CN109932764A - A kind of function surface lens of energy vernier focusing - Google Patents
A kind of function surface lens of energy vernier focusing Download PDFInfo
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Abstract
It is a kind of can be by the function surface lens of regular light beam vernier focusing, belong to one kind of non-spherical lens, it is divided into A type Type B and AA type three types by unpolarized light beam situation difference, this function surface lens is compared with plano-convex spherical lens, when focusing directional light light beam, this function surface lens focus precision is higher than plano-convex spherical lens.The absolute value of the tangent slope at any point can be calculated with YZQ tangent formula on the refractive curvature of this function surface lens, and the coordinate value of a series of point on this function surface lens refractive curvature can link calculating method with differential or differential solves equation calculating method and is calculated.This function surface lens can also be fabricated to the form of Fei Nier lens, be fabricated to Fei Nier form of lens and have no effect on focusing accuracy.Because function surface lens focus precision is higher thus, thus the optical instrument of manufacture degree of precision or the Salar light-gathering lens etc. for manufacturing Fei Nier form of lens can be used to.
Description
Technical field
The present invention relates to a kind of new aspheric lens, this lens can be by regular light beam vernier focusing.
Background technique
One side surface be plane spherical lens be known as " plano-convex spherical lens ", the lens that the present invention provides hereinafter referred to as
For " this lens ".
The height of lens focus precision in some situations, will directly influence the quality of lens functions performance, such as thoroughly
Mirror is used in the occasion for focusing laser.Plano-convex spherical lens are compared with this lens, when directional light light beam is focused, plano-convex ball
The focusing accuracy of face lens is lower, and the focusing accuracy of this lens is higher, this can give in terms of two and prove.
One is being compared in terms of the accuracy of focal length of lens calculation formula.Geometry in College Physics teaching material
In one chapter of optics, the calculation formula for deriving single plano-convex spherical lens focal length is had ready conditions limitation, one of conditional be into
Penetrating light is " paraxial rays ", and so-called " paraxial rays " refers to: the height h of light refraction point to optical axis (lens centre axis) is very
Low, h/r very little when light refraction, r here refers to the spherical radius of spherical lens, and h is then equivalent to lens radius.In geometry
In optical theory, the light beam that " object point " is issued in unlimited distance when directional light light beam is regarded as, and as one of condition, it derives
The calculation formula of image space focal length is gone out.When " paraxial rays " this condition is not able to satisfy, with the plano-convex spherical lens derived
The calculated focal length of the calculation formula of image space focal length has uncertainty.And the focometer of this lens is calculated in analytic equation, then
There is no the limitation of " paraxial rays ", the derivation of this lens refractive curvature analytic equation is detailed in this specification Summary.
In the entire section of this lens centre axis transverse direction, unique restrictive condition is: the incidence angle of incident ray, which is less than, to be totally reflected
Angle.
The second is can be emulated to draw to give with computer CAD proves.Lens refracted light is drawn with computer CAD mapping software
Index path is the Xiang Faming of the present inventor, not from any data.Because AutoCAD mapping software has a set of multiple behind
The support of miscellaneous accurate mathematic system, the accuracy and correctness for the figure drawn are by countless people in all trades and professions
Confirmation is given, so the geometric figure drawn out with CAD is proved to be for reasoning Mathematics Proof.It is drawn and is rolled over CAD
When penetrating light path of light figure, " Object Snap " function in CAD need to be opened, and be arranged endpoint, intersection point, midpoint, intersection point, the center of circle and
The Object Snaps such as circular arc point of contact are opened, and are also needed to open orthogonal picture straight line function when drawing vertically and horizontally straight line, also be needed size
The precision setting of measurement is effective for 8 bit digitals after highest level, that is, decimal point, and draws at 1: 1 in proportion.Specific drafting spherical surface is saturating
The sequence and principle of mirror refracted light index path are as follows: referring to Figure 11, into 2004 or more version of AutoCAD mapping software, first with
The spherical radius R0 of spherical lens is radius, draws a semicircle by the center of circle of G point, after G one horizontal line DJ of strokes and dots, partly after this
One vertical straight line GY of round heart G strokes and dots, (" orthogonal " the picture straight line function of CAD need to be used by drawing DJ and GY straight line), in GY straight line
A horizontal line EF is drawn in upper appropriate location, then draws one and incident ray HP, the HP straight line of GY straight line parallel meets at P with half-round curve
Point reconnects G point and P and points with the finger or gesticulate straight line GP, then using P point is that a complete circle using R as radius (R < R0) is drawn in the center of circle, this circle and GP
Straight line meets at U point, after U one straight line UT vertical with incident ray HP of strokes and dots and meets at T point with HP straight line.Then CAD is used
Included dimensioning operation, measures the length of straight line UT and is set as X1, then calculate X1*n=X2 with calculator, n is lens
Relative index of refraction of the material relative to the light of air, then recycle CAD in draw extended line operation, by GP straight line extend to with
R is that V point is intersected and intersected in the other side of the circle of radius, then using V point as the center of circle, a complete circle is drawn by radius of X2, after P
Point is made as the tangent line of the circle of radius and to meet at Q point using X2, and (pair at the automatic capture point of contact carried in CAD will be used by drawing this tangent line
As capture function), it then recycles in CAD and draws extended line operation, straight line PQ is extended to and intersects with straight line EF and intersects at L
Point, straight line PL are the refracted light of spherical lens.Principle is: straight line GV is normal of the plano-convex spherical lens in P point, straight line HP
Be incident ray, had according to the refractive index formula of light: sin (c)/sin (a)=n, (c and a in this formula correspond in Figure 11
Angle c and angle a), if can prove that: sin (c)/sin (a)=n, PL straight line be refracted light.Referring to Figure 11.
It proves: because sin (c)/sin (a)=(X2/R)/(X1/R)=X2/X1, and because are as follows: X2=X1*n,
So: X2/X1=n, so sin (c)/sin (a)=n, so straight line PL is refracted light.
The a plurality of refracted light of spherical lens when incident ray is directional light light beam can be drawn according to this technique of painting, then is used
What CAD was carried measures size function, can measure the size of focusing focus hot spot.Figure 12 is that a plano-convex spherical drawing out is saturating
The example of mirror refracted light index path.Lens radius in Figure 12 is 50 millimeters, the spherical radius R113.69 of spherical lens be through
Cross what repeatedly examination picture just obtained, when this spherical radius can make 50 millimeters of lens radius and n=1.5, minimum light spot position is rigid
It appears in well near 200 millimeters of lens plane, error is less than 1 millimeter, and focus spot is having a size of 6.01 millimeters or so.
