CN111220177A - Method for verifying star point image sub-pixel positioning accuracy - Google Patents
Method for verifying star point image sub-pixel positioning accuracy Download PDFInfo
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Abstract
The embodiment of the invention discloses a method for verifying the positioning accuracy of star point image sub-pixels. The verification method comprises the steps of determining the period of the earth rotation by 360 degrees and the focal length of an optical system to be verified; aligning a main optical axis of an optical system to a fixed star with declination as a first preset value for integration, carrying out multiple times of observation within a preset time interval and keeping the optical system still in the observation process; calculating the position of each star point image by adopting a sub-pixel positioning algorithm to be verified, and calculating the distance between two adjacent star point images by adopting a distance formula; obtaining the included angle between the incident light of the fixed star and the main optical axis of the light system during the first observation; calculating the rotation angle of the earth, the included angle of the visual axis and the moving distance of the star image point on the image surface in two adjacent observation time points; and calculating the positioning precision of the sub-pixel positioning algorithm to be verified. The verification method has stability and high precision.
Description
Technical Field
The invention relates to the technical field of remote sensor optical design, in particular to a method for verifying the positioning accuracy of a star point image sub-pixel.
Background
Various optical instruments taking the position information of the star point image as an observation target need to perform test experiments on the positioning precision of the star point image. Currently, the means of testing the experiments include: performing simulation test by adopting ground equipment and a light source; and a two-dimensional turntable is adopted to carry out high-precision scanning and shooting of the space target. For an instrument with high positioning accuracy requirement, high-accuracy ground simulation equipment not only needs high cost, but also the accuracy of the simulation equipment can influence the accuracy of the whole measurement process and the test of the positioning accuracy of the instrument.
Therefore, aiming at the problems of high cost and high precision and stability of simulation equipment with high positioning precision in the prior art, a verification method for the positioning precision of the star point image sub-pixel with high stability and high precision is needed.
Disclosure of Invention
Aiming at the problems of high cost and high precision and stability of simulation equipment with high positioning precision in the prior art, the embodiment of the invention provides a method for verifying the positioning precision of a star point image sub-pixel with high stability and high precision. The verification method for the positioning accuracy of the sub-pixel of the star point image utilizes the earth as a high-accuracy rotating platform to observe the star point image of the fixed star, so that ultra-high-accuracy scanning accuracy can be provided, and the field angle of the star point image of the earth as the fixed star is smaller than 0.01 angular second, so that a high-accuracy point light source can be provided for an instrument.
The specific scheme of the method for verifying the positioning accuracy of the star point image sub-pixel is as follows: a method for verifying the positioning accuracy of star point image sub-pixels comprises the following steps of S1: determining the period of the earth rotation by 360 degrees as T and the focal length of the optical system to be verified as f; step S2: the main optical axis of the optical system is aligned with a fixed star with declination as a first preset value to carry out integration, and the integration time is t0N observations are made during a time interval t and the optical system remains stationary during said observations, where t is greater than t0(ii) a Step S3: calculating the position of each star point image by adopting a sub-pixel positioning algorithm to be verified, obtaining the position coordinates of each star point image, and calculating the distance between two adjacent star point images by adopting a distance formula; step S4: calculating an included angle between the incident light of the fixed star and the main optical axis of the light system in the 1 st observation in the step S2; step S5: calculating the angle of the earth rotation in the two adjacent observation time points and the visual axis included angle of the two adjacent observations, and calculating the moving distance of the image points of the two adjacent observations on the image surface according to the angle of the earth rotation and the visual axis included angle of the two adjacent observations; step S6: and calculating the positioning precision of the sub-pixel positioning algorithm to be verified according to the moving distance of the star image points observed twice on the image surface.
Preferably, the expression of the distance formula in step S3 is
Wherein lk' is the distance between two adjacent satellite points at the k-th time, (x)k,yk) Is the position coordinate of the kth star point image.
Preferably, the formula in step S4 is
and the angle alpha is an included angle between the incident light of the fixed star and the main optical axis of the light system, the distance d is the distance from the star image point to the focal point of the camera, and the distance f is the focal length of the optical system to be verified.
