CN105954872A - Optimization design method for extended pyramid - Google Patents
Optimization design method for extended pyramid Download PDFInfo
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- CN105954872A CN105954872A CN201610556666.4A CN201610556666A CN105954872A CN 105954872 A CN105954872 A CN 105954872A CN 201610556666 A CN201610556666 A CN 201610556666A CN 105954872 A CN105954872 A CN 105954872A
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- reflecting mirror
- incident angle
- pyramid
- angle
- optimization design
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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 invention provides an optimization design method for an extended pyramid. The light incident angle of a reflecting mirror 1 is determined from the perspective of use convenience. The light incident angle of a reflecting mirror 2 and a reflecting mirror 3 is determined from the perspective of optical performance according to the mutually perpendicular relation of the reflecting mirror 1, the reflecting mirror 2 and the reflecting mirror 3 in the extended pyramid and the minimization principle of the light incident angle. The space coordinates of the light incident points P1, P2 and P3 of the three reflecting mirrors in a Cartesian coordinate system XYZ are solved by adopting a vector triangle method according to the determined light incident angle of the three reflecting mirrors and the space position used by the extended pyramid. Therefore, the optimization design of the space internal light path of the extended pyramid can be realized. According to the method, the scale of the reflecting mirrors can be reduced and the optical processing efficiency can be enhanced through the minimization design of the incident angle so that the profile quality of the reflecting mirrors can be enhanced; and furthermore, the difficulty of film coating can be greatly reduced by reducing the incident angle, and the optimization design method has obvious effect in the aspect of enhancing beam transmission efficiency of the extended pyramid.
Description
Technical field
The invention belongs to the technical field such as optical engineering, Application Optics, be specifically related to a kind of Optimization Design extending pyramid.
Background technology
Extension pyramid is mainly used in the optical device of limited space, by parallel for the segment beam in optical device extraction, and not
Affected by extension pyramid installation accuracy.Extension pyramid is the equal of the part intercepted along light path in prism of corner cube.Expanded in the past
Incident angle is not optimized by the design of exhibition pyramid, not only affects optical manufacturing face shape, also can bring difficulty to optical coating, make
The efficiency of transmission of extension pyramid is restricted.And use the method that the incident angle in extension pyramid is optimized design, permissible
It is greatly improved processing and the service efficiency of extension pyramid.
Summary of the invention
For problem present in above extension pyramid design, proposing a kind of Optimization Design extending pyramid, the method can
Solve the problems referred to above.
In order to realize the purpose of the present invention, the present invention provides a kind of Optimization Design extending pyramid, comprises the following steps:
Step (1), the incident angle α of reflecting mirror 11It is set to 45 degree；
Step (2), with the incidence point P of reflecting mirror 11Set up cartesian coordinate system XYZ for initial point, determine under this coordinate system
The normal vector M of reflecting mirror 11, and reflecting mirror 2 and the incidence point position P undetermined of reflecting mirror 32And P3；
Reflecting mirror 2 and the normal vector undetermined of reflecting mirror 3 under cartesian coordinate system XYZ in step (3), establishment step (2)
M2And M3, make M1·M2=0, M1·M3=0 and M2·M3=0 three equation is set up simultaneously, sets up the incident illumination of reflecting mirror 1
Direction vector R1, the incident illumination direction vector R of reflecting mirror 22Emergent light direction vector R with reflecting mirror 34；
The face system equation of lower three mirror plane 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), determined the incident angle α undetermined of reflecting mirror 2 respectively by vector angle formula2=acos (M2·(-R2)
/(|M2|·|-R2|)) and the incident angle α undetermined of reflecting mirror 33=acos (M3·R4/(|M3|·|R4|)), and calculated α by extreme value algorithm2
And α3Make two angle of incidence sums α2+α3Minimum；
Step (6), the incident angle α of three reflecting mirrors determined according to step (1) and step (5)1, α2And α3, by
Amount triangulation method and the cosine law solve vector triangle Δ P1P2P3With Δ P2P3P4In two summit P2And P3In coordinate system
Coordinate figure under XYZ, wherein summit P4It it is obligatory point known to coordinate.