In order to be compared plano-convex spherical lens with this lens, the refracted light optical path of this lens is next drawn again
Figure.The calculating of the value of this lens curved surface curvilinear coordinate is written as VB program by the present inventor, can be obtained by operation VB program
Obtain the coordinate value of the point on this lens curved surface curve.What VB program can be convenient calculates the sheet for being separated by one thousandth mm in width
The coordinate value of a series of point on lens curved surface curve is big by expending if these coordinate values put all drawn in CAD
The time is measured, can not be accomplished, so will use in the method for straight line broken line substitution smooth curve herein, this lens is drawn in CAD
Focus spot situation, and determine spot size.Compare for convenience, this lens selects ginseng identical with plano-convex spherical lens
Number, i.e. lens radius are 50 millimeters, and the distance of focus to this lens plane is 200 millimeters, and the relative index of refraction of the light of lens is n
=1.5.Then the Curve On The Surface of this lens is divided into 10 sections by 5 millimeters of width again, this 10 sections of straight lines can be obtained in operation VB program
The coordinate value of turning point is 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).
Broken line this lens drawn out according to the coordinate of this 11 broken line turning points are as shown in figure 13, indicate X's in Figure 13
For X reference axis, indicating Y is Y-coordinate axle.It is a straight line rather than curve between every two coordinate points, this 10 straight lines are this
The refracting interface line of lens.In Figure 13 Y-coordinate axle be this lens of broken line central axis, the broken line part on the central axis left side with
Broken line part on the right of central axis is mirror symmetry, can use " image copying " operation in CAD, straight by mirror shaft of Y-coordinate axle
The line segment for connecing duplication the right obtains.How can prove that the broken line lens in Figure 13 are exactly this lens? there is a method that can demonstrate,prove
It is bright, exactly: the slope k of each section of refracting interface straight line can be checked, it is public to see whether slope k meets a simple mathematics
Formula, i.e., | k |=sin (b)/[n-cos (b)], the b in this mathematical formulae be the straightway to be checked midpoint with it is given parallel
The angle that the line of light light beam focusing focus (focal coordinates are X=0, Y=200 in this example) intersects with lens centre axis again, n
It is relative index of refraction (in this example be n=1.5) of the given lens relative to the light of air.It, can be straight with two-point in checking computations
The slope calculation method of line calculates the slope k of straightway, and the slope k calculated in this way is a negative value, should be by this negative value
It takes absolute value, then the value of this absolute value is compared its result with the value calculated with formula sin (b)/[n-cos (b)]
Answer equal or error very little.This of broken line lens in Figure 13 is characterized in one of feature of this lens, this feature can be by
Broken line lens for proving in Figure 13 are exactly this lens.
The refracted light index path of this lens of lower iso-surface patch Figure 13 middle polyline, to determine the size of focusing focus hot spot.It draws
The method of refracted light is similar with the spherical lens picture method of refracted light, first draws each section of refracting interface straightway midpoint
Refracted light, incident ray be directional light light beam.The specific method for drawing refracted light is referring to Figure 14.First from one section of refracting interface
The centerline axis parallel of midpoint P strokes and dots one incident ray HP, the HP incident ray and broken line lens of line JK, (drawing HP straight line needs
Use CAD automatic capture midpoint and " orthogonal " pictures straight line function), then using P point as the center of circle, grown be slightly less than JK line segment 1/2
The R of degree is that radius draws a complete circle, then JK straightway is rotated by 90 ° centered on P point, obtains new straight line, this straight line with
R is that the circle of radius meets at 2 points of U, G, and straight line UG is normal of the refracting interface line JK in P point, reconnects 2 points of J, K, repaints
JK straight line.Make the vertical line of straight line HP after U point and meets at T point, then the dimensioning function of being carried with CAD, measurement with HP straight line
The length of UT straight line and it is set as X1 out, then calculates X2=X1*n with calculator, then using X2 as radius, using G point as the center of circle, draws one
Complete circle is made to take X2 as the tangent line of the circle of half warp and meet at Q point (catching automatically of carrying in CAD will be used by drawing this tangent line after P point
Catch the Object Snap function at point of contact).Then it recycles in CAD and draws extended line operation, straight line PQ is extended to and is intersected with straight line EF
And L point is intersected at, straight line PL is the refracted light of this lens of broken line, and EF straight line is that this lens centre axis mutually hangs down with broken line
Directly, distance is located at one section of straight line slightly above focal point.EF linear position is referring to Figure 15.This can be drawn out with this drawing practice
10 refracted lights of the refracted light at 10 refracting interface line midpoints in example, the Y-coordinate axle left side can be used " image copying " to obtain.
The refracted light index path that 20 refracted lights obtain after all finishing is as shown in figure 15.Next the measuring scale small achievement of available CAD
It is capable of measuring the size of focusing focus hot spot.Computer mouse cursor is moved on near focal point, the runner on continuous rotation mouse will be burnt
The image of point continuously amplifies, and after amplifying to a certain extent, CAD mapping software no longer enlarged drawing can click CAD drawing at this time
" view (V) // re-generate (G) " order in drop-down menu in software, is rotated further by mouse wheel, and image continues to amplify,
If occurred the case where image no longer amplifies again, " view (V) // re-generate (G) " life in drop-down menu can also be again tapped on
It enables, until seeing the focus image of diverging, the size for measuring size functional measurement focus spot of CAD can be used at this time, survey
Amount the result is that: the size of focus spot is less than 0.0001 millimeter.So far, the size of focus spot is not also final determines, each
There are also the refracted lights of the point in each 2.5 millimeters of sections in left and right to be not drawn into other than midpoint for section refracting interface straightway, these
As shown in Figure 16 schematic diagram, the refracted light at these points is parallel with the refracted light of midpoint for the drafting of refracted light at point
(because incident ray is parallel) obtains the size of the practical focusing focus hot spot of each section of refracting interface line in this way to omit
Less than 5 millimeters, and this width for being slightly less than 5 millimeters is using focusing focus as midpoint.In view of 20 refracted light focuses
Hot spot is there are 0.0001 millimeter of slight error, the ruler of the focusing focus hot spot of broken line this lens in the Figure 13 finally obtained in this way
Very little is 5.0001 millimeters or so, this size is less than the size of plano-convex spherical lens focusing focus hot spot under the conditions of equivalent parameters
6.01 millimeter.
Moreover, the size of broken line this lens focus focus spot in Figure 13 can also reduce again, and method is will be every
The width of one section of refracting interface line reduces again, reruns VB program, obtains the coordinate value of more straightway turning points, and
Operation above is reformed in CAD mapping software according to the above method.It is emulated by the CAD of this lens of broken line and plano-convex spherical lens
It draws, it can be deduced that such a conclusion, this lens of broken line influence the master of focus spot size when focusing directional light light beam
To be partially the width of refracting interface straightway, if the width of refracting interface straightway significantly reduced, focus spot
Size will significantly reduce therewith, and plano-convex spherical lens do not have this characteristic then.
Summary of the invention
For the new type lens that the description present invention of accurate image provides, this specification gives this lens one name
Cry: " function surface lens ", the curved surface for refering in particular to this lens meet mathematical function analytic expression described in some this specification,
It is distinguished also for spherical lens and non-spherical lens.
