CN109932764B

CN109932764B - Function curved lens capable of accurately focusing

Info

Publication number: CN109932764B
Application number: CN201811072337.8A
Authority: CN
Inventors: 杨兆强
Original assignee: Individual
Current assignee: Individual
Priority date: 2018-09-03
Filing date: 2018-09-03
Publication date: 2021-11-02
Anticipated expiration: 2038-09-03
Also published as: CN109932764A

Abstract

A function curved lens capable of accurately focusing regular light beams belongs to one of aspheric lenses, and is divided into an A type B type and an AA type according to different incident light beam conditions. The absolute value of the tangent slope of any point on the refraction curved surface of the function curved surface lens can be calculated by a YZQ tangent formula, and the coordinate values of a series of points on the refraction curved surface of the function curved surface lens can be calculated by a differential link calculation method or a differential solution equation calculation method. The functional curved lens can also be manufactured into a Fresnel lens form, and the focusing precision is not influenced. Since the functional curved lens has high focusing accuracy, it can be used to manufacture optical instruments with high accuracy or solar condenser lenses in the form of Fresnel lenses.

Description

Function curved lens capable of accurately focusing

Technical Field

The invention relates to a novel aspheric lens which can accurately focus a regular light beam.

Background

A spherical lens having a plane surface on one side is called a "plano-convex spherical lens", and the lens of the present invention is hereinafter referred to simply as "the present lens".

The accuracy of the lens focus is directly affected by the performance of the lens in some cases, for example, the lens is used in the case of focusing laser light. The plano-convex spherical lens has a lower focusing accuracy when focusing a parallel light beam than the present lens, and the present lens has a higher focusing accuracy, which can be demonstrated from two points.

One is to make a comparison in terms of the accuracy of the lens focal length calculation formula. In the chapter of geometric optics in university physics textbooks, the calculation formula for deriving the focal length of a single plano-convex spherical lens is conditionally limited, where one of the conditions is that the incident light is "paraxial light", and the term "paraxial light" refers to: the height h from the light refraction point to the optical axis (central axis of the lens) is very low, h/r when the light is refracted is very small, wherein r refers to the spherical radius of the spherical lens, and h corresponds to the lens radius. In the geometric optics theory, a parallel light beam is regarded as a beam emitted from an object point at infinity, and a calculation formula of an image space focal length is derived on the condition that the beam is taken as one of the beams. When the condition of paraxial rays cannot be met, uncertainty exists in the focal length calculated by using the deduced calculation formula of the image space focal length of the plano-convex spherical lens. The mathematical analytic formula of the lens for calculating the focal length is not limited by paraxial rays, and the derivation of the mathematical analytic formula of the refraction curved surface of the lens is detailed in the invention content part of the specification. The only constraints are that, over the entire interval transverse to the central axis of the lens: the incident angle of the incident light is smaller than the angle at which total reflection occurs.

Secondly, the computer CAD simulation drawing can be used for proving. The invention relates to a method for drawing a lens refraction ray path diagram by computer CAD drawing software, which is an invention of the inventor and does not come from any data. Because the AutoCAD drawing software is supported by a complex and accurate mathematical system, and the accuracy and correctness of the drawn graph are proved by countless people in various industries, the geometric graph drawn by the CAD is used for reasoning and proving mathematically. When a refraction ray optical path diagram is drawn by using the CAD, an object capturing function in the CAD needs to be opened, and objects such as end points, intersection points, middle points, feet, circle centers, arc tangent points and the like need to be set for capturing and opening, an orthogonal straight line drawing function needs to be started when vertical and horizontal straight lines are drawn, the precision of size measurement needs to be set to be the highest level, namely 8 digits behind decimal points are effective, and drawing is carried out according to the proportion of 1: 1. The sequence and principle for drawing the light path diagram of the refracted rays of the spherical lens are as follows: referring to fig. 11, in the version above AutoCAD drawing software 2004, a spherical radius R0 of a spherical lens is taken as a radius, a semicircle is drawn with a G point as a center of a circle, a horizontal line DJ is drawn through the G point, a vertical straight line GY is drawn through the G point at the center of the semicircle, (drawing the straight lines DJ and GY need to draw a straight line function orthogonal to the CAD), a horizontal line EF is drawn at a proper position on the GY straight line, an incident light HP parallel to the GY straight line is drawn, the HP straight line intersects with the curve of the semicircle at a P point, the G point and the P point are connected to draw a straight line GP, a complete circle is drawn with the P point as a center of a circle and with the R as a radius (R < R0), the circle intersects with the straight line GP at a U point, and a straight line UT perpendicular to the incident light HP is drawn through the U point and intersects with the HP straight line at a T point. Then, the length of a straight line UT is measured by using the dimension marking operation of the CAD tape, the length of the straight line UT is set as X1, then a calculator is used for calculating X1X n X2, n is the relative refractive index of the lens material relative to the light of the air, then the straight line GP is extended to intersect with the other side of the circle with the radius of R and intersect at a point V by using the operation of drawing an extension line in the CAD, a complete circle is drawn with the radius of X2 as the center of the circle, then the tangent line of the circle with the radius of X2 is drawn at a point P and intersects at a point Q, (the tangent line is drawn to be used for the object capturing function of the self-contained automatic capturing tangent point in the CAD tape), and then the straight line PQ is extended to intersect with the straight line EF and intersect at a point L by using the operation of drawing the extension line in the CAD, and the straight line PL is the refracted ray of the spherical lens. The principle is as follows: the straight line GV is the normal of the plano-convex spherical lens at point P, the straight line HP is the incident ray, and the formula of the refractive index according to light is: sin (c)/sin (a) ═ n, (c and a in this formula correspond to angles c and a in fig. 11), if this can be demonstrated: sin (c)/sin (a), where PL is the refracted ray. See fig. 11.

And (3) proving that: because sin (c)/sin (a) (X2/R)/(X1/R) ═ X2/X1, and because: x2 ═ X1X n,

therefore: since X2/X1 is n, sin (c)/sin (a) is n, straight line PL is a refracted ray.

According to the drawing method, a plurality of refraction rays of the spherical lens when the incident ray is a parallel light beam can be drawn, and the size of a focus spot can be measured by using the measurement size function of the CAD. FIG. 12 is a schematic diagram showing an example of the optical path of the refracted ray of a plano-convex spherical lens. The lens radius in fig. 12 is 50 mm, and the spherical radius R113.69 of the spherical lens is obtained through a plurality of trial drawings, and the spherical radius enables the minimum spot position to be just about 200 mm from the lens plane when the lens radius is 50 mm and n is 1.5, the error is less than 1 mm, and the spot size of the focus is about 6.01 mm.

