CN114594484A

CN114594484A - Method for determining parameters of curved surface type reflector and coaxial laser radar

Info

Publication number: CN114594484A
Application number: CN202210198017.7A
Authority: CN
Inventors: 林建东; 任玉松; 单建勇; 白玉茹; 秦屹
Original assignee: Whst Co Ltd
Current assignee: Whst Co Ltd
Priority date: 2022-03-01
Filing date: 2022-03-01
Publication date: 2022-06-07

Abstract

The invention provides a parameter determination method of a curved reflector and a coaxial laser radar, wherein the curved reflector is a single-curved cylindrical curved reflector which is arranged on the coaxial laser radar, the coaxial laser radar comprises a cylindrical light-transmitting shell, and the method comprises the following steps: determining the curvature radius of a paraxial part of a curve corresponding to the curved surface type reflector according to the refractive index of the cylindrical light-transmitting shell to laser, the outer diameter length and the inner diameter length of the cylindrical light-transmitting shell, wherein the paraxial part is used for representing a preset area which is closest to the central axis of the cylindrical light-transmitting shell in the curve; substituting the curvature radius of the paraxial part of the curve and a preset conical coefficient into an aspheric curve standard equation to obtain an initial expression; and determining each aspheric surface coefficient in the initial expression by a damped least square method and a preset evaluation function to obtain a curve expression of the curve. The invention can improve the detection performance of the coaxial laser radar.

Description

Method for determining parameters of curved surface type reflector and coaxial laser radar

Technical Field

The invention relates to the technical field, in particular to a parameter determination method of a curved reflector and a coaxial laser radar.

Background

The laser radar, as a precise sensing system, has excellent performances such as high ranging precision, high angular resolution, high repetition frequency and the like, and is widely applied to the fields of intelligent robots, automatic tractors, intelligent/auxiliary driving, security and the like. At present, a laser radar generally utilizes the integral rotation of a transceiver module or the rotation of a plane reflector to enable a reflected light beam to rotate around a shaft for scanning detection, and compared with the former, the load driven by a motor of a scanning mode of the rotation of the plane reflector is smaller and lighter, so that the dynamic balance adjustment is easier, a whole system can realize higher scanning frequency, and the reliability is higher and is concerned.

The transparent shell is used as an important part of the laser radar, plays a role in protecting and supporting the radar, and ensures that the laser radar can work reliably for a long time. Because the light beam is circularly and symmetrically distributed in the rotating scanning process, the light-transmitting shell matched with the light beam is usually a cylindrical structure, but the introduction of the light-transmitting shell can affect the transmission characteristics of the light beam, and the detection angle resolution and the detection precision of the laser radar are reduced.

Disclosure of Invention

In view of this, the invention provides a method for determining parameters of a curved reflector and a coaxial laser radar, which can solve the problem of the detection performance reduction of the laser radar caused by a light-transmitting shell of the laser radar.

In a first aspect, an embodiment of the present invention provides a method for determining parameters of a curved mirror, where the curved mirror is a single-curved cylindrical curved mirror, the curved mirror is installed in a coaxial laser radar, and the coaxial laser radar includes a cylindrical transparent housing, and includes:

determining the curvature radius of a paraxial part of a curve corresponding to the curved surface type reflector according to the refractive index of the cylindrical light-transmitting shell to laser, the length of the outer diameter and the length of the inner diameter of the cylindrical light-transmitting shell, wherein the paraxial part is used for representing a preset area which is closest to the central axis of the cylindrical light-transmitting shell in the curve;

substituting the curvature radius of the paraxial part of the curve and a preset conical coefficient into an aspheric curve standard equation to obtain an initial expression;

and determining each aspheric surface coefficient in the initial expression by a damped least square method and a preset evaluation function to obtain a curve expression of the curve.

In a second aspect, embodiments of the present invention provide a curved mirror for mounting to a coaxial lidar including a cylindrical light-transmissive housing, the parameters of which are determined by a method as claimed in claims 1 to 6.

In a third aspect, embodiments of the present invention provide a coaxial lidar comprising a cylindrical light-transmissive housing and a curved mirror, the curved mirror being a single curved cylindrical curved mirror, wherein parameters of the curved mirror are determined by the method of claims 1 to 6.

In a fourth aspect, an embodiment of the present invention provides a terminal, including a memory, a processor, and a computer program stored in the memory and executable on the processor, where the processor implements the steps of the method according to the first aspect or any possible implementation manner of the first aspect when executing the computer program.

In a fifth aspect, the present invention provides a computer-readable storage medium, which stores a computer program, and when the computer program is executed by a processor, the computer program implements the steps of the method according to the first aspect or any one of the possible implementation manners of the first aspect.

Compared with the prior art, the embodiment of the invention has the following beneficial effects:

the embodiment of the invention provides a method for determining parameters of a curved reflector, which determines the curved surface of the curved reflector by determining each parameter of a curve on the curved surface of the curved reflector, compensates the effect of a cylindrical shell on a straight light beam by the curved reflector so as to reduce the influence of the cylindrical light-transmitting shell on a collimated detection light beam, solves the problem of light spot divergence caused by the practical application of the light-transmitting shell, improves the measurement precision of a laser radar and the receiving efficiency of a receiving and transmitting light path so as to increase the acting distance of the radar, does not introduce an additional optical calibration element to compensate the divergence caused by the alignment of the light-transmitting shell on the straight light beam, and compensates by modifying the surface shape of the reflector, so that the system structure is more compact, and the realization is more flexible and convenient.

Drawings

In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the embodiments or the prior art descriptions will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without inventive exercise.

FIG. 1 is a schematic diagram illustrating the effect of a cylindrical transparent housing of a lidar on the characteristics of a collimated light beam provided by an embodiment of the invention;

fig. 2 is a flowchart of an implementation of a method for determining parameters of a curved mirror according to an embodiment of the present invention;

FIG. 3 is a schematic horizontal cross-sectional view of a cylindrical light-transmissive envelope provided in accordance with an embodiment of the present invention;

FIG. 4 is a schematic diagram of Yz incident light of a cross section reflected by a curved mirror provided by an embodiment of the present invention;

FIG. 5 is a schematic diagram of paraxial ray transmission on a xoy projection plane provided by an embodiment of the invention;

FIG. 6 is a schematic diagram of an even aspheric equation curve in a y' oh coordinate system according to an embodiment of the present invention;

fig. 7 is a functional relationship diagram of the aspheric order terms in the y' oh coordinate system according to the embodiment of the present invention.

