CN105954872B - A kind of optimum design method of extension pyramid - Google Patents
A kind of optimum design method of extension pyramid Download PDFInfo
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- CN105954872B CN105954872B CN201610556666.4A CN201610556666A CN105954872B CN 105954872 B CN105954872 B CN 105954872B CN 201610556666 A CN201610556666 A CN 201610556666A CN 105954872 B CN105954872 B CN 105954872B
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- G—PHYSICS
- G02—OPTICS
- G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
- G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
- G02B27/0012—Optical design, e.g. procedures, algorithms, optimisation routines
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Abstract
The present invention proposes a kind of optimum design method of extension pyramid, from the angle of incidence of light of the determining speculum of property easy to use 1, from optical property, the angle of incidence of light of speculum 2 and speculum 3 is determined according to speculum 1, speculum 2 and 3 mutually orthogonal relationship of speculum and angle of incidence of light minimization principle in extension pyramid.The spatial position used according to the angle of incidence of light of three determining speculums and extension pyramid solves the light incidence point P of three speculums using vector triangle method1,P2And P3Space coordinate at cartesian coordinate system XYZ.It is achieved in the optimization design of light path inside extended corner cone space.This method is designed by the minimum of incident angle, is reduced the scale of speculum, is improved the efficiency of optical manufacturing, reflecting mirror surface shape quality is made to be improved；The difficulty of plated film more importantly can be substantially reduced by reducing incident angle, it is with obvious effects in terms of the beam Propagation efficiency for improving extension pyramid.
Description
Technical field
The invention belongs to the technical fields such as optical engineering, Application Optics, and in particular to a kind of optimization design of extension pyramid
Method.
Background technology
Extension pyramid is mainly used in the optical device of limited space, draws the segment beam in optical device is parallel
Go out, without being influenced by extension pyramid installation accuracy.It is the equal of one intercepted along light path in prism of corner cube to extend pyramid
Point.The design of previous extension pyramid does not optimize incident angle, not only influences optical manufacturing face shape, can also give optical coating band
It is next difficult, so that the efficiency of transmission of extension pyramid is restricted.And it is excellent to use this method to carry out the incident angle in extension pyramid
Change design, processing and the service efficiency of extension pyramid can be greatly improved.
Invention content
The problem of for the above extension pyramid design, proposes a kind of optimum design method of extension pyramid, the party
Method can solve the above problems.
In order to achieve the object of the present invention, the present invention provides a kind of optimum design method of extension pyramid, including following step
Suddenly：
The incident angle α of step (1), speculum 11It is set to 45 degree；
Step (2), the incidence point P with speculum 11Cartesian coordinate system XYZ is established for origin, is determined under the coordinate system
The normal vector M of speculum 11And the incidence point position P undetermined of speculum 2 and speculum 32And P3；
In step (3), establishment step (2) under cartesian coordinate system XYZ speculum 2 and speculum 3 normal vector undetermined
M2And M3, make M1·M2=0, M1·M3=0 and M2·M3=0 three equation is set up simultaneously, establishes the incident light direction of speculum 1
Vectorial R1, the incident light direction vector R of speculum 22With the emergent light direction vector R of speculum 34；
The face system equation of lower three mirror planes of cartesian coordinate system XYZ in step (4), establishment step (2)：M1·
[X,Y,Z]T=0, M2·[X,Y,Z]T=0 and M3·[X,Y,Z]T=0；
Step (5), the incident angle α undetermined for determining speculum 2 respectively by vector angle formula2=acos (M2·(-R2)/(|
M2|·|-R2|)) and speculum 3 incident angle α undetermined3=acos (M3·R4/(|M3|·|R4|)), and calculated by extreme value algorithm
α2And α3Make the sum of two incidence angles α2+α3It is minimum；
The incident angle α of step (6), three speculums determined according to step (1) and step (5)1, α2And α3, by vector three
Angular method and the cosine law solve vector triangle Δ P1P2P3With Δ P2P3P4In two vertex P2And P3At coordinate system XYZ
Coordinate value, wherein vertex P4It is obligatory point known to coordinate.