Wherein, in described step (1), the angle of incidence of reflecting mirror 1 is set to 45 °, to ensure incident illumination and the emergent light of reflecting mirror 1
It is mutually perpendicular to, more convenient when processing and installing and using.
Wherein, described step (5) asks for angle of incidence sum α2+α3Minima, work as α through solving2=α3Angle of incidence when=60 °
Sum α2+α3Minimum, now can omit step (3)～(5), step (6) directly determine two summit P2And P3Seat
Scale value.
The present invention compared with prior art has the advantage that
(1) present invention extends the incident angle of corner cube reflector 1 and is set to 45 °, brings convenience to processing and installing and using；
(2) by optimization method, the present invention determines that the incident angle of reflecting mirror 2 and reflecting mirror 3 can promote extension pyramid light beam
Efficiency of transmission.And incident angle is not made optimization by existing method.
Accompanying drawing explanation
Fig. 1 is the geometry solving schematic diagram of the extension pyramid Optimization Design that the present invention proposes.
Detailed description of the invention
For making the object, technical solutions and advantages of the present invention clearer, below in conjunction with specific embodiment, and referring to the drawings,
The present invention is described in more detail.
The present invention extends the method for pyramid optimization design, by optimizing the incident angle of each reflecting mirror, substantially increases extension pyramid
Beam Propagation efficiency.Its concrete implementation process is as it is shown in figure 1, specifically comprise the following steps that
The first step: set up cartesian coordinate system XYZ as shown in Figure 1, with the incidence point P of reflecting mirror 11For zero.
Second step: the angle of incidence of reflecting mirror 1 is defined as 45 °, as it is shown in figure 1, determine reflecting mirror 1 under coordinate system XYZ
Normal vector M1=[-1 ,-1,0], and the incident ray of reflecting mirror 1 and emergent ray direction vector be respectively R1=[0,1,0] and
R2=[-1,0,0].
3rd step: set up the light point position undetermined P of reflecting mirror 2 and reflecting mirror 3 under cartesian coordinate system XYZ2
And P3And reflecting mirror 2 undetermined and the plane normal direction vector M of reflecting mirror 32And M3；Set up reflecting mirror 2 and reflecting mirror 3
Incident and emergent light direction vector is respectively as follows: R2, R3And R3, R4。
4th step: had following relational expression: M by extension three reflecting surface mutually orthogonal relationships of pyramid1·M2=0, M1·M3=0
And M2·M3=0.The normal vector M of integrating step two1Determine M2=[1 ,-1, m], determines M3=[1 ,-1 ,-2/m], wherein m is for treating
Determine parameter；The relation being parallel to each other by extension pyramid incident beam and outgoing beam understands the direction vector of outgoing beam
R4=[0 ,-1,0].
5th step: set up the face system equation of lower three mirror plane 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: determined the angle of incidence undetermined of reflecting mirror 2 under cartesian coordinate system XYZ by vector angle formula respectively
α2=acos (M2·(-R2)/(|M2|·|-R2|)) and the incident angle α undetermined of reflecting mirror 33=acos (M3·(R4)/(|M3|·|R4|)),
Then α2+α3=acos ((1/ (m2+2))1/2)+acos((1/(4/m2+2))1/2), to this formula derivation, when m=± 21/2Time α2+α3There is minima
120 °, now α2=α3=60 °.
7th step: solved vector triangle Δ P by vector triangle method and the cosine law in cartesian coordinate system XYZ1P2P3
With Δ P2P3P4In two summit P2And P3Coordinate figure.I.e. solve | P1P3|2=| P1P2|2+|P2P3|2-2|P1P2||P2
P3|cos(2α2) and | P2P4|2=| P2P3|2+|P3P4|2-2|P2P3||P3P4|cos(2α3) P in two formulas2And P3Point is not
Know coordinate figure, wherein P4It it is obligatory point known to coordinate.