Described " regular light beam " is divided into three kinds of situations in this specification: first is that the composition that is parallel to each other between light and light
Light beam is referred to as " directional light light beam " in this specification；Second is that the light beam for a certain focus of directive that some object issues, this explanation
It is referred to as " focus on light beam " in book；Third is that being referred to as in this specification from the light beam of some object of the directive of a certain focus sending
" point light source light beam ".At three kinds of regular light beam, this specification takes one to the function surface lens of three types respectively
Name is: the function surface lens of directional light light beam vernier focusing are known as " A type function toroidal lens "；Focus on light beam is changed
The function surface lens of focus are known as " Type B function surface lens "；Point light source light beam is focused again in the lens other side
Function surface lens be known as " AA type function toroidal lens ".
Described " lens refractive curvature " refers in this specification: the surface curve that lens reflect light.
Described in this specification "Lens refractive curvature line" it is meant that:Lens refractive curvature lineAround center axis rotation 360
Spending the curved surface formed isLens refractive curvature, rightLens refractive curvatureMathematical analysis can be analyzed to pairLens refractive curvature line
Mathematical analysis, it is rightLens refractive curvature lineThe mathematical analysis made existsLens refractive curvatureOn will obtain identical result.
The function that function surface lens have is: regular light beam vernier focusing needs to manufacture and process this lens
First to derive the mathematical function analytic expression of lens refractive curvature, specific derivation is as follows:
(01) go out a refractive index deformation formula from the optical lens refractive index derivation of equation:
Referring to Fig. 1, the angle a is angle of incidence of light, and the angle c is light refraction angle, and PF is normal, and PA is incident ray, and PB is folding
Light is penetrated, PE is the extended line of incident ray, and the angle b adds the angle d to be equal to the angle c, and because the angle d is equal to the angle a, (vertical angles are equal), institute
With angle b=c-d=c-a, this specification plays one to the angle b and is named as: " deflection angle ".Lower section is optically denser medium in Fig. 1, and top is
Air, light are injected in air from optically denser medium, and n is the relative index of refraction of light, because testing actually measured n value is greater than 1, root
According to refractive index formula n=sin (c)/sin (a), so having: 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 index of refraction of light, is obtained by refractive index formula)
=sin (a+b)/sin (a)；(being obtained referring to Fig. 1, c=d+b=a+b)
=[sin (a) cos (b)+cos (a) sin (b)]/sin (a)；(being obtained by trigonometric function formula)
={ [sin (a) cos (b)]/sin (a) }+{ [cos (a) sin (b)]/sin (a) }；(bracket is unfolded to obtain)
=cos (b)+[sin (b)/tan (a)]；(being obtained by a angle tangent value tan (a)=sin (a)/cos (a)) is again by n
Formula that=cos (b)+[sin (b)/tan (a)] is derived or so transposition arranges abbreviation, available following formula:
Tan (a)=sin (b)/[n-cos (b)] ... ... (1)
Derived expression (1) gives the mathematical relationship between incidence angle a and deflection angle b and relative index of refraction n three, this
Formula is the deformation formula of refractive index formula, below to use in derivation process.
(02) YZQ tangent formula one is derived:
It is A type function toroidal lens by the index path of directional light light beam vernier focusing referring to Fig. 2, Fig. 2.Camber line is in figure
The other side of mirror refractive curvature line, lens is plane, and this plane is parallel with X-coordinate axle, and Y-coordinate axle is lens refractive curvature
Central axis.When incident light is directional light light beam and vertical with the plane side of lens, and is irradiated to the plane side of lens, enter
It penetrates light not reflect, incident light keeps original direction to enter lens interior.F point in Y-coordinate axle is the coke of lens refraction light
Point, f point is referred to as the focus of A type function toroidal lens refractive curvature in this specification.P point is any one on lens refractive curvature
Point, arrowed parallel lines are incident rays from bottom to top, and incident ray is parallel with Y-coordinate axle, and PE line is that incident ray is logical
The extended line of P point is crossed, PF line is normal of the lens refractive curvature in P point, and the G point in X-axis is that P point is cut on lens refractive curvature
The intersection point of line and X-coordinate axle, the R point in X-axis are the marginal points of lens, and O point is coordinate origin, refracted light Pf and PE straight line
Angle be the angle b because incident ray extended line PE is parallel with Y-coordinate axle, the angle of refracted light Pf and Y-coordinate axle
It is the angle b, the angle of (parallel lines alternate interior angle is equal), incident ray HP and normal PF is the angle angle of incidence of light a, tangent line PG and X-axis
Angle be the angle of contingence the supplementary angle angle d.Because two of the angle d are mutually perpendicular to respectively while with the two of the angle a, (tangent line perpendicular to
Normal, incident ray is perpendicular to X-axis), so there is the angle d to be equal to the angle a.Next we are the angle a angle b in Fig. 2 and a in Fig. 1
A comparison is made at the angle angle b, you are incidence angle and deflection angle, by Fig. 1, it can be seen that their physical characteristic is identical
The formula (1) derived equally is correct in Fig. 2.Again because the angle a is equal to the angle d in Fig. 2, the angle d is less than 90 degree, and d
Angle is the angle of tangent line and X-axis, so the absolute value of P point tangent slope | k |=tan (d)=tan (a), will | k | substitute into formula
(1) it is obtained in:
| k |=sin (b)/[n-cos (b)] ... ... (2).
Formula (2) is any point on the A type function toroidal lens refractive curvature by directional light light beam vernier focusing
The calculation formula of tangent slope absolute value.In order to describe convenience, one is played to formula (2) and is named as: " YZQ tangent formula one ",
(YZQ is that the first letter of the present inventor Yang Zhao triliteral Chinese phonetic alphabet by force connects together the abbreviation title of composition).This is public
In formula | k | for the absolute value of the tangent slope of any point P point on lens refractive curvature, b is corresponding tangent line point of contact P
The angle that point intersects with the central axis of lens refractive curvature again with the line of the focus f point of lens refractive curvature, n is lens material
Expect the relative index of refraction relative to air (light is projected from lens and got into the air) light.
