CN112598583B - Refractive index model distortion correction method - Google Patents
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Abstract
The invention discloses a refractive index model distortion correction method, which comprises the following steps: obtaining a plurality of sample points through mathematical modeling, wherein each sample point comprises a refraction value and a theoretical value of a solar facula centroid under a two-dimensional rectangular coordinate system of a detector; calculating a refraction module value and a theoretical module value of each sample point, and fitting the refraction module values and the theoretical module values of all the sample points to obtain a one-dimensional fitting curve from the refraction module values to the theoretical module values; calculating to obtain corrected module value information according to the one-dimensional fitting curve and the module value of any real measurement point; combining the corrected module value information and the corrected solar facula centroid coordinate information to calculate corrected solar facula centroid coordinate information under the two-dimensional rectangular coordinate system of the detector; and calculating to obtain a unit vector of the sun under the two-dimensional rectangular coordinate system of the detector according to the corrected centroid coordinate information of the solar facula. The method has the advantages of simple realization and small calculated amount.
Description
Technical Field
The invention relates to the technical field of photoelectricity, in particular to a refractive index model distortion correction method based on single parameter fitting.
Background
Many optical sensor lenses are provided with glass protection cover plates, when light passes through the glass cover plates, refraction occurs, the light path is caused to be refracted, and further, distortion occurs to image or light spot coordinates, and imaging quality or light spot coordinate calculation accuracy is affected.
By way of illustration in the field of aerospace control systems, a digital sun sensor (detector) is a high-precision sensor for measuring sun azimuth pointing, and can be used for realizing satellite triaxial high-precision attitude determination with horizon double-vector attitude determination, and can also be used as a sun-facing orientation attitude sensor.
When sunlight passes through the glass cover plate and reaches the digital solar detector, the traveling direction of the light is displaced and deviated due to the refraction effect of the glass cover plate, so that the measured sun azimuth is error, the larger the included angle between the light and the optical axis is, the larger the measurement error angle caused by displacement deviation is, and when the included angle between the optical axis of the light line diagram is 0, the measurement error angle caused by displacement deviation is also 0.
Aiming at correction of refractive index model distortion, the traditional method mainly comprises two-dimensional surface fitting correction and Newton iterative calculation method correction.
Wherein, for the two-dimensional curved surface fitting method: and obtaining a series of sample points through mathematical modeling, wherein the sample points are uniformly distributed in the whole detector area as much as possible. Each sample point has a corresponding real solar coordinate and an actual measurement coordinate obtained by the detector, and coordinate points in the planes are subjected to two-dimensional curved surface fitting to obtain fitting coefficients of corresponding orders. And combining the measured sun with two-dimensional curved surface fitting at any coordinate point in the detector to obtain corrected solar coordinates. The method has the advantages that the algorithm adaptation force is strong, and the method is applicable to refractive index models and other system error types; the disadvantage is that the number of parameters to be fitted is large, if a higher order fitting accuracy is desired, the number of fitting parameters is increased in a quadratic manner (for n-order two-dimensional surface fitting, the required fitting parameters are (n 2 +3n+2)/2), the software implementation is correspondingly complex. The two-dimensional curved surface fitting principle is simple, but the required fitting parameters are more, the correction algorithm is complex, and the calculated amount is large.
For newton's iterative method: according to the polar coordinate principle, points with equal distances from the center of the detector have the same system measurement error, the expression of the measured value in the two-dimensional rectangular coordinates is firstly converted into a polar coordinate system, and then the corresponding relation between the measured coordinates and the actual coordinates can be obtained according to the refractive index model. However, the equation for solving the actual coordinates through the solar actual measurement target is an overrunning equation, and has no direct expression, and the equation is obtained through multiple iterative calculations. The method has the advantages that only the related physical parameters of the refractive index model are needed, and the mathematical meaning is clear; the method has the defects that in one software running period, the corrected solar actual coordinates can be obtained through repeated iteration for a plurality of times, and the calculated amount is large. Namely, for correction of the Newton iteration calculation method, the equation is solved by repeated iteration calculation in a computer operation period, and the calculation amount is large.
Disclosure of Invention
Aiming at the defects of the two methods, the invention combines the advantages of the two methods and avoids the defects of the two methods, and provides a refractive index model distortion correction method based on single-parameter fitting, which has small calculation amount and low calculation complexity.
