ES2915923B2 - PROCEDURE FOR PROJECTION OF A POINT LIGHT BEAM ON A FINAL PROJECTION SURFACE AND CORRESPONDING SCANNING PROCEDURE - Google Patents

Description

DESCRIPTION

PROCEDURE FOR PROJECTION OF A POINT LIGHT BEAM ON A

FINAL PROJECTION SURFACE AND SCANNING PROCEDURE

CORRESPONDENT

field of invention

The invention relates to a method of projecting a beam of point light onto a final projection surface, said beam of point light having to pass through at least a first medium with a first refractive index and a second medium with a second refractive index and said first and second refractive indices being different from each other, said procedure comprising the steps of: [a] providing a light emitter to emit said beam of point light, and [b] providing means for redirecting light to redirect said spot light beam onto said final projection surface, said redirection means being arranged at a known distance with respect to said emitter and mounted so that they can rotate around a first and a second axes of rotation.

Likewise, the invention relates to a laser scanning method to obtain a characterization of the shape of a final projection surface.

State of the art

Driverless vehicles are becoming increasingly popular. An example is driverless land vehicles. Another, non-limiting example of these vehicles are driverless underwater vehicles, known by their English acronym UUVs (Unmanned Undewater Vehicles), which are increasingly used for economic and safety reasons. In particular, autonomous underwater vehicles, more commonly called AUVs (Autonomous Underwater Vehicles), are used for reconnaissance, inspection, navigation or handling work. To do this, these vehicles are equipped with 3D scanners based on acoustic (SONAR) or optical (LiDAR) systems. Optical systems are preferable due to their greater lateral resolution and refresh rate, since the working range of these vehicles is relatively small.

Underwater 3D detection basically faces two problems: the first lies in the rapid degree of attenuation of light underwater and the second the distortion in the light caused by the refractive elements that get in its way. This causes scanners that are applied on land and are therefore not subject to the effects of refraction, do not provide satisfactory results when used in an underwater environment, especially when used for operations such as mapping or manipulation of objects.

Therefore, it is necessary to have light beam projection devices that have high precision and a high update frequency.

Document EP3605012A1 discloses a set and method of underwater scanning using laser light that obtains a geometric characterization of the shape of a surface based on the principle of triangulation. The set comprises: a laser light emitter, diffraction means that transform the point laser light into a flat fan configuration, redirection means that redirect the fan and project it onto the surface to be explored. On the other hand, a light receiver is provided that captures a scanning area that contains the fan and control means that control the elements of the assembly. The receiver has its own processing means to detect the illuminated points in the captured image. The redirection means are assembled so that they can rotate around at least one fixed axis. The rotation of the first redirection means is controlled by the control means in a synchronized manner with the remaining elements. The points illuminated by the fan in the scanning area that form a line that, depending on the angle of rotation of the fan, becomes increasingly curved. This line is characterized by an elliptical cone, so that a triangulation is carried out by calculating the intersection of the projected fan with the elliptical cone. This procedure is repeated until the entire surface is characterized. The surface characterization procedure requires high computing power and therefore the system is not as fast as would be desirable.

Document GB2509247A discloses a method for calibrating a scanning system based on trigonometry in air and water. The trigonometry-based scanning system comprises a structured signal emitting device for emitting a structured signal and a sensor or receiver having a field of view for detecting the signals emitted by the structured signal emitting device. The structured signal emitting device and the sensor that have a geometric relationship measured in the air. The method comprising: a) determining, both in water and air, a sensor array, b) measuring the rotation and translation of an optical axis of the sensor with respect to a largely defined ideal optical axis of the sensor by a sensor housing in which the sensor is mounted, determining the rotation and translation of a sensor coordinate system in air and water simultaneously, to obtain a rotation/translation matrix for the field of view in air and water respectively; and c) measuring the rotation of an optical axis of the emitting device relative to an optical axis of the ideal emitting device substantially defined by the housing of the emitting device, determining a relative change in an angle of the structured signal, between the structured signal in the air and the structured signal in the water respectively, to generate a rotation matrix of the device that will be subsequently applied to the structured signal once it has been projected on the surface to be scanned. This procedure reacts with a delay and is difficult to provide a high refresh rate.

Summary of the invention

The purpose of the invention is to provide a method for projecting a point light beam onto a final projection surface of the type indicated at the beginning, which is faster than those known in the state of the art.

This purpose is achieved through a procedure for projecting a beam of point light onto a final projection surface of the type indicated at the beginning, characterized in that said procedure also includes the steps of: [c] previously calculating a pair formed by: [i ] a first angle (α _x ) of rotation to rotate said redirection means around said first axis (x) of rotation and [ii] a second angle (α _y ) of rotation to rotate said redirection means around said second axis (y) of rotation, [iii] including said first and second refractive indices in said calculation step so that said pair of first and second angles (α _x , α _y ) of rotation compensate for the refraction of said light beam redirected by said redirecting means upon passing through said second means, [d] rotating said redirecting means around said first and second axes of rotation according to said pair of first and second angles (α _x , α _y ) of rotation previously calculated, and [e] emit a beam of point light on said redirection means for said pair of first and second angles (α _x , α _y ), so that said beam of point light, once redirected by said means redirection, when passing through said second means, is contained in a target emission surface (0) and is projected onto said final projection surface.

As seen previously, in the state of the art the effect of refraction, for example, in underwater vehicles, when light passes from the first to the second medium it is deformed due to refraction, the only way to compensate for refraction is by subsequent post-processing, which consists of adjusting a model to the real projected image. That is, even though the sensor receives a deformed image due to refraction, this image is corrected a posteriori.