(03) YZQ tangent formula two is derived:
Referring to Fig. 3, Fig. 3 is the index path for the focus that Type B function surface lens change focus on light beam.Y-coordinate axle is
The central axis of lens refractive curvature, the F point in figure in Y-coordinate axle is focus on light beam focusing focus position when no lens reflect
It sets, F point is referred to as the virtual focus of Type B function surface lens refractive curvature in this specification.F point in Y-coordinate axle is incident focusing
Again the focus that is focused after light beam is reflected by Type B function surface lens, f point is referred to as that Type B function surface lens are rolled in this specification
Penetrate the focus of curved surface.Two curves are the lens curved surface lines of two side of Type B function surface lens in figure, and the R point in X-axis is lens
Marginal point, 0 point is coordinate origin, and lower section rectangle UV is the object for emitting light beam in figure.Object one of the lens towards transmitting light beam
The curved surface of side is the sphere curved surface of a segment standard, and the center of circle of sphere curved surface is located at virtual focus F point, and the other side of lens is that refraction is bent
Face, virtual focus F point and lens refractive curvature are located at the same side.The effect of sphere curved surface is: so that the directive F point that object UV is issued
All light being irradiated on sphere curved surface and lens sphere curved surface it is vertical everywhere, make incident light that original direction be kept to enter saturating
Inside mirror.Unirefringence only occurs when being reflected by Type B function surface lens for focus on light beam, and this structure is for simplifying mathematical analysis
Formula is critically important.P point is any point on lens refractive curvature, and PM is normal of the lens refractive curvature in P point, in X-coordinate axle
G point be refractive curvature in the tangent line of P point and the intersection point of X-axis, straight line PT was the P point auxiliary line parallel with Y-coordinate axle, the angle a
It is the angle of incident ray and normal, the angle b is the angle of the extended line PF and refracted light Pf of incident ray, and the angle d is P point tangent line
With the angle of X-coordinate axle.The angle h be the focus f point of tangent line point of contact P point and lens refractive curvature line again with lens refractive curvature
Central axis intersection angle, the angle g be the virtual focus F point of tangent line point of contact P point and lens refractive curvature line again with lens
The angle of the central axis intersection of refractive curvature, and because auxiliary line PT is parallel with Y-coordinate axle, straight line PT and incident ray
The angle of extended line PF is equal with the angle g, (parallel lines alternate interior angle is equal) and the angle g.The angle of normal PM and straight line PT is the angle e.
Because two of the angle e are mutually perpendicular to respectively while with the two of the angle d, (for tangent line perpendicular to normal, straight line PT is perpendicular to X-coordinate
Axis), so the angle e is equal to the angle d.Following relational expression can be derived by Fig. 3:
In triangle FfP, the angle angle the b=angle h- g ... ... (3)；(triangle exterior angle be equal to non-conterminous two interior angle it
With)
The angle angle the a=angle the g+ angle the e=angle g+ d ... ... (4)；(vertical angles are equal) and (the angle angle e=d) is obtained
The angle angle a b is incidence angle and deflection angle respectively, and the formula derived by Fig. 1 (1) is also that correctly, will push away in Fig. 3
Derived relational expression (3), (4) substitute into formula (1) and obtain:
Tan (g+d)=sin (h-g)/[n-cos (h-g)] ... ... (5)
It enables: sin (h-g)/[n-cos (h-g)]=W
Formula (5) left side of the equal sign is unfolded with trigonometric function, right side of the equal sign is equal to W, left and right transposition, and abbreviation substitutes into W value
It obtains:
Tan (d)=[W-tan (g)]/[1+W*tan (g)] ... ... (6)
Because the angle d is the angle of tangent line and X-axis, and the angle d is less than 90 degree, so the absolute value of P point tangent slope | k |
=tan (d), will | k | it substitutes into formula (6), obtains:
| k |=[W-tan (g)]/[1+W*tan (g)] ... ... (7)
W in formula (7) is: W=sin (h-g)/[n-cos (h-g)]
Formula (7) is that focus on light beam is changed any point on the Type B function surface lens refractive curvature of focus
Tangent slope absolute value calculation formula.In order to describe conveniently, one is played to formula (7) and is named as: " YZQ tangent formula
Two ".In this formula | k | for the absolute value of the tangent slope of any point P point on lens refractive curvature, h is corresponding cuts
The angle that line point of contact P point intersects with the central axis of lens refractive curvature again with the line of the focus f point of lens refractive curvature, g
It is the line central axis with lens refractive curvature again of the virtual focus F point of corresponding tangent line point of contact P point and lens refractive curvature
The angle of intersection, n are relative index of refraction of the lens material relative to air (light is projected from lens and got into the air) light.
(04) AA type function toroidal lens tangent slope formula illustrates:
It is the optical path that AA type function toroidal lens focuses point light source light beam again on the other side of the lens referring to Fig. 4, Fig. 4
Figure.AA type function toroidal lens is substantially to be combined to constitute to plane by two A type function toroidal lens planes.GM in figure
Straight line is the central axis of lens, f1 the and f2 point on straight line GM is the focus of two side of lens.When the luminous point of point light source light beam
When f1 point, according to the reversibility pricinple of light and A type function toroidal lens refractive light paths principle, the light beam quilt of point light source sending
Towards after the refractive curvature refraction of point light source side, directional light light beam will be become in lens interior, when directional light light beam is from lens
When other side refractive curvature projects, because being also and A type function toroidal lens towards the lens refractive curvature for focusing side again
The refractive curvature of same type, so directional light light beam will be completely refocused.It is also each with well known two side of spherical lens
Unlike the focus of an own identical focal length: the focal length of the focus of two side of AA type function toroidal lens can be not identical
's.Because the refractive curvature of two side of AA type function toroidal lens is the refractive curvature with A type function toroidal lens same type,
So the tangent slope absolute value analytic expression of refractive curvature and the cutting for A type function toroidal lens of two side of AA type function toroidal lens
Line slope absolute value analytic expression is identical, is all YZQ tangent formula one.
(05) it is fabricated to the function surface lens tangent slope formula explanation of Fei Nier form of lens:
The curved surface of Fig. 2, Fig. 3 and function surface lens shown in Fig. 4 is to be revolved by whole smooth lens curved surface line around central axis
Then at such function surface lens are referred to as " single-curved surface function surface lens " in this specification, or referred to as " function surface is saturating
Mirror ".Fig. 5, Fig. 6 and Fig. 7 are seen again, claim to be shown with a plurality of (2 and 2 or more) smooth song such as Fig. 5, Fig. 6 and Fig. 7 in this specification
The function surface lens that upper thread is constituted around center axis rotation are as follows: " the function surface lens of Fei Nier form of lens ".Fig. 5 is
It is fabricated to the schematic diagram of the A type function toroidal lens of Fei Nier form of lens, Fig. 6 is the B type for being fabricated to Fei Nier form of lens
The schematic diagram of three kinds of forms of function surface lens, three kinds of forms are respectively: sphere curved surface and refractive curvature are fabricated to Fei Nier
Form of lens；Refractive curvature is fabricated to Fei Nier form of lens and sphere curved surface is still single-curved surface form；Refractive curvature is still
It is single-curved surface form and sphere curved surface is fabricated to Fei Nier form of lens, the function surface lens of these three forms referred to as make
At the Type B function surface lens of Fei Nier form of lens.Fig. 7 is the AA type function toroidal lens for being fabricated to Fei Nier form of lens
The schematic diagram of two kinds of forms, two kinds of forms are respectively: two side refractive curvatures are fabricated to Fei Nier form of lens；Side refraction is bent
Wheat flour is made Fei Nier form of lens and other side refractive curvature is still single-curved surface form, and the function surface of this two kinds of forms is saturating
Mirror is referred to as the AA type function toroidal lens for being fabricated to Fei Nier form of lens.Because of the function of A type Type B and AA type three types
Folder of the tangent slope absolute value analytic equation of toroidal lens with the extended line and central axis of refracted light or incident ray
Angle (angle the b angle the h angle g) is related with refractive index n, and is divided into several Duan Wuguan with lens refractive curvature line, so the production of three types
At the function surface lens of Fei Nier form of lens, tangent slope analytic expression is cut with corresponding single-curved surface function surface lens
Line slope absolute value analytic expression is identical.