In order to solve the problems, the invention is realized by the following technical scheme:
a refractive index model distortion correction method comprising: s1, obtaining a plurality of sample points through mathematical modeling, wherein each sample point comprises a refraction value and a theoretical value of a solar facula centroid under a two-dimensional rectangular coordinate system of a detector. And S2, calculating the refraction mode value and the theoretical mode value of each sample point, and fitting the refraction mode values and the theoretical mode values of all the sample points to obtain a one-dimensional fitting curve from the refraction mode value to the theoretical mode value. And step S3, calculating to obtain corrected module value information according to the one-dimensional fitting curve and the module value of any real measurement point. And S4, combining the corrected module value information and the corrected solar spot centroid coordinate information to calculate and obtain the corrected solar spot centroid coordinate information under the two-dimensional rectangular coordinate system of the detector. And S5, calculating to obtain a unit vector of the sun under the two-dimensional rectangular coordinate system of the detector according to the corrected centroid coordinate information of the solar light spots.
Preferably, the step S1 includes: drawing m concentric circles by taking the center of the detector as the center, and taking the center of the circle as the starting point, and making a ray to intersect with the center of the circle to obtain m+1 collinear equidistant points;
the m+1 collinear equidistant points are theoretical values of the sample points, and m+1 sample point coordinate theoretical values are obtained;
wherein f represents the focal length of the detector, gamma represents the half cone angle for the field of view of the detector, and i is an integer from 0 to m; beta is the included angle between the ray and the x-axis in the two-dimensional rectangular coordinate system of the detector;
obtaining the actual coordinate values of m+1 sample points:
x′ i ＝((f-H0)·tan(θ i )+H0·tan(arcsin(sin(θ i )/n)))·i·cos(β)
y′ i ＝((f-H0)·tan(θ i )+H0·tan(arcsin(sin(θ i )/n)))·i·sin(β)
wherein n is the refractive index of the glass cover plate of the detector, H0 is the thickness of the glass cover plate, and f is the focal length of the detector; θ i For the theoretical incident angle corresponding to the ith concentric circle:
preferably, the step S2 includes: theoretical modulus M of the ith said sample point i The following formula is adopted for calculation:
wherein x is i And y i A theoretical value representing the i-th sample point; f represents the focal length of the detector, gamma represents the half cone angle for the field of view of the detector, and i is an integer from 0 to m;
the refractive index modulus of the ith sample point is calculated by the following formula:
wherein n is the refractive index of the glass cover plate, H0 is the thickness of the glass cover plate, and f is the focal length of the detector;
θ i for the theoretical incident angle corresponding to the ith concentric circle:
preferably, the step S3 includes:
for any solar spot centroid coordinates (sx ', sy') measured by the detector:
the actual measurement point modulus S' is calculated by adopting the following formula:
the corrected module value S is calculated by adopting the following formula:
wherein a is i Representing coefficients to be fitted, k representing the order of the polynomial fitting formula, i e (0, 1, …, k).
Preferably, the step S4 includes: the corrected centroid coordinate information of the solar light spots is calculated by adopting the following formula:
the corrected centroid coordinates of the solar spot are (sx, sy).
Preferably, the step S5 includes: the unit vector of the sun under the two-dimensional rectangular coordinate system of the detector is calculated by adopting the following formula:
thus, the unit vector of the sun under the two-dimensional rectangular coordinate system of the detector is
Preferably, the method further comprises: after the satellite processor obtains the unit vector of the sun in the detector coordinate system, the satellite processor can calculate and obtain the azimuth vector of the sun in the satellite coordinate system according to the installation matrix information of the detector and the satellite body, and the azimuth vector is used for satellite sun-to-sun orientation control and satellite attitude determination.
The invention has at least one of the following advantages:
compared with the traditional algorithm, the method simplifies the two-dimensional fitting into one-dimensional fitting (single-parameter fitting), the fitting order is equal to the number of fitting parameters, the software is simple to realize, and the calculated amount is small.
Drawings
FIG. 1 is a schematic flow chart of a distortion correction method based on a refractive index model according to an embodiment of the present invention;
FIG. 2 is a schematic diagram illustrating sample point selection according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of refractive index model generation according to an embodiment of the present invention;
fig. 4 is a schematic diagram of actual-point model calculation according to an embodiment of the invention.
