CN103292981A - Measuring device and calibration method for optical lens distortion - Google Patents

Abstract

Provided is a measuring device and a calibration method for optical lens distortion. The measuring device comprises a single star light simulator, an adjusting rack, a to-be-tested lens, a CCD (charge coupled device) camera, a one-dimensional air flotation turntable, an angle encoder, a computer and an optical platform. The calibration method includes the steps of using a centroid localization algorithm to determine centroid position coordinates of a star point image when the to-be-tested lens is under different fields of view, establishing a calibration model for the to-be-tested lens distortion based on the distribution of the centroid position coordinates of the star point image under the entire field of view, and realizing the calibration of the distorted to-be-tested lens. The measuring device and the calibration method for the optical lens distortion has the advantages that the device is simple; the method is convenient; measurement accuracy is high; and the optical lens distortion can be easily measured and calibrated.

Description

Measurement mechanism and the bearing calibration of optical lens distortion

Technical field

The present invention relates to optical lens, especially a kind of measurement mechanism and bearing calibration of optical lens distortion.

Technical background

Can there be distortion to a certain degree in general optical lens when imaging, be difficult to reach the perfect lens imaging effect, the size of distortion has determined the image quality of camera lens and the measuring accuracy of system to a great extent, can cause the geometric position distortion of image, and bring difficulty for feature extraction and the calculation of parameter of image, thereby influence the erroneous judgement of information, even can't clearly differentiate the object to be imaged.Therefore, be used for the optical lens of precision measurement system, it is particularly important that the measurement of its distortion and correction seem.

Known technology [1] wide-angle distortion testing system and method, the applying date is the Chinese patent 01256866.X in Dec 11 calendar year 2001.This method is to utilize light source to pass through the light-passing board of array light hole, through lens imaging to be measured to CCD, and use test software analysis optical spot centre position.Calculating is as near any distance between two optical spot centre corresponding with the edge between adjacent two optical spot centre and the cross center in edge, distortion is the ratio of two optical spot centre distance in edge with center two optical spot centre distances, judges the situation of lens distortion size to be measured according to comparative result.Before the distortion test, require the geometric center of light-passing board and the optical axis of camera lens to be measured to coincide, therefore the alignment error of light-passing board and camera lens to be measured can influence distortion measurement, the array light hole is not of uniform size on the light-passing board simultaneously also will influence measuring accuracy, and this method mainly is applicable to the measurement of big visual field optical lens distortion.

Image sensering device and the method for the distortion of known technology [2] energy compensating images, the applying date is the Chinese patent 98122712.0 on November 26th, 1998.This method is to read a correcting sheet earlier, has the chequered with black and white striped of scheduled volume on this correcting sheet, and the exact position of black streaking is known.After correcting sheet reads, can get the chequered with black and white striped of corresponding scheduled volume, calculate by judging, can get the black streaking position.Then, calculate the exact position of the chequered with black and white striped of this scheduled volume and the difference that image reads the back calculating location, namely get the amount of distortion of each reference point.Deposit the amount of distortion of each reference point in the storer end correcting sheet fetch program.Carry out image when reading, each amount of distortion that is stored in the storer is removed at every turn, to revise the pattern distortion that optical system causes.This bearing calibration be not to image each the point carried out distortion correction, its calibration result is not really accurate, can not obtain complete satisfactory correcting image.

Summary of the invention

The objective of the invention is to overcome the deficiency of above-mentioned technology formerly, proposed a kind of measurement mechanism and bearing calibration of optical lens distortion, this installation method is simple, convenient, measuring accuracy is high, is easy to realize measurement and the correction of optical lens distortion.

Technical solution of the present invention is as follows:

A kind of optical lens distortion measurement device, characteristics are that its formation comprises single star optical simulator 1, adjustment rack 2, camera lens to be measured 3, CCD camera 4, one dimension air-float turntable 5, angular encoder 6, computing machine 7 and optical table 8 compositions, and the position relation of above-mentioned component is as follows:

Described adjustment rack 2 and one dimension air-float turntable 5 place on the described optical table 8, described single star optical simulator 1 is made up of integrating sphere light source 101, parallel light tube 103 and the pin hole graticule 102 that is positioned on parallel light tube 103 focal planes, described single star optical simulator 1 is fixed on the described adjustment rack 2, described camera lens to be measured 3 and CCD camera 4 are fixed on the one dimension air-float turntable 5, and the entrance pupil face of camera lens 3 to be measured is overlapped with the revolving shaft of one dimension air-float turntable 5, described angular encoder 6 is used for the angle of the rotation of record one dimension air-float turntable 5; The described pin hole graticule 102 of optical illumination that is sent by described integrating sphere light source 101, light by pin hole graticule 102 is formed starlight by parallel light tube 103 collimations, this starlight produces the asterism picture by camera lens 3 to be measured, this asterism picture is surveyed by described CCD camera 4, and the output terminal of described CCD camera 4 links to each other with the input end of described computing machine 7.

The bearing calibration that the measurement mechanism that utilizes above-mentioned optical lens to distort is implemented lens distortion to be measured is to utilize the barycenter location algorithm to determine the centroid position coordinate of asterism picture under the different visual fields of camera lens to be measured, and at the centroid position coordinate distribution situation of asterism picture under the whole visual field, set up the peg model of lens distortion to be measured, realize the correction of lens distortion to be measured.

