Confocal optical protractor and method for determining angles with structured light illumination - Patents.com

Abstract

To provide a method for simultaneously measuring the roll angle, pitch angle and yaw angle of an element.SOLUTION: A step is included in which a laser beam is guided to a spiral phase plate resonator (SPPR) device and a light vortex intensity pattern having a center of gravity and a radial direction light peak is generated. After the laser beam propagates and passes through the SPPR device, the laser beam is reflected from an element so that the laser beam is guided to a camera that generates an image of the light vortex intensity pattern. The center of gravity position of the image is determined (176), the count having been aggregated along the radial direction from the center of gravity of the image is determined (178), and the position of the radial direction light peak in the image is determined using this aggregated count (180). The frequency of the laser beam is changed, the radial direction light peak is rotated, and the roll angle of the element is estimated from a frequency change (184).SELECTED DRAWING: Figure 24

Description

[Technical field]

[0001] Cross-reference to related applications

[0001] This application was filed on October 26, 2018, and relates to a Confocal Optical Protractor This is a continuation of U.S. patent application Ser. No. 16 / 171,883, entitled "Confocal Optical Protractor."

[0002] Field

[0002] This disclosure relates generally to a method for measuring the roll, pitch, and yaw angles of an element, and more particularly to a method for simultaneously measuring the roll, pitch, and yaw angles of an element. The method employs a spiral phase plate resonator (SPPR) device that generates an optical vortex pattern beam having an intensity peak. The optical vortex pattern beam is reflected from the element and incident on a camera or detector. PRIOR ART

[0003]

[0003] Non-contact measurement of angles, specifically roll, yaw, and pitch angles, is often important in manufacturing optical components, building aerospace components, system level metrology applications including alignment and tracking, 3D printing, lithography, sample part fabrication, etc. Most techniques employed in the art and used to measure angles employ mechanical devices including autocollimators, interferometers, and moving parts. Roll angle is the most difficult angle to measure, and therefore the number of systems capable of measuring roll angle with precision is limited.

[0004]

[0004] Although autocollimators have been successful in measuring pitch and yaw angles with high accuracy, the range over which these angles can be measured is limited. Furthermore, to measure the roll angle, a complex arrangement of autocollimators is required. Interferometers can measure pitch and yaw angles, but cannot measure roll angles without complex configurations of additional optical elements, such as deflection optics and prisms. Furthermore, many free-space optical elements are limited in their operation in harsh environments. Mechanical devices, such as mechanical protractors, require the system to be compact, severely limiting non-contact measurement of angles. Furthermore, systems that include moving parts are much more likely to fail during long periods of operation.

[0005]

[0005] Typically, roll angle is measured by placing a part on a rotatable mount that includes built-in angular ticks along its circumference and then rotating the mount to determine the roll angle of the part. This technique often works well when assembling small parts, but can be difficult when fabricating large parts or very heavy aerospace system parts. Another known roll angle measurement technique involves placing a mechanical protractor on the part and determining the angle of interest between two references. In this technique, the mechanical protractor contacts the surface to determine the roll angle, but this can be detrimental in applications that require non-contact measurement of the roll angle. To measure increasingly smaller angles in a limited space, the radius of the protractor needs to be increased (increasing the angular ticks) or gears are required on the mechanical protractor to amplify the accuracy of the measured angle. This means that mechanical protractors for high accuracy measurements tend to be large, which can be problematic when measuring angles in limited spaces. This task becomes even more challenging when measuring angles on curved surfaces. Furthermore, some applications such as 3D printing, lithography, and part fabrication in clean room environments require non-uniform measurement of the roll angle. Although some require contact determination, mechanical protractors make contact with the part being measured. If the surface is rotating at a constant speed, the roll angle and rotation rate cannot be inferred by a mechanical protractor.

[0006]

[0006] Optical systems provide the ability to make non-contact angle measurements between two stationary points or two stationary lines on a surface, even when the surface is curved and / or rough. Specifically, the coherent superposition of optical vortices embedded in a cylindrical symmetry can be used to perform non-contact angle measurements with very high precision and accuracy. The properties of the coherent superposition of optical vortices are such that they form a periodic intensity modulation as a function of the roll angle (azimuth angle), which can be projected onto the surface whose angle is being measured and detected by a detector.

