rotation axes are used, about a plurality of pivot points, and this rotation focus or other optical action when they are rotated relative to each other or relative to a fixed circular aperture centered on the optical axis OA. That is, in the general case where both of the two elements rotate, as shown in FIG. Similar arrangements are considered for other azimuthal angles, with the rotational fulcrum above or with both rotational fulcrums both above or below, and for other azimuthal angles. Differentiation of the individual analytical shapes To apply geometry, the intersection of the analytic function surface and the optical axis OA must first be determined. %XIY instead of
It is convenient to describe it as a power series. Furthermore, since a completely exact representation is not required, this power series can be truncated midway and made into a polynomial. If there are no poles within the area of the fan-shaped annular part to be used, the inner boundary is formed by concentric arcs centered on the singular point that includes the @ at the rotation fulcrum, so mathematically There will be no intermittent peculiarities. However, the accuracy of representing the analytical shape of a surface by a truncated power-law series or polynomial in x and y can mathematically depend on the relative distance to the pole or singularity at the origin in a polar coordinate system. , quite conceivable. This may be considered even if the poles are outside the entire aperture used, i.e. expressed in terms of the parameters of the optical device (with some coefficients representing the distance to the outside poles). The size of the curve will become thicker in proportion to the reciprocal of or in proportion to the power of As long as it is analytical in the domain and the number of terms in the polynomial is sufficiently thick (takes a truncated power series, i.e., the polynomial expression can be expressed with any precision required, ◎ converse In other words, due to the existence of external poles, the shape of the corresponding analytic function expressed in polar coordinates around such a pole is mathematically a form that cannot be expressed precisely in a power series. but nevertheless adequately describe the shape of the deformed surface.These mathematical forms expressed in polar coordinates are also analytic and do not have °C poles. It may be said that the deformed surface described by Since these surface holes are continuous, one is fixed with respect to the angle about the offset axis RA, and the other is 9°, the shape of each of these two surfaces, 1, σ,y)
and 11+, a mathematical method to represent (x, y) ℃
The form of a Begi series can be adopted. The coefficients of each term in this power series are undetermined. Next, a method of calculating all these coefficients to the required extent is established. In this case, as described in Section 5 below, it is assumed that all possible power terms of Ma and 7 exist. However, before proceeding with the mathematical processing, it is important to state here the important goals of the present invention. A pair of adjacent refractive confectionery whose shape is determined by an analytical function, and which may have an aspherical surface among its four surfaces, is used to create the shape shown at the bottom of the same figure. , the objective is to obtain the same optical effect as that of a pair of adjacent rotationally symmetrical refractive elements.One of the simulated pairs for this stain correction rotates around an eccentric rotation fulcrum and has a flat outer surface. , the other of the simulated pairs can be fixed and its outer surface is a rotationally symmetric refractive confection with or without an aspherical bevel.The inner opposing surfaces of these two elements are We have a surface shape described by an analytic function, which performs as much as possible the same optical action as the pair to be simulated.Furthermore, if for any given pair of object distances, the aperture, There is a corresponding set of adjacent rotationally symmetrical refractive elements that optimizes the optical properties of the objective to the required extent over the field and spectrum, and this rotationally symmetrical refractive element depends not only on its refractive power (aspherical If the forces also change and they are distributed in a favorable manner on its four surfaces, both the refractive and aspherical properties can be changed to make the optical behavior of the rotationally symmetric, refractive element pair as equal as possible. , must be replaced by a rotational movement about an axis parallel to the optical axis OA through at least one offset rotational fulcrum of the optical element of the invention.0 At the same time, the coefficients of the power series terms are 5 must be calculated to best simulate.The target values of the rotationally symmetric refractor to be simulated must be determined by conventional optical design.However, the calculation of this simulation is based on mathematical In this case, the first step is to determine the detailed optics of the required equipment,
By carrying out the design, a simulation is performed for the average object distance. Depending on the purpose of the camera, the average object distance that is adopted may be the median value within the focusing range, a value shifted to an area that is advantageous for long-distance photography, or a value that is a combination of values. Although it is h, it is a certain value close to the close distance. However, in the detailed design it must be planned in advance that at least one pair of adjacent surfaces will ultimately have, or at least be able to be incorporated mathematically, a polynomial form or form of an analytic function. If only one surface of a pair of simulated models can be rotated about an offset axis, then either the front or back surface is a simple element and lies in the first plane with respect to the other surface. or the polynomial form can be distributed on two sides. Rotatable surfaces should be in analytic function form or polynomial form. The overall optical design can have refractive power and an aspherical term in analytic function form or polynomial form on one or both of the inner opposing surfaces, if this proves preferable, and on the identification elements. The outer m surface can have refractive power and an aspherical term Y when necessary. In special cases, the conventional refractive surface of the rotatable element can be transferred or assigned to the outer surface of the identification element. This outer surface can already have a predetermined optical power and an aspherical term. In Figure 4, consider the mathematical reference line in i, de, i space. This reference line is a line parallel to the optical axis at 7 points with specified i and de values. It is for mathematical convenience only. This base f! All points on the L line have the same i, Te value Y, and only the i value varies. The actual light rays are refracted by successive surfaces of adjacent pairs of simulated surfaces. The pair of opposing inner narrow surfaces of the stiffness are deformed into the desired shape. In practice, the actual ray may be used as a reference line, in which case i and te will vary along the line segment between the spliced surfaces. If we were to expand it into a series with respect to i, te, i, a significant number of coefficients would appear and it would be unnecessarily