Corneal lenticule incision using a femtosecond laser with a smooth scanning trajectory connecting multiple sweeps

Abstract

An ophthalmic laser system and associated method for forming lenticule incisions in a corneal lens extraction procedure. The lenticule incisions are formed by multiple sweeps of a laser scan line along the meridian of longitude of the lenticule incision, with the end point of each sweep being connected to the start point of the next sweep by a smooth turning trajectory. The trajectory includes a first circular arc tangentially connected to the first sweep at its end point, a second circular arc tangentially connected to the next sweep at its start point, and a straight line segment tangentially connected to both arcs. The smooth trajectory is determined using given limits of the speed, acceleration, and jerk of the XY scanning motor without using high frequency filters to smooth the trajectory, thereby avoiding unknown changes to the original trajectory and achieving a highly accurate lenticule shape.

Description

[Technical field]

[0001] (CROSS-REFERENCE TO RELATED APPLICATIONS) This application claims the benefit of U.S. Patent Application No. 17 / 658,229, filed April 6, 2022, which is incorporated by reference herein in its entirety.

[0002] FIELD OF THEINVENTION FIELD OF THE DISCLOSURE

[0002] Embodiments of the present invention relate generally to laser-assisted ophthalmic procedures, and more particularly to systems and methods for making lenticule incisions in the cornea. [Background technology]

[0003] Vision defects such as myopia (nearsightedness), hyperopia, and astigmatism can be corrected using glasses or contact lenses. Alternatively, the cornea of ​​the eye can be surgically reshaped to provide the necessary optical correction. Eye surgery is becoming more common with some patients pursuing it as an elective procedure to avoid using contact lenses or glasses to correct refractive problems, and others pursuing it to correct deleterious conditions such as cataracts. And with recent developments in laser technology, laser surgery is becoming the technique of choice for ophthalmic procedures.

[0004] Different laser eye surgery systems use different types of laser beams for various procedures and indications. These include, for example, ultraviolet lasers, infrared lasers, and near-infrared, ultrashort pulse lasers. Ultrashort pulse lasers emit radiation with pulse durations as short as 10 femtoseconds and as long as 3 nanoseconds, and wavelengths between 300 nm and 3000 nm.

[0005] Conventional surgical approaches to reshape the cornea include laser assisted in situ keratomileusis (hereinafter "LASIK"), photorefractive keratectomy (hereinafter "PRK") and lenticule extraction.

[0006] In a LASIK procedure, an ultrashort-pulsed laser is used to cut a corneal flap, exposing the corneal stroma for photoablation by an ultraviolet beam from an excimer laser. Photoablation of the corneal stroma reshapes the cornea and corrects refractive conditions such as myopia, hyperopia, and astigmatism. In a PRK procedure, where no flap is created, the epithelial layer is removed first, and then some stromal material is removed by the excimer laser. The epithelial layer grows back within a few days after the procedure.

[0007] In a corneal lenticule extraction procedure, instead of ablating corneal tissue with an excimer laser after the creation of a corneal flap, this technique involves tissue removal with two or more femtosecond laser incisions that intersect to form a lenticule for extraction. Extraction of the lenticule changes the shape of the cornea and its refractive power to achieve vision correction. Extraction of the lenticule can be performed either with or without the creation of a corneal flap. In a flapless procedure, a refractive lenticule is formed in the intact portion of the anterior cornea and removed through a small incision. Methods for corneal lenticule extraction using a fast scan-slow sweep approach in a surgical ophthalmic laser system are described in U.S. Patent Application Publication No. 20160089270, entitled "Systems And Methods For Lenticular Laser Incision," published on March 31, 2016, and U.S. Patent Application Publication No. 20200046558, entitled "High Speed ​​Corneal Lenticular Incision Using A Femtosecond Laser," published on February 13, 2020. Summary of the Invention [Means for solving the problem]

[0008] An embodiment of the present invention provides a method of lenticule dissection using a scanning method in which sweeps along meridians of longitude are connected to each other by smooth trajectories, significantly reducing acceleration and jerks in the movement of the XY scanner.

[0009] In one aspect, an embodiment of the invention includes a laser source configured to generate a pulsed laser beam comprising a plurality of laser pulses; a laser delivery system configured to deliver the pulsed laser beam to a target tissue in an eye of a subject; a radio frequency scanner configured to scan the pulsed laser beam back and forth at a predefined frequency; an XY scanner configured to deflect the pulsed laser beam, the XY scanner being separate from the radio frequency scanner; a Z scanner configured to change a focal depth of the pulsed laser beam; and a controller configured to control the laser source, the radio frequency scanner, the XY scanner, and the Z scanner to sequentially form a plurality of sweeps that collectively form at least one lenticule incision in a lens of the subject's eye, the lens having a curved surface defining an apex and a central axis passing through the apex, each sweep being a scan line having a predefined length and being a straight line tangential to a parallel of latitude of the lens, the parallel of latitude being perpendicular to the central axis and having a defined distance to the apex. and controlling the XY scanner and the Z scanner to move a center of the scan line along a meridian of longitude of the lens, the meridian of longitude being a curve that passes through a vertex and has a predefined angular position about a central axis, the plurality of sweeps being formed successively along respective meridians of longitude that are different from one another, and the controller controls a first sweep of the plurality of sweeps. The ophthalmic surgical laser system is further configured to control the XY scanner to move a center of the scan line along a smooth turning trajectory connecting an end point of one sweep to a starting point of a second sweep of the plurality of sweeps, the turning trajectory including a first arc, a straight line segment, and a second arc, the first arc tangentially connected to the first sweep at an end point of the first sweep, the second arc tangentially connected to the second sweep at a starting point of the second sweep, and the straight line segment tangentially connected to both the first arc and the second arc.

[0010] In a preferred embodiment, the controller is further configured to control the laser source and / or the laser delivery system to blank the pulsed laser beam when the center of the scan line is moved along the orbit from the end point of the first sweep to the start point of the second sweep.