On the other hand, the method according to the invention solves the problem in a different way from known methods. The proposed solution does not involve correctly approximating the projected image, but on the contrary, it consists of rotating the redirection means by the necessary angle to compensate a priori for the effect of refraction before projecting the image onto the final projection surface. Thanks to this, the finally projected point corresponds to the position that this same point would have if there had not been a change of medium.

Obviously, this implies that the three-dimensional position of the projected point can be solved with a much simpler equation since, once the point light beam has been adjusted to the target emission surface, to determine the projection of the point on the final target surface, It is only necessary to calculate the intersection of the line corresponding to the point light beam with the ideal plane that represents the final projection surface, which results in a point.

Furthermore, the invention encompasses a series of preferred features that are the subject of the dependent claims and whose usefulness will be highlighted later in the detailed description of an embodiment of the invention.

Obviously, and for all types of applications, it is more interesting not only to project individual points, but also sets of points that define arbitrary curves, which allows illuminating the final projection surface with specific patterns, which can be used to facilitate the three-dimensional reconstruction of the scanned surface. To this end, in an embodiment that aims to achieve a fast projection speed, [a] in said calculation stage a plurality of pairs of: [i] first angles (α _x ) of rotation are previously calculated to rotate said redirection means around said first axis (x) of rotation and [ii] second angles (α _and ) of rotation to rotate said redirection means around said second axis (y) of rotation, [iii] being included in said stage of I calculate said first and second refractive indices so that each pair of first and second angles (α _x , α _y ) of rotation of said plurality of pairs of first and second angles (α _x , α _y ) of rotation compensates the refraction of each light beam redirected by said redirection means when passing through said second means, and once said calculation step is completed, for each pair of first and second angles (α _x , α _y ) of rotation, said steps are carried out sequentially. of: [b] rotating said redirection means around said first and second axes of rotation (x, y) according to said pairs of first and second angles (α _x , α _y ) of rotation previously calculated, and [c] issuing a point light beam on said redirection means for each pair of first and second angles (α _x , α _y ), and [d] repeat said steps [b] and [c] until the last pair of first and second angles (α _x , α _y ) of said plurality of pairs of first and second angles (α _x , α _y ), so that each point light beam, when passing through said second medium, is contained in said objective emission surface (Φ) .

In this embodiment, all the necessary angles of each of the light beams that will be projected onto the final projection surface are previously calculated, with the corresponding correction that allows each of the light beams to be contained in the surface of the projection. target emission. Thanks to this, the speed of operation of the light redirection means is maximized.

In an alternative embodiment said steps of: [c] previously calculating a couple formed by: [i] a first angle (α _x ) of rotation to rotate said redirection means around said first axis (x) of rotation and [ ii] a second angle (α _y ) of rotation to rotate said redirection means around said second axis (y) of rotation, [iii] said first and second refraction indices being included in said calculation step so that said pair of first and second angles (α _x , α _y ) of rotation compensate for the refraction of said light beam redirected by said redirection means when passing through said second means, [d] rotate said redirection means around said first and second axes of rotation (x, y) according to said pair of first and second angles (α _x , α _y ) of rotation previously calculated, and [e] emit a point light beam on said redirection means for said pair of first and second angles (α _x , α _y ), so that said point light beam, when passing through said second means, is contained in a target emission surface ( O), are carried out jointly and sequentially for a plurality of pairs of first and second angles (α _x , α _y ) of rotation, so that each beam of point light, when passing through said second medium, is contained in said target emission surface (0).

In an embodiment intended to facilitate scanning for autonomous vehicle orientation tasks, said target emission surface (0) is a plane. Thanks to this, straight lines are projected on the final projection surface which are easy to process in environmental mapping procedures.

In order to facilitate the projection of light in underwater environments, in a preferred embodiment, the method comprises at least a third medium with a third refractive index and said first, second and third refractive indices being different from each other.

According to another embodiment, which aims to be able to work in underwater environments, said first medium is air, said second medium is water and said third medium is a solid and transparent medium.

Particularly preferably said third means is a transparent peephole and especially preferably said third means is glass or plexiglass.

Finally, the invention also relates to a laser scanning method to obtain a characterization of the shape of a final projection surface comprising the steps of the method of projecting a point light beam according to the invention. Thus, the scanning procedure also includes the steps of:

[a] provide a light receiver,

[b] arrange said first redirection means and said light receiver separated by a known predetermined distance that defines a baseline, [c] capture a scanning area of said final projection surface that must be characterized through said receiver of light, said area containing said light beam projected onto said final projection surface, and

[d] synchronize the emission of the light beam and the capture by said light receiver through control means functionally associated with said emitter and said light receiver.

Preferably, said first and second axes of rotation (x, y) are perpendicular to each other.

Preferably, said spot light beam is a laser light beam.

Another relevant problem consists of optimizing the scanning assembly to work in media other than air and in particular, submerged in water. To do this, said casing is waterproof and said laser is green or blue. The green or blue laser attenuates less underwater than other types of lasers and therefore projects further away. In environments with clear or slightly turbid waters, it is especially preferred that the laser be blue since it presents less attenuation than the green laser, despite having more backscattenng, that is, the reflection of light towards itself. set. Alternatively, in the case of more turbid waters, it is preferable for the laser to be green, since despite having more attenuation than a blue laser, the green laser has less backscattering than the blue laser. Under conditions of a single projection medium, that is, projection in the air without change of medium, the flat fan is projected onto the surface as a straight line. This does not occur in cases where there is a change of medium, for example, air-water sight glass.