Fig. 8 is a dot alignment diagram of an exit surface and a 10m image surface of a field of view of which Vx is 0 ° and Vz is 0 ° in a sequence mode of a plane mirror provided by an embodiment of the present invention;

FIG. 9 is a schematic diagram of a coaxial optical path curved mirror transceiver system according to an embodiment of the present invention;

FIG. 10 is a model of a coaxial optical path provided by an embodiment of the present invention;

FIG. 11 is a graph of an optimized aspheric surface according to an embodiment of the present invention;

FIG. 12 is a graph of an optimized correction curve of aspheric terms of each order according to an embodiment of the present invention;

fig. 13(a) is a dot array diagram of the exit surface and the target surface of the field of view with Vx being 0 ° and Vz being 0 ° in the sequence mode provided by the embodiment of the present invention;

fig. 13(b) is a dot array diagram of the exit surface and the target surface of the field of view with Vx being 0 ° and Vz being 1 ° in the sequence mode provided by the embodiment of the present invention;

fig. 13(c) is a dot array diagram of the exit surface and the target surface of the field of view of Vx 0 ° and Vz-1 ° in the sequence mode according to the embodiment of the present invention;

fig. 13(d) is a dot array diagram of the exit surface and the target surface of the field of view with Vx being 1 ° and Vz being 0 ° in the sequence mode provided by the embodiment of the present invention;

fig. 13(e) is a dot array diagram of the exit surface and the target surface of the field of view of Vx-1 ° and Vz-0 ° in the sequence mode according to the embodiment of the present invention;

FIG. 14 is a graph illustrating the results of comparing a simulated flat mirror to a curved mirror in a non-sequential mode according to an embodiment of the present invention;

FIG. 15 is a schematic structural diagram of a device for determining parameters of a curved mirror according to an embodiment of the present invention;

fig. 16 is a schematic diagram of a terminal according to an embodiment of the present invention.

Detailed Description

In the following description, for purposes of explanation and not limitation, specific details are set forth, such as particular system structures, techniques, etc. in order to provide a thorough understanding of the embodiments of the invention. It will be apparent, however, to one skilled in the art that the present invention may be practiced in other embodiments that depart from these specific details. In other instances, detailed descriptions of well-known systems, devices, circuits, and methods are omitted so as not to obscure the description of the present invention with unnecessary detail.

To make the objects, technical solutions and advantages of the present invention more apparent, the following description will be made by way of specific embodiments with reference to the accompanying drawings.

Fig. 1 is a schematic diagram illustrating an influence of a cylindrical light-transmitting housing of a lidar on characteristics of a collimated light beam according to an embodiment of the present invention. As shown in fig. 1, since the optical beam is circularly symmetric in the rotational scanning, the light-transmissive envelope matched with the optical beam is generally a cylindrical structure.

In order to ensure the measurement accuracy of the laser radar, the laser radar must align the transmitting and receiving light paths before each measurement, so that the transmitting and receiving light paths are parallel to observe effective data, the process is called as the collimation process of light beams, and the obtained light beams are called as collimated light beams.

The introduction of a light-transmissive envelope has an effect on the beam transmission characteristics. Laser beams are collimated by the emitting lens and then transmitted in parallel along the z-axis direction, the plane reflector and the horizontal plane form an angle of 45 degrees and rotate by taking the z-axis as a rotating shaft, the beams are reflected by the reflector and then horizontally emitted, and the cylindrical light-transmitting shell has different influences on the beams on the vertical section parallel to the z-axis and the horizontal section vertical to the z-axis. As shown in fig. 1, the z-axis is a cylindrical axis, and in a section parallel to the cylindrical axis, such as a vertical section in fig. 1, the light-transmissive envelope functions as a parallel flat plate structure without changing the transmission direction of the light beam.

However, in a cross section perpendicular to the cylindrical axis, i.e., a horizontal cross section in fig. 1, the light-transmitting housing functions like a negative meniscus lens to diverge the light beam, the collimated light beam passes through the plane mirror and then through the cylindrical housing, and the light-transmitting housing functions to diverge the original collimated light beam to a certain extent, which greatly affects the detection angle resolution and accuracy of the laser radar system.

To solve this problem, an embodiment of the present invention provides a method for determining parameters of a curved mirror, and referring to fig. 2, it shows an implementation flowchart of the method for determining parameters of a curved mirror provided in the embodiment of the present invention, and the method is detailed as follows:

in step 201, a curvature radius of a paraxial portion of a curve corresponding to the curved mirror is determined according to a refractive index of the cylindrical light-transmitting casing to laser light, and an outer diameter length and an inner diameter length of the cylindrical light-transmitting casing, where the paraxial portion is used for representing a preset region closest to a central axis of the cylindrical light-transmitting casing in the curve.

In an embodiment of the invention, the curved mirror is a single curved cylindrical curved mirror mounted on a coaxial lidar comprising a cylindrical light transmissive envelope. Compared with a double-bending free-form curved surface reflector, the single-bending cylindrical curved surface reflector adopted by the embodiment of the invention has the advantages that the mirror surface structure is simpler, the processing technology is easier to realize, and the production cost is favorably reduced.

In one possible implementation, the refractive index of the cylindrical light-transmissive envelope for the laser light is determined based on the material of the cylindrical light-transmissive envelope and the operating wavelength of the laser light.

FIG. 3 is a schematic horizontal sectional view of a cylindrical light-transmitting envelope according to an embodiment of the present invention, with reference to FIG. 1 and FIG. 3, the cylindrical light-transmitting envelope has an outer diameter R₁Inner diameter of R₂。

In one possible implementation, the radius of curvature of the paraxial portion of the curved mirror is determined according to a first formula

Wherein R is_GThe curvature radius of the paraxial part of the curved reflector, n is the refractive index of the cylindrical light-transmitting shell to laser, R₁Is the outer diameter length, R, of the cylindrical light-transmitting envelope₂Is the length of the inner diameter of the cylindrical light-transmitting envelope.

The derivation process of the first formula is described below with reference to fig. 1, 3 to 5.

Referring to fig. 1, in the embodiment of the present invention, a cross section perpendicular to the x-axis is referred to as a vertical cross section, and a cross section perpendicular to the z-axis is referred to as a horizontal cross section. Fig. 4 is a schematic diagram of the reflection of incident light of yoz, which is a cross section perpendicular to the x-axis, by a curved mirror according to an embodiment of the present invention.

Considering the normal vector characteristic and the beam vector relationship of 0 for each of the sectional line equations F (0, y, z) of the curved mirror in a section perpendicular to the x-axis, where the beam on the y-axis is at the position (0, y,0) and the incident vector S is (0,0,1), and the sectional line equation F (0, y, z) of 0 and the yoz plane is 0, the sectional line equation F (0, y, z) is required to be 0 as a sectional line L equation:

where L0 is the length of the sectional line L, where the sectional line L coincides with the coordinate axis origin o.

After determining the sectional line equation, in conjunction with fig. 4, from the continuous relationship of the curved surfaces, a desired curved surface, i.e., the curved surface of the curved mirror in the embodiment of the present invention, can be formed by scanning along the curve G with the sectional line L as a generatrix. Assume the equation for curve G to be:

since the reflecting surface is a single curved surface, the curve G is in a plane perpendicular to the sectional line L, and the equation for the curve G can be:

the problem of solving the three-dimensional space curved surface is converted into the problem of solving the curve G through the analysis model, so that the system parameter relation and the design difficulty are greatly simplified, and the subsequent design optimization is facilitated.