complex. Therefore, as a second step, it is convenient to use a reference #' parallel to the axis, and to connect the intersection of the first of the four surfaces involved with the last of these four surfaces. It is convenient to calculate for the elementary refractive element the total optical thickness along this reference line between the intersection of . Overall, this optical thickness consists of three line segments. Two of the six line segments are in the medium and the middle line segment is in air. The optical thickness along the reference line can be determined by simply adding the geometric line segment multiplied by its refractive index. If the inner paired refractive surfaces of the lower element in Figure 4 are refolded by a polynomial or more generally an analytic function, the geometry along the same reference vein What should be selected by adding the products of the theoretical line segments and their respective refractive indices is the equation of i and te for the basic refractive device in which both elements are rotating bodies around the optical axis OA. This optical thickness is calculated analytically as a function. If the medium of both elements is the same, and if for convenience the outer surface is plane, then the line segment in the air, i.e. the central line segment, is the fundamental rotational refraction when the polynomial form is used. It can be seen that the element must have the same geometrical length as if it were used. The position of this line segment in air along the reference line moves, but as the thickness along the reference line increases for one element, it increases by decreasing the thickness for the other element. canceled out. Therefore, the total optical thickness along the reference line is the value for the elementary refractor to be simulated and the value for the elementary refractor to be simulated in principle at position 1, i.e. in the unrotated position. There is no difference between a converted polynomial device or an analytic function device. The most important point in the whole procedure is this translation in two directions of the central air purity at arbitrarily given values of i and te between the original rotating refractive element and the simulated polynomial device. It is movement. In fact, it is this flexibility of the i-position of the air line segment that makes it possible and useful to be represented by a polynomial device. Once the analytical function formula that accurately simulates the radial distance from the optical axis OA is known, stiffness is monovalent for a rotating device, and bivalent f and te for a polynomial device. However, it will be readily seen that relatively small aberrations that affect the optical properties only slightly are transferred to the polynomial device. In the present case, the basic refractor already has a constant residual imaging error and distortion error Z over the range of aperture, 4M field and spectral range. Similarly, the simulated polynomial device introduces even smaller errors or aberrations due to the inevitable and inherent movement along the oligocentric axis of the arbitrarily quadrupled air section from its original and possibly best position. be done. However, if this air space is small, such as when adjacent surfaces are very close together, the new aberrations will also be small;
Its main effect is to shift the tip laterally. There is also a prismatic variation along any ray due to the difference in slope at the intersection compared to the slope of the elementary refractive surface to be simulated, resulting in a relatively small refractive error. This aberration to be added in a polynomial device, i.e., a simulator, is relatively small for objectives with normal apertures, fields of view, and spectral ranges, such as in handheld cameras, and is It is only important for equipment where precision is required. Finally, imperfections in the simulation between the analytical function expression representing the deformed surface and the rotating refractive surface of the base device to be simulated result in small aberrations that add up. This incompleteness of the simulation is mainly caused by terminating the series in the middle. The second step started above is an algebraic calculation in which the total optical thickness of the refractor is expressed as a power series of x and y. That is, in the rotationally symmetric system of the basic refracting device, all variables are expanded into a power series containing up to a certain order (X2+72). A commonly used series formula, for a single rotationally symmetric refractive surface, is of the form: where C is the apex curvature of a particular refractive surface and β is the first non-conic coefficient. The quantity e2 is the square of the eccentricity for a particular cone. In the case of a spherical surface, both e2 and β are zero. The above equation can be further expanded into a Taylor series as follows. If we use the subscripts 1 and (i+1)'Y to designate the refractive surface Y that is immediately adjacent to the basic device, then the geometric length of the line segment in air along the reference axis 6
(see figure) is simply the difference between two such power series, and is expressed in the following form. (H1+x+ Hl) (X”+72) + −=where H is also the same for (i+1). On the other hand, the polynomial surface is defined as First, the following form is given: The length of a target line segment in air can be written as the simple difference in binary values for two very adjacent surfaces plus the on-axis spacing distance.The offset axis of rotation for the moving element is the optical axis. In the special case taken parallel to oA,
cos ψ −ai=rψ x = r s
Use the relational expression of inψ stiffness and set it from the equidominance of the power series! ,7. Z all 7. It can be seen that there is the following relationship between Z, Te, and i space. These relational expressions are the power series for the rotating refractive element,
It can be used to redefine a general power series for a polynomial surface by transforming it into polynomial space. As long as we are not dealing with the shapes of individual surfaces, but only their differences, in fact, in the simplest case, we only deal with the geometric length of the line segment in the air, Y, so we can fold the power series to the top side. Therefore, you can put
All previously unknown coefficients can be calculated sequentially. At this point, certain terms can be omitted, or at least ignored. This is because they are always zero as long as the equivalent terms of the transformed series for the rotationally refractive surface remain essentially zero. There are also other terms that are not directly important. It is a term in which the geometric length of a line segment in air remains the same no matter what value is assigned to it. These terms are those that have only the constant term A100 and those that have only the power of Te and which can be affected by the rotational change described by Te. Therefore, they will be zero when calculating the difference. Such terms can be assigned the value 7 of zero and are therefore eliminated. However, by assigning a finite value to such a term and proceeding in accordance with the method used,
It can be constructed more easily than polynomial surfaces. More importantly, these terms can be used in later optimization operations using Congenitan to improve the properties.