In order to compare the plano-convex spherical lens with the present lens, the light path of the refracted ray of the present lens is plotted next. The inventor writes the calculation of the coordinate value of the lens curve into a VB program, and can obtain the coordinate value of a point on the lens curve by running the VB program. The VB program can conveniently calculate the coordinate values of a series of points on the curved surface curve of the lens at a distance of one thousandth of a millimeter, if the coordinate values of the points are drawn in the CAD, a large amount of time is consumed, and the method cannot be realized, so that the method of replacing a smooth curve with a straight line broken line is adopted here, the condition of the focal spot of the lens is drawn in the CAD, and the spot size is determined. For comparison, the lens has the same parameters as the plano-convex spherical lens, namely the radius of the lens is 50 mm, the distance from the focal point to the plane of the lens is 200 mm, and the relative refractive index of the light of the lens is 1.5. Then dividing the curved surface curve of the lens into 10 sections according to the width of 5 mm, and operating a VB program to obtain the coordinate values of the turning points of the 10 sections of straight lines as follows:

(X＝0，Y＝12.31313986)，(X＝5，Y＝12.18002184)，

(X＝10，Y＝11.78207526)，(X＝15，Y＝11.12344882)，

(X＝20，Y＝10.21082107)，(X＝25，Y＝9.05307535)，

(X＝30，Y＝7.66089624)，(X＝35，Y＝6.04632717)，

(X＝40，Y＝4.22232648)，(X＝45，Y＝2.20235262)，(X＝50，Y＝0)。

the lens is shown in fig. 13, where X is the X coordinate axis and Y is the Y coordinate axis in fig. 13. Between every two coordinate points is a straight line instead of a curve, and the 10 straight lines are the refractive interface lines of the lens. In fig. 13, the Y coordinate axis is a central axis of the lens, and a broken line part on the left side of the central axis and a broken line part on the right side of the central axis are mirror images, and can be obtained by directly copying a line segment on the right side by using the Y coordinate axis as a mirror image axis through a mirror image copying operation in CAD. How can it be proved that the broken line lens in fig. 13 is the present lens? One method can prove that: the slope k of each segment of the straight refractive interface line can be checked to see whether the slope k conforms to a simple mathematical formula, i.e., | k | ═ sin (b)/[ n-cos (b) ], where b is the angle between the line connecting the midpoint of the straight segment to be checked and the given parallel light beam focusing focal point (in this case, the focal point coordinate is X ═ 0, and Y ═ 200) and the central axis of the lens, and n is the relative refractive index of the given lens with respect to the light of air (in this case, n ═ 1.5). During the checking, the slope k of the straight line segment can be calculated by a slope calculation method of a two-point straight line, the calculated slope k is a negative value, the negative value should be taken as an absolute value, and the absolute value should be compared with the value calculated by the formula sin (b)/[ n-cos (b) ] to obtain the same result or have small error. This feature of the broken line lens of fig. 13 is one of the features of the present lens, and can be used to prove that the broken line lens of fig. 13 is the present lens.

The refracted ray path of the broken line lens of fig. 13 is plotted below to determine the size of the focused focal spot. The method for drawing the refracted ray is similar to the method for drawing the refracted ray by the spherical lens, the refracted ray at the midpoint of the straight line segment of each segment of the refraction interface is drawn, and the incident ray is a parallel light beam. Referring to fig. 14, a method of refracting light is shown. Drawing an incident light HP from a midpoint P point of a section of refraction interface line JK, wherein the HP incident light is parallel to the central axis of a broken line lens, (drawing an HP straight line needs to use the functions of automatically capturing the midpoint and drawing a straight line in an orthogonal mode of CAD), drawing a complete circle by taking the P point as the center of a circle and taking R with the length being slightly less than 1/2 of the JK line segment as the radius, rotating the JK straight line segment by 90 degrees by taking the P point as the center to obtain a new straight line, wherein the straight line is intersected with the circle with the R as the radius at U, G two points, and the straight line UG is the normal line of the refraction interface line JK at the P point, is connected with J, K two points, and is used for redrawing the JK straight line. Then, the length of the UT straight line is measured and set as X1 by using the marking size function of the CAD self-contained, then the calculator calculates X2 ═ X1 × n, then a complete circle is drawn by using X2 as the radius and G point as the center of the circle, and then the tangent of the circle which uses X2 as the half-pass is drawn through P point and is intersected at Q point (the drawn tangent is used for the object capture function of automatically capturing the tangent point of the CAD self-contained). And then drawing an extension line in CAD to extend the straight line PQ to be intersected with a straight line EF and be intersected at a point L, wherein the straight line PL is a refracted ray of the broken line lens, and the straight line EF is a straight line which is perpendicular to the central axis of the broken line lens and is slightly beyond the focus. The EF straight line position is seen in fig. 15. The 10 refracted rays at the midpoint of the 10 refracted interface lines in this example can be plotted using this plotting method, and the 10 refracted rays to the left of the Y coordinate axis can be obtained using "mirror replication". The optical path diagram of the 20 refracted rays obtained after the drawing is shown in fig. 15. The dimensions of the focused focal spot can then be measured using the measurement dimensions function of the CAD. Moving a computer mouse cursor to the vicinity of a focus, continuously rotating a rotating wheel on a mouse, continuously amplifying an image of the focus, after the image is amplified to a certain degree, continuously amplifying the image by CAD drawing software, clicking a view (V)/regenerate (G) command in a pull-down menu in the CAD drawing software, then rotating the rotating wheel of the mouse, continuously amplifying the image, and if the image is not amplified again, clicking a view (V)/regenerate (G) command in the pull-down menu again until a divergent focus image is seen, at the moment, measuring the size of a focus light spot by using a CAD measurement size function, wherein the measurement result is as follows: the size of the focus spot is less than 0.0001 mm. So far, the size of the focal spot has not been determined finally, the refracted ray of each segment of the straight line segment of the refractive interface is not shown except for the midpoint, the refracted ray at the left and right points is drawn as shown in the schematic diagram of fig. 16, the refracted ray at the points is parallel to the refracted ray at the midpoint (because the incident rays are parallel), so that the size of the actual focused focal spot of each segment of the refractive interface is slightly smaller than 5 mm, and the width of slightly smaller than 5 mm is the width of the focused focal spot with the focused focal point as the midpoint. Considering that the 20 refracted ray focal spots have a slight error of 0.0001 mm, the size of the focal spot of the obtained polygonal-line lens in fig. 13 is about 5.0001 mm, and the size is smaller than the size of the focal spot of the plano-convex spherical lens under the same parameter condition by 6.01 mm.

