CN105259602A - Novel aspheric panoramic reflector design method - Google Patents

Abstract

The invention discloses a novel aspheric reflector design method for an omnidirectional vision system. The method is characterized by comprising steps: the diameter, the thickness and the maximum incidence angle of the reflector are determined, a proper sampling point number is selected according to the maximum incidence angle and required processing precision, the diameter and the thickness are subdivided according to the sampling point number, as for a cluster of coaxial hyperbolic curves with the same focus and with real axis lengths increased linearly, curve segments are intercepted horizontally for finite element splicing to obtain a surface-type curve meeting certain requirements, an iterative formula is substituted, coordinates of the sampling points are obtained, the sampling points generated by an iterative equation are used for fitting an aspheric contour curve equation, and the equation is converted into ZMAX recognition optical equation.

Description

A kind of new aspheric panorama mirror design method

Technical field

The invention belongs to omni-directional visual process field, particularly relate to a kind of new aspheric panorama mirror design method.

Background technology

Constantly perfect along with overall view visual system, panoramic vision technology has had preliminary application in vision and optical field.In indoor and outdoor surroundings, panoramic vision is just progressively applied to the field such as monitoring and long-range reality.Due to its angular field of view of 360 degree, overall view visual system in outdoor environment the most directly application be monitoring field application.Video camera based on omnibearing vision sensor has very outstanding advantage, its looking away (360 degree), Information Compression in a hemisphere visual field can be become piece image, the quantity of information of piece image is larger, any point in panoramic picture all corresponds to a certain point determined monitored in space, therefore space position calibration algorithm is simple, without run-home during monitoring, making the algorithm of the moving object in the acquisition of visual information, detection and tracking monitoring range more simple, is a kind of quick, reliable panoramic vision information acquisition means.But current panorama system, carrying out the very large pattern distortion of panoramic picture expansion existence, propose a lot of method for reducing and eliminating this distortion, improving curved surface of reflector profile is one relatively directly effective method, greatly can improve the linearity that mirror image launches.

Summary of the invention

The nonlinear distortion that method object in the present invention exists in being to provide a kind of direct effective method abatement panoramic picture to launch, realizes the accurate reproduction of image information.

The technical solution adopted in the present invention is: the new method that a kind of non-spherical reflector for fully-directional visual system designs, and determines the diameter of catoptron, thickness and maximum incident angle three parameters.According to the machining precision of maximum incident angle and requirement, choose suitable sampling number, diameter and thickness determine the size of the useful area of minute surface, according to sampling number, diameter and thickness are segmented, substitute into iterative formula, ask for the coordinate of sampled point, carry out curve fitting according to the coordinate of all sampled points afterwards, and be converted into the Optical equations of ZMAX identification.The coaxial hyperbolic curve that real axis length linear increases progressively to cluster focal length is identical, level intercepts segment of curve and carries out finite element splicing, expands the method for the good imaging area of the linearity under the condition meeting single view constraint.

The invention has the beneficial effects as follows: improve image quality, the distortion of horizontal direction and vertical direction in removal of images unfolding calculation by the curvature of curve improving mirror surface band portions corresponding.

Accompanying drawing explanation

In order to be illustrated more clearly in the embodiment of the present invention or technical scheme of the prior art, be briefly described to the accompanying drawing used required in embodiment or description of the prior art below, apparently, accompanying drawing in the following describes is only some embodiments of the present invention, for those of ordinary skill in the art, under the prerequisite not paying creative work, other accompanying drawing can also be obtained according to these accompanying drawings.

Fig. 1 is curved design conditional curve schematic diagram.

Embodiment

Below in conjunction with embodiment, the present invention is further described.

Embodiment 1

The new method that a kind of non-spherical reflector for fully-directional visual system designs, determine the diameter of catoptron, thickness and maximum incident angle three parameters, according to the machining precision of maximum incident angle and requirement, choose suitable sampling number, according to sampling number, diameter and thickness are segmented, the coaxial hyperbolic curve that real axis length linear increases progressively to cluster focal length is identical, level intercepting segment of curve carries out finite element splicing and is met necessarily required type curve, substitute into iterative formula, ask for the coordinate of sampled point, the sampled point generated by iterative equation simulates aspheric contour curve equation, and be converted into the Optical equations of ZMAX identification.