This is something that can be reintroduced. That is, the procedure used above is made easier by using a reference rM taken parallel to the optical axis OA. The strict optical situation is complicated. When optimization operations are performed correctly,
Non-zero values for these special terms of Te or powers of Te,
That is, any remaining improvements in aperture, field of view, and spectrum will be taken into account, with the exception of using a finite value. In the case of parallelism, the following relational expression can be changed by the above procedure. Aloo = 0 (or other possible value) A1□
. −〇Aio1=0 (or other possible value) personi2o
= -2(01+1-01)A1□1=0 For example -ΔAio2 Aio, 3=0 (or other possible value) A1□
t = −2(Hlax −Hl) A1□3; O A1゜4 = −(H1+1− T11) (for convenience) ten specifiable values, e.g. ΔA1o4 ALos = 0 (or other specified value) A1+
1. oo = 0 (or other specified value = Aio
o) Ai+x, ]o = O Ai+x, ol= 0 (or other specified value =
Ai, 01) Ai+1.20 = O Ai+1. ll =O A4+1.02=0+specified value=ΔA10PAi+
1.21 ” O Ai+1.Q3= 0+specified value=Ai03A1+
1・40°O Ai+1.2□=0 '1+1. xs = O Ai + bo4 = 0 + specified value = ΔA1G4A1+
1+41=0 Ai+x,,s=O Ai+1.05=0+specified value=Aios From these equations and from the conversion formula given above, ! ,,
? , a power series in m-space can be transferred to polar coordinate representation in r and phi (ψ). The poles outside the polylinear system indicated by the reciprocal term of (a + Te) and the transformation term of the inverse power term of (a + Te), the coefficients in the polar coordinate system of r and 7 eye no longer contain poles. It disappears in this way. In fact, the polar coordinate representation is no longer a complete power series, but equivalently represents, at least over the order of the power series adopted, the same shape of the surface as was previously obtained from the analytic numerical numbers with i and te. There is no loss of precision when converting to polar coordinates, which is no longer present in curved Cartesian coordinates. Expressed in polar coordinates, it is as follows. A similar formula holds true for 1+1K. If we look at the results of the formulas related to AK, we will see that a variable amount (a+te) appears in the denominator of various powers for many coefficients. The variable nature of such a term with respect to te invalidates the nature of the power series in its usual representation. In this case, such a reciprocal term t can be expanded into another power series, and the series can be manipulated by a new enlarged coefficient or adjustment, such as λ. The coefficient is erotic. Its convergence is slow. Therefore, the situation will remain that the polar coordinate representation is somewhat more precise than a recalibrated power series truncated at an appropriate level. This contradiction will reappear when performing an optimization in the s7a2 system and then back to the l-1i, Te,i, or polar coordinate systems. The conversion operation will yield the best result, where no poles will be included in the representation of the optimal functional form in polar coordinates, and will be precise according to the number of terms used.For polynomial surfaces i, power series of te-1: xmym2
It can also be converted to a similar power series in space. This is usually what computers do.
s 7 e ” space. In this case, X, 7.Z
In order for the result in the system to be a correct power series with a constant coefficient of variation By, it may be necessary to expand the reciprocal of (a+de) in advance. In the case of parallel and offset axes, it is expressed by the following equation within a fourth-order precision. zi = Bi30"+311g"7"+B151x37
+B113X73+ −-・=B11s = −((0
'l+1- ('i+x) -CC'i-01)]
-:= a θ (C'i -01)) a2°. In these equations, the factor 1/6 appears at all points. j is the rotation angle of the rotating element about the off-axis. For convenience, if other terms containing t appear, such as f) is small, then the contribution by higher order terms will be small, or will be partially canceled out by computer optimization.In any case, if only the tide term is left, then in the denominator The appearance of 〃 means that the designer can use small values of i, thereby defining relatively strongly deformed polynomial surfaces, or large values of θ for weakly deformed surfaces. χ means that χ can be used. In this latter case, the higher-order terms of the powers of i will make a larger contribution, so the property χ will be dangerous. We would like to emphasize that the 7 i are in the same polar coordinate system. The phi used above is the polar coordinate variable used to define the actual resting shape of the deformed surface in polar coordinates. On the other hand, i is 6 is the angular displacement of a predetermined deformed form for the movable or rotating element.6 is the characteristic of the basic device for a specified average object distance with other distance, preferably a special value of σ that transforms to infinity. In the above equation between the coefficients, the values of C and H are also required for at least one out-of-range inverse object distance that differs from the average distance. These values are calculated for a rotationally symmetric refractor at a second distance chosen relative to the object plane, which may conveniently be assumed to be infinite. However, in practice: The target values of C and H meet to be calculated for at least four object distances.These four
One of the two object distances is infinite. Such a value of H (in this calculation, if 02=1 for convenience, the value of β) is plotted against C. In the most common case, it will be a parabola, as shown in FIG. On the other hand, a straight line is actually preferred. In this case, a straight line should be drawn across this parabola so that the properties at the two selected distances are as favorable as possible. At this time, the target value along this tilted straight line is used in the calculation of the equation, but if infinity is used, this target value is the recalculated H (or β) for this infinity. It is. Depending on the required degree of properties, further steps can be carried out by means of a computer optimization operation, if necessary. During this operation, an array of image points must be acquired throughout the field of view, unless the two images are the same. And the rotational relationships of normal devices are suppressed. There is also a variation in the non-verbal eyes. There are two patterns in caliber and field of view compared to the requirement of a purely rotating device, and generally speaking, very long computer operations will be required. Therefore, the optimization is usually sufficient if performed at the average wavelength with an accuracy that is considered adequate. In optical devices where the highest properties are required, it is known in advance to be zero, either for reasons of convenience or because it is inherently zero in rotating devices, but this is no longer the case in modified devices. It is desirable to reintroduce all terms Z. The reintroduced stiff leaves are also included in ΔA1°k. In fact, we can use every possible term in the matrix of X, 7, but
Many terms will be small in magnitude. In this case, the computer may be overburdened. The final step is to transfer the fully computer-optimized form to polar coordinates in the ``17'' space. During this final transformation, we introduce a reasonable number of terms YN, but the inaccuracies due to the non-exact series representation are eliminated. The correct transformation formula must be used for each point to avoid reintroducing the The required effective aperture of the movable surface is clearly indicated.The variable part Y of the rotationally symmetrical refractor is simulated by one or more analytical function elements rotatable about a common rotational fulcrum. The essential form required for each analytic function surface of the invention is given in the x.y,z coordinate system as follows: where K1 is a specifiable constant, and If the rotationally symmetric device to be simulated has rotationally symmetric aspherical surfaces, then the essential form of each analytic function defining the simulated surface Y is as follows: where Kl t Kl + K3 + K4 is a constant to be determined, and 5 = 2 K4 + (residual value set as zero for convenience). From the above considerations, a number of optical devices have been designed. Among these devices Some of the contents of the invention will be described as illustrative examples.The first three examples are!,7
．． 'Z coordinate system, but the latter five examples are shown in the "+7+" coordinate system. Both embodiments are suitable for use as variable focus photographic objectives, with a focal length of 1251! It is scaled for use in 1, has a speed of f/10, and has a total viewing angle range of 50 degrees, measured diagonally across the format. However, before describing these embodiments in detail, the symbols used will be explained. The symbol f,1 usually indicates the equivalent focal length of the optical device,
This focal length is at the wavelength (L (587,6 nm)) and is determined by a paraxial ray for an object at infinity. (In the case of the device, f and f in Gauss optics are equal.) Therefore, fd is the equivalent focal length for the d-ray, that is, KFL (equivalent focal length).