[0011] In another aspect, an embodiment of the present invention provides a method for forming a lenticule incision using an ophthalmic surgical laser system, comprising: generating a pulsed laser beam comprising a plurality of laser pulses by a laser source; delivering the pulsed laser beam to a target tissue in a subject's eye; scanning the pulsed laser beam back and forth at a predefined frequency by a radio frequency scanner; deflecting the pulsed laser beam by an XY scanner, the XY scanner being separate from the radio frequency scanner; varying a focal depth of the pulsed laser beam by a Z scanner; and controlling the laser source, the radio frequency scanner, the XY scanner, and the Z scanner by a controller to sequentially form a plurality of sweeps that collectively form at least one lenticule incision in a lens in the subject's eye, the lens having a curved surface defining an apex and a central axis passing through the apex, each sweep comprising controlling the radio frequency scanner to deflect the pulsed laser beam to form a scan line, the scan line having a predefined length and being a straight line tangent to a parallel of latitude of the lens, the parallel of latitude being perpendicular to the central axis. a plurality of sweeps are formed by: controlling the XY and Z scanners to move a center of the scan line along a meridian of longitude of the lens, the meridian of longitude being a curve that passes through the apex and has a defined angular position about the central axis; and controlling the laser source to periodically blank the pulsed laser beam when the scan line is located within a central region of the lens, the plurality of sweeps being formed sequentially along respective different meridians of longitude. and controlling, by a controller, the XY scanner to move a center of the scan line along a smooth circular trajectory connecting an end point of a first sweep of the multiple sweeps and a starting point of a second sweep of the multiple sweeps, the circular trajectory including a first circular arc, a straight line segment, and a second circular arc, the first circular arc being tangentially connected to the first sweep at an end point of the first sweep, the second circular arc being tangentially connected to the second sweep at a starting point of the second sweep, and the straight line segment being tangentially connected to both the first circular arc and the second circular arc.

[0012] In a preferred embodiment, the controller controls the laser source and / or laser delivery system to blank the pulsed laser beam when the center of the scan line is moved along the orbit from the end point of the first sweep to the start point of the second sweep.

[0013] It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory and are intended to provide further explanation of the invention as claimed. [Brief description of the drawings]

[0014] The novel features of the invention are set forth in detail in the appended claims. A better understanding of the features and advantages may be facilitated by reference to the following detailed description that sets forth illustrative embodiments utilizing the principles of the invention, and the accompanying drawings, in which like numerals refer to like parts throughout the different views. However, like parts do not necessarily have like reference numerals. Moreover, the drawings are not to scale, with emphasis instead being placed on illustrating the principles of the invention. All figures are intended to convey concepts, with relative size, shape, and other detailed attributes being illustrated generally, rather than being depicted exactly or precisely. [Figure 1] FIG. 1 is a block diagram of a surgical ophthalmic laser system that may be used to perform a lenticule incision method, according to one embodiment of the present invention. [Diagram 2] FIG. 2 is another diagram of a surgical ophthalmic laser system that may be used to perform a lenticule incision method, according to one embodiment of the present invention. [Diagram 3] FIG. 2 is a simplified diagram of a controller for a surgical ophthalmic laser system that may be used to perform a lenticule incision method in accordance with an embodiment of the present invention. [Figure 4] 1 illustrates an exemplary scan of a surgical ophthalmic laser system, in accordance with one embodiment of the present invention. [Diagram 5]1 illustrates an exemplary surface incision using a fast scan-slow sweep method of a surgical ophthalmic laser system in accordance with an embodiment of the present invention. [Figure 6] 1 illustrates the geometric relationship between a fast scan line and an intended spherical incision surface of a surgical ophthalmic laser system in accordance with one embodiment of the present invention. [Figure 7] 1 illustrates an exemplary lenticule incision using a surgical ophthalmic laser system, according to one embodiment of the present invention. [Figure 8] FIG. 13 is a schematic diagram illustrating an exemplary corner-free smooth turning trajectory for connecting two sweeps, in accordance with one embodiment of the present invention. [Figure 9] 1 is a flowchart illustrating a method for generating a smooth trajectory for connecting two sweeps, according to an embodiment of the present invention. [Figure 10] 11 is another flowchart illustrating a method for generating a smooth trajectory for connecting two sweeps according to an embodiment of the present invention. [Figure 11] 1 shows a comparison of simulated position, velocity, acceleration, and jerk of an XY stage during the formation of a lenticule incision using a straight turning trajectory according to the prior art versus a smooth turning trajectory according to an embodiment of the present invention. [Figure 12] 1 shows a comparison of simulated position, velocity, acceleration, and jerk of an XY stage during the formation of a lenticule incision using a straight turning trajectory according to the prior art versus a smooth turning trajectory according to an embodiment of the present invention. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0015] SUMMARY OF THE DISCLOSURE Embodiments of the present invention are directed generally to systems and methods for laser-assisted ophthalmic procedures, and more specifically, to systems and methods for corneal lenticule incisions.

[0016] Referring to the drawings, FIG. 1 shows a system 10 for making an incision in a tissue 12 of a patient's eye. The system 10 includes, but is not limited to, a laser 14 capable of generating a pulsed laser beam, an energy control module 16 for varying the pulse energy of the pulsed laser beam, a fast scan line movement control module 20 for generating a fast scan line of the pulsed laser beam (described in more detail below), a controller 22, and a slow scan line movement control module 28 for moving and delivering the laser scan line to the tissue 12. The controller 22, such as a processor running suitable control software, is operably coupled to the fast scan line movement control module 20, the slow scan line movement control module 28, and the energy control module 16 to direct the scan line of the pulsed laser beam along a scan pattern on or within the tissue 12. In this embodiment, the system 10 further includes a beam splitter 26 and an imaging device 24 coupled to the controller 22 for a feedback control mechanism (not shown) of the pulsed laser beam. However, other feedback methods may also be used. In one embodiment, the pulse patterns may be compiled in machine-readable data in a tangible storage medium in the form of a treatment table, which may be adjusted according to feedback input from the automated image analysis system to the controller 22 in response to feedback data provided from a monitoring system feedback system (not shown).

[0017] The laser 14 may include a femtosecond laser capable of providing a pulsed laser beam that may be used in optical procedures such as localized photoablation (e.g., laser-induced optical breakdown). The localized photoablation may be located at or below the surface of tissue or other materials to generate high precision material processing. For example, a micro-optical scanning system may be used to scan the pulsed laser beam to generate incisions in materials, form flaps of material, form pockets in materials, form removable structures of material, etc. The terms "scan" or "scanning" refer to the movement of the focal point of a pulsed laser beam along a desired path or in a desired pattern.

[0018] In other embodiments, laser 14 may comprise a laser source configured to deliver an ultraviolet laser beam including multiple ultraviolet laser pulses capable of photolyzing one or more intraocular targets within the eye.