Detailed Description
The invention provides a refractive index model distortion correction method based on single parameter fitting, which is further described in detail below with reference to the accompanying drawings and the detailed description. The advantages and features of the present invention will become more apparent from the following description. It should be noted that the drawings are in a very simplified form and are all to a non-precise scale, merely for the purpose of facilitating and clearly aiding in the description of embodiments of the invention. For a better understanding of the invention with objects, features and advantages, refer to the drawings. It should be understood that the structures, proportions, sizes, etc. shown in the drawings are for illustration purposes only and should not be construed as limiting the invention to the extent that any modifications, changes in the proportions, or adjustments of the sizes of structures, proportions, or otherwise, used in the practice of the invention, are included in the spirit and scope of the invention which is otherwise, without departing from the spirit or essential characteristics thereof.
Refractive index model distortion is regular distortion, and if the refractive index model error is only related to the distance from the main point (light incidence point) of the position of light (solar rays) on the digital solar detector from the polar coordinate angle, the correction of the refractive index model error can be realized theoretically through single parameter fitting.
For a better understanding of the present invention, a method for correcting refractive index model distortion based on single parameter fitting is illustrated below by taking a digital sun sensor (digital sun detector) of an aerospace control system as an example, as shown in fig. 1. The method comprises the following steps: and the ground fitting parameter calculation and the on-board processing are two parts.
( Wherein, the steps S1 and S2 described below are ground fitting parts, and can be completed on the ground; the steps S3, S4, S5 described below are on-board processing parts, i.e. can be completed on-board. )
The method for correcting the distortion of the refractive index model provided by the embodiment comprises the following steps:
s1, obtaining a plurality of sample points through mathematical modeling, wherein each sample point comprises a refraction value and a theoretical value of a solar facula centroid under a two-dimensional rectangular coordinate system of a detector.
And S2, calculating the refraction mode value and the theoretical mode value of each sample point, and fitting the refraction mode values and the theoretical mode values of all the sample points to obtain a one-dimensional fitting curve from the refraction mode value to the theoretical mode value.
And step S3, calculating to obtain corrected module value information according to the one-dimensional fitting curve and the module value of any real measurement point.
And S4, combining the corrected module value information and the corrected solar spot centroid coordinate information to calculate and obtain the corrected solar spot centroid coordinate information under the two-dimensional rectangular coordinate system of the detector.
And S5, calculating to obtain a unit vector of the sun under the two-dimensional rectangular coordinate system of the detector according to the corrected centroid coordinate information of the solar light spots.
As shown in fig. 2, the step S1 includes: drawing m concentric circles by taking the center of the detector as the center and taking the center of the circle as the starting point, and taking a ray (as shown in fig. 2, when beta=0, the ray is the x axis in the two-dimensional rectangular coordinate system of the detector) to intersect with the center of the circle to obtain m+1 collinear equidistant points (as shown in 0,1 and 2 … m in fig. 2).
The m+1 collinear equidistant points are theoretical values of the sample points, and the obtained coordinate theoretical values of the m+1 sample points are expressed by adopting the following formula:
wherein f represents the focal length of the detector, gamma represents the half cone angle for the field of view of the detector, and i is an integer from 0 to m; beta is the included angle between the ray and the x-axis in the two-dimensional rectangular coordinate system of the detector. When i is 0,1,2 and … m, respectively, the theoretical coordinates of the sample point are (x 0 y 0 )，(x 1 y 1 )，···，(x m y m ) If the selected ray is the x-axis (β=0), the sample point may be written as theoretical coordinates (x 0 0)，(x 1 0)，···，(x m 0)。
As shown in fig. 3, the causes of the distortion in the refractive index model are as follows: the dotted area in fig. 3 represents the cover glass of a digital detector, which has a thickness H0 and a refractive index n (vacuum refractive index 1). The position B is a solar entrance port, sunlight is influenced by a glass medium and deviates from the original incident direction (BF) after entering the glass cover plate from the position B, the actual route in the glass cover plate is BC, and the sunlight irradiates on the detector D (actual point) after exiting the glass cover plate from the position C. If there is no influence of the glass cover plate, the light falls on the F point (theoretical point) of the digital detector, and the error between the actual point and the theoretical point is caused by the fact that the refractive index of the glass cover plate is inconsistent with the vacuum refractive index, so the distortion is called as a refractive index model.
The distance from B to the center (O) of the detector is f, called the focal length of the detector (detector). According to the geometrical relationship OF the refractive index model, the theoretical value is OF:
OF＝f×tan(θ) (2)
where θ represents the theoretical incident angle of sunlight.