A kind of measurement mechanism that utilizes optical lens to distort is realized the bearing calibration of lens distortion to be measured, and this method may further comprise the steps:

1. the demarcation of visual field, optical center to be measured: use internal focusing telescope to seek the optical axis of camera lens to be measured, and by being fixed on " ten " word graduation of the CCD camera collection internal focusing telescope on the camera lens back plane to be measured, be somebody's turn to do the position coordinates of " ten " word graduation point of crossing on CCD camera target surface, be visual field, optical center to be measured coordinate x ₀, y ₀

2. show the asterism picture: camera lens to be measured is fixed on the one dimension air-float turntable, aims at camera lens to be measured with single star optical simulator, the starlight that single star optical simulator produces to the target surface of CCD camera, forms an asterism as s through lens imaging to be measured ₀₀,

Regulate described adjustment rack, make the asterism of single star optical simulator generation as s ₀₀Aim at the coordinate x of the visual field, center of camera lens to be measured ₀, y ₀Rotation one dimension air-float turntable, and the angle of pitch of adjusting adjustment rack, the starlight that single star optical simulator is produced, through the asterism picture of lens imaging to be measured to the CCD camera target surface, drop on the position of CCD target surface l=1, k=1, be camera lens directions X-3.5 to be measured ° and Y-direction-3.5 ° visual field point, it is s that note asterism herein looks like ₁₁, and utilize the barycenter location algorithm, obtain asterism as s ₁₁Centroid position coordinate x ₁₁, y ₁₁

3. gather the asterism picture of-3.5 ° of visual fields on the camera lens Y-direction to be measured: with asterism as s ₁₁The present position is the one-dimensional scanning starting point, rotation one dimension air-float turntable, make camera lens to be measured along directions X from l=1, k=1 realizes one-dimensional scanning to 3.5 ° of visual field points of directions X, the analyzing spot that every interval is 0.3 ° is a collection position, collection position l=1, k=2 place with it the asterism of CCD camera collection correspondence to look like be s ₁₂, and calculate centroid position coordinate x ₁₂, y ₁₂..., collection position l=1, k=n place with it corresponding asterism to look like be s _1n, utilize the barycenter location algorithm to obtain centroid position coordinate x _1n, y _1n, simultaneously, angular encoder shows that the angle value that the one dimension air-float turntable rotates in real time should be ω mutually _X11, ω _X12..., ω _X1n, be the field angle on the one-dimensional scanning camera lens directions X to be measured;

4. regulate the angle of pitch of adjustment rack, make starlight look like to fall within the position of CCD target surface l=2, k=n by the asterism of lens imaging to be measured, and note asterism herein to look like be s _2n, the barycenter location algorithm can get its position coordinates x _2n, y _2nAgain with asterism as s _2nThe present position is the one-dimensional scanning starting point, rotation one dimension air-float turntable, make camera lens to be measured realize one-dimensional scanning from l=2, k=n to-3.5 ° in the other direction along X, the analyzing spot that every interval is 0.3 ° is a collection position, the CCD camera is successively during collection position l=2, k=n-1, k=n-2 ..., k=1 asterism to look like be s _{2 (n-1)}, s _{2 (n-2)}..., s ₂₁, a series of corresponding position coordinateses with it that utilize that the barycenter location algorithm obtains are x _{2 (n-1)}, y _{2 (n-1)}, x _{2 (n-2)}, y _{2 (n-2)}..., x ₂₁, y ₂₁, simultaneously, angular encoder shows that the angle value that the one dimension air-float turntable rotates in real time should be ω mutually _X2n, ω _{X2 (n-1)}..., ω _X21

5. change the position of one-dimensional scanning starting point, 3., 4. repeating step obtains a series of asterism pictures ... s _M1, s _M2S _MnCorresponding angle value with it ..., ω _Xm1, ω _Xm2..., ω _Xmn, the asterism that obtains until the CCD camera is as all being distributed on the CCD target surface, and by the obtainable asterism picture element of barycenter location algorithm heart position coordinates is ..., x _M1, y _M1, x _M2, y _M2..., x _Mn, y _Mn

6. set up lens distortion model to be measured:

The two-dimensional polynomial model of distortion correction as shown in the formula:

${\mathrm{\ω}}_{\mathrm{xlk}}=a_0+a_1{x}_{\mathrm{lk}}^{\′\′}+a_2{y}_{\mathrm{lk}}^{\′\′}+a_3{x_{\mathrm{lk}}^{\′\′}}^2+a_4{y_{\mathrm{lk}}^{\′\′}}^2+a_5{x}_{\mathrm{lk}}^{\′\′}{y}_{\mathrm{lk}}^{\′\′}+a_6{x_{\mathrm{lk}}^{\′\′}}^3+a_7{x_{\mathrm{lk}}^{\′\′}}^2{y}_{\mathrm{lk}}^{\′\′}+a_8{x}_{\mathrm{lk}}^{\′\′}{y_{\mathrm{lk}}^{\′\′}}^2+a_9{y_{\mathrm{lk}}^{\′\′}}^3$

Wherein, $\left\{\begin{array}{c}{x}_{\mathrm{lk}}^{\′\′}=x_{\mathrm{lk}}^{\′}-x_0\\ y_{\mathrm{lk}}^{\′\′}=y_{\mathrm{lk}}^{\′}-y_0\end{array}\right.,$

a ₀, a ₂, a ₃, a ₄, a ₅, a ₆, a ₇, a ₈, a ₉Be multinomial coefficient;