[0019] While the laser system 10 can be used to photomodify a variety of materials (e.g., organic, inorganic, or combinations thereof), the laser system 10 is suitable in some embodiments for ophthalmic applications. In these cases, focusing optics direct the pulsed laser beam toward the eye (e.g., on or into the cornea) for plasma-mediated (e.g., non-UV) photoablation of superficial tissue, or into the stroma of the cornea for intrastromal photodissection of tissue. In these embodiments, the surgical laser system 10 may also include a lens that changes the shape of the cornea (e.g., flattening or curving) before scanning the pulsed laser beam toward the eye.

[0020] FIG. 2 shows another exemplary diagram of the laser system 10. FIG. 2 shows the components of the laser delivery system, including a movable XY scanner (or movable XY stage) 28 of a compact femtosecond laser system. In this embodiment, the system 10 uses a femtosecond oscillator, or fiber oscillator based, low energy laser. This allows the laser to be much smaller. The laser-tissue interaction is in low density plasma mode. An exemplary set of laser parameters for such a laser includes pulse energy in the 40-100 nJ range and pulse repetition rate (or "repetition rate") in the 2-40 MHz range. A high speed Z scanner 25 and a resonant scanner 21 direct the laser beam to a scan line rotator 23. When used in ophthalmic procedures, the system 10 also includes a patient interface design with a fixed conical nose 31 and a contact lens 32 that engages the patient's eye. A beam splitter can be placed inside the patient interface cone 31 to allow the entire eye to be imaged via visualization optics. In some embodiments, the system 10 may use an optical system with a numerical aperture (NA) of 0.6 that produces a 1.1 μm Full Width at Half Maximum (FWHM) focal spot size, and a resonant scanner 21 that produces a scan line of 0.2-1.2 mm, where the XY scanner scans the resonant scan line into a field of 1.0 mm. A prism 23 (e.g., a Dove or Pechan prism, etc.) rotates the resonant scan line to any direction on the XY plane. A fast Z scanner 25 sets the incision depth. The slow scan line movement control module employs a movable XY stage 28 carrying an objective lens 27 with Z scanning capability, referred to as the slow Z scanner because it is slower than the fast Z scanner 25. The movable XY stage 28 moves the objective lens to achieve scanning of the laser scan line in the X and Y directions. The objective lens varies the depth of the laser scan line in the tissue. The energy control and auto-Z module 16 may include appropriate components for controlling the laser pulse energy, including attenuators, etc. It may also include an auto-Z module that employs a confocal or non-confocal imaging system to provide a depth reference.The compact femtosecond laser system 10 may be a desktop system in which the patient sits upright during treatment. This eliminates the need for certain opto-mechanical arm mechanisms and significantly reduces the complexity, size, and weight of the laser system. Alternatively, the compact laser system may be designed as a conventional femtosecond laser system in which the patient is treated while lying down.

[0021] 3 illustrates a simplified block diagram of an exemplary controller 22 that may be used by the laser system 10 according to one embodiment of the present invention to control the laser system 10 and perform at least some of the operations described in detail below. The controller 22 typically includes at least one processor 52 that may communicate with a number of peripheral devices via a bus subsystem 54. These peripheral devices may include a storage subsystem 56, including a memory subsystem 58 and a file storage subsystem 60, a user interface input device 62, a user interface output device 64, and a network interface subsystem 66. The network interface subsystem 66 provides an interface to an external network 68 and / or other devices. The network interface subsystem 66 may include one or more interfaces known in the art, such as LAN, WLAN, Bluetooth, and other wired and wireless interfaces.

[0022] User interface input devices 62 may include a keyboard, a pointing device (such as a mouse, trackball, touch pad, or graphics terminal), a scanner, foot pedals, joysticks, a touch screen integrated into a display, audio input devices (such as voice recognition systems, microphones, and other types of input devices). In general, the term "input device" is intended to include a variety of conventional and proprietary devices and methods for inputting information into controller 22.

[0023] The user interface output devices 64 may include a display subsystem, a printer, a fax machine, or a non-visual display such as an audio output device. The display subsystem may be a flat panel device such as a liquid crystal display (LCD), a light emitting diode (LED) display, a touch screen display, or the like. The display subsystem may also provide non-visual displays such as an audio output device. In general, the term "output device" is intended to include a variety of conventional and proprietary devices and methods for outputting information from the controller 22 to a user.

[0024] The storage subsystem 56 may store the basic programming and data constructs that provide the functionality of various embodiments of the present invention. For example, databases and modules that implement the functionality of the methods of the present invention, as described herein, may be stored in the storage subsystem 56. These software modules are generally executed by the processor 52. In a deployed environment, software modules may be stored on and executed by processors of multiple computer systems. The storage subsystem 56 typically includes a memory subsystem 58 and a file storage subsystem 60.

[0025] The memory subsystem 58 typically includes multiple memories, including a main random access memory (RAM) 70 for storing instructions and data during program execution, and a read only memory (ROM) 72 in which non-changing instructions are stored. A file storage subsystem 60 provides persistent (non-volatile) storage for program and data files. The file storage subsystem 60 may include hard disk drives with associated removable media, compact disk (CD) drives, optical drives, DVDs, solid state memory, and / or other removable media. One or more drives may be located in remote locations, other connected computers at other locations, coupled to the controller 22. Modules implementing the functionality of the present invention may be stored by the file storage subsystem 60.

[0026] The bus subsystem 54 provides a mechanism by which the various components and subsystems of the controller 22 can communicate with one another as intended. The various subsystems and components of the controller 22 need not be in the same physical location, but may be located in various locations within a collocated network. Although the bus subsystem 54 is shown generally as a bus, alternative embodiments of the bus subsystem may use multiple buses.

[0027] Due to the ever-changing nature of computers and networks, the description of controller 22 depicted in Figure 3 is intended as an example only for purposes of illustrating one embodiment of the present invention. Many other configurations of controller 22 are possible having more or fewer components than those depicted in Figure 3.

[0028] As should be understood by one of ordinary skill in the art, additional components and subsystems may be included with the laser system 10. For example, spatial and / or temporal integrators may be included to control the energy distribution within the laser beam. Ablation effluent aspirators / filters, aspirators, and other ancillary components of surgical laser systems are known in the art and may be included within the system. Additionally, an imaging device or system may be used to direct the laser beam.