Likewise, the invention also encompasses other detailed features illustrated in the detailed description of an embodiment of the invention and in the accompanying figures.

Description of the drawings

Other advantages and characteristics of the invention can be seen from the following description, in which, without any limiting character, some preferred embodiments of the invention are reported, making reference to the accompanying drawings. The figures show:

Fig. 1 shows a schematic graphic representation to explain the reflection phenomenon.

Fig. 2 shows a schematic graphic representation to explain the phenomenon of refraction.

Fig. 3, a schematic model of the geometric model of the projection procedure of a point light beam onto a final projection surface.

Figs. 4a to 4g, diagrams explaining the influence of poor calibration of each parameter of the model according to the invention.

Fig. 5. Schematic model of the geometric model, the viewpoint and the target are kept perpendicular to the outgoing light ray for α _x = α _y = 0° throughout the simulations.

Fig. 6, view of the projection point patterns on the final projection surface, distorted for different values of p at 1 m distance.

Fig. 7, diagram of the maximum deviation A from the desired pattern of straight lines for an increasing number of waypoints.

Figs. 8a to 8e, diagrams of the influence of the number of waypoints per line on the maximum deviation of straight light between waypoints.

Figs. 9a to 9e, diagrams of maximum line fit error when the actual final projection plane is not necessarily at the nominal distance of 1000 mm.

Fig. 10, diagram of the field of view (FoV) at a distance of 1 m.

Fig. 11, a schematic perspective view of a scanning assembly according to the invention with two medium changes, in a first scanning position.

Fig. 12, a schematic perspective view of a scanning assembly according to the invention with three medium changes, in a first scanning position.

Detailed description of an embodiment of the invention

Next, on the basis of Figures 1 to 10, the proposed geometric model for the projection of a point light beam 1 on a final projection surface 100 and for its application in the particular case of an underwater laser scanner is presented.

A. Geometric approximation

This section first brings together three well-known principles, namely reflection, refraction and intersection of the linear plane corresponding to the final projection surface 100, on which the mathematical model is built. Next, the composition of the coordinates is reviewed to transform the points and vectors in different reference frames, as well as the quaternions.

1) Reflection: as seen in Figure 1, the direction vector of the light beam resulting from the reflection of a ray with vector Vn on a surface with n normal (since Vn and n are unit vectors) is calculated as :

2) Refraction: in the second case, when a light beam 1 with vector Vn encounters a refraction surface with normal n that separates two media with differentiated refraction coefficients, (r and rout, respectively), and assuming that Vin and n are unit vectors, the direction vector of the resulting refracted ray can be expressed as:

3) Intersection of a line with a plane: the point of intersection P between a line l = Á ^v + lo and a plane n ^e n - x = d is calculated as:

4) Composition: The position of a coordinate frame A with respect to the world coordinate frame W is given by {W}^ { ^a > but for simplicity it will henceforth be called £ ^a . In three-dimensional space, it is composed of 6 degrees of freedom:

To change the reference frame in which the three-dimensional coordinates of a point are expressed, the following equation is generally used:

where {W}t{A> is the relative translation of {A} with respect to {W} and {W}R{ ^a } is the relative rotation of {A} with respect to {W}. This operation is called composition and can be expressed in a more compact form:

The coordinates of a vector can be expressed with respect to a different coordinate frame simply by rotating it:

Lines and planes can be characterized using a point and a vector. A line is defined by any arbitrary point on it and its direction vector, while a plane is represented by any arbitrary point on it and its normal vector. Therefore, the expression of a line or a plane with respect to a different reference system is reduced to the application of the transformation corresponding to its definition point and vector.

Quaternions: A normalized quaternion is a quaternion of the form:

Which meets the equation:

Quaternions can easily represent rotations around a given axis. The rotation of an angle Q about a unit axis u = [ux Uy Uz]T can be expressed with the normalized quaternion:

The 3x3 rotation matrix associated with a normalized quaternion is:

B. Model parameters

Figure 3 shows the geometric model to explain the procedure for projecting a point light beam 1 onto a final projection surface 100 for the case of three different media. In this particular case, the light beam 1 preferably refers to a light beam laser intended to be mounted on an underwater vehicle. The model is made up of 4 main elements: an emitter 6 of the light beam 1, as a laser point source, redirection means 8 such as, for example, a biα _x ial mirror or a MEMS mirror, a flat peephole 14 , referred to in the art as a viewing port or more commonly by its English version viewport, used as a transparent window that separates a first medium 2, which is air, and a second medium 4, which is water, and a consistent target to be scanned. on a final projection surface 100. Finally, the viewing window 14 represents a third medium that may be made of glass, plexiglass or the like. When building the model the following assumptions have been made:

1) Light beam 1: Light beam 1 in this case is a laser which is considered as a spot light beam 1. This emitted light beam 1 is modeled as a straight line, which represents the central longitudinal axis of the actual light beam 1. This light beam 1 is aligned with the x-axis of its local reference axis {L}.

2) Redirection means 8: The redirection means 8 are formed by a reflection surface to reflect the incident light beam 1, which can be rotated by a motorized drive. For example, it can be a MEMS mirror (from its English acronym Micro-electro-mechanical system) and in the figure they are modeled in the figure as a rectangular prism. These redirection means 8 can be rotated by the first and second rotation angles ( ax, ay) , respectively around two of their axes ( x, y). The origin of its local reference frame {M} is located at the center of rotation 16. The reflection surface of the redirection means 8 of the mirror is then represented by the plane

^wm , which is at a distance tM from the center of rotation, and whose normal is aligned with the local direction z'.