(06) differential link calculating method explanation:
It is above-mentioned to be deduced at three kinds of regular light beam that any point is cut on function surface lens refractive curvature
The calculation formula of line slope absolute value, but our purpose is the X, Y coordinates value of every bit on lens refractive curvature line to be obtained,
To facilitate numerical control device to process or draw lens curved surface line.Next we see that how to link calculating method with differential calculates lens
The X, Y coordinates value of every bit on refractive curvature line.If the radius of lens is R, there is a particular point on lens refractive curvature line
Coordinate do not need calculate, here it is the coordinate of rims of the lens point (R, 0), just using this particular point as starting point, from starting point
Start to calculate.Coordinate system is first defined, using the central axis of lens refractive curvature as Y-coordinate axle, the marginal point of lens is located at X
On axis, lens refractive curvature line is located at coordinate system first quartile.Then a slight gap dx is set in X-direction, lens is rolled over
It penetrates camberline and is divided into many micro-segments by slight gap dx in X-direction, (dx value can according to need any setting) will be every
It is one section of straight line that one micro-segments, which is set to, and have several key points to be defined as follows on small linear segments: small linear segments are in X
The length projected on axis is dx, and the length projected in Y-axis is dy, and small linear segments are divided into starting point coordinate by computation sequence and are
(x1, y1), tangent line point of contact P point coordinate are (Xp, Yp), and end point coordinate is (x2, y2), are calculated since the marginal point of lens,
And rims of the lens point is located in coordinate system first quartile X-axis, lens refractive curvature line is single upper thread section, then has x2 small always
It is consistently greater than y1 in x1, y2, following several formula: x1-x2=dx, y2-y1=dy, dy=further can be obtained | k | * dx,
Dy1=| k1 | * dx, | k1 | it is with (x1, y1) point for tangent line point of contact, at calculated (x1, the y1) point of YZQ tangent formula
The absolute value of refractive curvature line tangent slope.The P point coordinate calculation formula of differential link calculating method are as follows:
P point coordinate X value: Xp=x1-dx/m ... ... (8)
P point coordinate Y value: Yp=y1+dy1/m ... ... (9)
M in this 2 calculation formula is greater than 1 real number, by artificially specifying, when the intermediate point for selecting small linear segments
When as the point position P, the calculation formula (8) of the P point coordinate of calculating method is linked, the m in (9) is m=2.
Dy=| k | in * dx calculation formula | and k | it is the absolute value of small linear segments slope, with the tangent slope of P point
Absolute value is equal, | k1 | and | k | then it is calculated with YZQ tangent formula one or YZQ tangent formula two.When some small straight line
The starting point coordinate value of segment be (x1, y1) be it is known, dx be it is known, end point coordinate value be (x2, y2) when, computation sequence
It is: calculates the absolute value of tangent slope at (x1, y1) point with YZQ tangent formula | k1 |, by | k1 | dy1 is calculated, by specifying
M value and x1, y1 and dy1 value, dx value, calculate Xp and Yp with the link P point coordinate calculation formula (8) of calculating method, (9)
Value, then calculate with YZQ tangent formula the absolute value of the tangent slope at (Xp, Yp) point | k |, then by | k | calculate dy,
X2 and y2 value is calculated by the value of dy, dx, x1 and y1 again.Point in A type and AA type function toroidal lens refractive curvature calculates
In, | k1 | and | k | it is calculated by YZQ tangent formula one, in the calculating of the point on Type B function surface lens refractive curvature, |
K1 | and | k | it is calculated by YZQ tangent formula two, enables the marginal point of lens refractive curvature in coordinate system first quartile X-axis,
It using the marginal point of lens refractive curvature as starting point, calculates from the off, each calculated small linear segments is terminated
Starting point coordinate value of the coordinate value of point as next small linear segments, continuously repeats calculating, needs to calculate until having been calculated
Lens refractive curvature line on all points for being divided into dx coordinate value until.These coordinate values be exactly we want it is saturating
The coordinate value of a series of point of dx is divided between on mirror refractive curvature line.Claim this calculating lens refractive curvature in this specification
The method of the coordinate value of point on line are as follows: " differential link calculating method ".When actually calculating, will be counted using computer program
It calculates, so there is no concern that small enough will increase difficulty in computation for what dx took to improve precision.Calculating method is linked with differential
Although calculated coordinate value is the approximation of the coordinate value of the point on lens refractive curvature line, but by means of modern high performance meter
Error can be reduced to micrometer level by the help of calculation machine, be the requirement for being fully able to meet lens.