Adjacent two incident ray space angles of regulation curved surface are △ θ=(β-α)/m, i.e. unlimited segmentation of catoptron actual observation angle, and m is sampling number; Separately establish △ x=r/m, for sampled point is in the step-length of minute surface horizontal direction displacement, with minute surface bottom centre for system coordinates initial point, n=1 ~ m, iteration asks for sampled point successively, and formula (3) (4) calculate the coordinate of current sampling point, and formula (7) calculates θ _nafter, n adds up automatically, n=n+1, gets back to the coordinate that formula (3) calculates next sampled point, and so forth,

x ₀＝y ₀＝0(1)

θ ₀＝0.5×(90°-α)(2)

x _n＝n×△x(3)

y _n＝y _n-1+tanθ _n-1×△x(4)

θ _sn＝(90°-α)+n×△θ+λ _n(6)

θ _n＝0.5×θ _sn-λ _n(7)

λ _nfor the angle of reflection ray and main shaft, θ _snbe the angle of n-th incident ray and corresponding reflection ray, the shape obtained through curve is as the equation of formula (8) form

x ²＝a ₁z+a ₂z ²+…+a _kz ^k+…(8)

A ₁=2r ₀, r ₀for the radius-of-curvature on summit, the secondary surface of revolution is had:

x ²＝2r ₀z-(1+e)z ²(9)

Formula (9) is made into as shown in the formula

z＝c ₁x ²+c ₂z ²(10)

Wherein: c ₁=1/2r ₀, c ₂=(1+e)/2r ₀, make x ₁=x ², x ₂=z ², turn to set { x _1i, x _2i, z _imultilinear fitting, obtain following formula

z＝c ₁x ₁+c ₂x ₂(11)

Derived (14) by formula (12) (13)

r ₀＝1/c ₁(12)

e＝2r ₀c ₂-1(13)

$z=\frac{{\mathrm{cx}}^2}{1+\sqrt{1-(1+e)c^2{x}^2}}+H\left(x^2\right)---\left(14\right)$

Formula (14) is aspheric contour curve equation.

The foregoing is only preferred embodiment of the present invention, not in order to limit the present invention, within the spirit and principles in the present invention all, any amendment done, equivalent replacement, improvement etc., all should be included in protection of the present invention.

Claims (2)

1. the new method that designs of the non-spherical reflector for fully-directional visual system, it is characterized in that, determine the diameter of catoptron, thickness and maximum incident angle three parameters, according to the machining precision of maximum incident angle and requirement, choose suitable sampling number, according to sampling number, diameter and thickness are segmented, the coaxial hyperbolic curve that real axis length linear increases progressively to cluster focal length is identical, level intercepting segment of curve carries out finite element splicing and is met necessarily required type curve, substitute into iterative formula, ask for the coordinate of sampled point, the sampled point generated by iterative equation simulates aspheric contour curve equation, and be converted into the Optical equations of ZMAX identification.

2. the new method of the non-spherical reflector design of fully-directional visual system according to claim 1, is characterized in that: the concrete steps of described aspheric contour curve equation are:

Adjacent two incident ray space angles of regulation curved surface are △ θ=(β-α)/m, i.e. unlimited segmentation of catoptron actual observation angle, and m is sampling number; Separately establish △ x=r/m, for sampled point is in the step-length of minute surface horizontal direction displacement, with minute surface bottom centre for system coordinates initial point, n=1 ~ m, iteration asks for sampled point successively, and formula (3) (4) calculate the coordinate of current sampling point, and formula (7) calculates θ _nafter, n adds up automatically, n=n+1, gets back to the coordinate that formula (3) calculates next sampled point, and so forth,

x ₀＝y ₀＝0(1)

θ ₀＝0.5×(90°-α)(2)

x _n＝n×△x(3)

y _n＝y _n-1+tanθ _n-1×△x(4)

θ _sn＝(90°-α)+n×△θ+λ _n(6)

θ _n＝0.5×θ _sn-λ _n(7)

λ _nfor the angle of reflection ray and main shaft, θ _snbe the angle of n-th incident ray and corresponding reflection ray, the shape obtained through curve is as the equation of formula (8) form

x ²＝a ₁z+a ₂z ²+…+a _kz ^k+…(8)

A ₁=2r ₀, r ₀for the radius-of-curvature on summit, the secondary surface of revolution is had:

x ²＝2r ₀z-(1+e)z ²(9)

Formula (9) is made into as shown in the formula

z＝c ₁x ²+c ₂z ²(10)

Wherein: c ₁=1/2r ₀, c ₂=(1+e)/2r ₀, make x ₁=x ², x ₂=z ², turn to set { x _1i, x _2i, z _imultilinear fitting, obtain following formula

z＝c ₁x ₁+c ₂x ₂(11)

Derived (14) by formula (12) (13)

r ₀＝1/c ₁(12)

e＝2r ₀c ₂-1(13)

$z=\frac{{\mathrm{cx}}^2}{1+\sqrt{1-(1+e)c^2{x}^2}}+H\left(x^2\right)---\left(14\right)$

Formula (14) is aspheric contour curve equation.