[0029] In a preferred embodiment, beam scanning can be achieved with a "fast scan-slow sweep" scanning scheme, also referred to herein as the fast scan line scheme, which consists of two scanning mechanisms: first, a high frequency fast scanner is used to scan the beam back and forth to generate a short fast scan line (e.g., resonant scanner 21 in FIG. 2), and second, the fast scan line is slowly swept by a much slower X, Y, and Z scanning mechanism (e.g., objective lens 27 with movable XY stage 28 and slow Z scan, and fast Z scanner 25). FIG. 4 illustrates a scanning example of the laser system 10 using an 8 kHz (e.g., 7 kHz to 9 kHz, more typically, 0.5 kHz to 20 kHz) resonant scanner 21 to generate a fast scan line 410 of about 1 mm (e.g., 0.9 mm to 1.1 mm, more typically, 0.2 mm to 1.2 mm) and a scan speed of about 25 m / s, and an X, Y, and Z scanning mechanism with a scan speed (sweep speed) smaller than about 0.1 m / s. The fast scan line 410 may be perpendicular to the light beam propagation direction, i.e., it is always parallel to the XY plane. The trajectory of the slow sweep 420 can be any three-dimensional curve traced by the X, Y, and Z scanning devices (e.g., the XY scanner 28 and the fast Z scanner 25). The advantage of the "fast scan-slow sweep" scanning scheme is that it uses only small field optics (e.g., a field diameter of 1.5 mm) that can achieve high focus quality at a relatively low cost. Large surgical fields (e.g., field of view diameter of 10 mm or more) are achieved using an XY scanner, which may be unlimited.

[0030] In the preferred embodiment shown in Fig. 5 and Fig. 7, the laser system 10 uses a "fast scan-slow sweep" scanning method under the preferred procedure to form a smooth lenticle cut. First, in a three-dimensional lenticle cut, the fast scan line is preferably placed tangent to the latitude line of 510 on the surface of the lenticle. The latitude line is a circle on the surface of the lens that is perpendicular to the Z axis (axis parallel to the depth direction of the eye) and has a defined distance to the apex (highest point in the Z direction). For example, in the laser system 10 of Fig. 2, this can be realized by adjusting the prism 23 to a corresponding orientation via software, e.g., via the controller 22. Second, the slow sweep trajectory preferably moves along the meridian of longitude 520 on the surface of the lenticle. The meridian is a curve that passes through the intersection of the surface with a plane passing through the Z axis, i.e., the apex, and has a defined angular direction with respect to the Z axis. For example, in the laser system of FIG. 2, this can be done by adjusting the XY scanner 28 and the fast Z scanner 25 via software, e.g., via the controller 22. The procedure starts with a scan line parallel to the XY plane and sweeps the apex of the lens according to the curvature with the largest diameter (see also FIG. 7). Multiple sweeps are performed at successive angular orientations relative to the Z axis to form the entire lenticule, for example, as realized by rotating the prism 23 between successive sweeps. In this preferred procedure, there are no vertical "steps" in the incision and vertical side cuts are eliminated. As will be analyzed below in the present invention, the deviation between the laser focus position and the intended spherical incision is also minimized.

[0031] 6 illustrates the geometric relationship between a fast scan line 610 and an intended spherical cut surface 620 of, for example, a lens, in particular the distance deviation (δ) between an end point B of the scan line 610 and a point A on the intended cut surface 620. The maximum deviation δ is the distance between points A and B and is given by (Equation (1)):

[0032]

number

[0033] Although the maximum deviation analysis above is for spherical surfaces, the scanning method can also be used to create smooth cuts having non-spherical shapes, such as ellipsoidal shapes, in which case the parallels of latitude and / or meridians of longitude may not be circular.

[0034] In the exemplary case of myopia correction, the radius of curvature of the surface incision may be determined by the amount of correction ΔD using the following formula (Equation (2)):

[0035]

number

[0036]

number

[0037] Using such a "fast scan-slow sweep" scanning scheme, each sweep of the fast scan line forms a curved band, which is equivalent to bending a flat rectangle so that its long side forms an arch shape (the shape of a meridian of longitude) while its short side remains straight. Figure 7 shows a top view 750 of a lenticule incision 700 and a top view 780 of one exemplary sweep. CUT denotes the incision diameter and w denotes the width of the sweep.

[0038] 7 shows three exemplary sweeps (1A-1B), (2A-2B), and (3A-3B), each passing through (i.e., over) the lenticule incision apex 755. To form these sweeps, the trajectory of the center point of the scan line moves along the meridian of the incision 700 from a starting point 1A on the periphery to an opposite end point 1B on the periphery, then moves (in a counterclockwise direction) from point 1B to a nearby starting point 2A on the periphery, which move along the meridian of the incision on the periphery to an opposite end point 2B, then moves (in a counterclockwise direction) from point 2B to a nearby starting point 3A on the periphery, which move along the meridian of the incision on the periphery to an opposite end point 3B, and so on.

[0039] According to an embodiment of the present invention, when the center point of the scan line is moved from the end point of one sweep (e.g., 1B) to the start point of the next sweep (e.g., 2A), it is moved along a smooth curve without corners, rather than along a straight line connecting the two points. As mentioned above, the center of the scan line is moved by the movable XY stage 28 and high-speed Z scanner 25 of the ophthalmic laser system. Moving the center point in a straight line from each end point to the next start point creates many sharp turning points that introduce undesirable high acceleration and jerk (rate of change of acceleration) to the XY stage motion. In the mechanical system of the XY stage, large changes in velocity and acceleration require large changes in the XY actuator torque, which can cause very jerky movements and violent vibrations in the stage. This can result in high trajectory errors and undesirable system vibrations. In an embodiment of the present invention, by moving from the end point to the next start point in a smooth trajectory without corners, the irregularity and magnitude of acceleration and jerk are significantly reduced, thus improving the corneal lenticule incision quality. This is accomplished without unnecessarily slowing movement along the trajectory, so that the overall time required for lenticule incision is not significantly increased.

[0040] FIG. 8 illustrates a schematic diagram of an exemplary corner-free smooth turning trajectory (i.e., the movement of the center point of the scan line) according to an embodiment of the present invention. In FIG. 8, the first sweep proceeds along a trajectory from point S through vertex O to point A, and the next sweep proceeds along a trajectory from point E through vertex O to point F. The end point A of the first sweep is smoothly connected to the start point E of the next sweep by a turning trajectory ABDE, where AB is a circular arc, BD is a straight line, and DE is another circular arc. The first circular arc AB is tangent to both lines OA and BD, and the second circular arc DE AB is tangent to both lines BD and EO. The entire curve including the two sweeps and the turning trajectory ABDE is differentiable.