Preferably, in step S5, the calculation formula of the angle that the earth rotates at the two adjacent observation time points is Δ ═ 360 · T/T, where T is the length of the time interval between n observations, and T is the period of 360 degrees of the earth' S rotation.
Preferably, the calculation formula of the visual axis angle of the two adjacent observations in the step S5 is
wherein Δ is an angle rotated by the earth in two adjacent observation time points, and β is the first preset value in step S2.
Preferably, the calculation formula of the moving distance in step S5 is
lk＝f·(tan(α+kx)-tan(α+(k-1)x),...k∈[1..n-1]and f is the focal length of the optical system to be verified, α is the included angle between the incident light of the fixed star and the main optical axis of the optical system, and x is the included angle between the visual axes of two adjacent observations.
Preferably, the positioning accuracy includes an error mean and a variance.
Preferably, the calculation formula of the error mean value is as follows:
the method isThe difference is calculated as:
wherein lk' is the distance between two adjacent satellite points at the kth time, lkIs the moving distance of the k-th two adjacent star image points on the image surface.
Preferably, n is a natural number greater than 2.
According to the technical scheme, the embodiment of the invention has the following advantages:
according to the verification method for the positioning accuracy of the sub-pixel of the star point image, provided by the embodiment of the invention, the star point image of the fixed star is observed by using the earth as a high-accuracy rotating platform, so that high-accuracy scanning accuracy can be provided, the opening angle of the fixed star can be maintained within 0.01 arc second, and a high-accuracy point light source can be provided for an optical system. The method for verifying the positioning accuracy of the sub-pixel of the star point image provided by the embodiment of the invention can be suitable for testing the positioning accuracy of the star point image of an optical system without relative movement between an optical axis and a body.
Drawings
FIG. 1 is a schematic flow chart of a method for verifying the positioning accuracy of a sub-pixel of a star point image according to an embodiment of the present invention;
fig. 2 is a schematic diagram of a partial result of the stellera diffuse spot positioning photography provided in the embodiment of the present invention;
FIG. 3 is a schematic diagram of a verification experiment principle of the method for verifying the positioning accuracy of the sub-pixel of the star point image provided in the embodiment of the present invention.
Detailed Description
In order to make the technical solutions of the present invention better understood, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The terms "first," "second," "third," "fourth," and the like in the description and in the claims, as well as in the drawings, if any, are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It will be appreciated that the data so used may be interchanged under appropriate circumstances such that the embodiments described herein may be practiced otherwise than as specifically illustrated or described herein. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed, but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
As shown in fig. 1, a schematic flow chart of a method for verifying the positioning accuracy of a star point image sub-pixel provided in the embodiment of the present invention is shown. In this embodiment, the method for acquiring the scattered spot of the star point image includes six steps, and the specific content in each step is as follows.
Step S1: and determining the period of the earth rotating for 360 degrees as T and the focal length of the optical system to be verified as f. The period T of 360 degrees of earth rotation can be obtained based on common sense, and T is 23 hours, 56 minutes, 4.09 seconds, and can be approximately 24 hours. The focal length f of the optical system to be verified can be determined according to the selected optical system.
Step S2: the main optical axis of the optical system is aligned with a fixed star with declination as a first preset value to carry out integration, and the integration time is t0N observations are made during a time interval t and the optical system remains stationary during said observations, where t is greater than t0in this embodiment, n is a natural number greater than 2.
Step S3: calculating the position of each star point image by adopting a sub-pixel positioning algorithm to be verified to obtain the position coordinates (x) of each star point image1,y1)、(x2,y2)…(xn,yn) And calculating by using a distance formulaThe distance between two adjacent star image points. The expression of the distance formula is shown in the formula:
wherein lk' is the distance between two adjacent satellite points at the k-th time, (x)k,yk) Is the position coordinate of the kth star point image.