Make A=[a ₀a ₁A ₉] ^T, ψ _x=[ω _X11ω _X12ω _Xmn] ^T,

$P=\left[\begin{array}{cccccccccc}1& x_{11}^{\&prime;\&prime;}& y_{11}^{\&prime;\&prime;}& {x_{11}^{\&prime;\&prime;}}^2& {y_{11}^{\&prime;\&prime;}}^2& x_{11}^{\&prime;\&prime;}{y}_{11}^{\&prime;\&prime;}& {x_{11}^{\&prime;\&prime;}}^3& {x_{11}^{\&prime;\&prime;}}^2{y}_{11}^{\&prime;\&prime;}& x_{11}^{\&prime;\&prime;}{y_{11}^{\&prime;\&prime;}}^2& {y_{11}^{\&prime;\&prime;}}^3\\ 1& x_{12}^{\&prime;\&prime;}& y_{12}^{\&prime;\&prime;}& {{\mathrm{<figure-callout\; id="12"\; label="x"\; filenames="HDA00003227957800012.png"\; state="\{\{state\}\}">x</figure-callout>}}_{12}^{\&prime;\&prime;}}^2& {y_{12}^{\&prime;\&prime;}}^2& x_{12}^{\&prime;\&prime;}{y}_{12}^{\&prime;\&prime;}& {x_{12}^{\&prime;\&prime;}}^3& {x_{12}^{\&prime;\&prime;}}^2{y}_{12}^{\&prime;\&prime;}& x_{12}^{\&prime;\&prime;}{y_{12}^{\&prime;\&prime;}}^2& {y_{12}^{\&prime;\&prime;}}^3\\ \&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;& & & & & & & & & \\ 1& x_{\mathrm{mn}}^{\&prime;\&prime;}& y_{\mathrm{mn}}^{\&prime;\&prime;}& {x_{\mathrm{mn}}^{\&prime;\&prime;}}^2& {y_{\mathrm{mn}}^{\&prime;\&prime;}}^2& x_{\mathrm{mn}}^{\&prime;\&prime;}{y}_{\mathrm{mn}}^{\&prime;\&prime;}& {x_{\mathrm{mn}}^{\&prime;\&prime;}}^3& {x_{\mathrm{mn}}^{\&prime;\&prime;}}^2{y}_{\mathrm{mn}}^{\&prime;\&prime;}& x_{\mathrm{mn}}^{\&prime;\&prime;}{y_{\mathrm{mn}}^{\&prime;\&prime;}}^2& {y_{\mathrm{mn}}^{\&prime;\&prime;}}^3\end{array}\right]$

Wherein, m 〉=9, n 〉=9.

Following formula can get each coefficient of correcting distorted two-dimensional polynomial model:

A＝P ^-1ψ _x

Again the every coefficient of polynomial expression is brought in the correcting distorted two-dimensional polynomial model, i.e. the distortion of recoverable camera lens to be measured.

This model is used for match and produces the centroid position of asterism picture by camera lens to be measured, and it can effectively reduce barycenter location inaccuracy error, improves the distortion correction precision.

Compare with technology formerly, technique effect of the present invention is as follows:

1. this method is measured the optics lens distortion, need not complicated alignment procedures, is subjected to artifical influence factor less, applicable to the distortion measurement of middle small field of view optical lens.

2. this method has been set up a strict mathematics model, can realize the correction that distorts under the different visual fields of optical lens, and its mathematical model simply is suitable for, correction accuracy is high, provides accuracy guarantee for optical lens is used for precision measurement.

3. this method realizes the measurement of optical lens distortion by the one-dimensional scanning mode, and it is simple to have a measuring equipment, simple operation, characteristics such as measuring accuracy height; Be specially adapted to the correction of optical lens in the precision measurement system, for example the correction of star sensor barycenter distortion.

Description of drawings

Fig. 1 is the structural representation of the present invention's lens distortion measurement mechanism to be measured

Fig. 2 for asterism in the present invention's lens distortion measuring process to be measured as the gatherer process synoptic diagram

Fig. 3 is the present invention's lens distortion measurement model to be measured synoptic diagram

Embodiment

Below in conjunction with drawings and Examples the present invention is described in further detail, but should limit protection scope of the present invention with this.

See also Fig. 1 earlier, Fig. 1 is the present invention's lens distortion measurement mechanism to be measured structural representation.As seen from the figure, optical lens distortion measurement device of the present invention, formation comprises single star optical simulator 1, adjustment rack 2, camera lens to be measured 3, CCD camera 4, one dimension air-float turntable 5, angular encoder 6, computing machine 7 and optical table 8 compositions, and the position relation of above-mentioned component is as follows:

Described adjustment rack 2 and one dimension air-float turntable 5 place on the described optical table 8, described single star optical simulator 1 is made up of integrating sphere light source 101, parallel light tube 103 and the pin hole graticule 102 that is positioned on parallel light tube 103 focal planes, described single star optical simulator 1 is fixed on the described adjustment rack 2, described camera lens to be measured 3 and CCD camera 4 are fixed on the one dimension air-float turntable 5, and the entrance pupil face of camera lens 3 to be measured is overlapped with the revolving shaft of one dimension air-float turntable 5, described angular encoder 6 is used for the angle of the rotation of record one dimension air-float turntable 5; The described pin hole graticule 102 of optical illumination that is sent by described integrating sphere light source 101, light by pin hole graticule 102 is formed starlight by parallel light tube 103 collimations, this starlight produces the asterism picture by camera lens 3 to be measured, this asterism picture is surveyed by described CCD camera 4, and the output terminal of described CCD camera 4 links to each other with the input end of described computing machine 7.