(07) differential solves equation calculating method explanation:
Differential solves equation calculating method and needs YZQ tangent formula being converted into the form that X, Y coordinates solve equation.A type function is bent
Face lens are referring to Fig. 9, and Type B function surface lens are referring to Figure 10.It needs for lens refractive curvature line to be segmented before conversion formula
It is similar to link the way in calculating method to differential, first defines coordinate system for processing, using the central axis of lens refractive curvature as
The marginal point of Y-coordinate axle, lens is located in X-axis, and lens refractive curvature line is located at coordinate system first quartile.Then it is set in X-direction
Lens refractive curvature line is divided into many segments by interval dx in X-direction by a fixed interval dx, and (dx value, which can according to need, appoints
Meaning setting), it is one section of straight line that each segment, which is set to, and have several key points to be defined as follows on linear segments: linear segments are in X
The length projected on axis is dx, and the length projected in Y-axis is dy, and linear segments are divided into starting point coordinate by computation sequence and are
(x1, y1), tangent line point of contact P point coordinate are (Xp, Yp), and end point coordinate is (x2, y2), are calculated since the marginal point of lens,
And rims of the lens point is located in coordinate system first quartile X-axis, lens refractive curvature line is single-curved surface section, then has x2 to be consistently less than
X1, y2 are consistently greater than y1, and following several formula further can be obtained: x1-x2=dx, y2-y1=dy solve equation the P of calculating method
Point coordinate calculation formula are as follows:
P point coordinate X value: Xp=x1-dx/m ... ... (10)
P point coordinate Y value: Yp=y1+dy/m ... ... (11)
The real number that the m in the calculation formula of the P point coordinate of calculating method is greater than 1 is solved equation, by artificially specifying, when selection is straight
When the intermediate point of line segment is as the point position P, solving equation the m in the calculation formula of the P point coordinate of calculating method is m=2.It is right
Turn in A type and AA type function toroidal lens by the available following 2 A type function toroidal lens trigonometric function of mark in Fig. 9
Change equation:
By the P point coordinate calculation formula (10) for solving equation calculating method, (11) and the A type function toroidal lens triangle derived
Function conversion equation (12), (13) are updated in YZQ tangent formula one in the expression formula of right side of the equal sign, and arranging by abbreviation can be with
Obtain one only include variable x1, y1, dx, dy and constant f, n, m the absolute value expression of tangent slope, by this expression formula letter
The expression of change are as follows: T1 (x1, y1, dx, dy), while by the slope absolute value of linear segments | k | be expressed as | dy/dx |, then YZQ is cut
It is as follows that line formula one can be exchanged into another expression-form:
| dy/dx |=T1 (x1, y1, dx, dy) ... ... (15)
Write expression formula (15) as solve equation form are as follows:
| dy/dx |-T1 (x1, y1, dx, dy)=0 ... ... (16)
In equation (16), dx is artificially arranged, so being known, because coordinate calculating is from rims of the lens point
Start calculating, is coordinate value of the end point coordinate value of each linear segments as next linear segments starting point later, so
For the linear segments for preparing to calculate, x1, y1 are also known.In this way with regard to only one unknown number in equation (16)
Dy, by solving equation available dy value to equation (16).Equation (16) is a unitary polynomial equation formula.Common solution
Equation method cannot solve this equation, this equation can be solved with computer program, with the program source of this equation of VB program solution
Code can be as follows:
This section of program is solved equation with test method(s), that is, dy value is allowed to incrementally increase, when dy value increases to a certain value, meter
Calculation machine program learns Abs (dy/dx)-T1 (x1, y1, dx, dy)=0 or Abs (dy/dx)-T1 (x1, y1, dx, dy) by calculating
Absolute value less than 0.000001 when, program jumps out circulation, and dy value at this time is non trivial solution, and program continues to run, calculate
End point coordinate x2 and the y2 value of this line segment out.
For Type B function surface lens, by the available following 6 Type Bs function surface lens triangle of the mark in Figure 10
Function converts equation:
By the Type B function surface lens trigonometric function derived convert equation (20), (21), (22), (23), (24),
(25) the P point coordinate calculation formula (10) of equation calculation method is conciliate, (11) are updated to right side of the equal sign in YZQ tangent formula two
In expression formula, by abbreviation arrange available one only include variable x1, y1, dx, dy and constant f, F, n, m tangent line it is oblique
The absolute value expression of rate, the expression that this expression formula is simplified are as follows: T2 (x1, y1, dx, dy), and the slope of linear segments is absolute
Value | k | be expressed as | dy/dx |, then it is as follows to can be exchanged into another expression-form for YZQ tangent formula two:
| dy/dx |=T2 (x1, y1, dx, dy) ... ... (26)
Write expression formula (26) as solve equation form are as follows:
| dy/dx |-T2 (x1, y1, dx, dy)=0 ... ... (27)
Because x1, y1, dx for preparing the linear segments calculated are it is known that only one is not in equation (27)
Know that several dy, equation (27) are a unitary polynomial equation formulas, this equation can be solved with computer program, obtains dy
Value.
Above-mentioned two equations (16) and (27) are solved equation after finding out dy value, and because (x1, y1) is known, then answer
End point coordinate (x2, y2) value that this linear segments can be calculated with formula x1-x2=dx and y2-y1=dy, will calculate
Each linear segments end point starting point coordinate value of the coordinate value as next linear segments, continuously repeat calculating, directly
To having been calculated on calculative lens refractive curvature line until the coordinate value of all points for being divided into dx.Claim this in this specification
The method of the coordinate value of point on kind calculating lens refractive curvature line are as follows: " differential solves equation calculating method ".In dx value infinite approach
Under conditions of 0, the coordinate value that the point on the calculated a series of refractive curvature line of calculating method is solved equation by differential is one
Exact value.
(08) YZQ tangent formula can there are many plant different form of expression explanations:
It is above-mentioned to give two kinds of YZQ tangent formula explanations, there are also any it should be understood that above-mentioned YZQ tangent formula can
With the form of expression different there are many kind, such as in tangent slope absolute value calculation formula, can be replaced just with tangent function
String function or cosine function, or YZQ tangent formula etc. is described with the form of X, Y coordinates, but howsoever change, last meter
Calculating result will be consistent with YZQ tangent formula.So to judge whether tangent slope absolute value calculation formula belongs to model of the present invention
Interior tangent slope absolute value calculation formula is enclosed, calculated result is seen and cannot only see the form of expression.
(09) function surface lens how to be defined and ordinary lens method illustrates:
The differential link calculating method or differential provided with this specification solves equation calculating method and can calculate certain function surface
The coordinate value of a series of point on lens refractive curvature line reflects bent using calculated coordinate data as stencil value with lens
The coordinates measurements of actually active point are compared on face, if matched, then it is assumed that this lens is and function toroidal lens
Identical lens.Here the word that " matches " has two meanings, first is that identical as stencil value not less than the measured value of 95% point
Or error is then considered to match in allowed limits, because there is error, stencil value and measurement in processing and measurement
Value can not 100% it is identical；Second is that error is then considered kissing within the allowable range when Entity measurement value is compared with stencil value
Close, this allowable range of error can be within 1/10th millimeters within 1 percent millimeters or one thousandth millimeter with
It is interior, which allowable range of error grade is specifically selected, premised on it can demonstrate the fact, a biggish error is selected to allow
Range level.
(10) the superior place of function surface lens:
Because function surface lens can precision surpasses by regular light beam vernier focusing, and in terms of by directional light light beam focusing
Plano-convex spherical lens have been crossed, and the form of Fei Nier lens can also be made into, therefore function surface lens can be used to
It manufactures the optical instrument of higher precision and is used to the Salar light-gathering lens etc. of manufacture Fei Nier form of lens.Also as letter
Number toroidal lens refractive curvature can carry out parsing with the function analytic expression provided in this specification and coordinate calculates, therefore can be square
Calculated coordinate value being input in numerical control device just, and then what be can be convenient processes required function surface lens.
Detailed description of the invention
Fig. 1 is the index path that light injects light refraction in air from optically denser medium
Fig. 2 is A type function toroidal lens by the index path of directional light light beam vernier focusing.
Fig. 3 is the index path for the focus that Type B function surface lens change focus on light beam.
Fig. 4 is the index path that AA type function toroidal lens focuses point light source light beam again on the other side of the lens.
Fig. 5 is the schematic diagram for being fabricated to the A type function toroidal lens of Fei Nier form of lens.