Moreover, the size of the focusing focus spot of the lens with the broken line in fig. 13 can be further reduced by further reducing the width of each segment of the refractive interface line, re-running the VB program to obtain more coordinate values of the turning points of the straight line segments, and repeating the above operations in the CAD drawing software according to the above method. Through CAD simulation drawing of the polygonal-line-shaped lens and the plano-convex spherical lens, a conclusion can be drawn that when the polygonal-line-shaped lens focuses parallel light beams, the main part influencing the size of a focus spot is the width of a straight line segment of a refraction interface, if the width of the straight line segment of the refraction interface is greatly reduced, the size of the focus spot is greatly reduced, and the plano-convex spherical lens does not have the characteristic.

Disclosure of Invention

For the purpose of accurately and visually describing the novel lens of the present invention, the present specification gives the lens a name: "functional curved lens" means that the curved surface of the lens conforms to a mathematical function analytical formula described in this specification, and is also to be distinguished from a spherical lens and an aspherical lens.

The "regular beam" referred to in this specification is divided into three cases: the first is a light beam formed by parallel light rays, which is called as a parallel light beam in the specification; secondly, a light beam emitted by a certain object and emitted to a certain focus is called as a focusing light beam in the specification; and thirdly, a light beam emitted from a certain focus and emitted to a certain object is called a point light source light beam in the specification. In three cases of regular light beams, the specification gives three types of functional curved lenses a name: the function curved lens for accurately focusing the parallel light beams is called as an A-type function curved lens; the function curved lens which changes the focal length of a focusing light beam into a focal length is called as a 'B-type function curved lens'; the functional curved lens which refocuses the point light source beam on the other side of the lens is called an AA type functional curved lens.

The "lens refractive curved surface" referred to in the present specification means: the lens is a surface curved surface which refracts light rays.

In this specification, the term "Lens refraction curve lineThe meaning of "is:lens refraction curve lineThe curved surface formed by rotating 360 degrees around the central axis isCurved surface of lens refractionTo, forCurved surface of lens refractionCan be decomposed into pairsLens refraction curve lineMathematical analysis of (2), toLens refraction curve lineMake a mathematical analysis inCurved surface of lens refractionThe same results will be obtained.

The functional curved lens has the functions of: the regular light beams are accurately focused, and a mathematical function analytical formula of a lens refraction curved surface is firstly deduced in order to manufacture and process the lens, wherein the mathematical function analytical formula is specifically deduced as follows:

(01) deriving a refractive index distortion equation from the optical lens refractive index equation:

referring to fig. 1, angle a is a light ray incident angle, angle c is a light ray refraction angle, angle PF is a normal line, PA is an incident light ray, PB is a refracted light ray, PE is an extended line of the incident light ray, angle b plus angle d is equal to angle c, and since angle d is equal to angle a, (opposite angles are equal), angle b is equal to angle c-d, and angle b is equal to angle c-a, and the description gives the name: "deflection angle". In fig. 1, the lower part is a light-tight medium, the upper part is air, light enters the air from the light-tight medium, n is a relative refractive index of the light, and since an experimentally actually measured value of n is greater than 1, the following formula n ═ sin (c)/sin (a) is provided: the angle c is greater than the angle a, and the angle b is greater than zero.

n ═ sin (c)/sin (a); (n is the relative refractive index of light, obtained from the refractive index equation)

Sin (a + b)/sin (a); (see fig. 1, available from c + d + b + a + b)

(ii) sin (a) cos (b) + cos (a) sin (b) ]/sin (a); (derived from trigonometric functions)

{ [ sin (a) cos (b) ]/sin (a) } + { [ cos (a) sin (b) ]/sin (a) }; (the bracket is unfolded to get)

Cos (c) (b) ++ [ sin (b)/tan (a); the left and right terms of the formula derived from the tangent value of a (tan (a) ═ sin (a)/cos (a)) are simplified, and the following formula can be obtained:

tan(a)＝sin(b)/[n-cos(b)]…………(1)

the derivation formula (1) gives the mathematical relationship among the incident angle a, the deflection angle b and the relative refractive index n, and the formula is a deformation formula of the refractive index formula and is used in the following derivation process.

(02) Deducing a YZQ tangent formula I:

referring to fig. 2, fig. 2 is an optical path diagram of a type a function curved lens for precisely focusing a parallel light beam. The arc line in the figure is the refraction curve line of the lens, the other side of the lens is a plane, the plane is parallel to the X coordinate axis, and the Y coordinate axis is the central axis of the refraction curve line of the lens. When the incident light is a parallel light beam and is vertical to one side of the plane of the lens and irradiates one side of the plane of the lens, the incident light is not refracted, and the incident light enters the inside of the lens in the original direction. The f point on the Y coordinate axis is the focal point of the lens refraction light, and the f point is called as the focal point of the A-type function curved surface lens refraction curved surface in the specification. The point P is any point on the lens refraction curved surface, a parallel line marked with an arrow from bottom to top is an incident ray, the incident ray is parallel to a Y coordinate axis, a PE line is an extension line of the incident ray passing through the point P, a PF line is a normal line of the lens refraction curved surface at the point P, a G point on an X axis is an intersection point of a tangent line of the point P on the lens refraction curved surface and the X coordinate axis, a R point on the X axis is an edge point of the lens, a point O is a coordinate origin, an included angle between a refracted ray Pf and a PE straight line is an angle b, the incident ray extension line PE is parallel to the Y coordinate axis, the included angle between the refracted ray Pf and the Y coordinate axis is also an angle b, (parallel lines are equal in offset angles), the included angle between the incident ray HP and the normal line PF is a ray incident angle a, and the included angle between the tangent line PG and the X axis is a complementary angle d of the tangent line angle. Because the two sides of the angle d and the two sides of the angle a are perpendicular to each other (the tangent is perpendicular to the normal, and the incident ray is perpendicular to the X-axis), there is an angle d equal to the angle a. Next we compare angle a and angle b in fig. 2 with angle a and angle b in fig. 1, and you will find that their physical properties are identical, both angle of incidence and angle of deflection, and that equation (1) derived from fig. 1 is also true in fig. 2. Since the angle a is equal to the angle d, the angle d is smaller than 90 degrees, and the angle d is the angle between the tangent and the X-axis in fig. 2, the absolute value | k | ═ tan (d) ═ tan (a) of the slope of the tangent at point P is obtained by substituting | k | into equation (1):

|k|＝sin(b)/[n-cos(b)]…………(2)。

the formula (2) is a calculation formula of the absolute value of the tangent slope of any point on the refraction curved surface of the A-type function curved lens for accurately focusing the parallel light beams. For descriptive convenience, formula (2) is given a name: "YZQ tangent formula one" (YZQ is the abbreviation name formed by connecting the first letters of the Chinese pinyin of three characters of Yang Mega of the inventor). In the formula, | k | is the absolute value of the slope of the tangent line at any point P on the lens refractive curved surface, b is the included angle between the connecting line of the corresponding tangent point P and the focal point f of the lens refractive curved surface and the central axis of the lens refractive curved surface, and n is the relative refractive index of the lens material relative to the air (the light rays are emitted from the lens into the air).