[0041] In Figure 8, point M is the intersection of the extension of line OA and line DB, and point N is the intersection of line OE and line DB. These points are used in the calculations described below, but note that line segments AM, MB, DN, and NE are not part of the turning trajectory. The XY coordinate system shown in Figure 8 is the machine coordinate system defined by the laser system.

[0042] The conditions and steps for calculating the turning trajectory will be described later.

[0043] The coordinates of points O, M, and N (X O ,Y O ), (X M ,Y M ) and (X N ,Y N ) are given as inputs for the calculation, respectively. In some embodiments, points M and N are at equal distances from vertex O, but this is not required. Constraints used in the calculation include: (1) Geometric configuration: the distance from point M to the straight line segment connecting points A and B (i.e., the chord of the arc AB) should be within a predefined limit ZW. (2) Acceleration and velocity: the velocity and acceleration at turning points A and B should be within predefined limits. It is preferred that the magnitude of the linear velocity of the movement at point A (entrance point of the arc AB) and the magnitude of the linear velocity of the movement at point B (exit point of the arc AB) are equal. Preferably, the magnitude of the linear velocity of the movement along the entire turning trajectory is approximately constant.

[0044] Since the arc AB is tangent to the line OA at point A and to the line BD at point B, the line C1A is perpendicular to the line OM, the line C1B is perpendicular to the line DM, and C1 is the center of the circle that defines the arc AB. The coordinates of the circle center C1 (X C1 ,Y C1 ) and the radius r of the arc AB are calculated as follows:

[0045] The angle α of the line segment OM in the (X,Y) coordinate system is α = arctan(slope OM )

[0046]

number

[0047]

number

[0048] angle

[0049]

number

[0050]

number

[0051]

number

[0052] As an example, if we use the maximum value ZW as the distance from point M to chord AB, then the length of the line segment AM is:

[0053]

number

[0054] Coordinate X of point A A and Y A is calculated from the length of the line segment AM and the angle α. X A =X M -AM * cos(α) Y A =Y M -AM * sin(α)

[0055] Similarly, the coordinates of point B are B and Y B is calculated from the length of the line segment BM (which is equal to the length of the line segment AM) and the angle β. X B =X M -B.M. * cos(β) Y B =Y M -B.M. * sin(β)

[0056] (X A ,Y A ) and (X B ,Y B ), the length of the chord AB is:

[0057]

number

[0058] Next, the radius of the circle, r, is calculated as follows:

[0059]

number

[0060] The coordinates of the circle center C1 are as follows: X C1 =X A -r * sin(α) Y C1 =Y A +r * cos(α)

[0061] From the calculated center coordinates and radius values, the coordinates of the trajectory waypoints along the arc AB can be calculated as follows: X i =X C1 -r * sin(α+i*delta_α) Y i =Y C1 +r * cos(α+i*delta_α) where delta_α is the incremental angle value along the arc, and i denotes the i-th sampling point after point A.

[0062] The incremental angle value delta_α can be calculated from the value of the moving velocity and the sampling frequency when a constant linear velocity is used. A Using the radius r of the arc, the angular velocity of the motion is ω=v A / r Sample frequency f s With , the incremental angle value is delta_α=ωf s

[0063] The coordinates of the arc DE and the trajectory waypoints along it can be calculated in a similar manner. A straight line segment is then defined by point B (the exit point of the first arc AB) and point D (the entry point of the second arc DE), and the coordinates of the trajectory waypoints along the line BD can be calculated using the linear velocity and the sampling frequency.

[0064] Preferably, after computing the trajectory, Gaussian smoothing is applied to the trajectory data points by performing a convolution with a Gaussian kernel function. This smoothing step serves to suppress high frequency signals and emphasize low frequency data. The Gaussian kernel function is defined by the following equation, where σ is the standard deviation of the sampled data points:

[0065]

number

[0066] A Gaussian kernel function has the desirable properties, symmetry, being a smooth function with an infinite number of derivatives, a convolution of a Gaussian kernel function itself being a Gaussian function, and a 2D convolution can be performed by two 1D convolutions.

[0067] The calculation of the smooth turning trajectory between the two sweeps described above will be summarized with reference to the flowchart in Fig. 9. First, a point M located along the direction of the first sweep and located near the intended end point of the first sweep, and a point N located along the direction of the second sweep and located near the intended start point of the second sweep are defined as inputs (step S901). Each of these points may be defined by the angular position of the respective sweep around the apex O and the distance from the apex, which is set slightly larger than the desired radius of the lenticule incision to be formed. The two reference points may be the same or different distances from the apex.

[0068] Next, using the coordinates of points O, M, and N and the predefined distance from point M to the chord of the arc, the circle center C1, radius r, entry point A, and exit point B of the first arc AB (associated with point M) are calculated (step S902) such that the arc AB is tangent to the line OM at the entry point A and to the line MN at the exit point B. The second arc DE associated with point N is similarly calculated (step S903) such that the arc DE is tangent to the line NM at the entry point D and to the line NO at the exit point E. A straight line segment BD is formed between the exit point B of the first arc and the entry point D of the second arc (step S904). The first arc AB, the straight line segment BD, and the second arc DE together form a smooth, corner-free turning trajectory ABDE that connects the end point of the first sweep (point A) and the start point of the next sweep (point E).

[0069] The coordinates of the waypoints along the turning trajectory ABDE may be calculated based on a defined (preferably constant) linear velocity of movement along the trajectory and a sampling frequency (step S905). Optionally, Gaussian smoothing is applied to the calculated turning trajectory by performing a convolution with a Gaussian kernel function (step S906).

[0070] In the above embodiment, the coordinates of points M and N (intersections of the two sweep directions with the straight line segments of the smooth turning trajectory) are taken as input, and the distances of points M and N to the chords of the corresponding arcs are used as the limiting geometric parameters to calculate the coordinates of points A, B, D, and E (entrance and exit points of the two arcs of the smooth turning trajectory). In a first alternative embodiment, the coordinates of points A and E (entrance point of the first arc and exit point of the second arc) are taken as input, and the coordinates of B and D (exit point of the first arc and entry point of the second arc) are calculated using the radius of the arc circle as the limiting geometric parameter. More specifically, for the arc AB, the center C1 of the circle can be calculated from the coordinates of the reference point A, the angle of the line OA, and the radius r of the circle based on the tangent relationship between the circle and the line OA. The center C2 of the arc DE can be calculated similarly. The coordinates of points B and D can be calculated from the direction and radius r of line C1C2 based on the tangent relationship between the straight line segment BD and the two circles.