[0007]

[0007] Various methods exist in the art for creating a coherent superposition of optical vortices, including the use of spatial light modulators, helical phase plates in interferometers, helical phase mirrors in interferometers, etc. However, these methods cannot control the yaw angle of the optical vortex without mechanically rotating selected parts of the optical system, which has limited resolution. Alternatively, the optical system consists of a complex structure of optical elements, including motorized stages, i.e., in the case of helical mirrors, q-plates, helical phase plates, etc. Methods employing spatial light modulators (SLMs) require a computer to control the SLM and its resolution, and the generation of angular displacement is limited by the pixelated SLM screen and the finite range of phase changes of the SLM. Due to these challenges, there is no clear way to miniaturize the system while maximizing the accuracy of the angle measurement without further complicating the design of the optical system.

[0008]

[0008] A resonator based on a spiral phase plate, i.e. a spiral phase plate resonator (SPPR) device, is a miniaturized optical element that can generate a coherent superposition of optical vortices by reflecting light off or through the device. There is basic science research showing the effect of resonators on low-reflectivity SPPR devices. There is also research on rotation sensors based on rotational Doppler shift. However, a complete optical protractor system for technical applications, such as determining roll angle against a reference in manufacturing and production, aerospace systems or otherwise, has not yet been demonstrated in the art.

[0009]

[0009] Titled "Optical Protractor To Measure Roll Angle On A Static Surface And Rotating Surface," U.S. Patent Application No. 15 / 943,240, filed April 2, 2018, and assigned to the assignee of the present application, discloses an optical protractor employing a spiral phase plate resonator (SPPR) device to measure roll angles between two points on a stationary or rotating surface, the contents of which are incorporated herein by reference. The protractor includes an adjustable laser source that generates a laser beam and an optical component that responds to and converts the laser beam into a single mode laser beam. The SPPR device includes opposing reflective surfaces that receive the single mode laser beam and reflect the beam back and forth within the device. One of the reflective surfaces includes a spiral step index, and multiple reflected beams with different phases are combined into an output beam from the device having an optical vortex intensity pattern, where the intensity pattern includes radial light intensity lines. The protractor includes a lens that projects the output beam onto an element, a detector that detects light reflected from the element, and a processor responsive to signals from the detector. The processor generates an image of the reflected light that includes the optical vortex intensity pattern projected onto the element and causes the laser source to change the frequency of the laser beam so that one of the intensity lines is aligned with a first of two points. The processor then determines whether the one intensity line is aligned with a first of two points. Then, have the laser source again change the frequency of the laser beam so that it aligns with the second of the two points, and use the difference between the frequencies of the laser beams to determine the angle between the points. Summary of the Invention [Means for solving the problem]

[0010]

[0010] The following discussion discloses and describes a method for simultaneously measuring the roll, pitch, and yaw angles of an element. The method directs a frequency tunable laser beam through a spiral phase plate resonator (SPPR) device. The SPPR device includes opposing reflective surfaces that reflect the laser beam back and forth within the device, one of the reflective surfaces including a spiral step index, combining multiple reflected amplitudes with different phases to generate an optical vortex intensity pattern defined by the phases of the multiple amplitudes. The intensity pattern includes a singularity centroid in the center of the beam and radial optical peaks. The SPPR device reflects or transmits a first beam and transmits a second beam. The method includes reflecting the first beam off a closed shutter to direct the first beam to a first camera that produces an image of the optical vortex intensity pattern, directing the second beam to a second camera that produces an image of the optical vortex intensity pattern, determining an initial frequency of the laser beam according to an angular position of a radial optical peak in the images produced by the first and second cameras, and synchronizing registration between the images produced by the first and second cameras. The method includes determining a position of a center of gravity in the image produced by the first camera and determining a position of a center of gravity in the image produced by the second camera. The method further includes determining a count tallied along a radial direction from the center of gravity in the image produced by the first camera as a function of a yaw angle of the beam, and using the tallied counts to determine a position of the radial optical peak in the image produced by the first camera. The method also includes determining a count tallied along a radial direction from the center of gravity in the image produced by the second camera as a function of a yaw angle of the beam, and using the tallied counts to determine a position of the radial optical peak in the image produced by the second camera. The method then includes opening a shutter such that the first beam propagates through the open shutter to the element, and directing the first beam reflected from the element to a first camera, the first camera capturing an optical vortex. and again generating an image including the intensity pattern. The method again determines a location of the center of gravity in the image generated by the first camera and again determines counts tallied along a radial direction from the center of gravity in the image generated by the first camera as a function of the beam roll angle. The method varies the frequency of the laser beam to rotate the radial optical peak of the optical vortex intensity pattern in the image generated by the first camera and estimates the roll angle of the element from the frequency change.