length). If the mean object plane is at some specified finite distance, then the symbol t6y, which becomes the "scale focal length", or more precisely the "scale factor" is adopted. If this specified object distance is infinite, then fd and Fd will be equal in the first case and mean the same thing, i.e. apply to a scale focal length or an object at infinity. FtFL ya-
means. It can also be adapted to have a distortion over the average part of the field of view (with focal length calibrated for objects at infinity) by the amount fd as a scale factor. Even if the symbol fd is applied for a specified average object distance, the optical device will also have the normal fd of the optical system. In this case, for numerical purposes, the object plane is temporarily moved to infinity. For the form of focusing carried out here, fd is used for a fixed and specified position of the image plane, and fd for the associated but ever-varying apparatus is such that it obtains h
As long as the
The meanings of all coefficients have already been explained herein and will not be repeated. all prices jd
standardized against. The first embodiment is a pair of analytic function elements used in combination with an objective as shown in FIG. The table of its structural data is as follows. When the element ■ is laterally rotated by an angle θ around the shifted point to refocus at infinite object distance, rd = 0.9983 ((1, "K kept constant)
It can be seen that it is. The coefficients of rotationally symmetric surfaces are as follows. Beta2 = 1.754X10' Beta. =
-1,528X 101 is 2 = 7-[331X
I Q-3 Gamma 4 = -2,862X 10-2 Delta p = -1,750X10-7 Delta 4 = -4,
491X 10-'Element whose back surface is a polynomial surface■
is fixed (not rotationally symmetric). Element (2), whose front surface is a polynomial surface, is centered at a specified offset point and rotates around a laterally offset axis parallel to the optical axis. The coefficients for surfaces that are not rotationally symmetric are as follows. do do l turtle do l＞
IQ! t l 1 false? ?
? +rrr! × × ×
× × × ×口IIIIIIIIIIII
IIIIIIIIIIIIIIIFr F
P? +r? ? ? r? r W r v-W
f××××× ×××XX××××××× Here, the prime (′) is A with two parts as before.
It is used to distinguish the term Y. The second embodiment is a pair of analytic function elements used in combination with three elements, as shown in FIG. The structural data is as follows. It can be seen that by rotating the element (2) laterally by an angle θ around the shifted point, the time to refocus for an infinite object distance is 〒 =0.9987 (dF is kept constant). The coefficients for rotationally symmetric surfaces are the following formula: ××× II II ll ××× II II II
Rotates around a specified offset point and around an axis parallel to the optical axis and laterally offset. The coefficients of a non-rotationally symmetric surface are given as: A620: OA'FO20=0 A602"OA'FO2=0 A630=4.519X10-2/4
Avso=4.519X10-”/I VA621:
': Omufu2180A612=1.356X10-1/2F), Tsu12=1.356X10-''/IIA'640:0
M1F40: 0Ae4
Q"OAW40" 0 Muro31=-4-519X10-2/? F
A? 31shi 4.519X10-2/! i5622”'O
A〒22=0 Muro04"OA704"" O A'65g"--2,259X10-3/l A'
? 50"<2.259X10-3/?A650=-3,
234X10-1/! F A7so=-3,234
x10-1/Fmu'641: OA'〒4180 A6 No. 18゛ 0
Muff 41: 0'5sa=-1,078x10'/y
Mufu 5z = -1,078x100/11 Muro zs = OAIFss = 0 Muro z 4 = -1-617x100/y Ay1
4=-1,617x10'/y where prime (')
is used to distinguish an A term that has two parts, as before. Example S, which is the last example in the quantity, Te, - system, consists of a pair of analytic function elements combined with triplet elements, as shown in FIG. It is. The structural data is as follows: When the 0 element ■ rotates laterally around a point shifted by an angle θ and refocuses at an infinite object distance, ? , = 0.9996 (d8 is kept constant). The coefficients of rotationally symmetric surfaces are as follows: 0II II
II I+ λ The element ■ whose back surface is a polynomial surface is fixed (not rotationally symmetric) 0 The element ■ whose front surface is a polynomial surface is
Rotates around a specified offset point and a laterally offset axis parallel to the optical axis. The coefficients of a non-rotationally symmetric surface are as follows. A4to= OAl520:0 A402”0 Mu302=OA43゜=
4.739x10″″2/iF A,. = 4.
739x10-"/FA421"" OAsa1= 0 A412= 1.422x10""l/# A, 0
．． = 1.422x10″″1/imu’44G” OA
'+540=:0 A440= 0.743x10' As4o=
0n431=-4,739x10-”/?F A,
531=-4,739x10-2/4A4□2=1.