Wherein, the incidence angle of speculum 1 is set to 45 ° in the step (1), to ensure incident light and the outgoing of speculum 1
Light is mutually perpendicular to, more convenient when processing and installation uses.
Wherein, the sum of incidence angle α is sought in the step (5)2+α3Minimum value, through solve work as α2=α3Enter at=60 °
The sum of firing angle α2+α3Minimum can be omitted step (3)~(5) at this time, and two vertex P are directly determined by step (6)2And P3Coordinate
Value.
The present invention has the following advantages that compared with prior art：
(1) incident angle of present invention extension corner cube reflector 1 is set to 45 °, is brought convenience to processing and installation use；
(2) present invention determines that the incident angle of speculum 2 and speculum 3 can promote extension pyramid light by optimization method
The efficiency of transmission of beam.And existing method does not make optimization to incident angle.
Description of the drawings
Fig. 1 is the geometry solving schematic diagram of extension pyramid optimum design method proposed by the present invention.
Specific implementation mode
To make the objectives, technical solutions, and advantages of the present invention clearer, below in conjunction with specific embodiment, and reference
Attached drawing, the present invention is described in more detail.
The method that the present invention extends pyramid optimization design substantially increases expansion by optimizing the incident angle of each speculum
Open up the beam Propagation efficiency of pyramid.Its specific implementation process is as shown in Figure 1, be as follows：
The first step：Cartesian coordinate system XYZ as shown in Figure 1 is established, with the incidence point P of speculum 11For coordinate origin.
Second step：The incidence angle of speculum 1 is determined as 45 °, as shown in Figure 1, determining the speculum 1 at coordinate system XYZ
Normal vector M1=[- 1, -1,0], and the incident ray of speculum 1 and emergent ray direction vector are respectively R1=[0,1,0]
And R2=[- 1,0,0].
Third walks：The light incidence point position P undetermined of speculum 2 and speculum 3 is established at cartesian coordinate system XYZ2
And P3And the plane normal direction vector M of speculum 2 undetermined and speculum 32And M3；Establish speculum 2 and speculum 3 incidence and
Emergent light direction vector is respectively：R2, R3And R3, R4。
4th step：There is following relational expression by three reflecting surface mutually orthogonal relationships of extension pyramid：M1·M2=0, M1·M3
=0 and M2·M3=0.In conjunction with the normal vector M of step 21Determine M2=[1, -1, m], determines M3=[1, -1, -2/m], wherein m
For undetermined parameter；The direction vector R of outgoing beam known to the relationship be mutually parallel by extension pyramid incident beam and outgoing beam4
=[0, -1,0].
5th step：Establish the face system equation of lower three mirror planes of cartesian coordinate system XYZ：M1·[X,Y,Z]T=0,
M2·[X,Y,Z]T=0 and M3·[X,Y,Z]T=0.
6th step：Determine the incident angle α undetermined of speculum 2 respectively by vector angle formula at cartesian coordinate system XYZ2
=acos (M2·(-R2)/(|M2|·|-R2|)) and speculum 3 incident angle α undetermined3=acos (M3·(R4)/(|M3|·|R4
|)), then α2+α3=acos ((1/ (m2+2))1/2)+acos((1/(4/m2+2))1/2), to the formula derivation, when m=± 21/2When α2+
α3There is 120 ° of minimum value, at this time α2=α3=60 °.
7th step：Vector triangle Δ is solved by vector triangle method and the cosine law in cartesian coordinate system XYZ
P1P2P3With Δ P2P3P4In two vertex P2And P3Coordinate value.Solve | P1P3|2=| P1P2|2+|P2P3|2-2|P1P2||P2P3
|cos(2α2) and | P2P4|2=| P2P3|2+|P3P4|2-2|P2P3||P3P4|cos(2α3) P in two formulas2And P3The unknown coordinates of point
Value, wherein P4It is obligatory point known to coordinate.
