CN105698819A - Calibration method for multi-camera polarized light sensor - Google Patents

Abstract

The invention discloses a calibration method for a multi-camera polarized light sensor.The calibration method comprises the steps that firstly, a measuring error equation for the multi-camera polarized light sensor is established; secondly, linear regression equations of cameras are established; thirdly, linear parameters of the cameras are acquired by solving the equations; fourthly, a target optimization function for polarizing film installation error angles is established; fifthly, the installation error angles of a polarizing film are solved in an iteration mode based on Gauss-Newton.Calibration of the multi-camera polarized light sensor is finished, nonuniformity errors of the multi-camera polarized light sensor and the installation error angles of the polarizing film are compensated, the measuring precision of the polarized light sensor can be effectively improved, and the calibration method has the advantages that principles are simple, operation is easy and convenient, and the application range is wide and has broad application prospects for achieving orientation positioning of the bionic polarized light.

Description

A kind of scaling method for polyphaser polarized light sensor

Technical field

The present invention relates to polarized light sensor fields of measurement, particularly to a kind of scaling method for polyphaser polarized light sensor。

Background technology

Currently, although the classical airmanship such as inertial navigation, satellite navigation, geomagnetic matching navigation achieves significant progress, plays great function in the application being each suitable for；But in the face of low cost, in high precision, strongly disturbing special environment, classical airmanship still can not fully meet the demand that the autonomous navigation of motion platform, intelligent operation and safety are maked a return voyage。No matter have in mind from the trend of airmanship self high speed development, or from urgent demand, be required for expanding new thinking, New Research Method, seek the airmanship new, adaptive capacity to environment is strong, to adapt to constantly progressive new demand。

Based on the bionical cognition technology of simulation of the Nature biosystem, the new development for airmanship provides enlightenment。A lot of insecticides and the birds polarized light information by special physiological structure perception sky in nature, thus being navigated activity。Such as, desert Formica fusca determines azimuth information by detecting the polarization mode in air, it is possible to linearly accurately returning from the place of distance nest hundreds of meters, the insecticide such as Apis, butterfly realizes navigator fix also by intensity and the direction of perception sky polarized light。Compared with classical airmanship, bionical polarotactic navigation utilizes the sky polarization mode with natural quality, strong interference immunity, error do not accumulate, the advantage such as applied widely, when being relatively suitable for the long boat under complex environment, remote independent navigation, the application for fields such as vehicle, boats and ships, aircraft has extensive prospect。

Accurately measuring the distribution of sky polarized light pattern is the basis realizing bionical polarotactic navigation。Two kinds can be divided into according to measurement means polarized light sensor, a kind of polarization luminous point measurement apparatus being based on photodiode, sensors with auxiliary electrode simple in construction, the impact that light intensity changes can be overcome, be conducive to long-time measurement, but detection region is limited, measurement result is subject to the impact of the factors such as weather, the second is based on the polarized light sensor of polyphaser, sensors with auxiliary electrode has the advantage of multichannel, many pixels, it is capable of the fine polarization mode in whole day territory to measure, closer to the polarized light detection organ of Compound Eye of Insects mechanism。The demarcation of polarized light sensor is the necessary means realizing accurately measuring。From the document published at present, rarely have document that the demarcation of polarized light sensor is furtherd investigate。Therefore it is carried out deep theory and applied research is necessary。

Generally speaking, effect in research and utilization polarized light is navigated is far from reaching the biological level using polarotactic navigation at present, organ and acceptance research thereof for biological perception polarized light are relatively more abundant, have been able to realize imitating in engineering the sensor of the polarized light detection brake of insecticide。But the demarcation for polarized light sensor is studied very few, greatly affects the certainty of measurement of sensor, it is therefore desirable to the demarcation of bionical polarized light sensor is studied。

Summary of the invention

The technical problem to be solved in the present invention is that the compensation of nonuniformity error and the polaroid error of fixed angles how realizing polyphaser polarized light sensor。

For solving above-mentioned technical problem, the solution that the present invention proposes is:

A kind of scaling method for polyphaser polarized light sensor, it is characterised in that comprise the following steps:

(1) measuring error equation of polyphaser polarized light sensor is set up；

(2) equation of linear regression of each camera is set up；

(3) solving equation obtains the linear dimensions of each camera；

(4) the objective optimization function of polaroid fix error angle is set up；

(5) based on the fix error angle of Gauss-Newton iterative polaroid。

As a further improvement on the present invention, the output equation measuring equation and sensor that in above-mentioned steps (1), measuring error equation comprises the measuring error equation of pixel in each camera, each camera channel contains polaroid fix error angle；