[0071] In the smooth turning trajectory described above, the circular radii of the two arcs are identical. In alternative embodiments, they may have different radii as long as the tangential relationship between the arcs and the trajectory of the sweep is maintained as well as the straight line segments.

[0072] Although it is possible to smoothly connect two sweeps with an infinitely differentiable curve, an embodiment of the present invention uses a smooth turning trajectory with two circular arcs connected by one straight line segment, where each circular arc is tangent to both the corresponding sweep trajectory and the straight line segment. Such a turning trajectory can be explicitly calculated from the pre-determined maximum speed, maximum acceleration, and maximum jerk of the system. In other words, the trajectory determined using this algorithm automatically satisfies the system motor characteristics. Compared with the usual general filtering techniques for angle smoothing, the proposed method does not introduce implicit, usually unknown changes to the originally intended trajectory. Therefore, using this algorithm, the shape accuracy of the lenticule and the maximum speed, acceleration, and maximum jerk of the system can be achieved simultaneously.

[0073] The flowchart of Fig. 10 is a more general overview of a method for calculating a smooth turning trajectory between two sweeps according to an embodiment of the present invention. First, a first reference point is defined (step S1001) that is located at or outside the intended edge of the lenticule incision along the direction of the first sweep, and a second reference point is defined (step S1001) that is located at or outside the intended edge of the lenticule incision along the direction of the second sweep. These reference points may be points M and N as in the embodiment of Fig. 9, or points A and E as in the first alternative embodiment described above. Each reference point may be defined by the angular position of the respective sweep around the apex of the lenticule incision and the distance from the apex.

[0074] Then, based on the coordinates of the two reference points and the coordinates of the vertices, and at least one predefined geometric parameter, two arcs and a straight line segment are calculated (step S1002), such that the first arc is tangent to both the straight line and the straight line segment from the vertex to the first reference point, and the second arc is tangent to both the straight line and the straight line segment from the vertex to the second reference point. The predefined geometric parameter may be the distance from the reference point to the chord of the corresponding arc, as in the embodiment of FIG. 9, or the radius of the circle of the arc, as in the first alternative embodiment. The first arc, the straight line segment, and the second arc together form a smooth, corner-free turning trajectory that connects the end of the first sweep and the start of the next sweep.

[0075] The coordinates of the waypoints along the turning trajectory may be calculated based on a defined (preferably constant) linear velocity of movement along the trajectory and a sampling frequency (step S1003). Optionally, Gaussian smoothing is applied to the calculated turning trajectory by performing a convolution with a Gaussian kernel function (step S1004).

[0076] The multiple sweeps along the meridians of the lenticule, connected to each other by the smooth swivel trajectory described herein, collectively form a scan pattern for performing the lenticule incision. The movable XY stage 28 and the high-speed Z scanner 25 are controlled to move the center of the laser scan line according to the scan pattern. During the treatment scan, the laser beam is blanked during the period corresponding to the swivel trajectory between the sweeps (blanking can be achieved by controlling the optical components of the laser itself and / or the laser delivery system). In other words, the laser cutting stops at the end point A, resumes at the start point E, and so on. Thus, the start and end points of all the sweeps collectively define the periphery of the lenticule incision (which may include both the optical zone and the ring-shaped transition zone).

[0077] In summary, an embodiment of the present invention employs a turning trajectory that includes two circular arcs and a straight line segment between them, where each arc is tangent to both the corresponding sweep trajectory and the straight line segment, and applies Gaussian kernel smoothing to the trajectory waypoints to generate a smooth lenticular cut trajectory that reduces XY actuator acceleration and jerk.

[0078] Simulations using actual mechanical parameters for an exemplary XY stage showed that a smooth pivot trajectory according to an embodiment of the present invention can reduce the magnitude of acceleration by more than half, compared to using a straight connection. A comparison of simulated XY stage behavior is shown in Figures 11 and 12. Figure 11 shows the simulated position, velocity, acceleration, and jerk of the X stage (panel (a)) and Y stage (panel (b)) during the formation of a lenticule incision using a straight pivot trajectory according to the prior art. Figure 12 shows a comparison of the simulated position, velocity, acceleration, and jerk of the X stage (panel (a)) and Y stage (panel (b)) during the formation of each lenticule incision using a straight pivot trajectory (solid line) versus a smooth pivot trajectory (dotted line) according to an embodiment of the present invention.

[0079] In some embodiments, the entire lenticule incision procedure is performed in the following steps. 1. Calculate the radius of curvature of the lenticule based on the amount of optical correction, for example using equation (3) for myopia correction. 2. Select the diameter of the lenticule to be excised. 3. Select the laser and optical system parameters, including the laser pulse energy and scan line step parameters described above. 4. Perform a bottom cut, whereby the fast scan line is preferably kept tangential to the parallel of latitude, and the slow sweep trajectories traced by the X, Y, and Z scanning devices move along the meridians of longitude near the South Pole in a sequence of 1A to 1B (first sweep of the lenticle cut), 2A to 2B (second sweep of the lenticle cut), 3A to 3B (third sweep of the lenticle cut), etc., connected by a smooth turning trajectory as described above, until a complete bottom cut surface is generated. 5. A lenticule lateral (edge) incision is performed. 6. Perform the top incision in a similar manner as the bottom incision is made. 7.Perform the entrance incision.

[0080] Although the method for generating a smooth turning trajectory has been described above in connection with forming a lenticule incision for a corneal lenticule extraction procedure, the method may also be used for other laser-assisted ophthalmic procedures that include a trajectory in which the laser scanning pattern has a sharp turning point. For example, a LASIK procedure involves, among other things, forming a corneal flap by making a flat bed cut in the cornea. The bed cut may include multiple sweeps that may be connected together using a smooth turning trajectory similar to that described above.

[0081] All patents and patent applications cited herein are hereby incorporated by reference in their entirety.

[0082] While certain embodiments of the present disclosure have been shown and described in illustrative form with a certain degree of particularity, those skilled in the art will understand that the embodiments are provided by way of example only, and that various changes may be made without departing from the spirit or scope of the invention. Accordingly, the present disclosure is intended to embrace all modifications, alternative constructions, changes, substitutions, alterations, combinations and arrangements of parts, structures, and steps that fall within the spirit and scope of the invention as generally expressed by the following claims and their equivalents.