(03) Deducing a YZQ tangent formula II:

referring to fig. 3, fig. 3 is an optical path diagram of a B-type function curved lens for changing a focal length of a focused light beam. The Y coordinate axis is the central axis of the lens refraction curved surface, and the point F on the Y coordinate axis in the figure is the position of a focusing focus when no lens refraction exists, and the point F is called as the virtual focus of the B-type function curved surface lens refraction curved surface in the specification. The f point on the Y coordinate axis is the focus of the incident focusing beam which is refocused after being refracted by the B-type function curved lens, and the f point is called as the focus of the B-type function curved lens refraction curved surface in the specification. The two curves in the figure are the lens curve lines on both sides of the B-type function curve lens, the point R on the X-axis is the edge point of the lens, the point 0 is the origin of coordinates, and the lower rectangular UV in the figure is the object emitting the light beam. The curved surface of one side of the lens, which faces to the object emitting the light beam, is a section of standard spherical curved surface, the circle center of the spherical curved surface is located at a virtual focus F point, the other side of the lens is a refraction curved surface, and the virtual focus F point and the refraction curved surface of the lens are located at the same side. The spherical curved surface has the following functions: all light rays emitted by the object UV and emitted to the point F and irradiated on the spherical curved surface are perpendicular to the spherical curved surface of the lens, so that the incident light enters the lens in the original direction. The focusing light beam is refracted only once by the B-type function curved lens, and the structure is important for simplifying a mathematical analytic expression. The point P is any point on the lens refraction curved surface, the point PM is the normal line of the lens refraction curved surface at the point P, the point G on the X coordinate axis is the intersection point of the tangent line of the refraction curved surface at the point P and the X axis, the straight line PT is an auxiliary line passing through the point P and being parallel to the Y coordinate axis, the angle a is the included angle between the incident ray and the normal line, the angle b is the included angle between the extension line PF of the incident ray and the refraction ray Pf, and the angle d is the included angle between the tangent line of the point P and the X coordinate axis. The angle h is the included angle of the intersection of the connecting line of the tangent point P and the focus point F of the lens refraction curved surface and the central axis of the lens refraction curved surface, the angle g is the included angle of the intersection of the connecting line of the tangent point P and the virtual focus point F of the lens refraction curved surface and the central axis of the lens refraction curved surface, and because the auxiliary line PT is parallel to the Y coordinate axis, the included angle of the straight line PT and the incident ray extension line PF is equal to the angle g (the offset angle in the parallel line is equal), and is also the angle g. The angle of the normal PM to the straight line PT is the angle e. Because the two sides of the e-angle are perpendicular to the two sides of the d-angle, respectively, (tangent line is perpendicular to normal, straight line PT is perpendicular to the X coordinate axis), the e-angle is equal to the d-angle. From fig. 3, the following relationship can be derived:

in triangle FfP, angle b-angle h-angle g … … … … (3); (triangle outer angle equals sum of two non-adjacent inner angles)

Angle a + angle e-angle g + angle d … … … … (4); (equal for vertex angles) and (angle e ═ angle d) are obtained

Angle a and angle b are the incident angle and the deflection angle, respectively, and equation (1) derived from fig. 1 is also true in fig. 3, and substituting the derived relations (3), (4) into equation (1) yields:

tan(g+d)＝sin(h-g)/[n-cos(h-g)]…………(5)

order: sin (h-g)/[ n-cos (h-g) ], W

And (3) expanding the left side of the equal sign of the formula (5) by using a trigonometric function, enabling the right side of the equal sign to be equal to W, moving terms from left to right, simplifying, and substituting the W value into the formula:

tan(d)＝[W-tan(g)]/[1+W*tan(g)]…………(6)

since the d-angle is the angle between the tangent and the X-axis and the d-angle is smaller than 90 degrees, the absolute value | k | ═ tan (d) of the slope of the tangent at point P, and | k | is substituted into equation (6), resulting in:

|k|＝[W-tan(g)]/[1+W*tan(g)]…………(7)

w in formula (7) is: w is sin (h-g)/[ n-cos (h-g) ]

Equation (7) is a calculation equation of the absolute value of the slope of the tangent at any point on the refractive curved surface of the B-type function curved lens for changing the focal length of the focused light beam. For descriptive convenience, formula (7) is given a name: "YZQ tangent equation two". In the formula, | k | is the absolute value of the slope of the tangent line at any point P on the lens refractive curved surface, h is the included angle between the line connecting the corresponding tangent point P and the focal point F of the lens refractive curved surface and the central axis of the lens refractive curved surface, g is the included angle between the line connecting the corresponding tangent point P and the virtual focal point F of the lens refractive curved surface and the central axis of the lens refractive curved surface, and n is the relative refractive index of the lens material relative to the light of the air (the light is emitted from the lens into the air).

(04) The formula of the tangent slope of the AA type function curved lens shows that:

referring to fig. 4, fig. 4 is an optical path diagram of an AA-type function curved lens to refocus a point light source beam on the other side of the lens. The AA type function curved lens is formed by two pieces of A type function curved lens which are combined together in a plane-to-plane mode. The straight line GM in the figure is the central axis of the lens and the f1 and f2 points on the straight line GM are the focal points on both sides of the lens. When the light emitting point of the point light source light beam is at the point f1, according to the principle of reversibility of light and the principle of refraction light path of the A-type function curved lens, the light beam emitted by the point light source is refracted by the refraction curved surface facing one side of the point light source and then becomes a parallel light beam inside the lens. Unlike the known spherical lens, which also has two focal points with the same focal length on both sides: the focal lengths of the focal points on both sides of the AA-type function curved lens may be different. Because the refractive curved surfaces on the two sides of the AA type function curved surface lens are the same type of refractive curved surfaces as the A type function curved surface lens, the absolute value analytic expressions of the tangent slopes of the refractive curved surfaces on the two sides of the AA type function curved surface lens are the same as the absolute value analytic expressions of the tangent slopes of the A type function curved surface lens, and are the YZQ tangent formula I.