The measurement mechanism that utilizes above-mentioned optical lens to distort is implemented the bearing calibration of lens distortion to be measured, and this method may further comprise the steps:

1. the demarcation of visual field, camera lens 3 center to be measured: use internal focusing telescope to seek the optical axis of camera lens 3 to be measured, and by being fixed on " ten " word graduation picture of the CCD camera 4 collection internal focusing telescopes on camera lens 3 back planes to be measured, be somebody's turn to do the position coordinates of " ten " word graduation point of crossing on the target surface of CCD camera 4, be the coordinate x of the visual field, center of camera lens 3 to be measured ₀, y ₀

2. show the asterism picture: described camera lens 3 to be measured is star sensor optical systems, gather the track while scan of asterism picture as shown in Figure 2, camera lens 3 to be measured is fixed on the one dimension air-float turntable 5, aim at camera lens 3 to be measured with single star optical simulator 1, the starlight that single star optical simulator 1 produces, be imaged onto on the target surface of CCD camera 4 through camera lens 3 to be measured, form an asterism as s ₀₀,

Regulate adjustment rack 2, make the asterism of single star optical simulator 1 generation as s ₀₀Aim at the coordinate x of the visual field, center of camera lens 3 to be measured ₀, y ₀Rotation one dimension air-float turntable 5, and the angle of pitch of adjusting adjustment rack 2, the starlight that single star optical simulator 1 is produced, process camera lens 3 to be measured is imaged onto the asterism picture on CCD camera 4 target surfaces, drop on the position of CCD target surface l=1, k=1, be camera lens 3X direction-3.5 to be measured ° and Y-direction-3.5 ° visual field point, it is s that note asterism herein looks like ₁₁, and utilize the barycenter location algorithm, obtain asterism as s ₁₁Centroid position coordinate x ₁₁, y ₁₁

3. gather the asterism picture of-3.5 ° of visual fields on the camera lens 3Y direction to be measured: with asterism as s ₁₁The present position is the one-dimensional scanning starting point, rotation one dimension air-float turntable 5, make camera lens 3 to be measured along directions X from l=1, k=1 realizes one-dimensional scanning to 3.5 ° of visual field points of directions X, the analyzing spot that every interval is 0.3 ° is a collection position, collection position l=1, k=2 place with it CCD camera 4 to gather that corresponding asterism looks like be s ₁₂, and calculate centroid position coordinate x ₁₂, y ₁₂..., collection position l=1, k=n place with it corresponding asterism to look like be s _1n, utilize the barycenter location algorithm to obtain centroid position coordinate x _1n, y _1n, simultaneously, angular encoder 6 shows that the angle value that one dimension air-float turntable 5 rotates in real time should be ω mutually _X11, ω _X12..., ω _X1n, be the field angle on the one-dimensional scanning camera lens 3X to be measured direction;

4. regulate the angle of pitch of adjustment rack 2, make starlight look like to fall within the position of CCD target surface l=2, k=n by the asterism of camera lens 3 imagings to be measured, and note asterism herein to look like be s _2n, the barycenter location algorithm can get its position coordinates x _2n, y _2nAgain with asterism as s _2nThe present position is the one-dimensional scanning starting point, rotation one dimension air-float turntable 5, make camera lens 3 to be measured realize one-dimensional scanning from l=2, k=n to-3.5 ° in the other direction along X, the analyzing spot that every interval is 0.3 ° is a collection position, CCD camera 4 is successively during collection position l=2, k=n-1, k=n-2 ..., k=1 asterism to look like be s _{2 (n-1)}, s _{2 (n-2)}..., s ₂₁, a series of corresponding position coordinateses with it that utilize that the barycenter location algorithm obtains are x _{2 (n-1)}, y _{2 (n-1)}, x _{2 (n-2)}, y _{2 (n-2)}..., x ₂₁, y ₂₁, simultaneously, angular encoder 6 shows that the angle value that one dimension air-float turntable 5 rotates in real time should be ω mutually _X2n, ω _{X2 (n-1)}..., ω _X21

5. change the position of one-dimensional scanning starting point, 3., 4. repeating step obtains a series of asterism pictures ... s _M1, s _M2S _MnCorresponding angle value with it ..., ω _Xm1, ω _Xm2..., ω _Xmn, the asterism that obtains until CCD camera 4 is as all being distributed on the CCD target surface, and by the obtainable asterism picture element of barycenter location algorithm heart position coordinates is ..., x _M1, y _M1, x _M2, y _M2..., x _Mn, y _Mn

6. set up the distortion correction model:

The distortion measurement model as shown in Figure 3, set up cartesian coordinate system O-XY: the visual field, center with camera lens 3 to be measured is the cartesian coordinate system that true origin is set up the CCD target surface, because camera lens 3 to be measured is imperfection optical systems, it can not reflect tested interasteric position relation really, and starlight always departs from ideal position by the asterism picture that camera lens 3 to be measured is imaged onto on the CCD camera 4.As shown in Figure 3, O is the true origin (x on the CCD target surface ₀, y ₀), X-axis and Y-axis be line direction and the column direction on the CCD target surface of corresponding camera lens 3 to be measured respectively.After supposing that starlight is by camera lens 3 imagings to be measured, the barycenter of its asterism picture is displaced to a p ' by a p, and the position coordinates of p point, p ' correspondence is made as (x respectively _Lk, y _Lk) and (x ' _Lk, y ' _Lk), then the distortion deviation of camera lens 3 to be measured is Δ, and Δ x, Δ y are respectively camera lens 3 to be measured in directions X and the Y-direction deviation that distorts, and other establishes Δ θ and is vector