487X10' A322= 0A404= 0
．． 743X10'A304=0A'. Ko2
．． 370x10-'force A16. . =-2,370X1
0-'/4mm4,5゜==-1,487x10-"/a
l A350=-1,487X10-"/!l'mu'441"'OA'l541=OA,41=-1,487X10'mu541=0
*, 52=-4,955x10-"/?F as
z=-4,955X10-1/? A423>1.487
x10' Ai5,3=0A414=-7,4
33X10-1/ff Aa14=-7,433x
10-1/iF where the % prime (') is used to distinguish the two-part A term as before. The following three examples are all shown in the X r 7 + Z coordinate system (the rotational fulcrum is on the +X axis λ). They are a pair of analytical function elements combined with two other elements.If these three examples are referred to as a fourth example, a fifth example, and a sixth example, their non-rotationally symmetric surfaces Although the values of the coefficients are different from each other, the basic device is otherwise the same, and its structural data is as follows: is an important polynomial surface and the values of its coefficients must be specified.0 The values of the coefficients of the non-rotationally symmetric surfaces for surfaces 4 and 5 of the fourth embodiment having the basic device described above are as follows. There is 0 xxx xxxx xxxxx xxxx
xxxxxxxxxxxx xxxxxxxxx xx
xxxII II II II II II II
II II II II II II II
II lj II II It II
II 11xxxxxxxxx
xII II II II II II II
II II II II II II II
II II 11 Yen IQ Both Yen Yen Yen Yen Yen Yen Both Yen Both Yen Yen Yen Yen In this example, when the offset distance of the rotating element ■ is 14.5 (0,570 inches), it is approximately 64 α (approximately 25 inches) from infinity. ). The values of the coefficients of the non-rotationally symmetrical surface for the fifth embodiment are as follows. xxx xxxx xxxxxx xxxx
xx Ning Yamauchi - Uchiuchi Heiyama Heihei Uchiuchi Yamauchi x
xxxxxxx xxxxxx Rorororororororororororo 1I II II II II II I
I II II II II II XXX
xxxx II II II II II II 1
Using these values for the first surface 4 and the surface 5, the ninth
According to the basic device shown in the figure, for a displacement of about 50° along the arc between the center points of the rotatable element aperture and a point distance of 15 m (0,6 in), from the distance about 66 cm (about 26 in) It is possible to focus up to The values of the coefficients of the non-rotationally symmetric surfaces for the six embodiments shown again in FIG. 9 and having the basic arrangement described above are constant. xxx xxxx xxxxxxxxxx
xxxxxxxxx xxxxxxII II
II II II II II II II
II II II II II II II
II II II II
xxxxxx II II II II II II
II II II II II It I
This device is also capable of focusing up to approximately 66 cm (26 inches), but its rotation point distance is 25 van
(1,0 inch) 0 The case in which all three elements are Zolexiglass devices is shown in Figure 10 0 Its structural data is the following system 0 The coefficients of rotationally symmetric surfaces are the following system It is. Beta, = 1.928 x 101 gamma 2
= 1.018 x 10” delta 2 =
1.191 x 10' Ezocilone a = 1.
When optimization is performed over the entire 258 x 10' plane 3, surface 4, and surface 5, surface 3 can also be a polynomial surface. It should be noted that the surface 5 includes as a basic device an implicit refractive ring and a corrective rotationally symmetric aspherical term. Both of these are later replaced by polynomial coefficients given to the first order and included therein. xx xxx xxxxx xxxxxx
xxxxxxxxxx xxx xxxx xxx
x'x xxxxxxxX
X X X X X X X X
X X XXXXXXXXXI II II
II ++ ・++ n ++ '++
++ i++ ++ ++ n ++ ＋
+ n n ++ n ++ ++xxxxxxxxx
xxxxxx 4xxxxxxxxxxxxxx II I
I On II If II II II
II:In II II 11111110
1111111 As the last embodiment, that is, the eighth embodiment. FIG. 11 shows an objective device capable of focusing four elements. This device uses a pair of glass elements in place of the front Plexiglas element of the seventh embodiment to provide improved correction for chromatic aberrations. The structural data of this device is as follows. ::l--th ≧ -ni-ni%-191I-
The Niduichi rotationally symmetric surface coefficient is as follows. Beta, = 1.508 x 101 gamma number = 1.363 x 101 delta,
= 1.030 x 10' Ezocilone a =
1.046 x 10' Surfaces 6 and 7 are polynomial surfaces. However, when optimization is performed over the entire surface 5, surface 6, and surface 7, it is possible to use the surface 5 as a polynomial surface. It should be noted that the surface 7 contains as a basic device an implicit refractive ring and a corrective rotationally symmetric aspherical term. Both of these are later replaced by nine polynomial coefficients given as first order and included among them. xx xxx xxx, x xxxxx xx
xxxxxxx xxx xxxx xxxxxx
XXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXII II II II
II II II II II II II II II
II II II It II II II
II' II II II 11xxxxxxxx
XXXXXXXXXXXXXXXXXII I
I II II II II it II I White I
II II II II II II II II II
II II' II II II II II It is obviously possible to make other dimensions of the embodiment described. In this case, it is necessary to re-determine the numerical value for one new physical dimension. In the simplest application, when all numbers are given in physical lengths, such as inches or millimeters, changing other dimensional scales can change dimensions such as radius, spacing distance, or clear aperture. It simply means multiplying the represented quantity by a constant factor. However, there are nonlinear quantities such as the aspheric coefficients beta, gamma, delta, etc. Reciprocal quantities, such as curvature, must be scaled in the opposite direction. Furthermore, if we change the length of one unit to the length of another unit, e.g. of one device? If 4 were to be converted to another value in another device, the rescaling required in that case would become more complex. However, by converting the two devices through the English scale or metric scale as an intermediate,
You can always check. ? ,=1.250″From a device with Ik?,=1.000
Assume that you want to convert to a device with . All you need to do is divide all dimensions by 1.250, t or 0.