As seen in Figure 3, the underwater laser scanner model of this embodiment is drawn in 2D only for simplicity. In reality, the y directions of the different coordinate axes do not have to be parallel.

Table I: Model parameters.

3) Sight Glass 14: Sight glass 14 plane is also modeled as a rectangular prism. The mean XY plane n ^v is the symmetry plane passing through the origin of its local reference coordinate axis {V}. Parallel to it are the inner and outer refraction planes (nv0 and nv1, respectively) at a distance t ^v /2 from it. Both bend the light beam 1 according to the three respective refractive indices r]0, n ^v and ^{n 1} . The normal vectors of the 3 planes are parallel to the local z direction.

4) Final projection surface 100: The object to be scanned is represented by a plane that represents the final projection surface 100, w ^r . The plane defining the final projection surface 100 passes through the origin of its local reference coordinate frame {T} and its normal n ^r is aligned with the local z direction.

The different elements of the model are parameterized according to Table I. Once the model is built, according to the invention, the only parameters that can be varied to scan a target are the first and second angles (α _x , α _y ) of rotation of redirection means 8. Therefore, all other parameters are assumed to be constant and are defined as r = [& % ^m t ^M & t ^v n n ^v n1 <ír].

As a complementary note, it should be noted that the model presented for underwater scanning can be immediately applied to scanning in air without the need for a sight glass 14, adjusting the respective refractive indices as follows: n ⁰ = n ^v = n1.

Algorithm 1 Calculation of a point S in {W} based on the

model parameters

C. Application of the model

The first objective of the model is to express the position of the scanned point S with respect to the global reference frame, as a function of all the model parameters. It is important to note that the point S corresponds to the intersection between the final projection surface 100 and the light beam 1, and is contained in a target emission surface 0, which is preferably a plane. Under normal operating conditions, the final projection surface 100 is not known a priori. This fact does not constitute in any case a limitation of the process according to the invention. In such cases, it is enough to define a final surface of projection 100 as a hypothetical arbitrary projection plane and calculate the point S as the intersection between said final projection surface 100 and the light beam 1. Since the objective emission surface 0 contains both the point S and the direction vector of the beam of light 1 rv1, the point S resulting from the intersection of light beam 1 with any arbitrary final projection surface 100 will always be contained in the target emission surface 0.

Typically, such a hypothetical projection plane is defined as parallel to the sight plane. It is also common to choose a distance of 1000 mm from the sight glass. Note that such decisions are arbitrary and therefore not essential to the invention.

Formally, {W}S = f (E[α _x α _y ]). Since all parameters in rs e are assumed constant, for a given scanner configuration, the final illuminated point S only depends on a pair of first and second angles ( ax, ay) of rotation of the redirection means 8:

The implementation of the function f is shown conceptually in Algorithm 1. From now on, all variables are assumed to be referred to the global coordinate axis {W}, unless explicitly stated otherwise. Please note that this implementation is conceptual. For example, r ^L ^ £ ^l @ {LV ^l in line 3 of the algorithm, it means that the laser light beam 1 r ^L in the world coordinate frame is obtained from the laser position % ^l and its equation relative to the frame local ^{L} r ^L . In reality, this operation is carried out as explained in section A-4).

The rotation matrix R (α _x , α _y ) in line 6 of the algorithm is constructed as a multiplication of two matrices: one expressing the rotation around the y axis of the redirection means 8 and another around x. The first matrix R ^y (α _y ) is the typical 3x3 rotation matrix of the first angle α _and rotation around the y axis. However, the construction of the second matrix is not as straightforward, because the rotation occurs around the unrotated x-axis, rather than x' (see Figure 3). This rotation can be expressed by a quaternion (see previous section A-5). The values Q = α _x y u = [cos α _y 0 sinα _y ]r can be introduced into equation 10. The value of u is the projection of the original local x-axis of the MEMS about the rotated reference frame {x', y', z'} (see figure 3). The resulting quaternion can then be converted to a rotation matrix Rx ( ax, α _y ) with equation 11 (note that its dependence on ay is introduced by u). The final rotation matrix is obtained by multiplying both matrices:

D. Application of the inverse model

The proposed model is used in the invention to solve the inverse problem: given a predetermined scanning point S, which pairs of first and second angles [ax ay] should the redirection means 8 rotate? This is a very relevant problem because solving it allows the laser light beam to be projected in any arbitrary direction within its field of view, also called in the FoV technique, by its English acronym Field of View. This is directly applicable to 3D scanning: when a target is scanned, the laser light beam must be directed to project a given pattern onto the scene. This pattern is a set of known setpoints that the laser needs to illuminate in a particular order. Using redirection means 8 such as, for example, a biα _x ial MEMS mirror and solving the aforementioned inverse problem, in principle, any arbitrary pattern can be projected.

As has been expressed in the previous section, under normal operating conditions, the final projection surface 100 is not known a priori. However, this fact does not constitute in any case a limitation of the system according to the invention. In such cases, it is enough to define a hypothetical arbitrary projection plane (see for example Figure 11) and calculate the curve defined by the intersection between said plane and the target emission surface 0:

Then, any point S that is contained in said curve and that is within the field of view FoV of the system is taken:

Solving the inverse problem means inverting the function f in equation (12). However, doing it analytically is a very complex task because the variables of the pair of first and second angles [ α _x , α _y ] of rotation appear several times with different exponents and within different trigonometric functions. Therefore, preferably a numerical approach is based on the invention.

1) A single point: The pair of first and second angles [α* _x , α* _y ] of rotation that achieves the projection of point S on the objective, that is, on the final projection surface 100, must comply with the equation:

These values can be computed iteratively using the Ceres nonlinear least squares solver, such as the one found on the site http://ceres-solver.org/. To do this, the residual error to minimize is the following:

As with any iterative solver, an initial guess is required. In this problem, starting with α _x = α _y = 0° is usually good enough for the solver to converge to the solution.