Fig. 6 is the schematic diagram for being fabricated to Type B function surface three kinds of forms of lens of Fei Nier form of lens.
Fig. 7 is the schematic diagram for being fabricated to AA type function two kinds of forms of toroidal lens of Fei Nier form of lens.
Fig. 8 is the VB flow chart that differential link calculating method is written as to computer VB program in embodiment.
Fig. 9 be A type function toroidal lens refractive curvature line application differential solve equation calculating method carry out calculate parsing schematic diagram.
Figure 10 be Type B function surface lens refractive curvature line application differential solve equation calculating method carry out calculate parsing signal
Figure.
Figure 11 is that plano-convex spherical lens application CAD draws refracted light index path schematic diagram.
Figure 12 is that plano-convex spherical lens application CAD draws refracted light index path instance graph.
Figure 13 is broken line this lens refracting interface straightway coordinate diagram.
Figure 14 is this lens of broken line using CAD drafting refracted light index path schematic diagram.
Figure 15 is this lens of broken line using CAD drafting refracted light index path instance graph.
Figure 16 is the refracted light index path schematic diagram of each point on broken line this lens refracting interface line.
Specific embodiment
Specific embodiment will design the Salar light-gathering lens for the Fei Nier form of lens that a piece of diameter is 30 centimetres, referring to
Fig. 5.We can regard sunlight as directional light light beam.Lens are made with glass, select the size of glass are as follows: 30 lis of diameter
Rice, 2 centimetres of thickness.Related data is searched, determines that the refractive index n of glass is 1.65.The focal length for designing lens is 50 centimetres, is considered
If maximum height will be more than 2 centimetres of (thickness of glass in the middle part of lens to the function surface lens that lens are fabricated to single-curved surface
Degree), it can not make, so selection is fabricated to the A type function toroidal lens type of Fei Nier form of lens.By lens refractive curvature
Line is divided into three sections, and the X value of three sections of refractive curvature line starting points is respectively R1, R2 and R3, as shown in Figure 5.It will be in refractive curvature
Mandrel is as Y-coordinate axle.Next differential link calculating method is written as computer VB program, calculated every on lens refractive curvature
The coordinate value of a bit.It is the unit of number that one thousandth millimeter is used in VB program, and dx=1, lens maximum radius R1 are
150000 (1 centimetre=10000 arithemetic units), focal length 500000, refractive index n=1.65, lens curved surface are divided into three sections, three sections
The X value of camberline starting point and end point is respectively 15 to 12 centimetres, and 12 to 8 centimetres, 8 to 0 centimetre.It is by this scale segment
In view of keeping the attainable maximum y value of each section of camberline of substantially equal.When calculating tangent slope, each small straight line is specified
The position close to intermediate point of segment is the position of tangent line point of contact P point.Fig. 8 is that differential link calculating method is written as computer VB
The VB flow chart of program.First start VB6 programmed environment software, a standard engineering program file is created, in form1 forms
A middle placement one order button Command1 and text box Text1, then according to program chart or following VB program source generation
Code writes VB program, program, the order button in window is run after writing, program starts to be calculated as required, greatly
The end of the program after about more than ten seconds obtains a filename on E disk are as follows: the file of abc.txt is beaten with organizer program
This file is opened, every a line there are 2 numbers in file, and first digit is the X-coordinate value of certain point, and second digit is same point
Y-coordinate value, one shares the coordinate value of the point on 150000 lens refractive curvature lines, and X value precision is one thousandth millimeter, Y value
Precision is micron order.We can be by abc.txt this data file copies into the computer of numerical control device, numerical control device energy
Enough according to coordinate value lens working.It is the source code of the VB program of embodiment as follows, pf line segment refers in VB program: lens folding
Any point P point is penetrated in camberline to the line segment of focus f point.
Claims (8)
1. a kind of can be non-spherical surface by the function surface lens of regular light beam vernier focusing, the refractive curvature of this lens, this
Lens are divided into three types by unpolarized light beam situation difference, can be known as the function surface lens of directional light light beam vernier focusing
The function surface lens that focus on light beam changes focus can be known as Type B function surface lens, energy by A type function toroidal lens
The function surface lens that point light source light beam focuses again on the other side of the lens are known as AA type function toroidal lens, these three classes
The function surface lens of type can also be made into the function surface lens of Fei Nier form of lens, the letter of these three types respectively
Number toroidal lens and the corresponding function surface lens for being fabricated to Fei Nier form of lens are common feature is that lens refraction is bent
The coordinate value of every bit with calculating method is linked with differential or solves equation every bit obtained from calculating method calculates with differential on face
Coordinate value matches, and solving equation the calculating of tangent slope absolute value in calculating method with differential in differential link calculating method is by YZQ
Tangent formula one or YZQ tangent formula two (or there is identical calculations result by with YZQ tangent formula one or YZQ tangent formula two
Other forms mathematical formulae) calculated.
2. A type function toroidal lens described in claim 1 and the A type function toroidal lens for being fabricated to Fei Nier form of lens,
Be characterized in: lens side is plane, and the lens other side is refractive curvature or the refractive curvature for being fabricated to Fei Nier form of lens.
3. Type B function surface lens described in claim 1 and the Type B function surface lens for being fabricated to Fei Nier form of lens,
Be characterized in: lens side is that accurate sphere curved surface or the accurate sphere curved surface for being fabricated to Fei Nier form of lens, lens are another
Side is refractive curvature or the refractive curvature for being fabricated to Fei Nier form of lens, and the center of circle of sphere curved surface is located at lens centre axis
Virtual focus (F point), virtual focus (F point) and lens refractive curvature are located at the same side, the virtual focus (F point) of lens refractive curvature
It is focusing focus of the incident focus on light beam when no lens reflect.
4. AA type function toroidal lens described in claim 1 and the AA type function toroidal lens for being fabricated to Fei Nier form of lens,
It is characterized in that: lens are to be combined to constitute to plane by two A type function toroidal lens planes, two side refractive curvature of lens is equal
For refractive curvature identical with A type function toroidal lens refractive curvature, this two sides refractive curvature or side refractive curvature can be with
It is fabricated to Fei Nier form of lens, the focus of this two sides refractive curvature can be different.
5. YZQ tangent formula one described in claim 1, it is characterized in that: formula is | k |=sin (b)/[n-cos (b)], in formula
| k | it is the tangent slope at A type function toroidal lens or any point (P point) on AA type function toroidal lens refractive curvature
Absolute value, b be the focus (f point) of corresponding tangent line point of contact (P point) and lens refractive curvature line again with lens refractive curvature
Central axis intersection angle, n is lens material relative to the opposite of air (light is projected from lens and got into the air) light
Refractive index.