With vector

Angle, be called the centroid motion angle of asterism picture, be the angle offset of camera lens 3 distortion to be measured, θ is made as vector

Along dextrorotation to the X-axis angle.Then have:

$\left\{\begin{array}{c}{x}_{\mathrm{lk}}=\left|o\stackrel{\&RightArrow;}{p}\right|\cos (\mathrm{\&theta;}+\mathrm{\&Delta;\&theta;})\\ y_{\mathrm{lk}}=\left|o\stackrel{\&RightArrow;}{p}\right|\sin (\mathrm{\&theta;}+\mathrm{\&Delta;\&theta;})\end{array}\right.,$ $\left\{\begin{array}{c}{x}_{\mathrm{lk}}^{\&prime;}=\left|o{\stackrel{\&RightArrow;}{p}}^{\&prime;}\right|\cos \left(\mathrm{\&theta;}\right)\\ y_{\mathrm{lk}}^{\&prime;}=\left|o{\stackrel{\&RightArrow;}{p}}^{\&prime;}\right|\sin \left(\mathrm{\&theta;}\right)\end{array}\right.---\left(2\right)$

Wherein

Be respectively vector

Mould.

$\left\{\begin{array}{c}\frac{x_{\mathrm{lk}}}{y_{\mathrm{lk}}}=\frac{\left|o\stackrel{\&RightArrow;}{p}\right|\cos (\mathrm{\&theta;}+\mathrm{\&Delta;\&theta;})}{\left|o\stackrel{\&RightArrow;}{p}\right|\sin (\mathrm{\&theta;}+\mathrm{\&Delta;\&theta;})}=\frac{\cos \left(\mathrm{\&theta;}\right)\cos \left(\mathrm{\&Delta;\&theta;}\right)-\sin \left(\mathrm{\&theta;}\right)\left(\mathrm{\&Delta;\&theta;}\right)}{\sin \left(\mathrm{\&theta;}\right)\cos \left(\mathrm{\&Delta;\&theta;}\right)+\cos \left(\mathrm{\&theta;}\right)\sin \left(\mathrm{\&Delta;\&theta;}\right)}\\ \frac{x_{\mathrm{lk}}^{\&prime;}}{y_{\mathrm{lk}}^{\&prime;}}=\frac{\left|o{\stackrel{\&RightArrow;}{p}}^{\&prime;}\right|\cos \left(\mathrm{\&theta;}\right)}{\left|o{\stackrel{\&RightArrow;}{p}}^{\&prime;}\right|\sin \left(\mathrm{\&theta;}\right)}=\frac{\cos \left(\mathrm{\&theta;}\right)}{\sin \left(\mathrm{\&theta;}\right)}\end{array}\right.---\left(3\right)$

$\frac{x_{\mathrm{lk}}}{y_{\mathrm{lk}}}=\frac{x_{\mathrm{lk}}^{\&prime;}\cos \left(\mathrm{\&Delta;\&theta;}\right)-y_{\mathrm{lk}}^{\&prime;}\sin \left(\mathrm{\&Delta;\&theta;}\right)}{y_{\mathrm{lk}}^{\&prime;}\cos \left(\mathrm{\&Delta;\&theta;}\right)+x_{\mathrm{lk}}^{\&prime;}\sin \left(\mathrm{\&Delta;\&theta;}\right)}---\left(4\right)$

The two-dimensional polynomial model of distortion correction as shown in the formula:

${\mathrm{\&omega;}}_{\mathrm{xlk}}=a_0+a_1{x}_{\mathrm{lk}}^{\&prime;\&prime;}+a_2{y}_{\mathrm{lk}}^{\&prime;\&prime;}+a_3{x_{\mathrm{lk}}^{\&prime;\&prime;}}^2+a_4{y_{\mathrm{lk}}^{\&prime;\&prime;}}^2+a_5{x}_{\mathrm{lk}}^{\&prime;\&prime;}{y}_{\mathrm{lk}}^{\&prime;\&prime;}+a_6{x_{\mathrm{lk}}^{\&prime;\&prime;}}^3+a_7{x_{\mathrm{lk}}^{\&prime;\&prime;}}^2{y}_{\mathrm{lk}}^{\&prime;\&prime;}+a_8{x}_{\mathrm{lk}}^{\&prime;\&prime;}{y_{\mathrm{lk}}^{\&prime;\&prime;}}^2+a_9{y_{\mathrm{lk}}^{\&prime;\&prime;}}^3$

Wherein, $\left\{\begin{array}{c}{x}_{\mathrm{lk}}^{\&prime;\&prime;}=x_{\mathrm{lk}}^{\&prime;}-x_0\\ y_{\mathrm{lk}}^{\&prime;\&prime;}=y_{\mathrm{lk}}^{\&prime;}-y_0\end{array}\right.,$

a ₀, a ₂, a ₃, a ₄, a ₅, a ₆, a ₇, a ₈, a ₉Be multinomial coefficient;