2) Approximate function: Actual 3D scan patterns can be composed of hundreds or thousands of fit points. A direct way to calculate the pairs of first and second angles (α _x , α _y ) of rotation required would be to calculate each pair of first and second angles (α _x , α _y ) of rotation corresponding to each adjustment point, as has been seen before. This approach, however, would not be efficient. In principle, find a more approach efficient could allow the projection pattern to be changed in real time. This would allow the sensor responsible for capturing the projected light pattern to increase its resolution in interesting areas of the FoV as it scanned or to decrease its resolution to speed up the 3D reconstruction.

An arbitrary pattern Q consisting of n points can be expressed as:

Where:

Consequently, to project the pattern, the set of pairs of first and second angles (α _x , α _y ) required of rotation can be calculated as:

As before, finding the analytical expression of the inverse function f-1 is complex. Instead, it would be very beneficial to find a simpler and more approximate function g , which would produce approximate values for the pair of first and second angles [áx áy] corresponding to an arbitrary projection point S on the final projection surface 100:

These values would then be used to project an approximate fit point S onto the final projection surface, which would be close enough to the original S :

This would be done for all points in the pattern:

More specifically, the function g is chosen to be a 5th degree polynomial in Sx and Sy:

Ox and Oy are the vectors of the polynomial coefficient that give the corresponding approximate angles áx and áy, respectively. The z component of S is not used because it is a redundant parameter that is determined by the position of the target plane nT on the final projection surface 100.

The Ox and Oy coefficient vectors are found numerically using the Ceres solver, available online at http://ceres-solver.org. First, an arbitrary pattern Q containing n fit points is defined. Then, the residual that is passed to the solver is:

where and á are calculated using equations (22) and (23). The resulting joint formal expression for the optimized coefficient vectors t0-*- ay\ is then:

To evaluate the performance of the proposed approximate function, a pattern consisting of 50x50 equidistant adjustment points spread over the entire field of view or FoV is used. The values of all the different sensor parameters are collected in Table II. Note that in this embodiment the final projection surface 100 is located at a distance of 1 m from the redirection means 8, i.e. the MEMS mirror.

Table II, nominal values for the model parameters.

Units are expressed in millimeters for lengths and in degrees for angles.

The calculation of each pair of first and second angles (α _x , α _y ) of rotation corresponding to each of the adjustment points requires around 7 s for a pattern of this type. If a pattern change was required, new pairs of angles would have to be calculated again, unless some of the adjustment points could be reused or interpolated. Using the approximate approach, the time needed to compute all pairs of first and second angles (α _x , α _y ) of rotation is greatly reduced to 7 ms for the same pattern. In terms of accuracy, the maximum and average point-to-point distances between Desired and approximate patterns are 0.013 mm and 0.002 mm, respectively. The resulting pairs of angles calculated with the approximate function are also very similar to those obtained, point by point: their maximum and average differences are 0.12° and 0.07°, respectively. These results confirm that the 5th degree polynomial is a suitable approximation function for f 1, since it allows reducing the calculation time while maintaining a very high precision. Calculating the vectors of the Ox and Oy coefficients takes about 1 minute, but it only needs to be done once because they would only vary if some of the sensor parameters changed.

The 5th degree of the polynomial g has been chosen heuristically. Additional research could be conducted to detect potentially more appropriate functions. However, since the evaluation times of the different polynomial degrees are very similar, their use would probably not noticeably increase the performance of the sensor.

E. Study of the influence of parameters

This section aims to examine the influence that each of the model parameters has on the overall performance. In order to study the individual effect of each parameter, they will be modified one by one while keeping the rest constant. The nominal values of all the parameters are shown in Table II, shown above. The poses <f of all elements are referred to the world coordinate frame {W}. The angles of rotation around the local y axes of the redirection means 8, the viewport and the objective are represented by 0 ^m , 0y and 0 ^t , respectively. 5 is the displacement of the mirror reference frame {M} in the world y and z directions. lv the position of the reference frame of the sight in the direction of the world z.

Please note that in this configuration:

where is the angle defined by the laser light beam 1 and the normal of the plane of the redirection means 8 when ax = ay = 0 (see figure 3).

In this embodiment, the various refractive indices n are chosen from air, plexiglass and water, respectively. The maximum mechanical turning angle for both axles of The redirection means 8, that is, the MEMS mirror, is 5°, which makes the horizontal and vertical mechanical field of view, also called Field of View (FoV), equal to 10°. This is a typical value for MEMS mirrors.

The section is structured as follows: first, section E.1 explains the magnitude of the error that results from poor calibration of each parameter individually. Other sources of error in the final projection are described below in section E.4. Finally, the effect of the parameters on the FoV of the scanner is studied in section E.4.

E.1 Effect of calibration error of individual parameters.

The model presented aims to evaluate and reduce the projection errors of light beam 1 of an underwater scanner.

The main source of projection errors is poor calibration of parameters. A parameter is miscalibrated when its actual value differs from its nominal value. The projection error introduced by this poor calibration is defined as the distance between the nominal (expected) position of a point S and its deviated (actual) position Sm.