Multiply by 800. K like this, and
=1.250/1.250 was requested? d=1.00
becomes 0. For example, if R1 = 2.500, then R4 = 2.000 in a rescaled device. That is, immediately K R1 = 2.50 x O, 800 = 2.
000 ◇ Beta has a scale of 3, gamma has a scale of 5, and delta has a scale of 7, but they are inverse powers. That is, in the above example, beta is (0,800)3, gamma is (0,800)s,
fkll is c O, 800) 7! It will be clear to those skilled in the art that there are no modifications to the embodiments described above within the scope of the present invention.
In the design of any optical device used, it is desirable to have at least one pair of immediately adjacent but opposing refractive surfaces of the preferred analytic function shape on the surface of each immediately adjacent lens element. Must. Then, at least one of the pair of elements rotates around a rotation fulcrum that is offset by a specified distance from the optical axis. Therefore, it rotates laterally about one axis parallel to the optical axis. Any such rotating element has a plane surface outside its area, and the refractive effect of this transverse plane, Kl!, is caused by a transverse rotation about offset parallel axes. It does not cause any appreciable change, or in special cases,
The action of an analytic function surface can be distributed from any one surface to both surfaces of the element. Conversely, if one of the pair of elements remains fixed and all imaging effects are obtained by lateral rotation of the other element's offset axis, then the outer surface of the fixed element is It can be designed identically to the other extra-regional refractive indexes or refractive elements of this optical device and can therefore have advantageous rotationally symmetrical refractive and aspherical powers. In special cases, the work of a fixed analytic function surface can be distributed over the two surfaces of the element. In this case, the action of the analytic function surface arranged in ttc4 is as follows. It is superimposed on the fundamental refractive power and the aspherical force of the outer surface of the fixed element. The reverse is also done. In the most general case, both elements of a pair are rotated individually about their respective offset rotational supports and offset parallel axes. The rotations may be rotations of the same magnitude but in opposite directions, or, if necessary, proportional rotations in the same or opposite directions, in selected embodiments of significant changes. % or nonlinear in the same or opposite direction if controllable 2
It can also be a heavy rotation. Therefore, all elements that rotate laterally in this way either rotate into their own plane and have an extraterrestrial plane that has no optical effect, or the function of each analytic function surface distributed on each surface t - Must have 0 [Effect of the invention] Therefore, if the correct parameters are selected for the adjacent analytic function surfaces, it can be used with sufficient precision and mathematical The refractive action of a rotationally symmetrical refractive lens can be controlled. Also, when necessary, other corrections, usually performed by using rotationally symmetric aspherical terms on one or more immediately fixed rotationally symmetric surfaces, can be applied to surfaces acting in concert. It has also been shown that it can be incorporated into the calculation of analytical functions that determine the shape of the fixed surface. That is, if we are dealing with two analytical refractive surfaces that are already aspheric in the broad sense, there is no need to use one or more other nearby rotationally symmetric aspheric surfaces. This fixed analytic function can be combined with a fixed pair of analytic surface pairs that are different from each other for that purpose. Therefore, this fixed analytic function is
It has superimposed rotationally symmetric refractive and aspherical powers that are not distributed by the shape of the analytic function of the moving or rotating opposing surfaces. Accordingly, all content disclosed in the foregoing description and all matter shown in the accompanying drawings is intended to be illustrative only and should not be construed as limiting.

[Brief explanation of drawings]

Fig. 1 is a schematic perspective view showing the overall characteristics of the optical element of the present invention, Fig. 2 is a schematic perspective view of a pair of optical elements of the present invention, and Fig. 3 shows a novel surface of the optical element of the present invention. FIG. 4 is a perspective view of the coordinate system used for the explanation, showing the element pair of the present invention on the upper side and the rotationally symmetrical refractive element pair simulated by the element pair of the present invention on the lower side. 5 is a schematic diagram of a graph of related parameters of a certain device, and FIGS. 6 to 11 are schematic sectional views of an optical device implementing the present invention. [Explanation of reference symbols] 20.22 Optical element 16 First surface 18 Second aspheric surface RA Rotation axis OA Optical axis

Claims (38)

[Claims] (1) An optical component having a shape expressed by an analytical function having at least one transparent element arranged along an optical axis, the element having a predetermined shape that is at least a portion of a rotating surface. on one side, and a second aspherical surface that is non-rotationally symmetric and mathematically described by a preselected polynomial having a non-zero term of at least fourth order. the first surface of the element such that the element can be displaced generally laterally relative to the optical axis by rotation of the element about an axis of rotation different from the optical axis; and the second surface of the element is configured such that when the element moves relative to the optical axis, the second surface of the element causes a continuous change in an optical property of the component. and, while the first surface of the element remains optically unchanged when the element is moved relative to the optical axis and does not have any effect on the optical properties of the component. An optical component that has a shape expressed by a function. (2) The optical component according to claim 1, which has a shape expressed by an analytical function in which the first surface is a plane. (3) The optical component according to claim 1, wherein the rotation axis is parallel to the optical axis but has a shape expressed by an analytical function at a different position. (4) In claim 1, the polynomial describing the second surface is a constant that can be specified by K_1 in Cartesian coordinates, K_2=-(1/3a)K_1, K_3=-(1/a )