Embodiment described above is only limitted to explain the present invention, and protection scope of the present invention should include the full content of claim,
And the full content of the claims in the present invention i.e. can be realized by embodiment person skilled in art.
Claims (3)
1. the Optimization Design extending pyramid, it is characterised in that comprise the following steps:
Step (1), the incident angle α of reflecting mirror 11It is set to 45 degree；
Step (2), with the incidence point P of reflecting mirror 11Set up cartesian coordinate system XYZ for initial point, determine under this coordinate system
The normal vector M of reflecting mirror 11, and reflecting mirror 2 and the incidence point position P undetermined of reflecting mirror 32And P3；
Reflecting mirror 2 and the normal vector undetermined of reflecting mirror 3 under cartesian coordinate system XYZ in step (3), establishment step (2)
M2And M3, make M1·M2=0, M1·M3=0 and M2·M3=0 three equation is set up simultaneously, sets up the incident illumination of reflecting mirror 1
Direction vector R1, the incident illumination direction vector R of reflecting mirror 22Emergent light direction vector R with reflecting mirror 34；
The face system equation of lower three mirror plane 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), determined the incident angle α undetermined of reflecting mirror 2 respectively by vector angle formula2=acos (M2·(-R2)
/(|M2|·|-R2|)) and the incident angle α undetermined of reflecting mirror 33=acos (M3·R4/(|M3|·|R4|)), and calculated α by extreme value algorithm2
And α3Make two angle of incidence sums α2+α3Minimum；
Step (6), the incident angle α of three reflecting mirrors determined according to step (1) and step (5)1, α2And α3, by
Amount triangulation method and the cosine law solve vector triangle Δ P1P2P3With Δ P2P3P4In two summit P2And P3In coordinate system
Coordinate figure under XYZ, wherein summit P4It it is obligatory point known to coordinate.
The Optimization Design of extension pyramid the most according to claim 1, it is characterised in that: anti-in described step (1)
The angle of incidence penetrating mirror 1 is set to 45 °, is mutually perpendicular to the incident illumination and emergent light ensureing reflecting mirror 1, is processing and is installing and using
Time more convenient.
The Optimization Design of extension pyramid the most according to claim 1, it is characterised in that: described step is asked in (5)
It is taken into firing angle sum α2+α3Minima, work as α through solving2=α3Angle of incidence sum α when=60 °2+α3Minimum, now can omit
Step (3)～(5), directly determined two summit P by step (6)2And P3Coordinate figure.
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109814082A (en) * | 2019-01-21 | 2019-05-28 | 上海禾赛光电科技有限公司 | Optical receiver module and laser radar system |
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 |
|---|
| ANNA BURVALL,ET AL.: "Linearity of the pyramid wavefront sensor", 《OPTICS EXPRESS》 * |
| JIANXIN WANG,ET AL.: "Comparison between non-modulation four-sided and two-sided pyramid wavefront sensor", 《OPTICS EXPRESS》 * |
| OLE WULFF,ET AL.: "Nonlinear control for pyramid sensors in adaptive optics", 《PROC. OF SPIE》 * |
| RENATE KUPKE,ET AL.: "Implementation of the pyramid wavefront sensor as a direct phase detector for large amplitude aberrations", 《PROC. OF SPIE》 * |
| 王建新 等: "无调制两面锥波前传感器的衍射理论分析和数值仿真", 《物理学报》 * |
| 陈欣扬 等: "基于四 棱锥传感器的波前检测仿真设计", 《天文学进展》 * |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109814082A (en) * | 2019-01-21 | 2019-05-28 | 上海禾赛光电科技有限公司 | Optical receiver module and laser radar system |
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