In conjunction with the above analysis, the transversal L equation F (0, y, z) is 0, i.e.

Its normal vector is

The reflection vector R (0,0,0) — 0,1,0), the rays of this curve are all collimated through the light-transmissive envelope with the angle remaining constant.

In order to obtain a suitable radius of curvature of the curve G in the vicinity of the section yoz, it is assumed that the curve G has a radius of curvature R at the paraxial portion_GThe equation for (a) can be expressed as:

the curved surface formed by scanning is a conical surface, and the equation is as follows:

the normal vector is:

for the light ray at the paraxial region position P (x', 0,0), the light ray transmission characteristics of the paraxial light path on the projection plane xoy are analyzed, and fig. 5 is a schematic diagram of the paraxial light ray transmission on the xoy projection plane provided by the embodiment of the invention. With reference to FIGS. 4 and 5, the intersection of the light ray at position P (x', 0,0) and the reflecting surface is

The normal vector at the reflection point is:

the reflected ray vector is:

with reference to fig. 5, according to the paraxial ray tracing relation on the projection plane xoy, it can be calculated that the included angle between the emergent ray and the y axis is:

the equivalent radius of curvature on the projection surface can be obtained

It is also possible to pass the relationship of the combined lenses, the outer diameter R₁Inner diameter R₂The shell with the refractive index n forms an equivalent focal length at the center of a circle

The reflector of the concave lens has the same size at the circle center o and accords with the opposite focal length-f', so that the infinite combined focal length of the reflector and the shell does not generate the angle deflection effect on the light beam, and the concave lens is obtained

From the paraxial relationship of the reflected ray vectors:

this gives:

in step 202, the curvature radius of the paraxial portion of the curve and the preset conic coefficient are substituted into the standard equation of the aspheric curve to obtain an initial expression.

In the embodiment of the invention, from the perspective of the spatial projection relationship, the paraxial region of the curve G has a curvature radius R_GThe cross section of the light ray on the x axis and the reflecting curved surface isElliptical shape with a ratio of major axis to minor axis of

With a radius of curvature at the apex of

After the curvature radius of the paraxial region is determined, appropriate mirror surface parameters need to be obtained through optimization calculation. The curved reflective surface formed by curve G is a single curved cylinder with a straight generatrix parallel to the z ' axis on a coordinate system xy ' z ' rotated 45 ° clockwise about the x-axis of coordinate system xyz. According to the structural characteristics of the system, the curve G is symmetrically distributed about the bus L, and an even aspheric curve can be used to approximate the ideal curve G. Because the even aspheric curve has more parameter variables needing to be determined, the even aspheric curve is easy to fall into a local minimum value through the optimization of the damping least square method, and an ideal result is difficult to obtain when the variables are more and more under the condition of no proper initial value, so the thought of the optimization design is to reduce the number of the variables as much as possible and set the proper initial value.

In order to facilitate understanding of the present invention, in the embodiment of the present invention, a coordinate system involved in the embodiment of the present invention is described, fig. 1 shows an initial coordinate system oxyz, and a z-axis and a y-axis in the initial coordinate system are rotated clockwise by 45 ° with respect to an x-axis to obtain a coordinate system oxyz', as shown in fig. 4. The curve G corresponding to the curved mirror is symmetrical with respect to the sectional line L, i.e. the y' axis. Based on this, a y 'oh coordinate system is established, in the y' oh coordinate system, the y 'axis is the y' axis in fig. 4, the intersection point of the curve G and the y 'axis is the origin in the y' oh coordinate system, the curve G and the y 'axis form a plane, and the h axis is on the plane and passes through the origin of the y' oh and is perpendicular to the y 'axis in the y' oh coordinate system. After the expression of the curve G is determined, the sectional line L is used as a generatrix to scan along the curve G to form a desired curved surface, i.e., the curved surface of the curved mirror in the embodiment of the present invention. Based on this, in the embodiment of the present invention, the parameter determining process of the curved mirror is a process of determining each parameter of the curve expression of the curve G.

At this time, the ideal curve G can be approximated by an even-order aspherical curve.

According to the standard equation form of the even aspheric curve:

wherein y ' (h) is used for representing the mapping relation between the value of y ' and the value of h in a y ' oh coordinate system, the y ' axis is vertical to the h axis, o is the origin of the y ' oh coordinate system, curves are symmetrically distributed around the y ' axis, o is the intersection point of the curves and the y ' axis, k is a cone coefficient, r is the curvature radius of the paraxial part of the curves, a₄、a₆、a₈、a₁₀、a₁₂、a₁₄Are aspheric coefficients of each order. The ideal curvature radius of the center of the reflecting curved surface can be determined by combining the paraxial beam analysis, and the curve G is a spherical curve near the section yoz. The aspheric terms corresponding to the aspheric coefficients of each order can be considered as modifying the curve G with different functional relationships to approximate an ideal curve.

Fig. 6 is a schematic diagram of an even-order aspheric equation curve in a y 'oh coordinate system according to an embodiment of the present invention, and fig. 7 is a functional relationship diagram of each order term of an aspheric surface in the y' oh coordinate system according to an embodiment of the present invention. FIG. 7 shows that when the aspheric coefficients of each order are all 1, the aspheric terms and the normalized radial distance h/h_mRelation, h_mFor maximum radial distance, higher order coefficients are more pronounced for large radial distance corrections and less aspheric for small radial distances. In order to analyze the influence of each order coefficient, taylor expansion is carried out on the standard equation form of the even-order aspheric surface curve, and the following can be obtained:

from the above equation, the conic coefficient k has an influence on each order higher-order term.

Based on this, the initial expression is:

wherein y ' (h) is used for representing the mapping relation between the value of y ' and the value of h in a y ' oh coordinate system, the y ' axis is vertical to the h axis, o is the origin of the y ' oh coordinate system, curves are symmetrically distributed around the y ' axis, o is the intersection point of the curves and the y ' axis, k is used for representing a preset cone coefficient, r is used for representing the curvature radius of the paraxial part of the curves, and a is used for representing the curvature radius of the paraxial part of the curves₄、a₆、a₈、a₁₀、a₁₂、a₁₄Are aspheric coefficients.

It can be seen that, in order to determine the curve expression of the curve, the values of r and k and the aspheric coefficients a of each order need to be determined₄、a₆、a₈、a₁₀、a₁₂、a₁₄The value of (c).

Wherein R is the curvature radius of the paraxial part of the curve corresponding to the curved reflector, i.e. R ═ R_G。

In one possible implementation, k is a preset value, such as an empirical value. In another possible implementation, as can be seen from the above analysis, the conic coefficient k has an influence on each order of higher-order term, and for simplification of calculation, k is equal to-1, and the initial expression is:

wherein y ' (h) is used for representing the mapping relation between the value of y ' and the value of h in a y ' oh coordinate system, the y ' axis is vertical to the h axis, o is the origin of the y ' oh coordinate system, curves are symmetrically distributed around the y ' axis, o is the intersection point of the curves and the y ' axis, r is used for representing the curvature radius of the paraxial part of the curves, a₄、a₆、a₈、a₁₀、a₁₂、a₁₄Are aspheric coefficients.