As K_1, z=K_1(xy^2+(1/3)x^3)-K_2x
An optical component having a shape expressed by an analytical function expressed as ^3y+K_3xy^3. (5) In claim 1, the polynomial describing the second surface is K_1, K_2 in Cartesian coordinates,
Let K_3 and K_4 be constants that can be specified, and K_5-2
K_4 plus the residual value, which is conveniently set as zero, z = K_1(xy^2+(1/3)x^3)-K_2x
^3y+K_3xy^3+K_4x^4+K_5x^2
An optical component having a shape expressed by an analytical function expressed as y^2. (6) at least one arranged vertically along the optical axis;
An optical component having a shape described by an analytic function having a pair of transparent elements, the elements having a first surface having a predetermined shape, which is at least a portion of a rotating surface, on one side. and having on the other side a second aspherical surface that is rotationally symmetric and mathematically described by a preselected polynomial having non-zero terms of order at least fourth; or both are different from the optical axis 1
The first surface and the second surface of the element are configured such that the element can be displaced generally laterally relative to each other by rotation about one or more axes of rotation, wherein the element The second surface of the element imparts a continuous change to an optical property of the component when moving relative to the element, while the first surface of the element causes a continuous change in an optical property of the component when the element moves relatively. 1. An optical component having a shape expressed by an analytic function that remains unchanged and does not affect the optical properties of said component in any way. (7) The optical component according to claim 6, which has a shape expressed by an analytical function in which the first surface is a plane. (8) The optical component according to claim 6, wherein one or more of the rotation axes are parallel to the optical axis but have a shape expressed by an analytic function at different positions. (9) In claim 6, the polynomial describing the second surface is a constant that can be specified by K_1 in Cartesian coordinates, K_2=-(1/3a)K_1, K_3=-(1/a)
As K_1, z=K_1(xy^2+(1/3)x^3)-K_2x
An optical component having a shape expressed by an analytical function expressed as ^3y+K_3xy^3. (10) In claim 6, the polynomial describing the second surface is K_1, K_2 in Cartesian coordinates.
, K_3 and K_4 are constants that can be specified, and K_5=
2K_4 plus the residual value, which is conveniently set as zero, z=K_1(xy^2+(1/3)x^3)-K_2x
^3y+K_3xy^3+K_4x^4+K_5x^2
An optical component having a shape expressed by an analytical function expressed as y^2. (11) An optical component having a shape expressed by an analytical function including a plurality of transparent elements arranged vertically along the optical axis, the outer side of the outer element among the elements being each of the facing sides having a predetermined shaped surface that is at least a portion of the rotating surface, while the facing sides of the outer element and the opposing sides of the remaining elements of the elements one or more of said elements each having an aspherical surface that is non-rotationally symmetric and mathematically described by a preselected polynomial having non-zero terms of order at least fourth; the surface of the element is configured such that the element can be displaced generally laterally relative to the element by rotation about one or more rotational axes different from the optical axis;
The non-rotationally symmetric aspherical surface of the element imparts a continuous change in certain optical properties of the component when the elements move relative to each other, while the An optical component having a shape described by an analytic function in which the outer surface remains optically unchanged and does not have any influence on the optical properties of the component. (12) The optical component according to claim 11, which has a shape expressed by an analytical function in which the first surface is a plane. (13) The optical component according to claim 11, wherein one or more of the rotational axes are parallel to the optical axis but have a shape expressed by an analytic function at different positions. (14) In claim 11, the polynomial describing the second surface is a constant that can be specified by K_1 in Cartesian coordinates, K_2=-(1/3a)K_1, K_3=-(1/a)
As K_1, z=K_1(xy^2+(1/3)x^3)-K_2x
An optical component having a shape expressed by an analytical function expressed as ^3y+K_3xy^3. (15) In claim 11, the polynomial describing the second surface is K_1, K_1 in Cartesian coordinates.
2. Let K_3 and K_4 be constants that can be specified, and K_5
=2K_4 plus z as the residual value, which is conveniently set as zero
=K_1(xy^2+(1/3)x^3)-K_2x^
3y+K_3xy^3+K_4x^4+K_5x^2y
An optical component having a shape expressed by an analytical function expressed by ^2. (16) An optical device comprising an optical component having a shape expressed by an analytical function and having at least one transparent element arranged along an optical axis, the element being at least a portion of a rotating surface. the first with a predetermined shape
a second aspherical surface on one side and a second aspherical surface that is non-rotationally symmetric and mathematically described by a preselected polynomial having a non-zero term of order at least fourth; the first surface of the element and the first surface of the element such that rotation of the element about a rotational axis different from the optical axis causes the element to be displaced generally laterally relative to the optical axis; the second surface is configured, wherein the second surface of the element continuously changes certain optical properties of the optical device as the element moves relative to the optical axis; , while the first surface of the element remains optically unchanged when the element moves relative to the optical axis, and has no effect on the optical properties of the optical device. An optical device equipped with an optical component having a shape represented by . (17) The optical device according to claim 16, wherein the first surface is a flat surface. (18) The optical device according to claim 16, wherein the rotation axis is parallel to the optical axis but at a different position. (19) In claim 16, the polynomial representing the second surface is a Cartesian coordinate, and K_1 is a constant that can be specified, and K_2=-(1/3a)K_1, K_3=-(1/a)
As K_1, z=K_1(xy^2+(1/3)x^3)-K_2x
An optical device represented by ^3y+K_3xy^3. (20) In claim 16, the polynomial representing the second surface is K_1, K_2 in Cartesian coordinates.