Projection errors due to miscalibrated parameters are shown in Figure 4. The metric used on all vertical axes is the average distance between the nominal and miscalibrated projection for each projected point (for n waypoints in total, with n = 100):

Several conclusions can be drawn from these figures. First, it can be seen that 0 ^m (directly related to p, see equation (26)) is a very critical parameter: a slight deviation from its nominal value of only 0.2° causes the error to increase rapidly (see figure 4a). Similarly, a deviation in the value of Q ^v of only half a degree causes an average error much greater than 1 mm (see Figure 4d). Regarding the index of refraction of water, it should be noted that, in general, it depends on different factors, such as the wavelength of light, salinity and temperature. For a green laser source of wavelength Á = 532 nm, the refractive index of seawater is between 1330 and 1345 for a wide range of salinity values. A discrepancy of this order would imply an average error of around 1 mm (see Figure 4g).

Furthermore, the possible variations of 5 and tM considered are up to 1.5 mm, since that is on the order of the diameter of a typical MEMS mirror. These values are sufficient to cause noticeable deviations, especially if the required precision is submillimeter (see figures 4b and 4c).

On the other hand, the influence of a slightly miscalibrated sight glass thickness is not too high (1 cm deviation means an average error of about 0.3 mm, see Figure 4f). Similarly, an error in sight distance of up to 1 cm would not increase the average error by more than 0.4 mm (see Figure 4e). In these last two cases, there are standard measuring instruments that can easily provide length measurements with an accuracy of better than 1 cm.

E.2 Other sources of error

The presented model allows the investigation of different sources of errors, apart from poor calibration of the parameters. This section studies the magnitude of projection errors with perfectly calibrated parameters. The sources of error considered depend on the number of waypoints used per line (section E.2-1 below) and the actual distance to the final projection surface 100 (section E.2-2 below). The goal of this section is to help get a deeper insight into what nominal parameter values are optimal.

In the following results, both the sight glass and the final projection surface 100 remain perpendicular to the outgoing reflected laser light beam 1 when α _x = α _y = 0° (see Figure 5). Therefore:

) The number of waypoints per line: The model presented can be used to compensate for the distortions introduced by redirection means 8, such as biα _x ial mirror, and by the double refraction of this embodiment, which depend mainly on fi (see figure 8). In this way, you can calculate the angles necessary to project a given number of waypoints, also called waypoints, to your desired positions. However, the movement of the redirection means 8 between the waypoints follows the distorted trajectories shown in Figure 7, introducing a distortion with respect to the corresponding straight line.

The deviation A of the actual light pattern from the desired one depends largely on the number of waypoints used per line, as shown in Figure 7. The curved lines show the actual paths of light beam 1 once projected onto the surface end of projection 100 between waypoints. Intuitively, the deviation A should decrease when more waypoints are used per line: the smaller the distance between two consecutive waypoints, the smaller the deviation A. The actual evolution is shown in Figure 8.

Some conclusions can be drawn from these plots. In general, the greater the number of waypoints per line, the smaller the deviation. However, this introduces a trade-off, since increasing the number of waypoints per line can mean, in principle, greater requirements for computing memory capacity and scanning time.

The deviation can also be minimized by reducing fi (see Figure 8a). This is an expected result, as a smaller fi naturally introduces less drift, as seen in Figure 6. However, this reduction is often limited in practice by the laser module (or an alternative combination of mirrors), which would obstruct the reflected light for fi ^0°. Another reason to keep fi as small as possible is to increase the effective reflective surface of the mirror (actually a 1 laser light beam has a certain beam diameter and is not a 1D line).

Similarly, increasing θ _v in the negative direction has a positive influence on the pattern deviation (see Fig. 8c). However, making θ _v ≠ 0° has other implications (see next section). The rest of the parameters (5, l ^v and tv) have a much smaller influence (see Figures 8b, 8d and 8e).

2) Different distance from the target: The set of angles needed to project straight lines depends on the distance to the final projection surface 100, so a certain value must be chosen as nominal. However, during the actual scan, the target may be at a different distance, which is not known a priori. This fact means that the projection points corresponding to the same line are not exactly on top of each other, since the final projection surface does not have to be a plane. The reason for this is that the double refraction produced by changing the medium twice means that the points R ⁱ in figure 3 do not form a perfectly straight line. Therefore, the protruding light planes are actually curved surfaces with very slight curvatures.

In order to evaluate the actual magnitude of the error, a straight line was fitted using least squares to each line of route points Si. The metric used is the maximum distance from the pattern points to their corresponding fitted line. The results are shown in figure 9.

It can be seen that the most influential parameters are the distance and orientation of the peephole. With a correct choice of a small observation distance l ^v and with θ _v = 0°, the maximum distance to the corresponding fitted line is much less than 0.05 mm (see Figures 9c and 9d), even if the scanned target It is located at a distance of 4 m (while the angles have been calibrated for 1 m). The rest of the parameters ( fi, 5 and t ^v ) have a much smaller influence on the magnitude of this error (see Figures 9a, 9b and 9e).

3) Field of view (FoV)

A relevant characteristic of a scanner's performance is its field of view, more commonly called FoV , which should be as large as possible. In the presented model, the area covered by the FoV depends mainly from 3, as shown in Figure 10. According to this graph, reducing 3 also contributes to increasing the FoV of the scanner.

Next, on the basis of Figure 11, it shows a scanning assembly 102 through which the procedure according to the invention applied to its most general form, which is in which a single change of medium occurs, is explained in detail. It should be noted that Figure 4 is a schematic representation intended to facilitate understanding of the procedure according to the invention.

The invention provides for a method of projecting a point light beam 1 onto the final projection surface 100, the light beam 1 having to be a point light beam such as, for example, a laser light. In order to simply explain the invention, the final projection surface 100 is represented as a plane. In practice, the final projection surface 100 may have any shape and be completely irregular.