In each camera, the measuring error equation of each pixel is:

In formula, j=1,2,3,4 represent the numbering of camera, k_j、b_jRepresenting linear dimensions, respectively scale factor and constant value zero are partially, I_cjFor the response value of pixel, n_jFor measuring white noise；

The measurement equation that each camera channel contains polaroid fix error angle is:

In formula, j represents that camera channel is numbered, and I is incident polarization light intensity, and d is degree of polarization, and φ is the angle of polarization, ε_jFor the fix error angle of polaroid, α in each passage of jth_jFor the established angle of polaroid, υ_jFor measuring white noise；

The measurement of polyphaser polarized light sensor is output as:

In formula,α₁=0 °, α₂=45 °, α₃=90 °, α₄=135 °

Then the angle of polarization of sensor measurement and degree of polarization are respectively as follows:

In formula,WithForComponent。

As a further improvement on the present invention, in above-mentioned steps (2), the equation of linear regression of each camera is:

In formula, i represents pendulous frequency,The intensity of input light,For the response value of corresponding camera pixel point, k_j、b_jFor needing the linear dimensions of each pixel demarcated。

As a further improvement on the present invention, in above-mentioned steps (4), the optimization object function of polaroid fix error angle is:

In formula,Representing the fix error angle of polaroid and initial polarization test error respectively, n is pendulous frequency, and r (x) is rotation error vector。

As a further improvement on the present invention, in above-mentioned steps (5), the equation that Gauss-Newton iterative method carries out error update is utilized to be

In formula,Jacobi matrix for error vector。

Compared with prior art, it is an advantage of the current invention that:

(1) polyphaser polarized light sensor has systematically been demarcated by the present invention first, the nonuniformity error of effective compensation camera and polaroid error of fixed angles, and the certainty of measurement for improving sensor provides theoretical direction and realizes method；

(2) present invention adopts linear regression that the linear dimensions of camera is demarcated, and based on the fix error angle of Gauss-Newton iterative polaroid, has and calculates the advantage simple, easy and simple to handle, accuracy rate is high。

Accompanying drawing explanation

Fig. 1 is the schematic flow sheet of the inventive method；

Fig. 2 be the inventive method specifically demarcate flow chart；

Fig. 3 is the experimental provision of the inventive method calibration for cameras linear dimensions；

Fig. 4 is the experimental provision that the inventive method demarcates polaroid fix error angle。

Detailed description of the invention

Below with reference to Figure of description and specific embodiment, the present invention is described in further detail。

As depicted in figs. 1 and 2, a kind of scaling method for polyphaser polarized light sensor that the present invention relates to, the first special construction according to polyphaser polarized light sensor for: the method, set up measuring error equation；Then according to each camera varying strength light irradiate under pixel response, solve each camera equation of linear regression obtain each pixel linear dimensions；The angle of polarization variable quantity recorded according to polarized light sensor again, sets up the optimization object function of polaroid fix error angle, adopts the fix error angle of Gauss-Newton iterative polaroid, thus completing the demarcation of polyphaser polarized light sensor。

In conjunction with concrete application example, the idiographic flow of the present invention is:

1. set up the measuring error equation of polyphaser polarized light sensor, comprise the measuring error equation of pixel in each camera, the output equation measuring equation and sensor that each camera channel contains polaroid fix error angle；

In each camera, the measuring error equation of each pixel is:

In formula, j=1,2,3,4 represent the numbering of camera, k_j、b_jRepresenting linear dimensions, respectively scale factor and constant value zero are partially, I_cjFor the response value of pixel, n_jFor measuring white noise；

The measurement equation that each camera channel contains polaroid fix error angle is:

In formula, j represents that camera channel is numbered, and I is incident polarization light intensity, and d is degree of polarization, and φ is the angle of polarization, ε_jFor the fix error angle of polaroid, α in each passage of jth_jFor the established angle of polaroid, υ_jFor measuring white noise；

The measurement of polyphaser polarized light sensor is output as:

In formula,α₁=0 °, α₂=45 °, α₃=90 °, α₄=135 °

Then the angle of polarization of sensor measurement and degree of polarization are respectively as follows:

In formula,ForComponent。

2. set up the equation of linear regression of each camera；

The linear dimensions of each camera is for compensating the output nonuniformity error that camera causes because optical characteristics is different, and concrete demarcation example experiment is as shown in Figure 3。For avoiding the impact of external light source, experiment carries out in airtight darkroom。Polarized light sensor is placed under uniform integration ball light source, allow in the largest light intensity of input at camera, gradually increase the size of input light intensity, record the pixel response of each camera simultaneously, response according to different input light intensity magnitude Yu camera pixel point, sets up the equation of linear regression of each pixel of each camera:

In formula, i represents pendulous frequency,The intensity of input light,For the response value of corresponding camera pixel point, k_j、b_jFor needing the linear dimensions of each pixel demarcated。

3. solving equation obtains the linear dimensions of each camera；

Formula (6) is solved by the principle minimum according to error sum of squares, can obtain corresponding linear dimensions。

Owing to the nonuniformity error useable linear parameter of each camera goes to compensate, then the linearity of calibrating parameters can weigh calibration result。After demarcation, in each camera, the linearly dependent coefficient of each pixel is:

In formula,For the measurement vector after pixel matching each in jth camera, I₀For input light dominant vector, λ_jFor linearly dependent coefficient。

When weighing the linear dimensions calibration result of camera, if linearly dependent coefficient λ_jBeing closer to 1, then show that the linearity is more strong, calibration result is more accurate。Owing to each camera contains multiple pixel, the index that can adopt pixel percentage ratio weighs overall calibration result, such as in this example experiment, calibration result is: in each camera, the linearly dependent coefficient of the pixel of 99% is all higher than 0.999, it is seen that the method can realize essence highly linear parameter calibration。

4. set up the objective optimization function of polaroid fix error angle；

The demarcation example experiment of polaroid fix error angle is as shown in Figure 4。First polarized light sensor is fixed on accurate multiteeth indexing table, place it under the standard polarized light source being made up of polaroid and uniform integration ball light source, by the angle that multiple rotary circular dividing table is different, read the rotational angle of circular dividing table, as reference rotational angle；Then the measurement result of sensor time according to different rotary position, calculates corresponding angle of polarization angle changing according to formula (3)～(4), then the error between reference rotational angle and the angle changing of sensor measurement is:

In formula, k represents kth time and rotates,For polarization sensor measure the angle of polarization,WithThe respectively initial measurement angle of polarization and error thereof, Δ_kFor reference rotational angle, can be obtained by accurate multiteeth indexing table。

The fix error angle defining each polaroid is estimation difference vector x with initial measurement angle of polarization error, in example experiment, contains 4 cameras containing sensor, then estimation difference vector is represented by:

Can obtaining according to above formula, the optimization object function of polaroid fix error angle is:

In formula, n is pendulous frequency, and r (x) is rotation error vector。

5. based on the fix error angle of Gauss-Newton iterative polaroid；

By formula (8)～(10) it can be seen that the optimization object function of polaroid fix error angle has non-linear, elder generation's linearization process when solving, carry out first order Taylor expansion:

Then optimization object function can be written as:

Above-mentioned optimization problem is dissolved and is converted into unconfined Linear least squares minimization problem, and the Gauss-Newton iterative method of classics can be adopted to solve。According to optimum theory it can be seen that formula (12) has solution must to be fulfilled for equation:

By above formula being solved the iterative equation that can obtain optimal solution:

In a word, the idiographic flow of above-mentioned demarcation can be obtained by Fig. 2。

The above is only the preferred embodiment of the present invention, and protection scope of the present invention is not limited merely to above-described embodiment, and all technical schemes belonged under thinking of the present invention belong to protection scope of the present invention。It should be pointed out that, for those skilled in the art, some improvements and modifications without departing from the principles of the present invention, these improvements and modifications also should be regarded as protection scope of the present invention。

Claims (5)

1. the scaling method for polyphaser polarized light sensor, it is characterised in that include following step:

(1) measuring error equation of polyphaser polarized light sensor is set up；

(2) equation of linear regression of each camera is set up；

(3) solving equation obtains the linear dimensions of each camera；

(4) the objective optimization function of polaroid fix error angle is set up；

(5) based on the fix error angle of Gauss-Newton iterative polaroid。

2. a kind of scaling method for polyphaser polarized light sensor according to claim 1, it is characterised in that: the measuring error equation of described step (1) comprises the measuring error equation of pixel in each camera, each camera channel contains the measurement equation of polaroid fix error angle and the output equation of sensor；

In each camera, the measuring error equation of each pixel is:

${\tilde{I}}_j=k_j{I}_{cj}+b_j+n_j$

In formula, j=1,2,3,4 represent the numbering of camera, k_j、b_jRepresenting linear dimensions, respectively scale factor and constant value zero are partially, I_cjFor the response value of pixel, n_jFor measuring white noise；

The measurement equation that each camera channel contains polaroid fix error angle is:

${\tilde{I}}_j=\frac{1}{2}I(1+dcos(2\mathrm{\φ}-2\left({\mathrm{\α}}_j-{\mathrm{\ϵ}}_j\right)\left)\right)+{\mathrm{\υ}}_j$

In formula, j represents that camera channel is numbered, and I is incident polarization light intensity, and d is degree of polarization, and φ is the angle of polarization, ε_jFor the fix error angle of polaroid, α in each passage of jth_jFor the established angle of polaroid, υ_jFor measuring white noise；

The measurement of polyphaser polarized light sensor is output as:

$\tilde{Q}={\left({\tilde{A}}^T\tilde{A}\right)}^{-1}{\tilde{A}}^T\tilde{U}$

In formula, $\tilde{A}=\left[\begin{array}{ccc}\cos 2({\mathrm{\α}}_1-{\mathrm{\ϵ}}_1)& \sin 2({\mathrm{\α}}_1-{\mathrm{\ϵ}}_1)& 1\\ \cos 2({\mathrm{\α}}_2-{\mathrm{\ϵ}}_2)& \sin 2({\mathrm{\α}}_2-{\mathrm{\ϵ}}_2)& 1\\ \cos 2({\mathrm{\α}}_3-{\mathrm{\ϵ}}_3)& \sin 2({\mathrm{\α}}_3-{\mathrm{\ϵ}}_3)& 1\\ \cos 2({\mathrm{\α}}_4-{\mathrm{\ϵ}}_4)& \sin 2({\mathrm{\α}}_4-{\mathrm{\ϵ}}_4)& 1\end{array}\right],$ $\tilde{U}={\[{\begin{array}{cccc}{\tilde{I}}_1& {\tilde{I}}_2& {\tilde{I}}_3& \tilde{I}\end{array}}_4\]}^T,$ α₁=0 °, α₂=45 °, α₃=90 °, α₄=135 °

Then the angle of polarization of sensor measurement and degree of polarization are respectively as follows:

$\widetilde{\mathrm{\φ}}=\frac{1}{2}\arctan \left(\frac{{\tilde{q}}_2}{{\tilde{q}}_1}\right)$

$\tilde{d}=\frac{\sqrt{{\tilde{q}}_1+{\tilde{q}}_2}}{{\tilde{q}}_3}$

In formula,WithForComponent。

3. a kind of scaling method for polyphaser polarized light sensor according to claim 1, it is characterised in that: in described step (2), the equation of linear regression of each camera is:

$min\underset{i}{\Σ}{\left({\tilde{I}}_j^i\right(k_j,b_j)-I_0^i)}^2,i\≥2$

In formula, i represents pendulous frequency,The intensity of input light,For the response value of corresponding camera pixel point, k_j、b_jFor needing the linear dimensions of each pixel demarcated。

4. a kind of scaling method for polyphaser polarized light sensor according to claim 1, it is characterised in that: in described step (4), the optimization object function of polaroid fix error angle is:

$\min f\left(x\right)=\left|\right|r\left(x\right)\left|\right|=\underset{k=1}{\overset{n}{\Σ}}{\left(r_k\right(x\left)\right)}^2,n\≥num\left(x\right)$

In formula, $x=\[\begin{array}{ccccc}{\mathrm{\ϵ}}_1& {\mathrm{\ϵ}}_2& {\mathrm{\ϵ}}_3& {\mathrm{\ϵ}}_4& \mathrm{\δ}{\widetilde{\mathrm{\φ}}}_0\end{array}\],$ Representing the fix error angle of polaroid and initial polarization test error respectively, n is pendulous frequency, and r (x) is rotation error vector。

5. a kind of scaling method for polyphaser polarized light sensor according to claim 1, it is characterised in that: in described step (5), utilize the equation that Gauss-Newton iterative method carries out error update to be

$x_{m+1}=x_m-{(\▿r{\left(x_m\right)}^T\▿r(x_m\left)\right)}^{-1}\▿r{\left(x_m\right)}^{T}r\left(x_m\right)$

In formula,Jacobi matrix for error vector。