(05) The formula for the tangent slope of a functional curved lens fabricated in the form of a fresnel lens illustrates:

the curved surface of the functional curved lens shown in fig. 2, 3 and 4 is formed by rotating the whole smooth lens curved surface line around the central axis, and the functional curved lens is referred to as a "single-curved-surface functional curved lens" in the present specification, or simply referred to as a "functional curved lens". Referring to fig. 5, 6 and 7, in this specification, a functional curved lens formed by rotating a plurality of (2 or more than 2) smooth curved lines around a central axis as shown in fig. 5, 6 and 7 is referred to as: "functional curved lens in the form of a Fresnel lens". Fig. 5 is a schematic view of a type a function curved lens fabricated in a fresnel lens form, and fig. 6 is a schematic view of three forms of a type B function curved lens fabricated in a fresnel lens form, the three forms being: the spherical curved surface and the refraction curved surface are both manufactured into a Fresnel lens form; the refraction curved surface is made into a Fresnel lens form, and the spherical curved surface is still in a single curved surface form; the refractive curved surface is still in the form of a single curved surface and the spherical curved surface is made into the form of a fresnel lens, and the three forms of the functional curved surface lenses are all called B-type functional curved surface lenses made into the form of the fresnel lens. Fig. 7 is a schematic diagram of two forms of AA-function curved lenses fabricated in the form of fresnel lenses, the two forms being: both the two side refraction curved surfaces are made into a Fresnel lens form; the functional curved lenses of both forms are called AA type functional curved lenses made in the form of fresnel lenses. Since the absolute value analytic expressions of the tangential slopes of the three types of functional curved lenses, i.e., type a, type B, and type AA, are related only to the angle (angle B, angle h, angle g) between the extended line of the refracted or incident light and the central axis and the refractive index n, and are not related to the division of the lens refractive curved line into several segments, the analytic expressions of the tangential slopes of the three types of functional curved lenses manufactured in the form of a fresnel lens are the same as the absolute value analytic expressions of the tangential slopes of the corresponding single-curved-surface functional curved lenses.

(06) Differential chaining algorithm description:

the above has derived the calculation formula of the absolute value of the tangent slope of any point on the refractive surface of the functional curved lens under three conditions of regular light beams, but we aim to obtain X, Y coordinate values of each point on the refractive surface of the lens for facilitating the numerical control equipment to process or draw the curve line of the lens. Next we see how we calculate X, Y coordinate values for each point on the refractive surface line of the lens using differential chaining computation. Let the radius of the lens be R, the coordinates of a special point on the refraction curved surface line of the lens do not need to be calculated, namely the coordinates (R, 0) of the edge point of the lens, and the special point is taken as a starting point and is calculated from the starting point. A coordinate system is defined firstly, the central axis of the lens refraction curved surface is taken as a Y coordinate axis, the edge point of the lens is positioned on an X axis, and the line of the lens refraction curved surface is positioned in a first quadrant of the coordinate system. Then, a tiny interval dx is set in the X direction, the curved refractive surface line of the lens is divided into a plurality of tiny fragments in the X direction according to the tiny interval dx, (the dx value can be arbitrarily set according to the requirement), each tiny fragment is defined as a straight line, and a plurality of key points on the tiny straight line fragment are defined as follows: the length of the projection of the tiny straight line segment on the X axis is dx, the length of the projection on the Y axis is dy, the tiny straight line segment is divided into coordinates of a starting point (X1, Y1), coordinates of a tangent point P point (Xp, Yp), coordinates of an ending point (X2, Y2) according to the calculation sequence, the calculation is started from an edge point of the lens, the edge point of the lens is located on the X axis of a first quadrant of a coordinate system, the refraction curve line of the lens is a single curve section, then X2 is always smaller than X1, Y2 is always larger than Y1, and further the following formulas can be obtained: x1-x2 ═ dx, y2-y1 ═ dy, dy ═ k | ×, dy 1| k1| dx, | k1| is the absolute value of the tangent slope of the refraction curve line at the (x1, y1) point calculated by the YZQ tangent formula, with the point (x1, y1) being the tangent point. The P-point coordinate calculation formula of the differential link calculation method is as follows:

p-point coordinate X value: xp ═ x1-dx/m … … … … (8)

P-point coordinate Y value: yp-y 1+ dy1/m … … … … (9)

M in the 2 calculation formulas is a real number larger than 1, and is artificially specified, and when the middle point of the minute straight line segment is selected as the position where the point P is located, m in the calculation formulas (8) and (9) linking the coordinates of the point P in the calculation method is m-2.

In the calculation formula of dy ═ k | × dx, | k | is the absolute value of the slope of the segment of the tiny straight line, and is equal to the absolute value of the slope of the tangent at the point P, | k1| and | k | are calculated by the first YZQ tangent formula or the second YZQ tangent formula. When the coordinate values of the starting point of a certain tiny straight line segment are known as (x1, y1), dx is known, and the coordinate values of the ending point are (x2, y2), the calculation sequence is as follows: the absolute value | k1| of the tangent slope at the point (x1, y1) is calculated by YZQ tangent formula, dy1 is calculated by | k1|, the values of Xp and Yp are calculated by P-point coordinate calculation formulas (8) and (9) of the link calculation method from the specified value m and the values of x1, y1, and dy1, the absolute value | k | of the tangent slope at the point (Xp, Yp) is calculated by YZQ tangent formula, dy is calculated by | k |, and the values of dy, dx, x1, and y1 are calculated to obtain the values of x2 and y 2. In the calculation of points on the refraction curved surface of the A-type and AA-type function curved surface lenses, | k1| and | k | are calculated according to a first YZQ tangent formula, in the calculation of points on the refraction curved surface of the B-type function curved surface lens, | k1| and | k | are calculated according to a second YZQ tangent formula, the edge point of the refraction curved surface of the lens is on the X axis of a first quadrant of a coordinate system, the edge point of the refraction curved surface of the lens is taken as a starting point, the calculation is started from the starting point, the coordinate value of the end point of each calculated tiny straight line segment is taken as the coordinate value of the starting point of the next tiny straight line segment, and the calculation is continuously repeated until the coordinate values of all points with the interval of dx on the refraction curved surface line of the lens which need to be calculated are calculated. These are the coordinate values of a series of points on the refractive surface line of the lens which we want to obtain at intervals dx. In this specification, the method for calculating the coordinate value of a point on the refraction curve line of the lens is referred to as: "differential chaining calculation method". In actual calculation, a computer program is used for calculation, so that there is no fear that the calculation difficulty is increased by taking dx to be small enough to improve the accuracy. Although the coordinate values calculated by the differential link calculation method are approximate values of the coordinate values of the points on the refraction curve line of the lens, the errors can be reduced to a micron level by the aid of a modern high-performance computer, and the use requirements of the lens can be completely met.