6. YZQ tangent formula two described in claim 1, it is characterized in that: formula is | k |=[W-tan (g)]/[1+W*tan (g)],
W in this formula is: W=sin (h-g)/[n-cos (h-g)], in formula | k | on Type B function surface lens refractive curvature
Any point (P point) tangent slope absolute value, h is the focus of corresponding tangent line point of contact (P point) and lens refractive curvature
The angle that the line of (f point) intersects with the central axis of lens refractive curvature again, g are corresponding tangent line point of contact (P point) and lens
The angle that the line of the virtual focus (F point) of refractive curvature intersects with the central axis of lens refractive curvature again, n is lens material phase
For the relative index of refraction of air (light is projected from lens and got into the air) light.
7. differential described in claim 1 links calculating method, it is characterized in that: using the central axis of lens refractive curvature as Y-coordinate axle,
The marginal point of lens is located in X-axis, and lens refractive curvature line is located at coordinate system first quartile, lens refractive curvature line in the side X
It is divided into many micro-segments to by slight gap dx, (dx value can according to need any setting) determines each micro-segments
To be one section of straight line, it is (x1, y1), tangent line point of contact P that the key point on small linear segments, which is divided into starting point coordinate by computation sequence,
Point coordinate is (Xp, Yp) and end point coordinate is (x2, y2), using formula x1-x2=dx, y2-y1=dy, dy=| k | * dx,
Dy1=| k1 | * dx, Xp=x1-dx/m and Yp=y1+dy1/m can calculate dy value and x2, y2 by x1, y1 value and dx value
Value, computation sequence is: the absolute value of tangent slope at (x1, y1) point is calculated with YZQ tangent formula | k1 |, by | k1 | it calculates
Dy1 calculates the value of Xp and Yp by the value and dx value of specified m value and x1, y1 and dy1, then is calculated with YZQ tangent formula
The absolute value of tangent slope at (Xp, Yp) point out | k |, then by | k | dy is calculated, then is calculated by the value of dy, dx, x1 and y1
X2 and y2 value, in the point in A type and AA type function toroidal lens refractive curvature calculates, | k1 | and | k | press YZQ tangent formula one
It is calculated, in the calculating of the point on Type B function surface lens refractive curvature, | k1 | and | k | it is carried out by YZQ tangent formula two
It calculates, enables the marginal point of lens refractive curvature in coordinate system first quartile X-axis, the marginal point with lens refractive curvature is
Point, calculates from the off, using the coordinate value of each calculated small linear segments end point as next small straight
The starting point coordinate value of line segment, continuously repeats calculating, until all intervals on calculative lens refractive curvature line have been calculated
Until coordinate value for the point of dx.
8. differential described in claim 1 solves equation calculating method, it is characterized in that: using the central axis of lens refractive curvature as Y-coordinate
The marginal point of axis, lens is located in X-axis, and lens refractive curvature line is located at coordinate system first quartile, lens refractive curvature line in X
Direction is divided into many segments by interval dx, and (dx value can according to need any setting), it is a Duan Zhi that each segment, which is set to,
Line, if the marginal point of lens refractive curvature in coordinate system first quartile X-axis, using the marginal point of lens refractive curvature as starting point,
It calculates from the off, linear segments starting point coordinate is set as (x1, y1), tangent line point of contact P point coordinate is (Xp, Yp), linear sheet
The end point coordinate of section is set as (x2, y2), for A type and AA type function toroidal lens, using the P point coordinate for solving equation calculating method
Calculation formula and the A type function toroidal lens trigonometric function derived convert equation, can be converted to YZQ tangent formula one only
Include the mathematic(al) representation of x1, y1, dx, dy variable and necessary constant, and be denoted as T1 (x1, y1, dx, dy), while by straight line
The slope absolute value of segment | k | be expressed as | dy/dx |, because prepare calculate linear segments x1, y1 and dx value be it is known that
So can be by equation | dy/dx |-T1 (x1, y1, dx, dy)=0 is solved equation, and obtains dy value, for Type B function surface
Lens, using the P point coordinate calculation formula for solving equation calculating method and the Type B function surface lens trigonometric function derived conversion etc.
Formula, YZQ tangent formula two can be converted to only include x1, y1, dx, dy variable and necessary constant mathematic(al) representation, and
It is denoted as T2 (x1, y1, dx, dy), while by the slope absolute value of linear segments | k | be expressed as | dy/dx | because prepare to calculate
X1, y1, dx value of linear segments are known, it is possible to by equation | dy/dx |-T2 (x1, y1, dx, dy)=0 solution
Equation obtains dy value, after finding out dy value, reapplies the end that formula x1-x2=dx and y2-y1=dy calculate this linear segments
Point coordinate (x2, y2) value, using the coordinate value of each calculated linear segments end point rising as next linear segments
Point coordinate value, continuously repeats calculating, until point that all are divided into dx has been calculated on calculative lens refractive curvature line
Until coordinate value.
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Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPH02236513A (en) * | 1989-03-10 | 1990-09-19 | Hoya Corp | Glass mold aspherical single lens |
| JPH11203712A (en) * | 1998-01-09 | 1999-07-30 | Toshiba Corp | Lens capable of generating evanescent wave |
| CN1409129A (en) * | 2001-09-17 | 2003-04-09 | 大日本印刷株式会社 | Resin composition for optical element, optical element and projection screen |
| TW200841043A (en) * | 2006-12-06 | 2008-10-16 | 3M Innovative Properties Co | Fresnel lens |
| US20120147476A1 (en) * | 2010-12-10 | 2012-06-14 | Hui-Hsiung Lin | Collimating optical element, collimating optical assembly, collimating optical array and collimating optical module |
| CN103022205A (en) * | 2012-12-12 | 2013-04-03 | 成都钟顺科技发展有限公司 | Line condensing lens |
-
2018
- 2018-09-03 CN CN201811072337.8A patent/CN109932764B/en active Active
Patent Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPH02236513A (en) * | 1989-03-10 | 1990-09-19 | Hoya Corp | Glass mold aspherical single lens |
| JPH11203712A (en) * | 1998-01-09 | 1999-07-30 | Toshiba Corp | Lens capable of generating evanescent wave |
| CN1409129A (en) * | 2001-09-17 | 2003-04-09 | 大日本印刷株式会社 | Resin composition for optical element, optical element and projection screen |
| TW200841043A (en) * | 2006-12-06 | 2008-10-16 | 3M Innovative Properties Co | Fresnel lens |
| US20120147476A1 (en) * | 2010-12-10 | 2012-06-14 | Hui-Hsiung Lin | Collimating optical element, collimating optical assembly, collimating optical array and collimating optical module |
| CN102540495A (en) * | 2010-12-10 | 2012-07-04 | 财团法人工业技术研究院 | Collimating optical element, assembly, array and collimating optical module |
| CN103022205A (en) * | 2012-12-12 | 2013-04-03 | 成都钟顺科技发展有限公司 | Line condensing lens |
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| CN109932764B (en) | 2021-11-02 |
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