Step S4: the included angle between the incident light of the star and the main optical axis of the light system at the 1 st observation in step S2 is obtained. In this embodiment, the expression of the angle between the incident light of the star and the principal optical axis of the light system is shown in formula 2:
and the angle alpha is an included angle between the incident light of the fixed star and the main optical axis of the light system, the distance d is the distance from the star image point to the focal point of the camera, and the distance f is the focal length of the optical system to be verified.
Step S5: and calculating the angle of the earth rotating in the two adjacent observation time points and the visual axis included angle of the two adjacent observations, and calculating the moving distance of the image points of the two adjacent observations on the image surface according to the angle of the earth rotating and the visual axis included angle of the two adjacent observations.
In this embodiment, the expression for calculating the angle of rotation of the earth in two adjacent observation time points is shown in equation 3:
Δ ═ 360. T/T (equation 3)
Wherein T is the length of the time interval for n observations, and T is the period of 360 degrees of earth rotation.
In this embodiment, the formula for calculating the viewing axis angle of two adjacent observations is shown in formula 4:
wherein Δ is an angle rotated by the earth in two adjacent observation time points, and β is the first preset value in step S2.
In this embodiment, the expression for calculating the moving distance of the star image point on the image plane in two adjacent observations is shown in formula 5:
lk＝f·(tan(α+kx)-tan(α+(k-1)x),...k∈[1..n-1](formula 5)
and f is the focal length of the optical system to be verified, α is the included angle between the incident light of the fixed star and the main optical axis of the optical system, and x is the included angle between the visual axes of two adjacent observations.
Step S6: and calculating the positioning precision of the sub-pixel positioning algorithm to be verified according to the moving distance of the star image points observed twice on the image surface. In this embodiment, the positioning accuracy includes an error mean V and a variance D.
In this embodiment, the calculation expression of the error mean is shown in equation 6:
in this embodiment, the calculation expression of the variance is as shown in equation 7:
wherein lk' distance between two adjacent satellite points at kth, /)kIs the moving distance of the k-th two adjacent star image points on the image surface.
The sub-pixel location algorithm to be verified includes many algorithms, which are not exemplified herein. In the embodiment of the invention, the verification process of the star point image sub-pixel positioning accuracy provided by the invention is explained by taking a distance center positioning algorithm as a specific sub-pixel positioning algorithm to be verified and a sirius as an observation fixed star as a specific embodiment.
As described in conjunction with fig. 2 and 3, the process of acquiring and verifying the stellera star point image diffuse spot is as follows:
determining the focal length f of the optical instrument to be60mm, the size of detector pixels is 5.5 mu m, the number of detector pixels is 4288 multiplied by 2848, and the observation target is sirius. The celestial coordinates of the celestial star are declination angle of-16 degrees 42 '47.315' and right ascension angle of 06 h45m9.2499s. The integration time 1s and the interval time 2s are used to continuously shoot 8 sirius star point images, as shown in fig. 2. In fig. 2, (a) shows a 0-second image, (b) shows a 2-second image, (c) shows a 4-second image, and (d) shows a 6-second image. The positions of 8 star point images are solved by adopting a distance center algorithm as follows: t is1(1648.207,1474.284)、T2(1648.967,1475.665)、T3(1649.613,1476.900)、T4(1650.350,1478.384)、T5(1651.084,1479.645)、T6(1651.870,1480.991)、T7(1652.543,1482.336)、T8(1653.259,1483.734). Calculating according to formula 1 to obtain the sequential distance between each point as: t is21Is 1.579 pixel, T32Is 1.397 th pixel, T43Is 1.659 pixel, T54Is 1.463 pixel, T65Is 1.562 pixel, T76Is 1.507 pixel, T87Is 1.574 picture elements.
if the focal point of the optical instrument is located in the (2144, 1424) pixel, the angle α between the fixed star incident ray and the main optical axis of the optical system during the 1 st observation is 2.616 ° according to formula 2.