[0083] [Embodiment] (1) An ophthalmic surgical laser system, comprising: a laser source configured to generate a pulsed laser beam comprising a plurality of laser pulses; a laser delivery system configured to deliver the pulsed laser beam to a target tissue in an eye of a subject; a radio frequency scanner configured to scan the pulsed laser beam back and forth at a predefined frequency; an XY scanner configured to deflect the pulsed laser beam, the XY scanner being separate from the radio frequency scanner; a Z scanner configured to vary the focal depth of the pulsed laser beam; a controller configured to control the laser source, the radio frequency scanner, the XY scanner, and the Z scanner to sequentially form a plurality of sweeps that collectively form at least one lenticule incision in a lens in the subject's eye, the lens having a curved surface defining a vertex and a central axis passing through the vertex; Each sweep is controlling the high frequency scanner to deflect the pulsed laser beam to form a scan line, the scan line being a straight line having a predefined length and tangent to a parallel of latitude of the lens, the parallel of latitude being a circle on a surface of the lens perpendicular to the central axis and having a defined distance to the apex; controlling the XY scanner and the Z scanner to move a center of the scan line along a meridian of longitude of the lens, the meridian of longitude being a curve that passes through the vertex and has a defined angular position about the central axis; the plurality of sweeps are formed successively along respective different meridians of longitude, The controller is further configured to control the XY scanner to move the center of the scan line along a smooth circular trajectory connecting an end point of a first sweep of the plurality of sweeps and a starting point of a second sweep of the plurality of sweeps, the circular trajectory including a first arc, a straight line segment, and a second arc, the first arc tangentially connected to the first sweep at the end point of the first sweep, the second arc tangentially connected to the second sweep at the starting point of the second sweep, and the straight line segment tangentially connected to both the first arc and the second arc. (2) An ophthalmic surgical laser system as described in embodiment 1, wherein the controller is further configured to control the laser source and / or the laser delivery system to blank the pulsed laser beam when the center of the scan line is moved along the orbit from the end point of the first sweep to the start point of the second sweep. (3) the controller is further configured to calculate the turning trajectory, the calculation comprising: receiving as input coordinates of a first reference point, a second reference point, and the vertex, the first reference point being located at a distance from the vertex along the first sweep direction and the second reference point being located at another distance from the vertex along the second sweep direction; An ophthalmic surgical laser system as described in embodiment 1, comprising a step of calculating the first and second arcs and the straight line segments based on the coordinates of the first and second reference points and the vertices, and based on at least one predefined geometric parameter. (4) An ophthalmic surgical laser system as described in embodiment 3, wherein the controller is further configured to calculate a plurality of waypoints located along the orbit between the end point of the first sweep and the start point of the second sweep based on a linear velocity of movement and a sampling frequency. (5) An ophthalmic surgical laser system as described in embodiment 3, wherein the controller is further configured to apply Gaussian smoothing to the trajectory.

[0084] (6) An ophthalmic surgical laser system as described in embodiment 3, wherein the straight line segment is on a straight line between the first reference point and the second reference point, and the at least one geometric parameter is a distance from the first reference point to a chord of the first circular arc. (7) An ophthalmic surgical laser system as described in embodiment 3, wherein the first reference point is the end point of the first sweep, the second reference point is the start point of the second sweep, and the at least one geometric parameter is a radius of a circle of the first arc. (8) A method for forming a lenticule incision using an ophthalmic surgical laser system, comprising: generating a pulsed laser beam with a laser source, the pulsed laser beam comprising a plurality of laser pulses; delivering the pulsed laser beam to a target tissue in a subject's eye; scanning the pulsed laser beam back and forth at a predefined frequency with a high frequency scanner; deflecting the pulsed laser beam by an XY scanner, the XY scanner being separate from the radio frequency scanner; Varying the focal depth of the pulsed laser beam by a Z scanner; controlling, by a controller, the laser source, the radio frequency scanner, the XY scanner, and the Z scanner to sequentially form a plurality of sweeps that collectively form at least one lenticule incision of a lens in the subject's eye, the lens having a curved surface defining a vertex and a central axis passing through the vertex, each sweep comprising: controlling the high frequency scanner to deflect the pulsed laser beam to form a scan line, the scan line being a straight line having a predefined length and tangent to a parallel of latitude of the lens, the parallel of latitude being a circle on a surface of the lens perpendicular to the central axis and having a defined distance to the apex; controlling the XY scanner and the Z scanner to move a center of the scan line along a meridian of longitude of the lens, the meridian of longitude being a curve that passes through the vertex and has a defined angular position about the central axis; controlling the laser source to periodically blank the pulsed laser beam when the scan line is located within a central region of the lens; the plurality of sweeps being formed successively along respective different meridians of longitude; controlling, by the controller, the XY scanner to move the center of the scan line along a smooth circular trajectory connecting an end point of a first one of the plurality of sweeps and a starting point of a second one of the plurality of sweeps, the circular trajectory including a first circular arc, a straight line segment, and a second circular arc, the first circular arc tangentially connected to the first sweep at the end point of the first sweep, the second circular arc tangentially connected to the second sweep at the starting point of the second sweep, and the straight line segment tangentially connected to both the first and second circular arcs. (9) The method of embodiment 8, further comprising controlling, by the controller, the laser source and / or the laser delivery system to blank the pulsed laser beam when the center of the scan line is moved along the orbit from the end point of the first sweep to the start point of the second sweep. (10) A step of calculating the turning trajectory by the controller, receiving as input coordinates of a first reference point, a second reference point, and the vertex, the first reference point being located at a distance from the vertex along the first sweep direction and the second reference point being located at another distance from the vertex along the second sweep direction; 9. The method of claim 8, further comprising the steps of: calculating the first and second arcs and the straight line segments based on the coordinates of the first and second reference points and the vertices, and based on at least one predefined geometric parameter.

[0085] (11) The method of embodiment 10, further comprising the step of calculating, by the controller, a plurality of waypoints located along the orbit between the end point of the first sweep and the start point of the second sweep based on a linear velocity of movement and a sampling frequency. (12) The method of claim 10, further comprising applying Gaussian smoothing to the turning trajectory by the controller. (13) The method of embodiment 10, wherein the straight line segment is on a straight line between the first reference point and the second reference point, and the at least one geometric parameter is a distance from the first reference point to a chord of the first circular arc. (14) The method of embodiment 10, wherein the first reference point is the end point of the first sweep, the second reference point is the start point of the second sweep, and the at least one geometric parameter is a radius of the circle of the first arc.