Make A=[a ₀a ₁A ₉] ^T, ψ _x=[ω _X11ω _X12ω _Xmn] ^T,

$P=\left[\begin{array}{cccccccccc}1& x_{11}^{\&prime;\&prime;}& y_{11}^{\&prime;\&prime;}& {x_{11}^{\&prime;\&prime;}}^2& {y_{11}^{\&prime;\&prime;}}^2& x_{11}^{\&prime;\&prime;}{y}_{11}^{\&prime;\&prime;}& {x_{11}^{\&prime;\&prime;}}^3& {x_{11}^{\&prime;\&prime;}}^2{y}_{11}^{\&prime;\&prime;}& x_{11}^{\&prime;\&prime;}{y_{11}^{\&prime;\&prime;}}^2& {y_{11}^{\&prime;\&prime;}}^3\\ 1& x_{12}^{\&prime;\&prime;}& y_{12}^{\&prime;\&prime;}& {x_{12}^{\&prime;\&prime;}}^2& {y_{12}^{\&prime;\&prime;}}^2& x_{12}^{\&prime;\&prime;}{y}_{12}^{\&prime;\&prime;}& {x_{12}^{\&prime;\&prime;}}^3& {x_{12}^{\&prime;\&prime;}}^2{y}_{12}^{\&prime;\&prime;}& x_{12}^{\&prime;\&prime;}{y_{12}^{\&prime;\&prime;}}^2& {y_{12}^{\&prime;\&prime;}}^3\\ \&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;& & & & & & & & & \\ 1& x_{\mathrm{mn}}^{\&prime;\&prime;}& y_{\mathrm{mn}}^{\&prime;\&prime;}& {x_{\mathrm{mn}}^{\&prime;\&prime;}}^2& {y_{\mathrm{mn}}^{\&prime;\&prime;}}^2& x_{\mathrm{mn}}^{\&prime;\&prime;}{y}_{\mathrm{mn}}^{\&prime;\&prime;}& {x_{\mathrm{mn}}^{\&prime;\&prime;}}^3& {x_{\mathrm{mn}}^{\&prime;\&prime;}}^2{y}_{\mathrm{mn}}^{\&prime;\&prime;}& x_{\mathrm{mn}}^{\&prime;\&prime;}{y_{\mathrm{mn}}^{\&prime;\&prime;}}^2& {y_{\mathrm{mn}}^{\&prime;\&prime;}}^3\end{array}\right]$

Wherein, m 〉=9, n 〉=9.

Following formula can get each coefficient of correcting distorted two-dimensional polynomial model:

A＝P ^-1ψ _x

Again the every coefficient of polynomial expression is brought in the correcting distorted two-dimensional polynomial model, i.e. the distortion of recoverable camera lens 3 to be measured.

This model is used for match and produces the centroid position of asterism pictures by camera lens to be measured 3, and it can effectively reduce barycenter location inaccuracy error, improves the distortion correction precision.

According to the ideal image relation, the relation between any a bit corresponding optical system field angle in space and the ideal image point is expressed from the next:

$x_{\mathrm{lk}}=x_0-\frac{f^{\&prime;}\tan {\mathrm{\&omega;}}_{\mathrm{xlk}}}{M_x},$ $y_{\mathrm{lk}}=y_0-\frac{f^{\&prime;}\cot {\mathrm{\&omega;}}_{\mathrm{xlk}}}{M_y}---\left(7\right)$

F ' is the focal length of camera lens 3 to be measured in the formula, M _x, M _yBe the CCD Pixel Dimensions, by known coordinate (x _Lk, y _Lk), (x ' _Lk, y ' _Lk), can determine the angle offset Δ θ that the distortion of camera lens 3 to be measured causes:

$\mathrm{\&Delta;\&theta;}=\arctan \left(\frac{x_{\mathrm{lk}}^{\&prime;}{y}_{\mathrm{lk}}-x_{\mathrm{lk}}{y}_{\mathrm{lk}}^{\&prime;}}{x_{\mathrm{lk}}{x}_{\mathrm{lk}}^{\&prime;}+y_{\mathrm{lk}}{y}_{\mathrm{lk}}^{\&prime;}}\right)---\left(8\right)$

Emulation and error analysis

The star sensor basic parameter of emulation is:

Visual field: 2 ω=7 °;

Wavelength: 450nm～700nm;

Focal length: f '=50.978mm (predominant wavelength: 550nm);

CCD pixel dimension: 6.45 μ m * 6.45 μ m;

Resolution: 1382 * 1036.

Star sensor optical system imperfection will cause the change of blur circle distortion, picture point energy dispersal and asterism brightness center.Table one is depicted as the theoretical barycenter distortion size under the different visual fields of star sensor.Finish the correction to the distortion of star sensor barycenter, multinomial coefficient a ₂=-1.96, a ₇=0.068, a ₉=0.07, a ₀=a ₁=a ₃=a ₄=a ₅=a ₆=a ₈=0, star sensor barycenter deviations data as shown in Table 2, finish barycenter distortion calibration after, system's barycenter deviations is less than 0.6 ", obtained desirable calibration effect.