In step 203, each aspheric coefficient in the initial expression is determined by a damped least squares method and a preset evaluation function, so as to obtain a curve expression of the curve.

In one possible implementation, the merit function is:

by selecting s points (x) at the target surface_i，y_i)，i＝1，…，s，x_iAnd y_iRepresenting the horizontal and vertical distance of the target point from the optical axis, respectively, e.g. s-9, i.e. 9 points are selected at the target surface, where x₁＝-100mm，y₁＝-100mm；x₂＝-100mm，y₂＝0mm；x₃＝-100mm，y₃＝100mm；x₄＝0mm，y₄＝-100mm；x₅＝0mm，y₅＝0mm；x₆＝0mm，y₆＝100mm；x₇＝100mm，y₇＝-100mm；x₈＝100mm，y₈＝0mm；x₉＝100mm，y₉Dividing the light beam incident to the aperture of the receiving lens by the field of view corresponding to each point in the form of a Gaussian 3-ring 6 arm, calculating the distance V between the intersection point of the light beam and the receiving photosensitive surface and the intersection point of the principal ray and the receiving photosensitive surface, and the weight of each point is preset, then in the evaluation function F, W is calculated_iRepresents a weight, V_iIs the current value, T_iIs the target value.

The correction of the aspherical coefficient function of each order being separated, i.e. aspherical coefficient a of fourth order₄Correction of curve G only with h⁴Correlation when a₄When 0, the radial distance is four such terms h⁴No correction effect is generated on the curve. As can be seen from the paraxial relationship calculation, the curvature radius R of the paraxial portion of the curve is R_GThe cone coefficient k is selected as-1, the values of the curvature radius and the cone coefficient are determined to reduce two variables for aspheric surface optimization, and the aspheric surface reflector which has small influence on the curve by each order of aspheric surface item in the paraxial region and is optimized by optimizing the aspheric surface coefficient on the light beam far away from the paraxial region supplements the light beam divergence effect of the light-transmitting shell. The aspherical surface coefficients of each order were optimized as variables by the following order: a is to₄Is set as a variable, a₆、a₈、a₁₀、a₁₂、a₁₄System of aspheric surfaces of each orderThe number is set to zero, and the optimal a is obtained by optimizing the damping least square method of software₄Comparing the evaluation functions before and after optimization, and stopping optimization if the change of the evaluation functions does not exceed a threshold value delta F; if the evaluation function changes beyond the evaluation threshold δ F, a₄A value of (a) is fixed₆Setting the variable to be optimized continuously, and optimizing by a damped least square method to obtain the optimal a₆Comparing the evaluation functions before and after optimization, stopping optimization if the change of the evaluation function does not exceed the evaluation threshold value delta F, and if the change of the evaluation function exceeds the evaluation threshold value delta F, a₄、a₆A value of (a) is fixed₈Setting as variable, optimizing by damped least square method to obtain optimal a₈And repeating the steps until the change of the evaluation function does not exceed the threshold value, or until the optimization of the aspheric surface coefficients of each order is completed, and the whole optimization process is completed.

In the embodiment of the present invention, the process of obtaining the aspheric coefficients of each order is as follows:

a is to₄、a₆、a₈、a₁₀、a₁₂、a₁₄Arranging according to a preset sequence to obtain a sequencing result;

sequentially optimizing the aspheric coefficients in the sequencing result by a damped least square method until the absolute value of the variation of the evaluation function is less than or equal to a preset threshold, wherein when a is measured_xWhen optimizing, a_xSet as variable, and locate at a in the sorting result_xSetting the value of the coefficient which has been optimized before as the optimal solution of the coefficient, and positioning the coefficient at a in the sequencing result_xThe latter value is set to 0, a_xIs any one of the aspheric coefficients in the sorted result.

In one possible implementation manner, in the sorting result, each aspheric surface coefficient is a sequentially from front to back₄、a₆、a₈、a₁₀、a₁₂、a₁₄And sequentially optimizing the aspheric coefficients in the sequencing result by a damped least square method until the variation of the evaluation function is less than or equal to a preset threshold value, wherein the method comprises the following steps:

a is to₄Set as variable, a₆、a₈、a₁₀、a₁₂、a₁₄Is set to 0 and is optimized by a damped least squares method to obtain a₄To determine an optimization a₄The absolute value of the change of the function is evaluated before and after, if a is optimized₄If the absolute value of the variation of the front and rear evaluation functions is less than or equal to a preset threshold, the optimization is finished, a₄Has a value of₄The values of other aspheric coefficients are 0;

if optimize a₄The absolute value of the variation of the front and rear evaluation functions is larger than a preset threshold value, and a₆Set as variable, then a₄Is set to a₄Is a is₈、a₁₀、a₁₂、a₁₄Is set to 0 and is optimized by a damped least squares method to obtain a₆To determine an optimization a₆The absolute value of the variation of the evaluation function before and after the optimization of a₆If the absolute value of the variation of the front and rear evaluation functions is less than or equal to a preset threshold, the optimization is finished, a₄Has a value of₄Of an optimal solution of₆Has a value of₆The values of other aspheric coefficients are 0;

if optimize a₆The absolute value of the variation of the front and rear evaluation functions is larger than a preset threshold value, and a₈Set as variable, then a₄Is set to a₄Of a is₆Is set to a₆Is a is₁₀、a₁₂、a₁₄Is set to 0 and optimized by a damped least squares method to obtain a₈To determine an optimization a₈The absolute value of the variation of the evaluation function before and after the optimization of a₈If the absolute value of the variation of the front and rear evaluation functions is less than or equal to a preset threshold, the optimization is finished, a₄Has a value of₄Of an optimal solution of₆Has a value of₆Of an optimal solution of₈Has a value of₈The values of other aspheric coefficients are 0;

if optimize a₈The absolute value of the variation of the pre-evaluation function and the post-evaluation function is larger than the preset valueThreshold value, a₁₀Set as variable, then a₄Is set to a₄Is a is₆Is set to a₆Is a is₈Is set to a₈Is a is₁₂And a₁₄Is set to 0 and optimized by a damped least squares method to obtain a₁₀To determine an optimization a₁₀The absolute value of the variation of the evaluation function before and after the optimization of a₁₀If the absolute value of the variation of the front and rear evaluation functions is less than or equal to a preset threshold, the optimization is finished, a₄Has a value of₄Of an optimal solution of₆Has a value of₆Of optimal solution of a₈Has a value of₈Of optimal solution of a₁₀Has a value of₁₀The values of other aspheric coefficients are 0;