In this case, the light beam 1 must pass through a first medium 2 with a first refractive index and a second medium 4 with a second refractive index. In this embodiment the first medium is air, while the second medium may be water. Therefore, the first and second refractive indices are different from each other, such that under normal conditions this difference causes refraction in light beam 1 and therefore the deformation of light beam 1.

In the case of projecting a single point, the method comprises the steps of providing a light emitter 6 to emit the point light beam 1. As already mentioned, the light beam 1 is preferably a laser light beam 1. In addition, the invention also provides light redirection means 8 to redirect the spot light beam 1 onto the final projection surface 100. Preferably, to _maximize the projection speed, the redirection means 8 is a mirror. MEMS. However, within the scope of the invention, other solutions are contemplated such as conventional motorized mirrors, galvanometric mirrors or others.

The redirection means 8 are arranged at a known and constant distance D with respect to the emitter 6. This does not mean that the redirection means 8 are static or immobile, but rather that the relative linear distance between the exit point of the light beam of the emitter 6 and the first and second x, y axes of the redirection means 8 is constant. Thus, the redirection means 8 are mounted so that they can rotate around these first and a second x, y axes of rotation shown in Figure 4.

Thus, the method according to the invention comprises the additional steps of, knowing the refractive indices of the first and second media 2, 4, that is, air and water, previously calculating a pair of angles formed by a first angle α _x of rotation to rotate the redirection means 8 around the first x-axis of rotation and a second angle α _y of rotation to rotate the redirection means 8 around the second y-axis of rotation.

As already mentioned in the previous paragraphs, this calculation stage according to the algorithm explained in the previous paragraphs includes the first and second refractive indices to obtain the pair of first and second angles α _x , α _y of rotation. In this way, the first _and second angles _α .

Once the pair of first and second angles α _x , α _and rotation have been calculated, the redirection means 8 are rotated around the first and second axes of rotation x, and according to the pair _of first and second angles _α previously calculated turns.

In this way, once the redirection means 8 have been rotated around the first and second x and y axes of rotation to compensate for the refraction that the light will suffer when changing from the first to the second means 2, 4, the beam is emitted. of point light 1 on said redirection means 8 for the pair of first and second angles α _x , α _y .

Thanks to this, the point light beam 1, once redirected by the redirection means 8, when passing through the second means 4, is contained in a target emission surface 0. This target emission surface 0 corresponds to the surface in which the light beam 1 would be contained when it is projected in the desired direction to compensate for the refraction. That is, preferably the plane corresponding to the plane that compensates for the refraction of the light beam 1 when changing medium. Finally, the light beam 1 contained in the objective emission surface 0 is projected onto the final projection surface 100, that is, at the same time intersecting the light beam 1 previously rotated by the redirection means 8 with the final projection surface 100, the corresponding point S explained in the previous paragraphs, in particular in section D, is obtained.

In Figure 11, to facilitate the understanding of the invention, the point corresponding to the intersection of the light beam 1 is also indicated with the reference S', in case the redirection means 8 had not been rotated according to the pair of first and second angles (α _x , α _y ) of rotation that compensate for the refraction of light beam 1.

In the preferred form of the invention, the objective of the invention is to _maximize the projection speed. In the calculation stage, a plurality of pairs of first angles α _x of rotation are previously calculated to rotate the redirection means 8 around the first axis x of rotation. and second angles α _y of rotation for rotating the redirection means 8 around the second axis y of rotation.

As previously mentioned, the calculation step includes the first and second refractive indices so that each pair of first and second angles α _x , α _y of rotation of the plurality of pairs of first and second angles α _x , α _y of rotation compensates the refraction of each light beam 1 redirected by said redirection means 8 when passing through said second means 4, and once the calculation step is completed, for each pair of first and second angles α _x , α _and rotation _, the steps of rotating the redirection means 8 around the first and second axes of rotation x, and according to the pairs of first and second angles _α a point light beam 1 on the redirection means 8 for each pair of first and second angles α _x , α _y . Finally, the turning and casting steps now described are repeated until the last pair of first and second angles α _x , α _y of the plurality of pairs of first and second angles α _x , α _y . By doing this, each emitted point light beam 1, when passing through said second medium 4, is contained in the objective emission surface 0, that is, the effect of refraction is compensated for each and every one of the light beams. 1 issued for each pair of first and second angles α _x , α _y previously calculated, of the plurality of pairs of corresponding first and second angles α _x , α _y .

In an alternative embodiment of the process according to the invention the steps of: [c] previously calculate a pair formed by:

[i] a first angle α _x of rotation for rotating the redirection means 8 around the first axis x of rotation y

[ii] a second angle α _y of rotation to rotate said redirection means 8 around the second axis y of rotation,

[iii] including in the calculation stage the first and second refraction indices so that the pair of first and second angles α _x , α _y of rotation compensate the refraction of the light beam 1 redirected by the redirection means 8 when passing through the second half 4,

[d] rotate the redirection means 8 around the first and second axes of rotation x, y according to the pair of first and second angles α _x , α _y of rotation previously calculated, and

[e] emit a point light beam 1 on the redirection means 8 for the pair of first and second angles α _x , α _y , so that said point light beam 1, when passing through said second means 4, is contained on a target emission surface 0,

They are carried out jointly and sequentially for a plurality of pairs of first and second angles α _x , α _and rotation, so that each point light beam 1, when passing through said second means 4, is contained in said emission surface goal 0.

Finally, Figure 12 shows a schematic scan assembly, intended for an underwater vehicle. In this case, the assembly differs from the embodiment of Figure 11 in that three medium changes occur. Thus, the first medium 2 is air, the second medium 4 is water, while the third medium is the peephole formed by a solid and transparent medium, such as glass or plexiglass. For the rest of the elements, reference is made to the previous paragraphs referring to figure 11.