Below star sensor is carried out the test of barycenter distortion measurement and correction.Because factors such as optical-mechanical system debugs, variation of ambient temperature and impact shock can cause that the mechanical-optical setup of star sensor produces distortion, the change that also will cause light spot energy to distribute, bring uncertainty to spot location, make that the position of barycenter in certain pixel of asterism hot spot is at random, and in diverse location place barycenter bearing accuracy difference, the one dimension air-float turntable angle value ψ of rotation is in real time surveyed out in a plurality of different visual fields of one-dimensional scanning star sensor _xDui Ying asterism is as s with it _LkCoordinate (x ' _Lk, y ' _Lk), 4 groups of data of actual measurement are as shown in Table 3.By the correction to the distortion of star sensor barycenter, the angle offset Δ θ that this barycenter distortion causes:

$\left\{\begin{array}{c}\mathrm{\&Delta;\&theta;}=k{y}_{\mathrm{lk}}-0.00133x_{\mathrm{lk}}+0.291\\ k=\frac{x_0-(0.02867x_{\mathrm{lk}}-7.405)}{y_{\mathrm{lk}}-y_0},y_{\mathrm{lk}}\&NotEqual;y_0\end{array}\right.$

Star sensor barycenter deviations data after the correction as shown in Table 4, before the calibration, angle measurement accuracy is 22 "; After the calibration, angle measurement accuracy is less than 2 ", experimental result shows that calibration result is good, can satisfy the high-precision requirement of star sensor.

Table one barycenter distortion/μ m

Table two Δ θ/(")

Table three

Table four

Claims (2)

1. optical lens distortion measurement device, be characterised in that its formation comprises single star optical simulator (1), adjustment rack (2), camera lens to be measured (3), CCD camera (4), one dimension air-float turntable (5), angular encoder (6), computing machine (7) and optical table (8) composition, the position relation of above-mentioned component is as follows:

Described adjustment rack (2) and one dimension air-float turntable (5) place on the described optical table (8), described single star optical simulator (1) is by integrating sphere light source (101), parallel light tube (103) and the pin hole graticule (102) that is positioned on parallel light tube (103) focal plane are formed, described single star optical simulator (1) is fixed on the described adjustment rack (2), described camera lens to be measured (3) and CCD camera (4) are fixed on the one dimension air-float turntable (5), and the entrance pupil face of camera lens to be measured (3) is overlapped with the revolving shaft of one dimension air-float turntable (5), described angular encoder (6) is used for the angle of the rotation of record one dimension air-float turntable (5); The described pin hole graticule of optical illumination (102) that is sent by described integrating sphere light source (101), light by pin hole graticule (102) is formed starlight by parallel light tube (103) collimation, this starlight produces the asterism picture by camera lens to be measured (3), this asterism picture is surveyed by described CCD camera (4), and the output terminal of described CCD camera (4) links to each other with the input end of described computing machine (7).

2. the measurement mechanism that utilizes the described optical lens of claim 1 to distort is implemented the bearing calibration of lens distortion to be measured, it is characterized in that this method may further comprise the steps:

1. the demarcation of camera lens to be measured (3) visual field, center: use internal focusing telescope to seek the optical axis of camera lens to be measured (3), and by being fixed on " ten " word graduation picture of CCD camera (4) the collection internal focusing telescope on camera lens to be measured (3) back plane, be somebody's turn to do the position coordinates of " ten " word graduation point of crossing on the target surface of CCD camera (4), be the coordinate x of the visual field, center of camera lens to be measured (3) ₀, y ₀

2. show the asterism picture: camera lens to be measured (3) is fixed on the one dimension air-float turntable (5), aim at camera lens to be measured (3) with described single star optical simulator (1), the starlight that single star optical simulator (1) produces, be imaged onto on the target surface of CCD camera (4) through camera lens to be measured (3), form an asterism as s ₀₀,

Regulate described adjustment rack (2), make the asterism of single star optical simulator (1) generation as s ₀₀Aim at the coordinate x of the visual field, center of described camera lens to be measured (3) ₀, y ₀Rotate described one dimension air-float turntable (5), and regulate the angle of pitch of described adjustment rack (2), the starlight that described single star optical simulator (1) is produced, process camera lens to be measured (3) is imaged onto the asterism picture on CCD camera (4) target surface, drop on the position of CCD target surface l=1, k=1, be camera lens to be measured (3) directions X-3.5 ° and Y-direction-3.5 ° visual field point, it is s11 that note asterism herein looks like, and utilize the barycenter location algorithm, obtain asterism as s ₁₁Centroid position coordinate x ₁₁, y ₁₁

3. gather the asterism picture of-3.5 ° of visual fields on camera lens to be measured (3) Y-direction: with asterism as s ₁₁The present position is the one-dimensional scanning starting point, rotate described one dimension air-float turntable (5), make described camera lens to be measured (3) along directions X from l=1, k=1 realizes one-dimensional scanning to 3.5 ° of visual field points of directions X, the analyzing spot that every interval is 0.3 ° is a collection position, collection position l=1, k=2 place with it CCD camera (4) to gather that corresponding asterism looks like be s ₁₂, and calculate centroid position coordinate x ₁₂, y ₁₂..., up to collection position l=1, k=n place with it corresponding asterism to look like be s _1n, utilize the barycenter location algorithm to obtain centroid position coordinate x _1n, y _1n, simultaneously, described angular encoder (6) shows that the angle value that one dimension air-float turntable (5) rotates in real time should be ω mutually _X11, ω _X12..., ω _X1n, be the field angle on one-dimensional scanning camera lens to be measured (3) directions X;