if optimize a₁₀The absolute value of the variation of the front and rear evaluation functions is larger than a preset threshold value, and a₁₂Set as variable, then a₄Is set to a₄Is a is₆Is set to a₆Is a is₈Is set to a₈Is a is₁₀Is set to a₁₀Is a is₁₄Is set to 0 and optimized by a damped least squares method to obtain a₁₂To determine an optimization a₁₂The absolute value of the variation of the evaluation function before and after the optimization of a₁₂If the absolute value of the variation of the front and rear evaluation functions is less than or equal to a preset threshold, the optimization is finished, a₄Has a value of₄Of an optimal solution of₆Has a value of₆Of an optimal solution of₈Has a value of₈Of an optimal solution of₁₀Has a value of₁₀Of an optimal solution of₁₂Has a value of₁₂The values of other aspheric coefficients are 0;

if optimize a₁₂The absolute value of the variation of the front and rear evaluation functions is larger than a preset threshold value, and a₁₄Set as variable, then a₄Is set to a₄Is a is₆Is set to a₆Of a is₈Is set to a₈Is a is₁₀Is set to a₁₀Is a is₁₂Is set to a₁₂The optimal solution is optimized by a damped least square method to obtain a₁₄And (4) finishing optimization, wherein for any aspheric coefficient, the value of the aspheric coefficient is the optimal solution of the aspheric coefficient.

To facilitate understanding of the present invention, the embodiments of the present invention are described using an example. In other steps and other possible implementations of the embodiments of the present invention, if an example in this step is involved, the values of the parameters and the expression symbols of the parameters in this example are consistent before and after the description is omitted.

The transmit-receive lens of the coaxial optical path system can be generally realized by the following two ways: the first mode is that a transmitting-receiving lens with a vertical optical axis is combined with a semi-transmitting and semi-reflecting lens; the second mode is a mode of a receiving lens with a hole dug in the center of the optical axis and a transmitting lens placed in the hole. The embodiment of the invention selects a coaxial light path of a receiving lens with a hole dug in the center. In the embodiment of the invention, the reflector is the curved reflector, the receiving lens is provided with a hole in the center of the optical axis, and the transmitting lens is a conventional collimating lens and is arranged in the hole of the receiving lens.

The optical axes of the receiving lens and the transmitting lens are coincident, the transmitting lens with the aperture of d is arranged in the middle hole of the receiving lens, and the laser source is positioned on the focal plane f of the transmitting lens_eAfter the emergent light from the laser source is collimated by the emitting lens, the beam width at the target surface with the distance L is

d is the aperture of the transmitting lens, e is the width of the light source, and different target (detection) distances L correspond to different conjugate distances of the receiving lens according to the geometrical optics principle

Wherein f is_rThe width of the beam detected at the focal length of the receiving lens in the coaxial laser radar is

The position of the light-sensitive surface of the detector is corresponding to the maximum target distance L of the radar_mCorresponding conjugate distance

Rather than the focal plane location of the receive lens.

Simulation modeling analysis is performed through an optical sequence mode, in an example provided by the embodiment of the present invention, the material of the cylindrical light-transmitting housing of the laser radar is PMMA (polymethyl methacrylate), the laser operating wavelength of the laser radar is 905nm, and the refractive index n of the cylindrical light-transmitting housing to the laser is 1.484. Outer diameter length R of cylindrical light-transmitting housing₁20mm, inner diameter R₂18mm, Vx is 0 °, Vz is 0 °, namely, the field of view beam whose included angle with the x-axis and the z-axis is 0 ° is reflected by the plane mirror and transmitted through the transparent housing to the target surface with the maximum detection distance of 10m, fig. 8 is a point diagram of the exit surface of the field of view with Vx 0 ° and Vz being 0 ° and the image surface of 10m in the sequence mode when the mirror is a plane mirror in the prior art, and in combination with fig. 8, it can be known that the beam is not deflected substantially in the y direction, but has a large divergence effect in the x direction, and the beam deflection angle δ is larger than 14 mrad.

In order to compensate the deflection effect of the cylindrical light-transmitting shell on the light beam, the embodiment of the invention provides a coaxial light path curved surface reflector transceiving system, as shown in fig. 9, a planar reflector is changed into a curved surface reflector. And a coaxial light path model is established for optimization.

FIG. 10 is a model of a coaxial optical path according to an embodiment of the present invention, and in conjunction with FIG. 10, the focal length f of the transmitting lens_e10.08mm, 5.89mm for the transmitting lens aperture d, and f for the receiving lens focal length_r24.00mm and the aperture of the receiving lens is 26mm, wherein, in conjunction with fig. 10, the target plane AB is imaged by the receiving lens to obtain an imaging plane a ' B ', L ' is the distance from the receiving lens to a ' B ', L ' is obtained by calculation to 24.058mm, and L ' -f of the receiving detector is located behind the focal plane_r0.058mm, namely the conjugate plane of the maximum detection target plane,the curvature radius of the paraxial region of the curved reflector is calculated according to the formula to obtain R_G780.50mm, the system combined focal length is about-10¹⁰mm, and the condition of infinite combined focal length of the paraxial system is met.

The merit function was obtained by selecting 9 points (x) at the target surface as shown in FIG. 10_i，y_i)，i＝1，…，9，x_iAnd y_iRespectively representing the horizontal and vertical distances, x, of the target point from the optical axis₁＝-100mm，y₁＝-100mm；x₂＝-100mm，y₂＝0mm；x₃＝-100mm，y₃＝100mm；x₄＝0mm，y₄＝-100mm；x₅＝0mm，y₅＝0mm；x₆＝0mm，y₆＝100mm；x₇＝100mm，y₇＝-100mm；x₈＝100mm，y₈＝0mm；x₉＝100mm，y₉Dividing the light beam incident to the aperture of the receiving lens by the field of view corresponding to each point in the form of a gaussian 3-ring 6 arm, calculating the distance V between the intersection point of the light beam and the receiving photosensitive surface and the intersection point of the principal ray and the receiving photosensitive surface, and setting the weight of each point and the weight of each light beam to establish an evaluation function F, which can be generally expressed as:

wherein W_iRepresents a weight, V_iIs the current value, T_iIs the target value.

Determining the radius of curvature R ═ R of the paraxial portion of curve G from the above calculation_GAnd a cone coefficient k is-1, an evaluation function change threshold is set to be δ F0.1%, and the aspheric coefficients of the respective orders are optimized by software as variables through the following optimization sequence:

a is to be₄Is set as a variable, a₆、a₈、a₁₀、a₁₂、a₁₄The aspheric coefficients of all orders are set to be zero values, and the optimal a is obtained by optimizing the damping least square method of software₄Comparing the evaluation functions before and after optimization, and stopping optimization if the change of the evaluation functions does not exceed a threshold value delta F; if the merit function changesIf the evaluation threshold value delta F is exceeded, a is set₄A value of (a) is fixed₆Setting as variable to continue optimization, and optimizing by damping least square method to obtain optimal a₆Comparing the evaluation functions before and after optimization, stopping optimization if the change of the evaluation function does not exceed a threshold value delta F, and stopping a if the change of the evaluation function exceeds the evaluation threshold value₄、a₆A value of (a) is fixed₈Setting as variable, optimizing by damping least square method to obtain optimum a₈And repeating the steps until the change of the evaluation function does not exceed the threshold value, and finishing the whole optimization process. The optimization process optimizes the aspheric coefficients of each order from low order to high order one variable at a time, so that the optimization difficulty and the probability of trapping the optimization into the local minimum are reduced, because the more the number of the optimized variables is, the more the local minimum of the combination of the optimized variables is.