According to the formula 3, the rotation angle Δ of the earth in two adjacent observation time points is calculated to be 360 · 2/86164 to 0.008356 °. According to equation 4, the viewing angle of the two observations is calculated to be 0.008003 °, as shown in fig. 3. Calculating and obtaining the moving distance l of the image points of two adjacent observations on the image surface according to the formula 5k＝f·(tan(α+kx)-tan(α+(k-1)x),...k∈[1..n-1]. The mean value V and the variance D of the error of the positioning method can be obtained from equation 6 and equation 7, respectively:
in the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above are not necessarily intended to refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, various embodiments or examples and features of different embodiments or examples described in this specification can be combined and combined by one skilled in the art without contradiction.
Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention, and that variations, modifications, substitutions and alterations can be made to the above embodiments by those of ordinary skill in the art within the scope of the present invention.
Claims (9)
1. A verification method for the positioning accuracy of star point image sub-pixels is characterized in that the acquisition method comprises the following steps:
step S1: determining the period of the earth rotation by 360 degrees as T and the focal length of the optical system to be verified as f;
step S2: the main optical axis of the optical system is aligned with a fixed star with declination as a first preset value to carry out integration, and the integration time is t0N observations are made during a time interval t and the optical system remains stationary during said observations, where t is greater than t0；
Step S3: calculating the position of each star point image by adopting a sub-pixel positioning algorithm to be verified, obtaining the position coordinates of each star point image, and calculating the distance between two adjacent star point images by adopting a distance formula;
step S4: calculating an included angle between the incident light of the fixed star and the main optical axis of the light system in the 1 st observation in the step S2;
step S5: calculating the angle of the earth rotation in the two adjacent observation time points and the visual axis included angle of the two adjacent observations, and calculating the moving distance of the image points of the two adjacent observations on the image surface according to the angle of the earth rotation and the visual axis included angle of the two adjacent observations;
step S6: and calculating the positioning precision of the sub-pixel positioning algorithm to be verified according to the moving distance of the star image points observed twice on the image surface.
2. The method for verifying the positioning accuracy of the sub-pixel of the star point image as claimed in claim 1, wherein the distance formula in the step S3 is expressed as
Wherein lk' is the distance between two adjacent satellite points at the k-th time, (x)k,yk) Is the position coordinate of the kth star point image.
3. The method for verifying the positioning accuracy of the sub-pixels of the star point image as claimed in claim 1, wherein the formula in the step S4 is
and the angle alpha is an included angle between the incident light of the fixed star and the main optical axis of the light system, the distance d is the distance from the star image point to the focal point of the camera, and the distance f is the focal length of the optical system to be verified.
4. The method for verifying the positioning accuracy of the sub-pixel of the star point image according to claim 1, wherein the calculation formula of the angle that the earth rotates in the two adjacent observation time points in step S5 is Δ ═ 360 · T/T, where T is the length of the time interval between n observations, and T is the period of 360 degrees of the earth' S rotation.
5. The method for verifying the positioning accuracy of the sub-pixel of the star point image according to claim 4, wherein the formula for calculating the included angle between the visual axes of the two adjacent observations in the step S5 is
wherein Δ is an angle rotated by the earth in two adjacent observation time points, and β is the first preset value in step S2.
6. The method for verifying the positioning accuracy of the sub-pixels of the star point image as claimed in claim 5, wherein the calculation formula of the moving distance in step S5 is
lk＝f·(tan(α+kx)-tan(α+(k-1)x),...k∈[1..n-1]，
and f is the focal length of the optical system to be verified, α is the included angle between the incident light of the fixed star and the main optical axis of the optical system, and x is the included angle between the visual axes of two adjacent observations.
7. The method for verifying the positioning accuracy of the sub-pixel of the star point image according to claim 1, wherein the positioning accuracy comprises a mean error value and a variance error.
8. The method for verifying the positioning accuracy of the sub-pixel of the star point image according to claim 7, wherein the calculation formula of the mean error value is as follows:
the calculation formula of the variance is as follows:
wherein lk' is the distance between two adjacent satellite points at the kth time, lkIs the moving distance of the k-th two adjacent star image points on the image surface.
9. The method for verifying the positioning accuracy of the sub-pixel of the star point image according to claim 1, wherein n is a natural number greater than 2.
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