(07) The calculation method of the micro-decomposition equation shows that:

the differential solution equation calculation method requires that the YZQ tangent equation be converted into the form of the X, Y coordinate solution equation. The type a functional curved lens is shown in fig. 9, and the type B functional curved lens is shown in fig. 10. Before the formula is converted, the refraction curved surface line of the lens needs to be processed in a segmented mode, a coordinate system is defined firstly, the central axis of the refraction curved surface of the lens is used as a Y coordinate axis, the edge point of the lens is located on an X axis, and the refraction curved surface line of the lens is located in a first quadrant of the coordinate system. Then, setting a distance dx in the X direction, dividing the lens refraction curved line into a plurality of segments in the X direction according to the distance dx, (the value of dx can be arbitrarily set according to needs), and defining each segment as a straight line, wherein several key points on the straight line segment are defined as follows: the length of the projection of the straight line segment on the X axis is dx, the length of the projection on the Y axis is dy, the straight line segment is divided into coordinates of a starting point (X1, Y1), coordinates of a tangent point P point (Xp, Yp), coordinates of an ending point (X2, Y2) according to the calculation sequence, the calculation is started from the edge point of the lens, the edge point of the lens is positioned on the X axis of a first quadrant of a coordinate system, the refraction curve line of the lens is a single-curved-surface section, X2 is always smaller than X1, Y2 is always larger than Y1, and the following formulas can be further obtained: x1-x2 ═ dx, y2-y1 ═ dy, and the calculation formula of the coordinate of the point P of the calculation method of the solution equation is as follows:

p-point coordinate X value: xp ═ x1-dx/m … … … … (10)

P-point coordinate Y value: yp as y1+ dy/m … … … … (11)

M in the calculation formula of the P point coordinate of the solution equation calculation method is a real number larger than 1 and is specified by human, and when the middle point of the straight line segment is selected as the position of the P point, m in the calculation formula of the P point coordinate of the solution equation calculation method is m-2. For the type a and AA function curved lens, the following 2 trigonometric function conversion equations of the type a function curved lens can be obtained according to the notation in fig. 9:

substituting P point coordinate calculation formulas (10) and (11) of a solution equation calculation method and deduced trigonometric function conversion equations (12) and (13) of a function curved lens of A type into an expression on the right side of an equal sign in a YZQ tangent formula I, and obtaining a tangent slope absolute value expression only containing variables x1, y1, dx and dy and constants f, n and m through simplification and arrangement, wherein the expression is simplified and expressed as follows: t1(x1, y1, dx, dy), and expressing the absolute value of the slope of the straight line segment | k | as | dy/dx |, the YZQ tangent equation can be transformed into another expression as follows:

|dy/dx|＝T1(x1，y1，dx，dy)…………(15)

writing expression (15) to the form of a solution equation:

|dy/dx|-T1(x1，y1，dx，dy)＝0…………(16)

in equation (16), dx is artificially set and is known, and since the coordinate calculation is started from the lens edge point, followed by the end point coordinate value of each straight segment as the coordinate value of the start point of the next straight segment, x1 and y1 are also known for the straight segments to be calculated. Thus, equation (16) has only one unknown dy, and by solving the equation (16), the dy value can be obtained. Equation (16) is a one-dimensional multiple equation. The conventional equation solving method cannot solve the equation, the equation can be solved by a computer program, and the program source code for solving the equation by a VB program can be as follows:

this program is to solve the equation by a test method, i.e. let the dy value increase gradually, when the dy value increases to a certain value, the computer program calculates that the absolute value of Abs (dy/dx) -T1(x1, y1, dx, dy) is 0 or Abs (dy/dx) -T1(x1, y1, dx, dy) is less than 0.000001, the program jumps out of the loop, the dy value at this time is the solution of the equation, the program continues to run, and the end point coordinates x2 and y2 of this segment are calculated.

For the B-type function curved lens, the following 6 trigonometric function conversion equations of the B-type function curved lens can be obtained according to the notation in fig. 10:

substituting the derived trigonometric function conversion equations (20), (21), (22), (23), (24), (25) of the B-type function curved lens and the P-point coordinate calculation equations (10) and (11) of the solution equation calculation method into an expression on the right side of the middle and middle signs of the YZQ tangent equation II, and obtaining a tangent slope absolute value expression only containing variables x1, y1, dx and dy and constants F, F, n and m through simplification, wherein the expression is simplified and expressed as: t2(x1, y1, dx, dy), and expressing the absolute value of the slope of the straight line segment | k | as | dy/dx |, the YZQ tangent equation two can be transformed into another expression as follows:

|dy/dx|＝T2(x1，y1，dx，dy)…………(26)

writing expression (26) to the form of a solution equation:

|dy/dx|-T2(x1，y1，dx，dy)＝0…………(27)

since x1, y1, dx of the straight line segment to be calculated are known, there is only one unknown dy in equation (27), equation (27) is a one-dimensional multi-order equation, and this equation can be solved by a computer program to obtain the dy value.

After solving the equations of the above two equations (16) and (27) to obtain dy values, since (x1, y1) is known, the coordinate values of the ending points of the straight line segment (x2, y2) can be calculated by applying the equations x1-x 2-dx and y2-y 1-dy, and the calculated coordinate values of the ending points of each straight line segment are used as the coordinate values of the starting points of the next straight line segment, and the calculation is continuously repeated until the coordinate values of all the points on the refractive surface line of the lens which are required to be calculated and are separated by dx are calculated. In this specification, the method for calculating the coordinate value of a point on the refraction curve line of the lens is referred to as: "differential solution equation calculation method". Under the condition that the dx value is infinitely close to 0, the coordinate values of the points on a series of refraction curve lines calculated by the differential solution equation calculation method are accurate values.

(08) The YZQ tangent equation may be described in many different forms:

the above description gives two kinds of YZQ tangent formula descriptions, and it should be further explained that: the above-described YZQ tangent equation may take many different forms, for example, in the equation for absolute values of tangent slope, a tangent function may be used instead of a sine function or a cosine function, or X, Y coordinates may be used to describe the YZQ tangent equation, but the final calculation will be consistent with the YZQ tangent equation regardless of variations. Therefore, to determine whether the tangent slope absolute value calculation formula falls within the scope of the present invention, only the expression form is not considered but the calculation result is considered.

(09) How to define the functional surface lens and the general lens method are explained as follows:

the differential link calculation method or the differential solution equation calculation method provided by the specification can be used for calculating the coordinate values of a series of points on the refraction curve line of the lens with a certain function curve surface, the calculated coordinate data is used as a template value to be compared with the coordinate measurement value of the actual effective point on the refraction curve surface of the lens, and if the coordinate values are matched with the coordinate measurement value, the lens is considered to be the same as the lens with the function curve surface. The term "match" has two meanings, firstly, when comparing the measured value and the template value, the individual obvious points deviating from the smooth curve and belonging to the measurement or processing error need to be eliminated, on the basis, the template value and the measured value are 100% identical in the error allowable range; and secondly, when the actual measured value is compared with the template value, the error is considered to be identical within an allowable range, the allowable error range can be within one tenth millimeter or within one hundredth millimeter or within one thousandth millimeter, and specifically which error allowable range grade is selected, and a larger error allowable range grade is selected on the premise of clearly speaking the fact.