The actual value is at an OD from the center of the detector:
OD＝(f-H0)×tan(θ)+H0×tan(arcsin(sin(θ)/n)) (3)
the OD can be obtained by using an analytical expression through OF, but the OF cannot be directly obtained by using the analytical expression through OD, and the OD can be obtained by multiple iterative solutions, and the OD can be obtained by data fitting.
In this embodiment, the detector field of view range is determined, for example, the detector field of view range uses a half cone angle γ, and the maximum value of the detector coordinate system is obtained as follows: f.tan (. Gamma.).
The fitting order k is determined (the more the fitting order is, the higher the fitting precision is, but the larger the corresponding calculated amount is, and vice versa.) generally, when the fitting order is selected, the order is as small as possible under the condition of ensuring the fitting precision, and 4-5 orders are generally adopted in engineering. Determining the number of sample points m>k. Determining concentric circle radius differences
The actual values of the coordinates of m+1 of the sample points are obtained as follows:
wherein n is the refractive index of the glass cover plate of the detector, H0 is the thickness of the glass cover plate, and f is the focal length of the detector; θ i For the theoretical incident angle corresponding to the ith concentric circle:
the fitting algorithm described in the step S2 is a generally known algorithm, specifically, for a k-order polynomial fitting formula, the expression is:
wherein a is i And x is a parameter before fitting, and y is a parameter after fitting.
If the number of the sample points is m>k, it can be seen that the number of equations is larger than the coefficient a to be solved by simultaneous equations i There are innumerable solutions by which a set of a can be obtained by least squares i And finally, fitting to obtain a curve, so that the variance between the fitted value and the theoretical value is minimized at the sample position. Special: if the number of samples m=k, a can be directly solved by simultaneous equations i At the sample, the fitted value is equal to the theoretical value and the variance is 0.
The step S2 includes: theoretical modulus M of the ith said sample point i The following formula is adopted for calculation:
wherein x is i And y i A theoretical value representing the i-th sample point; f represents the focal length of the detector, gamma represents the half cone angle for the field of view of the detector, and i is an integer from 0 to m.
The refractive index modulus of the ith sample point is calculated by the following formula:
wherein n is the refractive index of the glass cover plate, H0 is the thickness of the glass cover plate, and f is the focal length of the detector;
θ i for the theoretical incident angle corresponding to the ith concentric circle:
it can be seen that the sample point theoretical mode and the refractive mode are independent of the x-axis angle of the selected ray with respect to the detector in a two-dimensional rectangular coordinate system.
The step S3 includes: as shown in fig. 4, for the detector, any solar spot centroid coordinates (sx ', sy') are measured:
the actual measurement point modulus S' is calculated by adopting the following formula:
the corrected module value S is calculated by adopting the following formula:
wherein a is i Representing coefficients to be fitted, k representing the order of the polynomial fitting formula, i e (0, 1, …, k).
The step S4 includes: the corrected centroid coordinate information of the solar light spots is calculated by adopting the following formula:
the corrected centroid coordinates of the solar spot are (sx, sy).
The step S5 includes: the unit vector of the sun under the two-dimensional rectangular coordinate system of the detector is calculated by adopting the following formula:
thus, the unit vector of the sun under the two-dimensional rectangular coordinate system of the detector is
It can be seen that the sun forms a spot on the detector that satisfies the principle of aperture imaging (as shown in fig. 3), so that the coordinates of the sun vector in the detector need to be inverted and normalized.
In this embodiment, further comprising: after the satellite processor obtains the unit vector of the sun in the detector coordinate system, the satellite processor can calculate and obtain the azimuth vector of the sun in the satellite coordinate system according to the installation matrix information of the detector and the satellite body, and the azimuth vector is used for satellite sun-to-sun orientation control and satellite attitude determination.
Thus, the digital sun sensor (digital sun detector or digital sun detector) is sensitive to obtain a unit vector (representing sun azimuth) of the sun in the digital sun coordinate system. After the satellite processor acquires the information, the azimuth vector of the sun in the satellite coordinate system can be calculated according to the installation matrix information of the satellite body and the satellite, and the azimuth vector is used for satellite sun-to-sun orientation control, satellite attitude determination and the like.
Compared with the traditional algorithm, the two-dimensional fitting is simplified into one-dimensional fitting (single-parameter fitting), the fitting order is equal to the number of fitting parameters, the software is simple to realize, and the calculated amount is small.
It should be noted that the apparatus and methods disclosed in the embodiments herein may be implemented in other ways. The apparatus embodiments described above are merely illustrative, for example, flow diagrams and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of apparatus, methods and computer program products according to various embodiments herein. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that in some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems which perform the specified functions or acts, or combinations of special purpose hardware and computer instructions.