[0011]

[0011] Further features of the present disclosure will become apparent from the following description and appended claims, taken in conjunction with the accompanying drawings. [Brief description of the drawings]

[0012] [Figure 1] FIG. 1 is a schematic block diagram of a confocal optical protractor in which a measurement beam is reflected from a spiral phase plate resonator (SPPR) device and then from an element to measure the roll, pitch, and yaw angles of the element. [Diagram 2] FIG. 2 is an isometric view of the SPPR device separated from the optical protractor shown in FIG. 1. [Diagram 3] FIG. 1 is a side view of an SPPR device showing an internally reflected beam. [Figure 4] FIG. 2 is a diagram of a single-pixel detector array including eight single-pixel detectors arranged in a circle. [Diagram 5] FIG. 2 is an optical vortex intensity profile image of a beam reflected from an SPPR device at the protractor shown in FIG. 1. [Figure 6] 2 is an optical vortex intensity profile image of a reference beam transmitted through an SPPR device in the protractor shown in FIG. 1. [Figure 7] Fig. 5 shows the optical vortex intensity profile image when the beam is reflected above the center point to measure the pitch angle. [Figure 8] Fig. 5 shows the optical vortex intensity profile image when the beam is reflected below the center point to measure the pitch angle. [Figure 9] FIG. 5 shows the optical vortex intensity profile image when the beam is moved to the right to measure the yaw angle. [Figure 10] FIG. 5 shows the optical vortex intensity profile image when the beam is moved to the left to measure the yaw angle. [Figure 11] Figure 5 shows the optical vortex intensity profile image when the beam is rotated in a clockwise direction to measure the roll angle. [Figure 12] Figure 5 shows the optical vortex intensity profile image when the beam is rotated in the counterclockwise direction to measure the roll angle. [Figure 13] FIG. 1 is a schematic diagram of a confocal optical protractor that transmits a measurement beam through an SPPR device to measure the roll, pitch, and yaw angles of an element. [Figure 14] 14 is an optical vortex intensity profile image showing a beam transmitted through the SPPR device in the protractor shown in FIG. 13. [Figure 15] FIG. 15 shows the optical vortex intensity profile image when the beam is reflected above the center point to measure the pitch angle. [Figure 16] FIG. 15 shows the optical vortex intensity profile image when the beam is reflected below the center point to measure the pitch angle. [Figure 17] FIG. 15 shows the optical vortex intensity profile image when the beam is moved to the right to measure the yaw angle. [Figure 18] FIG. 15 shows the optical vortex intensity profile image when the beam is moved to the left to measure the yaw angle. [Figure 19] FIG. 15 shows the optical vortex intensity profile image when the beam is rotated in a clockwise direction to measure the roll angle. [Figure 20] FIG. 15 shows the optical vortex intensity profile image when the beam is rotated in the counterclockwise direction to measure the roll angle. [Figure 21]FIG. 13 is a flow chart showing the process of finding the beam centroid of an optical vortex intensity profile image with high contrast interference fringes. [Figure 22] FIG. 13 is a flow chart showing the process of finding the beam centroid of an optical vortex intensity profile image with low contrast interference fringes. [Diagram 23] FIG. 1 is a flow chart showing a process for determining pitch and yaw angles. [Figure 24] FIG. 1 is a flow chart showing a process for determining roll angle. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0013]

[0030] The following discussion of embodiments of the present disclosure is directed to methods of simultaneously measuring the roll, pitch, and yaw angles of an element using an SPPR device. This discussion is merely exemplary in nature and is in no way intended to limit the disclosure or its application and uses.