(10) The function curved surface lens has the advantages that:

since the functional curved lens can precisely focus a regular beam and is more precise than a plano-convex spherical lens in focusing a parallel light beam and can also be made in the form of a fresnel lens, the functional curved lens can be used to manufacture optical instruments of higher precision and to manufacture solar condenser lenses in the form of a fresnel lens, etc. And the refraction curved surface of the functional curved surface lens can be analyzed and coordinate calculated by using a function analytic formula given in the specification, so that the calculated coordinate value can be conveniently input into a numerical control device, and the required functional curved surface lens can be conveniently processed.

Drawings

FIG. 1 is a diagram of the light path of light rays refracted from an optically dense medium into air

Fig. 2 is an optical path diagram of a type a function curved lens for accurately focusing a parallel light beam.

Fig. 3 is an optical path diagram of a B-type function curved lens for changing the focal length of the focal point of a focused light beam.

Fig. 4 is an optical path diagram of an AA-type function curved lens refocusing a point light source beam on the other side of the lens.

Fig. 5 is a schematic diagram of a type a function curve lens fabricated in the form of a fresnel lens.

Fig. 6 is a schematic diagram of three forms of a B-type function curve lens fabricated in the form of a fresnel lens.

Fig. 7 is a schematic diagram of two forms of AA-function curved lenses fabricated in the form of fresnel lenses.

Fig. 8 is a VB program block diagram in which the differential link calculation method is written as a computer VB program in the embodiment.

FIG. 9 is a schematic diagram of the calculation and analysis of the refraction curve line of the A-type function curve lens by applying the differential solution equation calculation method.

FIG. 10 is a schematic diagram of the calculation and analysis of the refraction curve line of the B-type function curve lens by applying the differential solution equation calculation method.

Fig. 11 is a schematic diagram of a refractive ray path diagram drawn by applying CAD to a plano-convex spherical lens.

Fig. 12 is a diagram of an example of drawing a refractive ray path diagram by applying CAD to a plano-convex spherical lens.

FIG. 13 is a graph of a broken line of the coordinates of a straight line segment of the refractive interface of the present lens.

FIG. 14 is a schematic diagram of a broken line lens using CAD to draw a path diagram of refracted rays.

FIG. 15 is a schematic diagram of an example of a broken line lens using CAD to draw a path diagram of refracted rays.

FIG. 16 is a schematic diagram of a light path of refracted light rays for points on a refracting interface line of the polygonal lens.

Detailed Description

Specific embodiment a solar collector lens in the form of a 30 cm diameter piece of fresnel lens will be designed, see fig. 5. We can view sunlight as a parallel light beam. The lenses were made of glass, the dimensions of the glass being chosen as: diameter 30 cm and thickness 2 cm. Searching the relevant data, and determining that the refractive index n of the glass is 1.65. The focal length of the lens is designed to be 50 cm, and considering that if the lens is made into a single-curved function curved lens, the maximum height of the middle part of the lens exceeds 2 cm (the thickness of glass), and the lens cannot be made, the type A function curved lens made into a Fresnel lens is selected. The refractive surface lines of the lens are divided into three segments, and the X values of the starting points of the three segments of the refractive surface lines are R1, R2 and R3, respectively, as shown in fig. 5. The central axis of the refractive curved surface is taken as the Y coordinate axis. And then, a differential link calculation method is written into a computer VB program, and the coordinate value of each point on the lens refraction curved surface is calculated. In the VB program, units of thousands of millimeters are used, dx is 1, the maximum radius R1 of the lens is 150000(1 centimeter is 10000 units of numbers), the focal length is 500000, the refractive index n is 1.65, the curved surface of the lens is divided into three sections, and the X values of the starting point and the ending point of the curved line of the three sections are respectively 15 to 12 centimeters, 12 to 8 centimeters and 8 to 0 centimeters. Segmenting at this scale allows for the maximum y-value that can be achieved for each segment of the curved line to be substantially equal. In calculating the tangent slope, the position near the middle point of each minute straight line segment is designated as the position of the tangent point P of the tangent. Fig. 8 is a VB program block diagram in which a differential link calculation method is written as a computer VB program. Firstly starting VB6 programming environment software, creating a standard engineering program file, placing a Command button Command1 and a Text box Text1 in a form1 window, then writing a VB program according to a program diagram or the following VB program source codes, running the program after writing, clicking the Command button in the window, starting the program to calculate according to requirements, and after about ten seconds, ending the program running to obtain a file name on an E disk, wherein the Command button is as follows: txt, which is opened by a notepad program, each row in the file has 2 numbers, the first number is the X-coordinate value of a certain point, the second number is the Y-coordinate value of the same point, there are a total of 150000 coordinate values of points on the lens refraction curve line, the X-value precision is one thousandth of a millimeter, and the Y-value precision is in the micron order. Txt can be copied into a computer of a numerical control device, and the numerical control device can process the lens according to the coordinate values. The source code of the VB program of the embodiment is as follows, and the pf line segment in the VB program refers to: and a line segment from any point P to the focus f on the lens refraction curved surface line.

Claims

1. A can focus the functional curved lens of the regular light beam accurately, the refraction curved surface of this lens is the aspheric surface curved surface, this lens is divided into three types according to the incident light beam situation differently, can focus the functional curved lens of the parallel light beam accurately and call A type functional curved lens, can focus the functional curved lens that the light beam changes the focal length and call B type functional curved lens, can focus the function curved lens of the light beam on another side of the lens again and call AA type functional curved lens, these three types of functional curved lens can also be made into the functional curved lens of the form of Fresnel lens separately, these three types of functional curved lens and correspondent function curved lens making into the form of Fresnel lens have common characteristics: the coordinate value of each point on the lens refracting curved surface is matched with the coordinate value of each point calculated by a differential link calculation method or a differential solution equation calculation method, the absolute value of the slope of the tangent in the differential link calculation method and the differential decomposition equation calculation method is calculated according to a first YZQ tangent formula or a second YZQ tangent formula (or other mathematical formulas having the same calculation result as the first YZQ tangent formula or the second YZQ tangent formula), the first YZQ tangent formula is | k | ═ sin (b)/n-cos (b) ], the | k | in the first YZQ tangent formula is the absolute value of the slope of the tangent of any point (P point) on the refractive curved surface of the A-type function curved lens or the AA-type function curved lens, and b in the first YZQ formula is the included angle between the connecting line of the corresponding tangent point (P point) and the focus (f point) of the lens refracting curved surface and the central axis of the lens refracting curved surface, the second YZQ tangent formula is | k | ═ W-tan (g) ]/[1+ W · tan (g) ], where W in the second YZQ tangent formula is W ═ sin (h-g)/[ n-cos (h-g) ], where | k | in the second YZQ tangent formula is an absolute value of a tangent slope at any point (P point) on the refractive surface of the B-type function curved lens, where h in the second YZQ tangent formula is an angle at which a line connecting a corresponding tangent point (P point) and a focal point (F point) of the refractive surface of the lens intersects the central axis of the refractive surface of the lens, where g in the second YZQ tangent formula is an angle at which a line connecting the corresponding tangent point (P point) and an imaginary focal point (F point) of the refractive surface of the lens intersects the central axis of the refractive surface of the lens, and where n in the first and second YZQ tangent formulas is a relative refractive index of the lens material with respect to light entering air (light rays).