In addition, considering that the aspheric coefficients of different orders have different correction effects on the curve G, the low-order aspheric coefficients have larger correction effects on the whole curve under the same normalization parameter condition, the optimization sequence is higher, and the aspheric parameters after optimization are as follows:

a₄＝-1.218×10^-6mm^-3

a₆＝-8.730×10^-11mm^-5

a₈＝-2.725×10^-13mm^-7

a₁₀＝0mm^-9

a₁₂＝0mm^-11

a₁₄＝0mm^-13

the curve is optimized by calculating the curvature radius R in the paraxial region satisfying the curve G_GThe parabolic equation begins to be used as an initial condition, the correction is gradually carried out from a fourth-order term, the lower-order aspheric terms have larger correction effect on the curve, and the lower-order aspheric terms have larger correction effect on the curve from a₄To a₈The term evaluation function changes smaller and smaller to a₈Optimization stops the higher order corrections no longer being made if the merit function changes below the threshold. FIG. 11 is a graph of an optimized aspheric surface according to an embodiment of the present invention, and FIG. 12 is a graph of the present inventionAs shown in fig. 11 and 12, the optimized aspheric term correction curves of each order provided by the embodiment of the present invention have the same analysis as above, in which the aspheric terms having higher coefficient orders have larger radial distance correction and smaller influence on small radial distance.

Fig. 13(a) to 13(e) are point diagrams of the curved mirror after simulation optimization in the sequence mode according to the embodiment of the present invention, corresponding to the exit surface of different fields of view and the target surface of 10 m. The calculation result shows that the geometric radius increment of the light beam is less than 10mm after the light beam is transmitted for 10m for the field of view of Vx being 0 degrees and Vz being 0 degrees, and the light deflection angle delta of the light beam is less than 1mrad after the light beam is introduced into the reflector for compensation, so that the simulation result of the plane reflector is greatly improved. For Vx 0 degree, Vz 1 degree field of view, after transmitting 10m, the beam geometric radius increment is less than 10mm, and the beam deflection angle delta is less than 1mrad after introducing the curved mirror for compensation; and for Vx 0 degree and Vz-1 degree, the geometric radius increment of the light beam is less than 30mm after the light beam is transmitted for 10m, and the light beam deflection angle delta of the light beam is less than 3mrad after the light beam is introduced into the curved mirror for compensation. For a field of view with Vx being 1 degree and Vz being 0 degree, the geometric radius increment value of a light beam is less than 30mm after the light beam is transmitted for 10m, and the light beam deflection angle delta is less than 3mrad after the light beam is introduced into a curved reflector for compensation; and for Vx-1 degree and Vz-0 degree, the geometric radius increment of the light beam is less than 30mm after the light beam is transmitted for 10m, and the light beam deflection angle delta of the light beam is less than 3mrad after the light beam is introduced into the curved mirror for compensation. As can be seen from the dot-sequence diagram, the optical system characteristics are symmetrically distributed about the x-axis field of view, which is consistent with the symmetry of the structure.

FIG. 14 is a graph illustrating the results of comparing a simulated flat mirror to a curved mirror in a non-sequential mode according to an embodiment of the present invention; the laser source adopts three-section luminous edge-emitting laser diode, the power is 25W, the size of a luminous area (W multiplied by H) is 120 mu m multiplied by 20 mu m, and the diameter of a photosensitive surface of a sensor is 500 mu m. The left side of the radar is used as a 0-degree angle reference, the clockwise direction is positive, the simulation position distance is 10m, and the characteristics of light beams on a light-sensitive surface of a receiving detector are compared, so that the light beams are emergent in the vertical direction when the plane reflector is scanned at a 90-degree scanning angle, the width of the light beams in the horizontal direction is small and is slightly influenced by a light-transmitting shell, the emitting light spots and the receiving light spots can also keep basic shapes and present three-section distribution, but the receiving light spots exceed the range of the light-sensitive surface and lose part of echo energy, and the states of the emitting light spots and the receiving light spots at other angles of 0 degrees, 30 degrees and 45 degrees are changed and cannot present three-section distribution. The contrast simulation result of the curved surface reflector is introduced to show that the transmitting and receiving light spots can also keep basic shapes at the scanning angles of 0 degree, 30 degrees, 45 degrees and 90 degrees and are distributed in three sections, the receiving light spots are all positioned in the range of a photosensitive surface, no echo energy loss exists, and the curved surface reflector well compensates the influence of the cylindrical shell on the coaxial transmitting and receiving light path.

It should be understood that, the sequence numbers of the steps in the foregoing embodiments do not imply an execution sequence, and the execution sequence of each process should be determined by its function and inherent logic, and should not constitute any limitation to the implementation process of the embodiments of the present invention.

An embodiment of the present invention further provides a curved mirror, where the curved mirror is installed in a coaxial lidar including a cylindrical light-transmitting housing, and parameters of the curved mirror are determined by an embodiment of a method corresponding to fig. 2. The curved reflector compensates the effect of the cylindrical shell on the alignment light beam so as to reduce the influence of the cylindrical light-transmitting shell on the alignment detection light beam, solve the problem of light spot divergence caused by practical application of the light-transmitting shell, improve the measurement precision of the laser radar and the receiving efficiency of a receiving and transmitting light path so as to increase the radar action distance.

The embodiment of the invention also provides a coaxial laser radar, which comprises a cylindrical light-transmitting shell and a curved reflector, wherein the curved reflector is a single-bent cylindrical curved reflector, and the parameters of the curved reflector are determined by the method of the embodiment corresponding to the figure 2.

In another possible implementation manner, the coaxial lidar further comprises a receiving lens and a transmitting lens, wherein the receiving lens is dug in the center of the optical axis, and the transmitting lens is arranged in the hole of the receiving lens.

The coaxial laser radar provided by the embodiment of the invention compensates the action of the cylindrical shell aiming at the straight light beam by installing the curved surface type reflector so as to reduce the influence of the cylindrical light-transmitting shell on the collimated detection light beam, solve the problem of light spot divergence caused by practical application of the light-transmitting shell, improve the measurement precision of the laser radar and the receiving efficiency of a receiving and transmitting light path so as to increase the radar action distance.

The following are embodiments of the apparatus of the invention, reference being made to the corresponding method embodiments described above for details which are not described in detail therein.