Claims

1. 1. An ophthalmic surgical laser system comprising: a laser source configured to generate a pulsed laser beam comprising a plurality of laser pulses; a laser delivery system configured to deliver the pulsed laser beam to a target tissue in an eye of a subject; a radio frequency scanner configured to scan the pulsed laser beam back and forth at a predefined frequency; an XY scanner configured to deflect the pulsed laser beam, the XY scanner being separate from the radio frequency scanner; a Z scanner configured to vary the focal depth of the pulsed laser beam; a controller configured to control the laser source, the radio frequency scanner, the XY scanner, and the Z scanner to sequentially form a plurality of sweeps that collectively form at least one lenticule incision in a lens in the subject's eye, the lens having a curved surface defining a vertex and a central axis passing through the vertex; Each sweep is controlling the high frequency scanner to deflect the pulsed laser beam to form a scan line, the scan line being a straight line having a predefined length and tangent to a parallel of latitude of the lens, the parallel of latitude being a circle on a surface of the lens perpendicular to the central axis and having a defined distance to the apex; controlling the XY and Z scanners to move a center of the scan line along a meridian of longitude of the lens, the meridian of longitude being a curve that passes through the vertex and has a defined angular position about the central axis; the plurality of sweeps are formed successively along respective different meridians of longitude, The controller is further configured to control the XY scanner to move the center of the scan line along a smooth circular trajectory connecting an end point of a first sweep of the plurality of sweeps and a start point of a second sweep of the plurality of sweeps, the circular trajectory including a first arc, a straight line segment, and a second arc, the first arc being tangentially connected to the first sweep at the end point of the first sweep, the second arc being tangentially connected to the second sweep at the start point of the second sweep, and the straight line segment being tangentially connected to both the first arc and the second arc.

2. 2. The ophthalmic surgical laser system of claim 1, wherein the controller is further configured to control the laser source and / or the laser delivery system to blank the pulsed laser beam when the center of the scan line is moved along the orbit from the end point of the first sweep to the start point of the second sweep.

3. The controller is further configured to calculate the turning trajectory, the calculation comprising: receiving as input coordinates of a first reference point, a second reference point, and the vertex, the first reference point being located at a distance from the vertex along the first sweep direction and the second reference point being located at another distance from the vertex along the second sweep direction; and calculating the first and second arcs and the straight line segments based on the coordinates of the first and second reference points and the vertices and based on at least one predefined geometric parameter.

4. 4. The ophthalmic surgical laser system of claim 3, wherein the controller is further configured to calculate a plurality of waypoints located along the orbit between the end point of the first sweep and the start point of the second sweep based on a linear velocity of movement and a sampling frequency.

5. The ophthalmic surgical laser system of claim 3 , wherein the controller is further configured to apply Gaussian smoothing to the trajectory.

6. 4. The ophthalmic surgical laser system of claim 3, wherein the straight line segment is on a straight line between the first reference point and the second reference point, and the at least one geometric parameter is a distance from the first reference point to a chord of the first circular arc.

7. 4. The ophthalmic surgical laser system of claim 3, wherein the first reference point is the end point of the first sweep, the second reference point is the start point of the second sweep, and the at least one geometric parameter is a radius of the circle of the first arc.

8. 1. A method for forming a lenticule incision using an ophthalmic surgical laser system, comprising: generating a pulsed laser beam with a laser source, the pulsed laser beam comprising a plurality of laser pulses; delivering the pulsed laser beam to a target tissue in a subject's eye; scanning the pulsed laser beam back and forth at a predefined frequency with a high frequency scanner; deflecting the pulsed laser beam by an XY scanner, the XY scanner being separate from the radio frequency scanner; Varying the focal depth of the pulsed laser beam by a Z scanner; controlling, by a controller, the laser source, the radio frequency scanner, the XY scanner, and the Z scanner to sequentially form a plurality of sweeps that collectively form at least one lenticule incision of a lens in the subject's eye, the lens having a curved surface defining a vertex and a central axis passing through the vertex, each sweep comprising: controlling the high frequency scanner to deflect the pulsed laser beam to form a scan line, the scan line being a straight line having a predefined length and tangent to a parallel of latitude of the lens, the parallel of latitude being a circle on a surface of the lens perpendicular to the central axis and having a defined distance to the apex; controlling the XY and Z scanners to move a center of the scan line along a meridian of longitude of the lens, the meridian of longitude being a curve that passes through the vertex and has a defined angular position about the central axis; controlling the laser source to periodically blank the pulsed laser beam when the scan line is located within a central region of the lens; the plurality of sweeps being formed successively along respective different meridians of longitude; controlling, by the controller, the XY scanner to move the center of the scan line along a smooth circular trajectory connecting an end point of a first one of the plurality of sweeps and a starting point of a second one of the plurality of sweeps, the circular trajectory including a first arc, a straight line segment, and a second arc, the first arc tangentially connected to the first sweep at the end point of the first sweep, the second arc tangentially connected to the second sweep at the starting point of the second sweep, and the straight line segment tangentially connected to both the first arc and the second arc.

9. 10. The method of claim 8, further comprising controlling, by the controller, the laser source and / or the laser delivery system to blank the pulsed laser beam when the center of the scan line is moved along the orbit from the end point of the first sweep to the start point of the second sweep.

10. Calculating the turning trajectory by the controller, receiving as input coordinates of a first reference point, a second reference point, and the vertex, the first reference point being located at a distance from the vertex along the first sweep direction and the second reference point being located at another distance from the vertex along the second sweep direction; 9. The method of claim 8, further comprising: calculating the first and second circular arcs and the straight line segments based on the coordinates of the first and second reference points and the vertices and based on at least one predefined geometric parameter.

11. 11. The method of claim 10, further comprising calculating, by the controller, a number of waypoints located along the trajectory between the end point of the first sweep and the start point of the second sweep based on a linear velocity of movement and a sampling frequency.

12. The method of claim 10 further comprising applying, by the controller, Gaussian smoothing to the turning trajectory.

13. 11. The method of claim 10, wherein the straight line segment lies on a straight line between the first reference point and the second reference point, and the at least one geometric parameter is a distance from the first reference point to a chord of the first circular arc.

14. 11. The method of claim 10, wherein the first reference point is the end point of the first sweep, the second reference point is the start point of the second sweep, and the at least one geometric parameter is a circle radius of the first arc.

Images