2. The functional curved lens of claim 1, wherein the type a functional curved lens and the type a functional curved lens manufactured as a fresnel lens are characterized in that: one side is a plane, and the other side of the lens is a refraction curved surface or a refraction curved surface manufactured into a Fresnel lens form.

3. The functional curved lens of claim 1, wherein said type B functional curved lens is in the form of a fresnel lens, and wherein: one side of the lens is an accurate spherical curved surface or an accurate spherical curved surface manufactured into a Fresnel lens form, the other side of the lens is a refraction curved surface or a refraction curved surface manufactured into a Fresnel lens form, the circle center of the spherical curved surface is located at an imaginary focus (F point) on the central axis of the lens, the imaginary focus (F point) and the refraction curved surface of the lens are located on the same side, and the imaginary focus (F point) of the refraction curved surface of the lens is also a focusing focus of an incident focusing beam when no lens refracts.

4. The functional curved lens of claim 1, wherein the AA-type functional curved lens is an AA-type functional curved lens manufactured in a fresnel lens form, and wherein: the lens is formed by combining two A-type function curved surface lens planes together, the two side refraction curved surfaces of the lens are refraction curved surfaces which are the same as the refraction curved surfaces of the A-type function curved surface lens, the two side refraction curved surfaces or one side refraction curved surface can also be made into a Fresnel lens form, and the focal lengths of the two side refraction curved surfaces can be different.

5. The functional surface lens of claim 1, wherein said differential chaining method comprises: taking the central axis of the lens refractive curved surface as a Y coordinate axis, the edge point of the lens is located on an X axis, the lens refractive curved surface line is located in a first quadrant of a coordinate system, the lens refractive curved surface line is divided into a plurality of micro segments at a micro interval dx in the X direction, (the dx value can be arbitrarily set as required), each micro segment is defined as a straight line, the key point on the micro straight line segment is divided into a starting point coordinate (X1, Y1), a tangent point coordinate (Xp, Yp) and an ending point coordinate (X2, Y2) according to the calculation sequence, the formulas X1-X2-dx, Y2-Y1 dy, dy | k | dx, dy 1| 1| dx, Xp | X1-dx/m and Yp 1+ dy1/m are applied, and the values X1, Y1, X and Y2 are calculated sequentially: calculating absolute values | k1| of tangential slopes at (X1, y1) points by YZQ tangent formula, dy1 by | k1| and dy1 by specified m values and values X1, y1 and dy1 and dx values, calculating values of Xp and Yp, calculating absolute values | k | of tangential slopes at (Xp, Yp) points by YZQ tangent formula, dy by | k | and calculating values X2 and y2 by values of dy, dx, X1 and y1, calculating points | k1| and | k | according to the first equation of refraction Q in calculation of points on the refraction surfaces of A-type and AA-type functional surface lenses, calculating | k1| and | k | according to the second equation of refraction Q in calculation of points on the refraction surfaces of B-type functional surface lenses, calculating the edge points of the first quadrant of the refraction surface by using the first axis of the first equation of refraction surface as the start point of a straight line, calculating the start point of a minute segment of a straight line from the start point of the straight line, and the segment of the start point of the straight line And continuously repeating the calculation until the coordinate values of all points with the interval dx on the lens refraction curved surface line needing to be calculated are calculated.

6. The functional surface lens of claim 1, wherein the differential solution equation calculation method comprises: taking the central axis of the lens refraction curved surface as a Y coordinate axis, the edge point of the lens is positioned on an X axis, the lens refraction curved surface line is positioned in a first quadrant of a coordinate system, the lens refraction curved surface line is divided into a plurality of segments according to an interval dx in the X direction, (the dx value can be set arbitrarily according to needs), each segment is defined as a straight line, the edge point of the lens refraction curved surface is set on the X axis of the first quadrant of the coordinate system, the edge point of the lens refraction curved surface is taken as a starting point, the starting point coordinates of the straight line segment are set as (X1, Y1), the P point coordinates of the tangent point are set as (Xp, Yp), the ending point coordinates of the straight line segment are set as (X2, Y2), for the A-type and AA-type function curved surface lenses, the P point coordinate calculation formula of the solution equation calculation method and the deduced A-type function curved surface lens trigonometric function conversion equation can convert the YZQ tangent formula into a lens trigonometric function conversion equation only containing X1, Y25, and A-type function curved surface, y1, dx, dy variables and necessary constants, and is denoted as T1(x1, y1, dx, dy), and the absolute value of the slope of the straight line segment | k | is denoted as | dy/dx |, and since the values of x1, y1, and dx of the straight line segment to be calculated are known, the dy value can be obtained by solving the equation for the equation | dy/dx | -T1(x1, y1, dx, dy) ═ 0, and for the B-type functional surface lens, applying the equation of solution calculation formula P-point coordinate calculation formula and the derived trigonometric function conversion equation for the B-type functional surface lens, the YZQ tangent equation two can be converted into a mathematical expression containing only the variables x1, y1, dx, dy and necessary constants, and is denoted as T2(x1, y1, dx, dy 1), and since the absolute value of the slope of the straight line segment | k is denoted as T3583, and since the absolute value of the slope of the straight line segment is calculated, The y1 and dx values are known, so the dy value can be obtained by solving the equation of equation | dy/dx | -T2(x1, y1, dx, dy) ═ 0, after the dy value is obtained, the coordinate value of the end point of the straight line segment (x2, y2) is calculated by applying the equations x1-x2 ═ dx and y2-y1 ═ dy, the coordinate value of the end point of each straight line segment calculated is used as the coordinate value of the start point of the next straight line segment, and the calculation is continuously repeated until the coordinate values of all points on the refractive surface of the lens to be calculated, which are separated by dx, are calculated.