Embodiment described above is only limitted to explain that the present invention, protection scope of the present invention should include the whole of claim
Content, and the full content of the claims in the present invention can be thus achieved by embodiment person skilled in art.
Claims (2)
1. a kind of optimum design method of extension pyramid, it is characterised in that include the following steps：
The incident angle α of step (1), the first speculum (1)1It is set to 45 degree；
Step (2), with the incidence point P of the first speculum (1)1Cartesian coordinate system XYZ is established for origin, is determined in the coordinate system
The normal vector M of lower first speculum (1)1And second speculum (2) and third speculum (3) incidence point position P undetermined2
And P3；
In step (3), establishment step (2) under cartesian coordinate system XYZ the second speculum (2) and third speculum (3) it is undetermined
Normal vector M2And M3, make M1·M2=0, M1·M3=0 and M2·M3=0 three equation is set up simultaneously, establishes the first speculum
(1) incident light direction vector R1, the incident light direction vector R of the second speculum (2)2With the emergent light side of third speculum (3)
To vectorial R4；
The face system equation of lower three mirror planes of cartesian coordinate system XYZ in step (4), establishment step (2)：M1·[X,Y,Z
]T=0, M2·[X,Y,Z]T=0 and M3·[X,Y,Z]T=0；
Step (5), the incident angle α undetermined for determining the second speculum (2) respectively by vector angle formula2=acos (M2·(-R2)/
(|M2|·|-R2|)) and third speculum (3) incident angle α undetermined3=acos (M3·R4/(|M3|·|R4|)), and by extreme value
Algorithm calculates α2And α3Make the sum of two incidence angles α2+α3It is minimum；
The incident angle α of step (6), three speculums determined according to step (1) and step (5)1, α2And α3, by vector triangle
Method and the cosine law solve vector triangle Δ P1P2P3With Δ P2P3P4In two vertex P2And P3Coordinate at coordinate system XYZ
Value, wherein vertex P4It is obligatory point known to coordinate.
2. the optimum design method of extension pyramid according to claim 1, it is characterised in that：First in the step (1)
The incidence angle of speculum (1) is set to 45 °, with ensure the first speculum (1) incident light and emergent light be mutually perpendicular to, processing and
It is more convenient when installing and using.
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Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101131477A (en) * | 2007-09-07 | 2008-02-27 | 武汉大学 | Pyramid prism design method based on surface shape compensation |
| CN104991299A (en) * | 2015-07-09 | 2015-10-21 | 西南科技大学 | Method for calculating reflected light intensity of cubic pyramid type retroflection material |
-
2016
- 2016-07-15 CN CN201610556666.4A patent/CN105954872B/en active Active
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101131477A (en) * | 2007-09-07 | 2008-02-27 | 武汉大学 | Pyramid prism design method based on surface shape compensation |
| CN104991299A (en) * | 2015-07-09 | 2015-10-21 | 西南科技大学 | Method for calculating reflected light intensity of cubic pyramid type retroflection material |
Non-Patent Citations (6)
| Title |
|---|
| Comparison between non-modulation four-sided and two-sided pyramid wavefront sensor;Jianxin Wang,et al.;《OPTICS EXPRESS》;20101220;第18卷(第26期);第27534-27549页 * |
| Linearity of the pyramid wavefront sensor;Anna Burvall,et al.;《OPTICS EXPRESS》;20061211;第14卷(第25期);第11925-11934页 * |
| Nonlinear control for pyramid sensors in adaptive optics;Ole Wulff,et al.;《Proc. of SPIE》;20060627;第6272卷;第62721S-1-10页 * |
| Renate Kupke,et al..Implementation of the pyramid wavefront sensor as a direct phase detector for large amplitude aberrations.《Proc. of SPIE》.2008,第7015卷第70155H1-11页. * |
| 基于四 棱锥传感器的波前检测仿真设计;陈欣扬 等;《天文学进展》;20061230;第24卷(第4期);第362-372页 * |
| 无调制两面锥波前传感器的衍射理论分析和数值仿真;王建新 等;《物理学报》;20111230;第60卷(第2期);第029501-1-6页 * |
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