, K_3 and K_4 are constants that can be specified, and K_3=
2K_4 plus the residual value, which is conveniently set as zero, z=K_1(xy^2+(1/3)x^3)-K_2x
^3y+K_3xy^3+K_4x^4+K_5x^2
Optical device represented by y^2. (21) An optical device including an optical component having a shape expressed by at least one pair of analytic functions arranged vertically along the optical axis, the shape being expressed by the analytic functions. each of the optical components having at least one transparent element disposed along the optical axis, each of the elements having a first surface having a predetermined shape that is at least a portion of a rotating surface; a second aspheric surface on the other surface which is non-rotationally symmetric and mathematically described by a preselected polynomial having non-zero terms of order at least fourth; said elements such that said elements can be generally laterally displaced relative to each other by rotation of one or both of the elements about one or more rotational axes different from said optical axis; wherein the first surface and the second surface of the
The second surface of the element continuously changes certain optical properties of the optical device when the elements move relative to each other, while the second surface of the element continuously changes certain optical properties of the optical device when the elements move relative to each other. 1. An optical device comprising an optical component having a shape described by at least one pair of analytic functions, one surface of which remains optically unchanged and has no influence on the optical properties of said optical device. (22) The optical device according to claim 21, wherein the first surface is a flat surface. (23) The optical device according to claim 21, wherein one or more of the rotational axes are parallel to the optical axis but at different positions. (24) In claim 21, the polynomial representing the second surface is a constant that can be specified by K_1 in Cartesian coordinates, K_2-(1/3a)K_1, K_3=-(1/a)K
As _1, z=K_1(xy^2+(1/3)x^3)-K_2x
An optical device represented by ^3y+K_3xy^3. (25) In claim 21, the polynomial representing the second surface is K_1=K_2 in Cartesian coordinates.
, K_3 and K_4 are constants that can be specified, and K_5−
2K_4 plus the residual value, which is conveniently set as zero, z=K_1(xy^2+(1/3)x^3)-K_2x
^3y+K_3xy^3+K_4x^4+K_5x^2
Optical device represented by y^2. (26) In claim 21, the optical device includes at least one optical device disposed along the optical axis and disposed in front of the pair of optical components having a shape expressed by an analytic function. An optical device having a positive concave and convex lens element. (27) In claim 21, the optical device includes one optical device disposed along the optical axis and in front of the pair of optical components having a shape expressed by an analytic function. An optical device having a glass concave and convex lens element. (28) The optical device according to claim 21, wherein all optical components having shapes expressed by the analytical functions are made of one material. (29) The optical device according to claim 28, wherein the one material is an optical plastic. (30) An optical device comprising an optical component having a shape expressed by an analytical function including a plurality of transparent elements arranged vertically along the optical axis, the outer side of the elements being each of the outwardly facing sides of the elements has a predetermined shaped surface that is at least a portion of the rotating surface, while the inwardly facing sides of said outer element and the remaining elements of said elements Each of the opposing sides has an aspheric surface that is not rotationally symmetric and is mathematically described by a preselected polynomial having non-zero terms of order at least 4; the surface of the element is configured such that rotation of the element about one or more rotational axes different from the optical axis causes a relative generally lateral displacement of the element; the non-rotationally symmetric aspherical surface of the element imparts a continuous change to certain optical properties of the optical device when the element moves relative to each other; , an optical device in which the outer surface of the outer element remains optically unchanged and does not have any effect on the optical properties of the optical device. (31) The optical device according to claim 30, wherein the first surface is a flat surface. (32) The optical device according to claim 30, wherein one or more of the rotational axes are parallel to the optical axis but at different positions. (33) In claim 30, the polynomial representing the second surface is a constant that can be specified by K_1 in Cartesian coordinates, K_2=-(1/3a)-K_1, K_3=-(1/a
)K_1 as z=K_1(xy^2+(1/3)-x^3)-K_2
An optical device represented by x^3y+K_3y+K_3xy^3. (34) In claim 30, the polynomial representing the second surface is K_1, K_2 in Cartesian coordinates.
, K_3 and K_4 are constants that can be specified, and K_5=
2K_4 plus the residual value, which is conveniently set as zero, z=K_1(xy^2+(1/3)x^3)-K_2x
^3y+K_3xy^3+K_4x^4+K_5x^2
Optical device represented by y^2. (35) An optical component having a shape expressed by an analytical function including a plurality of transparent elements arranged vertically along the optical axis, wherein one of the outer elements of the elements is 1
the outwardly facing sides of one element having a predetermined shaped surface which is at least a portion of the rotating surface, while the outwardly facing sides of the remaining outer elements and the inwardly facing sides of these said outer elements; each of the side surfaces and the opposing side surfaces of the remaining elements of the elements has an aspherical surface that is non-rotationally symmetric and mathematically described by a preselected polynomial having a non-zero term of at least fourth order; , such that rotation of one or more of the elements about one or more rotational axes that are different from the optical axis allows the elements to be displaced generally laterally relative to each other. The surfaces of the elements are configured such that when the elements move relative to each other the non-rotationally symmetric aspherical surfaces of the elements impart a continuous change in certain optical properties of the parts; When the elements move relative to each other, the above 1
An optical component having a shape described by an analytic function in which said outer surfaces of two outer elements remain optically unchanged and have no influence on the optical properties of said component. (36) The optical component according to claim 35, which has a shape expressed by an analytical function in which the first surface is a plane. (37) In claim 35, the polynomial representing the second surface is a constant that can be specified by K_1 in Cartesian coordinates, K_2=-(1/3a)K_1, K_3=-(1/a)
As K_1, z=K_1(xy^2+(1/3)x^3)-K_2x
An optical component having a shape expressed by an analytical function expressed as ^3y+K_3xy^3. (38) In claim 35, the polynomial representing the second surface is in Cartesian coordinates, K_1, K_
2. Let K_3 and K_4 be constants that can be specified, and K_5
=2K_4 plus z as the residual value, which is conveniently set as zero
=K_1(xy^2+(1/3)x^3)-K_2x^
3y+K_3xy^3+K_4x^4+K_5x^2y
An optical component having a shape expressed by an analytical function expressed by ^2.