4. regulate the angle of pitch of described adjustment rack (2), make starlight look like to fall within the position of CCD target surface l=2, k=n by the asterism of camera lens to be measured (3) imaging, and note asterism herein to look like be s _2n, the barycenter location algorithm can get its position coordinates x _2n, y _2nAgain with asterism as s _2nThe present position is the one-dimensional scanning starting point, rotate described one dimension air-float turntable (5), make described camera lens to be measured (3) realize one-dimensional scanning from l=2, k=n to-3.5 ° in the other direction along X, the analyzing spot that every interval is 0.3 ° is a collection position, CCD camera (4) is successively during collection position l=2, k=n-1, k=n-2 ..., k=1 asterism to look like be s _{2 (n-1)}, s _{2 (n-2)}..., s ₂₁, a series of corresponding position coordinateses with it that utilize that the barycenter location algorithm obtains are x _{2 (n-1)}, y _{2 (n-1)}, x _{2 (n-2)}, y _{2 (n-2)}..., x ₂₁, y ₂₁, simultaneously, described angular encoder (6) shows that the angle value that one dimension air-float turntable (5) rotates in real time should be ω mutually _X2n, ω _{X2 (n-1)}..., ω _X21

5. change the position of one-dimensional scanning starting point, 3., 4. repeating step obtains a series of asterism pictures ... s _M1, s _M2S _MnCorresponding angle value with it ..., ω _Xm1, ω _Xm2..., ω _Xmn, the asterism that obtains until CCD camera (4) is as all being distributed on the CCD target surface, and by the obtainable asterism picture element of barycenter location algorithm heart position coordinates is ..., x _M1, y _M1, x _M2, y _M2..., x _Mn, y _Mn

6. set up lens distortion model to be measured:

The two-dimensional polynomial model of distortion correction as shown in the formula:

${\mathrm{\&omega;}}_{\mathrm{xlk}}=a_0+a_1{x}_{\mathrm{lk}}^{\&prime;\&prime;}+a_2{y}_{\mathrm{lk}}^{\&prime;\&prime;}+a_3{x_{\mathrm{lk}}^{\&prime;\&prime;}}^2+a_4{y_{\mathrm{lk}}^{\&prime;\&prime;}}^2+a_5{x}_{\mathrm{lk}}^{\&prime;\&prime;}{y}_{\mathrm{lk}}^{\&prime;\&prime;}+a_6{x_{\mathrm{lk}}^{\&prime;\&prime;}}^3+a_7{x_{\mathrm{lk}}^{\&prime;\&prime;}}^2{y}_{\mathrm{lk}}^{\&prime;\&prime;}+a_8{x}_{\mathrm{lk}}^{\&prime;\&prime;}{y_{\mathrm{lk}}^{\&prime;\&prime;}}^2+a_9{y_{\mathrm{lk}}^{\&prime;\&prime;}}^3$

Wherein, $\left\{\begin{array}{c}{x}_{\mathrm{lk}}^{\&prime;\&prime;}=x_{\mathrm{lk}}^{\&prime;}-x_0\\ y_{\mathrm{lk}}^{\&prime;\&prime;}=y_{\mathrm{lk}}^{\&prime;}-y_0\end{array}\right.,$

a ₀, a ₂, a ₃, a ₄, a ₅, a ₆, a ₇, a ₈, a ₉Be multinomial coefficient;

Make A=[a ₀a ₁A ₉] ^T, ψ _x=[ω _X11ω _X12ω _Xmn] ^T, then

$P=\left[\begin{array}{cccccccccc}1& x_{11}^{\&prime;\&prime;}& y_{11}^{\&prime;\&prime;}& {x_{11}^{\&prime;\&prime;}}^2& {y_{11}^{\&prime;\&prime;}}^2& x_{11}^{\&prime;\&prime;}{y}_{11}^{\&prime;\&prime;}& {x_{11}^{\&prime;\&prime;}}^3& {x_{11}^{\&prime;\&prime;}}^2{y}_{11}^{\&prime;\&prime;}& x_{11}^{\&prime;\&prime;}{y_{11}^{\&prime;\&prime;}}^2& {y_{11}^{\&prime;\&prime;}}^3\\ 1& x_{12}^{\&prime;\&prime;}& y_{12}^{\&prime;\&prime;}& {x_{12}^{\&prime;\&prime;}}^2& {y_{12}^{\&prime;\&prime;}}^2& x_{12}^{\&prime;\&prime;}{y}_{12}^{\&prime;\&prime;}& {x_{12}^{\&prime;\&prime;}}^3& {x_{12}^{\&prime;\&prime;}}^2{y}_{12}^{\&prime;\&prime;}& x_{12}^{\&prime;\&prime;}{y_{12}^{\&prime;\&prime;}}^2& {y_{12}^{\&prime;\&prime;}}^3\\ \&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;& & & & & & & & & \\ 1& x_{\mathrm{mn}}^{\&prime;\&prime;}& y_{\mathrm{mn}}^{\&prime;\&prime;}& {x_{\mathrm{mn}}^{\&prime;\&prime;}}^2& {y_{\mathrm{mn}}^{\&prime;\&prime;}}^2& x_{\mathrm{mn}}^{\&prime;\&prime;}{y}_{\mathrm{mn}}^{\&prime;\&prime;}& {x_{\mathrm{mn}}^{\&prime;\&prime;}}^3& {x_{\mathrm{mn}}^{\&prime;\&prime;}}^2{y}_{\mathrm{mn}}^{\&prime;\&prime;}& x_{\mathrm{mn}}^{\&prime;\&prime;}{y_{\mathrm{mn}}^{\&prime;\&prime;}}^2& {y_{\mathrm{mn}}^{\&prime;\&prime;}}^3\end{array}\right]$

Wherein, m 〉=9, n 〉=9.

Following formula can get each coefficient of correcting distorted two-dimensional polynomial model:

A＝P ^-1ψ _x

Again the every coefficient of polynomial expression is brought in the correcting distorted two-dimensional polynomial model, i.e. the distortion of recoverable camera lens to be measured (3).

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