Fig. 15 is a schematic structural diagram of a parameter determining apparatus for a curved mirror according to an embodiment of the present invention, which only shows portions related to the embodiment of the present invention for convenience of explanation, and the details are as follows:

as shown in fig. 15, the parameter determining apparatus 15 for a curved mirror includes: a curvature radius determination module 151 and an expression determination module 152;

the curvature radius determining module 151 is configured to determine a curvature radius of a paraxial portion of a curve corresponding to the curved mirror according to a refractive index of the cylindrical light-transmitting casing to laser light, an outer diameter length and an inner diameter length of the cylindrical light-transmitting casing, where the paraxial portion is used to represent a preset region closest to a central axis of the cylindrical light-transmitting casing in the curve;

the expression determining module 152 is configured to substitute the curvature radius of the paraxial portion of the curve and a preset conic coefficient into the aspheric curve standard equation to obtain an initial expression; and determining each aspheric surface coefficient in the initial expression by a damped least square method and a preset evaluation function to obtain a curve expression of the curve.

The embodiment of the invention provides a parameter determining device of a curved surface type reflector, which determines the curved surface of the curved surface type reflector by determining each parameter of a curve on the curved surface of the curved surface type reflector, compensates the effect of a cylindrical shell to align a straight light beam by the curved surface type reflector so as to reduce the influence of the cylindrical light-transmitting shell to a collimated detection light beam, solves the problem of light spot divergence caused by the practical application of the light-transmitting shell, improves the measurement precision of a laser radar and the receiving efficiency of a receiving and transmitting light path so as to increase the acting distance of the radar, does not introduce an additional optical calibration element to compensate the divergence caused by the alignment of the light-transmitting shell to the straight light beam, and compensates by modifying the surface shape of the reflector, so that the system structure is more compact, and the realization is more flexible and convenient.

The apparatus for determining parameters of a curved mirror provided in this embodiment may be used to implement the above embodiments of the method for determining parameters of a curved mirror, and the implementation principle and technical effect are similar, which are not described herein again.

Fig. 16 is a schematic diagram of a terminal according to an embodiment of the present invention. As shown in fig. 16, the terminal 16 of this embodiment includes: a processor 160, a memory 161, and a computer program 162 stored in the memory 161 and executable on the processor 160. The processor 160, when executing the computer program 162, implements the steps of the above-described embodiments of the method for determining parameters of a curved mirror, such as the steps 201 to 203 shown in fig. 2. Alternatively, the processor 160 implements the functions of the modules/units in the above device embodiments, for example, the functions of the modules 151 to 152 shown in fig. 15, when executing the computer program 162.

Illustratively, the computer program 162 may be partitioned into one or more modules/units that are stored in the memory 161 and executed by the processor 160 to implement the present invention. The one or more modules/units may be a series of computer program instruction segments capable of performing certain functions, which are used to describe the execution of the computer program 162 in the terminal 16.

The terminal 16 may be a computing device such as a desktop computer, a notebook, a palm top computer, and a cloud server. The terminal 16 may include, but is not limited to, a processor 160, a memory 161. Those skilled in the art will appreciate that fig. 16 is merely an example of a terminal 16 and is not intended to be limiting of the terminal 16, and may include more or less components than those shown, or some components in combination, or different components, e.g., the terminal may also include input output devices, network access devices, buses, etc.

The Processor 160 may be a Central Processing Unit (CPU), other general purpose Processor, a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), a Field Programmable Gate Array (FPGA) or other Programmable logic device, discrete Gate or transistor logic device, discrete hardware component, or the like. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like.

The memory 161 may be an internal storage unit of the terminal 16, such as a hard disk or a memory of the terminal 16. The memory 161 may also be an external storage device of the terminal 16, such as a plug-in hard disk, a Smart Media Card (SMC), a Secure Digital (SD) Card, a Flash memory Card (Flash Card), and the like, which are provided on the terminal 16. Further, the memory 161 may also include both internal and external memory units of the terminal 16. The memory 161 is used for storing the computer program and other programs and data required by the terminal. The memory 161 may also be used to temporarily store data that has been output or is to be output.

It will be apparent to those skilled in the art that, for convenience and brevity of description, only the above-mentioned division of the functional units and modules is illustrated, and in practical applications, the above-mentioned function distribution may be performed by different functional units and modules according to needs, that is, the internal structure of the apparatus is divided into different functional units or modules to perform all or part of the above-mentioned functions. Each functional unit and module in the embodiments may be integrated in one processing unit, or each unit may exist alone physically, or two or more units are integrated in one unit, and the integrated unit may be implemented in a form of hardware, or in a form of software functional unit. In addition, specific names of the functional units and modules are only for convenience of distinguishing from each other, and are not used for limiting the protection scope of the present application. The specific working processes of the units and modules in the system may refer to the corresponding processes in the foregoing method embodiments, and are not described herein again.

In the above embodiments, the descriptions of the respective embodiments have respective emphasis, and reference may be made to the related descriptions of other embodiments for parts that are not described or illustrated in a certain embodiment.

Those of ordinary skill in the art will appreciate that the various illustrative elements and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware or combinations of computer software and electronic hardware. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the implementation. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present invention.

In the embodiments provided in the present invention, it should be understood that the disclosed apparatus/terminal and method may be implemented in other ways. For example, the above-described apparatus/terminal embodiments are merely illustrative, and for example, the division of the modules or units is only one logical division, and there may be other divisions when actually implemented, for example, a plurality of units or components may be combined or may be integrated into another system, or some features may be omitted, or not executed. In addition, the shown or discussed mutual coupling or direct coupling or communication connection may be an indirect coupling or communication connection through some interfaces, devices or units, and may be in an electrical, mechanical or other form.

The units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of the embodiment.

In addition, functional units in the embodiments of the present invention may be integrated into one processing unit, or each unit may exist alone physically, or two or more units are integrated into one unit. The integrated unit can be realized in a form of hardware, and can also be realized in a form of a software functional unit.

The integrated modules/units, if implemented in the form of software functional units and sold or used as separate products, may be stored in a computer readable storage medium. Based on such understanding, all or part of the flow of the method according to the above embodiments may be implemented by a computer program, which may be stored in a computer-readable storage medium, and when the computer program is executed by a processor, the steps of the embodiments of the method for determining parameters of each curved mirror may be implemented. Wherein the computer program comprises computer program code, which may be in the form of source code, object code, an executable file or some intermediate form, etc. The computer-readable medium may include: any entity or device capable of carrying the computer program code, recording medium, usb disk, removable hard disk, magnetic disk, optical disk, computer Memory, Read-Only Memory (ROM), Random Access Memory (RAM), electrical carrier wave signals, telecommunications signals, software distribution medium, and the like. It should be noted that the computer readable medium may contain other components which may be suitably increased or decreased as required by legislation and patent practice in jurisdictions, for example, in some jurisdictions, computer readable media which may not include electrical carrier signals and telecommunications signals in accordance with legislation and patent practice.

The above-mentioned embodiments are only used for illustrating the technical solutions of the present invention, and not for limiting the same; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; such modifications and substitutions do not substantially depart from the spirit and scope of the embodiments of the present invention, and are intended to be included within the scope of the present invention.