[0014]

[0031] As discussed in more detail below, the present disclosure provides an "all optical" measurement system that uses no moving parts to measure roll, pitch, and yaw angles with an element. An optical system, or optical protractor, is described that provides a process for measuring pitch, yaw, and roll angles of a variety of components and parts in manufacturing and production, such as for unmanned aerial vehicles, airplanes, aircraft carriers, ballistic missiles, and the like, where non-contact measurement of the pitch, yaw, and roll angles of the components is important, and that the optical system can measure these angles during pattern recognition. It can also be applied in machine vision, such as in robots and autonomous vehicles, to determine

[0015]

[0032] The key element of this optical system is a Spiral Phase Plate Resonator (SPPR) device, in which an optical beam of a particular frequency undergoes multiple round trips, creating an output beam with an angular intensity-modulated interference pattern as a function of beam angle. By precisely varying the wavelength of the beam incident on the SPPR device, angular intensity peaks are rotated in the pattern of the beam output from the SPPR device. When this beam is projected onto a stationary surface, it can be detected to measure the pitch, yaw, and roll angles. The intensity-modulated interference pattern in the output beam is the result of a coherent superposition of selected optical winding numbers emerging from the SPPR device. be.

[0016]

[0033] To ensure high accuracy of the measured angle even in harsh environments such as in the presence of vibrations and temperature gradients, a method is required to calibrate the optical system. This method involves calibrating the rotation angle of the optical vortex intensity pattern to the wavelength of the beam and monitoring the angular displacement of the optical intensity pattern with respect to a reference beam on a detector such as a CCD camera. Any spurious changes in the optical system such as changes in the beam wavelength from a laser source, changes in the refractive index of an optical element, or vibrations of the surface being measured can be compensated for during the measurement of the angle. The image from the CCD camera is read in real time using image processing algorithms, and errors in finding the center of the optical vortex and other forms of systematic errors in the determination of the angle are reduced. Using standard techniques such as phase-locked method, amplitude-locked method, etc., the frequency of the input beam to the SPPR device is fixed and then varied, and the intensity pattern is rotated by incremental frequency increments for measurement, calibration, and real-time monitoring.

[0017]

[0034] 1 is a schematic block diagram of an optical system 10 of the type previously discussed for simultaneously measuring roll, pitch, and yaw angles between reference lines on a stationary or rotating surface and determining the rotational rate of the rotating surface. System 10 includes a narrow linewidth laser source 12 that is tunable and launches a coherent laser beam, for example in the visible-IR frequency range, into a single mode optical fiber 14. Single mode optical fiber 14 may be, for example, a TEM 00 A Gaussian mode laser beam 18 is provided. In an alternative embodiment, a TEM 00 Instead of the single mode optical fiber 14, other optical elements may be employed to provide the Gaussian modes. For example, the beam 18 may be coupled to a TEM 00 To make the optical mode Gaussian or to purify it, a suitably designed aperture (not shown) can be used. The beam 18 emitted from the fiber 14 is collimated by a collimator 16 located at the end of the fiber 14, ensuring that the beam 18 propagates through the optical system 10 with minimal divergence. Light reflected back into the laser source 12 may generate beam jitter in the laser cavity, resulting in intensity fluctuations in the output laser beam 18 or spurious frequency shifts in the laser wavelength, which may cause mode instabilities in the laser cavity and may cause the laser source 12 to become unfixed. Therefore, an optical isolator 20 is placed after the output of the collimator 16 to prevent the laser beam 18 from being reflected back into the laser source 12.

[0018]

[0035] After propagating through the optical isolator 20, the single mode beam 18 is split by a beam splitter 22 such that a small portion of the beam 18 is sent to a high speed detector 24 that monitors the beam intensity, and the remaining portion of the beam 18 is sent to an SPPR device 26 where, as a result of its finite reflectivity, the beam 18 is reflected back and forth within the device 26. FIG. 2 is an isometric view of the device 26 isolated from the system 10, and FIG. 3 is a side view thereof. The device 26 includes an optically transparent block 28, such as glass, with a reflector 30, such as a coating of a smooth reflective material, at the input side of the block 28. The block 28 is sufficiently optically transparent to be reflected back and forth within the device 26. The device 26 also includes a step-wise spiral reflector 32, such as a polymer or glass layer having a reflective coating, with azimuthally varying steps 36 having a height Δh at the output side of the block 28. The block 28 is also sufficiently transparent to allow the output beam to propagate through and exit the device 26. While this design employs a smooth reflective coating to provide a reflective surface on the block 28, alternative designs may use nanoscale structures to enable reflection of the beam 18 at the block 28.