While the present invention has been described in detail through the foregoing description of the preferred embodiment, it should be understood that the foregoing description is not to be considered as limiting the invention. Many modifications and substitutions of the present invention will become apparent to those of ordinary skill in the art upon reading the foregoing. Accordingly, the scope of the invention should be limited only by the attached claims.
Claims (6)
1. A method for modifying refractive index model distortion, comprising:
step S1, obtaining a plurality of sample points through mathematical modeling, wherein each sample point comprises a refraction value and a theoretical value of a solar facula centroid under a two-dimensional rectangular coordinate system of a detector;
s2, calculating a refraction module value and a theoretical module value of each sample point, and fitting the refraction module values and the theoretical module values of all the sample points to obtain a one-dimensional fitting curve from the refraction module values to the theoretical module values;
s3, calculating to obtain corrected module value information according to the one-dimensional fitting curve and the module value of any real measurement point;
s4, combining the corrected module value information and corrected solar spot centroid coordinate information (sx ', sy'), and calculating to obtain corrected solar spot centroid coordinate information under the two-dimensional rectangular coordinate system of the detector;
the step S4 includes: the corrected centroid coordinate information of the solar light spots is calculated by adopting the following formula:
the corrected centroid coordinates of the solar spot are (sx, sy); wherein S' represents a real-time point model value; s represents the corrected module value;
and S5, calculating to obtain a unit vector of the sun under the two-dimensional rectangular coordinate system of the detector according to the corrected centroid coordinate information of the solar light spots.
2. The method for correcting distortion of refractive index model according to claim 1, wherein the step S1 comprises: drawing m concentric circles by taking the center of the detector as the center, and taking the center of the circle as the starting point, and making a ray to intersect with the center of the circle to obtain m+1 collinear equidistant points;
the m+1 collinear equidistant points are theoretical values of the sample points, and m+1 sample point coordinate theoretical values are obtained;
wherein f represents the focal length of the detector, gamma represents the half cone angle for the field of view of the detector, and i is an integer from 0 to m; beta is the included angle between the ray and the x-axis in the two-dimensional rectangular coordinate system of the detector;
obtaining the actual coordinate values of m+1 sample points:
x′ i ＝((f-H0)·tan(θ i )+H0·tan(arcsin(sin(θ i )/n)))·i·cos(β)
y′ i ＝((f-H0)·tan(θ i )+H0·tan(arcsin(sin(θ i )/n)))·i·sin(β)
wherein n is the refractive index of the glass cover plate of the detector, H0 is the thickness of the glass cover plate, and f is the focal length of the detector; θ i For the theoretical incident angle corresponding to the ith concentric circle:
3. the method for correcting refractive index model distortion as claimed in claim 2, wherein the step S2 comprises: theoretical modulus M of the ith said sample point i The following formula is adopted for calculation:
wherein x is i And y i A theoretical value representing the i-th sample point; f represents the focal length of the detector, gamma represents the half cone angle for the field of view of the detector, and i is an integer from 0 to m;
the refractive index modulus of the ith sample point is calculated by the following formula:
wherein n is the refractive index of the glass cover plate, H0 is the thickness of the glass cover plate, and f is the focal length of the detector;
θ i for the theoretical incident angle corresponding to the ith concentric circle:
4. the method for correcting refractive index model distortion as claimed in claim 3, wherein the step S3 comprises:
for any solar spot centroid coordinates (sx ', sy') measured by the detector:
the actual measurement point modulus S' is calculated by adopting the following formula:
the corrected module value S is calculated by adopting the following formula:
wherein a is i Representing coefficients to be fitted, k representing the order of the polynomial fitting formula, i e (0, 1, …, k).
5. The method for correcting refractive index model distortion as claimed in claim 4, wherein the step S5 comprises: the unit vector of the sun under the two-dimensional rectangular coordinate system of the detector is calculated by adopting the following formula:
thus, the unit vector of the sun under the two-dimensional rectangular coordinate system of the detector is
6. The method for correcting refractive index model distortion as claimed in claim 5, wherein,
further comprises: after the satellite processor obtains the unit vector of the sun in the detector coordinate system, the satellite processor can calculate and obtain the azimuth vector of the sun in the satellite coordinate system according to the installation matrix information of the detector and the satellite body, and the azimuth vector is used for satellite sun-to-sun orientation control and satellite attitude determination.
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