Claims

1. A method for determining parameters of a curved mirror, characterized in that the curved mirror is a single curved cylindrical curved mirror, the curved mirror is mounted on a coaxial lidar comprising a cylindrical light-transmitting housing, comprising:

2. The method of claim 1, wherein determining the radius of curvature of the paraxial portion of the curve corresponding to the curved mirror based on the refractive index of the cylindrical light-transmissive envelope for the laser light, the length of the outer diameter and the length of the inner diameter of the cylindrical light-transmissive envelope comprises:

determining a radius of curvature of a paraxial portion of the curve according to a first formula

Wherein R is_GIs the curvature radius of the paraxial part of the curve, n is the refractive index of the cylindrical light-transmitting shell to laser, R₁Is the length of the outer diameter, R, of the cylindrical light-transmitting envelope₂Is the length of the inner diameter of the cylindrical light-transmitting housing.

3. The method of claim 1, wherein the initial expression is:

wherein y ' (h) is used for representing the mapping relation between the value of y ' and the value of h in a y ' oh coordinate system, the y ' axis is vertical to the h axis, o is the origin of the y ' oh coordinate system, the curve is symmetrically distributed around the y ' axis, o is the intersection point of the curve and the y ' axis, k is used for representing a preset cone coefficient, r is used for representing the curvature radius of the paraxial part of the curve, a₄、a₆、a₈、a₁₀、a₁₂、a₁₄Are aspheric coefficients.

4. The method of claim 3, wherein k is equal to-1, and wherein the initial expression is:

5. the method according to claim 3 or 4, wherein the determining of the individual aspheric coefficients in the initial expression by damped least squares and a preset evaluation function comprises:

sequentially optimizing aspheric coefficients in the sequencing result by a damped least square method until the absolute value of the variation of the evaluation function is less than or equal to a preset threshold, wherein when a is measured_xWhen optimizing, a_xSetting the sequence result to be a in a variable_xSetting the value of the coefficient which has been optimized before as the optimal solution of the coefficient, and positioning a in the ordering result_xThe latter value is set to 0, a_xIs any aspheric coefficient in the sorting result.

6. The method according to claim 5, wherein in the sorting result, each aspheric surface coefficient is a sequentially from front to back₄、a₆、a₈、a₁₀、a₁₂、a₁₄Sequentially optimizing aspheric coefficients in the sequencing result by a damped least square method until the variation of the evaluation function is less than or equal to a preset threshold value comprises:

a is to₄Set as variable, a₆、a₈、a₁₀、a₁₂、a₁₄Is set to 0 and optimized by a damped least squares method to obtain a₄To determine an optimization a₄The absolute value of the amount of change of the evaluation function before and after, if a is optimized₄Front and rear placesIf the absolute value of the variation of the evaluation function is less than or equal to the preset threshold, the optimization is finished, a₄Has a value of₄The values of other aspheric coefficients are 0;

if optimize a₄The absolute value of the variation of the evaluation function before and after is larger than the preset threshold value, and a₆Set as variable, then a₄Is set to a₄Is a is₈、a₁₀、a₁₂、a₁₄Is set to 0 and optimized by a damped least squares method to obtain a₆To determine an optimization a₆The absolute value of the amount of change of the evaluation function before and after, if a is optimized₆The absolute values of the variation of the evaluation function before and after the evaluation are less than or equal to the preset threshold, the optimization is finished, a₄Has a value of₄Of optimal solution of a₆Has a value of₆The values of other aspheric coefficients are 0;

if optimize a₆The absolute value of the variation of the evaluation function before and after is larger than the preset threshold value, and a₈Set as variable, then a₄Is set to a₄Is a is₆Is set to a₆Is a is₁₀、a₁₂、a₁₄Is set to 0 and optimized by a damped least squares method to obtain a₈To determine an optimization a₈The absolute value of the amount of change of the evaluation function before and after, if a is optimized₈And (b) finishing the optimization if the absolute values of the variation of the evaluation functions before and after the optimization are less than or equal to the preset threshold value, and (a) finishing the optimization₄Has a value of₄Of an optimal solution of₆Has a value of₆Of an optimal solution of₈Has a value of₈The values of other aspheric coefficients are 0;

if optimize a₈The absolute value of the variation of the evaluation function before and after is larger than the preset threshold value, and a₁₀Set as variable, then a₄Is set to a₄Is a is₆Is set to a₆Is a is₈Is set to a₈Of (2) an optimal solutionA is to₁₂And a₁₄Is set to 0 and optimized by a damped least squares method to obtain a₁₀To determine an optimization a₁₀The absolute value of the amount of change of the evaluation function before and after, if a is optimized₁₀The absolute values of the variation of the evaluation function before and after the evaluation are less than or equal to the preset threshold, the optimization is finished, a₄Has a value of₄Of an optimal solution of₆Has a value of₆Of an optimal solution of₈Has a value of₈Of an optimal solution of₁₀Has a value of₁₀The values of other aspheric coefficients are 0;

if optimize a₁₀The absolute value of the variation of the evaluation function before and after is larger than the preset threshold value, and a₁₂Set as variable, then a₄Is set to a₄Is a is₆Is set to a₆Is a is₈Is set to a₈Is a is₁₀Is set to a₁₀Is a is₁₄Is set to 0 and optimized by a damped least squares method to obtain a₁₂To determine an optimization a₁₂The absolute value of the change of the evaluation function before and after a, if a is optimized₁₂The absolute values of the variation of the evaluation function before and after the evaluation are less than or equal to the preset threshold, the optimization is finished, a₄Has a value of₄Of an optimal solution of₆Has a value of₆Of optimal solution of a₈Has a value of₈Of an optimal solution of₁₀Has a value of₁₀Of an optimal solution of₁₂Has a value of₁₂The values of other aspheric coefficients are 0;

if optimize a₁₂The absolute value of the variation of the evaluation function before and after is larger than the preset threshold value, and a₁₄Set as variable, then a₄Is set to a₄Is a is₆Is set to a₆Is a is₈Is set to a₈Is a is₁₀Is set to a₁₀Is a is₁₂Is set to a₁₂Is best solution ofOptimizing by an over-damped least square method to obtain a₁₄And finishing optimization, wherein for any aspheric coefficient, the value of the aspheric coefficient is the optimal solution of the aspheric coefficient.

7. Curved mirror, characterized in that it is mounted on a coaxial lidar comprising a cylindrical light-transmitting housing, the parameters of which are determined by the method of claims 1 to 6.

8. A coaxial lidar comprising a cylindrical light-transmissive housing and a curved mirror, the curved mirror being a single curved cylindrical curved mirror, wherein parameters of the curved mirror are determined by the method of claims 1 to 6.

9. A terminal comprising a memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that the processor implements the steps of the method according to any of the preceding claims 1 to 6 when executing the computer program.

10. A computer-readable storage medium, in which a computer program is stored which, when being executed by a processor, carries out the steps of the method according to any one of claims 1 to 6.