Also on the basis of this embodiment, the laser scanning method according to the invention is described below. The procedure includes the steps of the procedure for projecting a point light beam 1 explained in the previous paragraphs. But in addition, it comprises the steps of providing a light receiver 10, arranging the first redirection means 8 and the light receiver 10 separated by a known predetermined distance that defines a baseline 18, capturing a scanning area 12 of the surface final projection 100 that must be characterized through of the light receiver 10, the area containing the light beam 1 projected on the final projection surface 100, and finally, synchronizing the emission of the light beam and the capture by the light receiver 10 through control means 14 functionally associated with the light emitter 6 and receiver 10.

Claims (6)

1.- Procedure for projecting a punctual light beam (1) onto a point (S) of a final projection surface (100), said punctual light beam (1) having to pass through at least one first medium (2) with a first refractive index and a second means (4) with a second refractive index and said first and second refractive indices being different from each other, said procedure comprising the steps of: [a] provide a light emitter (6) to emit said spot light beam (1), and [b] provide light redirection means (8) to redirect said spot light beam (1) onto said end surface of projection (100), said redirection means (8) being arranged at a known distance with respect to said emitter (6) and mounted so that they can rotate around a first and a second axes (x, y) of rotation, characterized in that said procedure also includes the steps of: [c] previously calculate a pair formed by: [i] a first angle (α _x ) of rotation to rotate said redirection means (8) around said first axis (x) of rotation and [ii] a second angle (α _y ) of rotation to rotate said redirection means (8) around said second axis (y) of rotation, [iii] said first and second refraction indices being included in said calculation step so that said pair of first and second angles (α _x , α _y ) of rotation compensate for the refraction of said light beam (1) redirected by said means of redirection (8) when passing through said second means (4), [d] rotate said redirection means (8) around said first and second axes of rotation (x, y) according to said pair of first and second angles (α _x , α _y ) of rotation previously calculated, and [e] emit a punctual light beam (1) on said redirection means (8) for said pair of first and second angles (α _x , α _y ), so that said punctual light beam (1), once redirected by said redirection means (8), when passing through said second means (4), is projected onto a point (S) of said final projection surface (100). 2. - Procedure according to claim 1, characterized in that [a] in said calculation stage, a plurality of pairs of: [i] first angles (α _x ) of rotation to rotate said redirection means (8) around said first axis (x) of rotation and [ii] second rotation angles (α _and ) to rotate said redirection means (8) around said second axis (y) of rotation, [iii] said first and second refraction indices being included in said calculation step so that each pair of first and second angles (α _x , α _y ) of rotation of said plurality of pairs of first and second angles (α _x , α _y ) of rotation compensates the refraction of each light beam (1) redirected by said redirection means (8) when passing through said second means (4), and Once said calculation stage is completed, for each pair of first and second angles (α _x , α _y ) of rotation, said stages of: [b] rotate said redirection means (8) around said first and second axes of rotation (x, y) according to said pairs of first and second angles (α _x , α _y ) of rotation previously calculated, and [c] emit a punctual light beam (1) on said redirection means (8) for each pair of first and second angles (α _x , α _y ), and [d] repeat said steps [b] and [c] until the last pair of first and second angles (α _x , α _y ) of said plurality of pairs of first and second angles (α _x , α _y ), so that each point light beam (1), passing through said second means (4), and is projected onto said corresponding point (S) of said final projection surface (100). 3. - Procedure according to claim 1, characterized in that said steps of: [c] previously calculate a pair formed by: [i] a first angle (α _x ) of rotation to rotate said redirection means (8) around said first axis (x) of rotation and [ii] a second angle (α _y ) of rotation to rotate said redirection means (8) around said second axis (y) of rotation, [iii] said first and second refraction indices being included in said calculation step so that said pair of first and second angles (α _x , α _y ) of rotation compensate for the refraction of said light beam (1) redirected by said means of redirection (8) when passing through said second means (4), [d] rotate said redirection means (8) around said first and second axes of rotation (x, y) according to said pair of first and second angles (α _x , α _y ) of rotation previously calculated, and [e] emit a punctual light beam (1) on said redirection means (8) for said pair of first and second angles (α _x , α _y ), so that said punctual light beam (1), when passing by said second means (4), is projected onto said point (S) of said final projection surface (100), are carried out jointly and sequentially for a plurality of pairs of first and second angles (α _x , α _y ) of rotation, so that each punctual light beam (1), when passing through said second means (4), is projected onto said corresponding point (S) of said final projection surface (100). 4. - Method according to any of claims 1 to 3, characterized in that it comprises at least a third medium with a third refractive index and said first, second and third refractive indices being different from each other. 5. - Method according to claim 4, characterized in that said first medium (2) is air, said second medium (4) is water and said third medium is a solid and transparent medium. 6. - Laser scanning procedure to obtain a characterization of the shape of a final projection surface (100), characterized in that it comprises the steps of the projection procedure of a point light beam (1) according to any of claims 1 to 5, and also includes the stages of: [a] provide a light receiver (10), [b] arrange said first redirection means (8) and said light receiver (10) separated at a known predetermined distance that defines a baseline (18), [c] capture a scanning area (12) of said final projection surface (100) that must be characterized through said light receiver (10), said area containing said light beam (1) projected on said final surface projection (100), and [d] synchronize the emission of the light beam and the capture by said light receiver (10) through control means (14) functionally associated with said emitter (6) and said light receiver (10).