[0019]

[0036] When beam 18 propagates through block 28 without surface reflection, an optical vortex beam with a well-defined number of turns is generated on the output face of device 26, where device 26 acts as a spiral phase plate. By providing finite reflections on both opposing sides of device 26 and providing reflectors 32 with a gradually varying azimuthal thickness, device 26 operates as a spiral phase plate resonator (SPPR), and the optical vortex beam is output from device 26 as a coherent superposition of optical vortices separated by a specific positive number of turns. In other words, each reflection of beam 18 within device 26 creates an individual optical vortex beam with a unique phase that is output from device 26. Each beam has a different number of turns, i.e., an orbital angular momentum, and an amplitude U 1 ~U N The beam has all the optical vortex beam amplitudes U with different winding numbers and different orbital angular momentum states. 1 ~U N In other words, the optical vortex intensity pattern is a superposition of the beam U 1 ~U N The periodic intensity interference pattern is based on the phase of the vortex beam and varies as a function of the angle of the vortex beam. The rotation of the intensity pattern is controlled by the frequency of beam 18.

[0020]

[0037] The optical vortex intensity pattern of beam 18 is output from the input of SPPR device 26 to beam splitter 22 as reflected measurement beam 40 and from the output of SPPR device 26 as transmitted reference beam 42 for calibration purposes. In this non-limiting embodiment, SPPR device 26 is a commercial off-the-shelf (COTS) device with an internal reflectivity of approximately 0.04. This reflectivity results in high contrast vortex intensity peaks in measurement beam 40 and low contrast vortex intensity peaks in transmitted reference beam 42. Using reflected beam 40 for angle measurement makes the peaks more prominent and allows background light to be more easily removed.

[0021]

[0038] The reference beam 42 is imaged by a lens 50 located 2× focal length from the SPPR device 26 onto a charge-coupled device (CCD) camera 54 through an attenuator 56 to provide a beam direction reference for roll angle calculation. The measurement beam 40 is reflected by the beam splitter 22 towards a second beam splitter 60 which directs a small portion of the measurement beam 40 to a detector 62. The detector 62 tracks the direction of the optical vortex measurement beam 40 and the intensity of the beam 40 reflected from the SPPR device 26. The detector 62 is shown as a multi-pixel detector, such as a CCD camera, but can be any detector suitable for the purposes discussed herein. For example, the detector 62 can be a multi-pixel detector arranged in a circle ring, as shown in FIG. 4. It could also be a single pixel detector array 76 including a single pixel detector 78. This annulus could allow for measuring the rotational displacement of the beam 40 with high accuracy.

[0022]

[0039] A major portion of the measurement beam 40 is imaged onto a platform 66 through a shutter 68 by a lens 64 or a series of lenses, which direct the beam 40 to image the platform 66 in a confocal imaging geometry. The reflected beam from the platform 66 is directed by the beam splitter 60 to a CCD camera 70, which provides an angular measurement. Lens 64 images the reflected beam onto a camera. A narrow band filter 72 positioned in front of camera 70 reduces sources of background light at other wavelengths. In addition, lens 64 narrows the field of view (FOV) of camera 70 and also reduces the amount of backscattered light incident on camera 70. When shutter 68 is closed, beam 40 is reflected through beam splitter 60 onto camera 70. When shutter 68 is open, beam 40 passes through shutter 68 and is reflected back from platform 66 to camera 70. CCD camera 70 also serves to calibrate the internal position of beam 40.

[0023]

[0040] An xyz coordinate system is shown for platform 66, where rotation about the x axis indicates the yaw angle, rotation about the y axis indicates the pitch angle, and rotation about the z axis indicates the roll angle. The optical vortex intensity profile of measurement beam 40 with high contrast interference fringes as imaged onto camera 70 is shown in FIG. 5. Here, device 26 measures |r 2 | 2 = 0.04, where r 2 is the Fresnel reflection coefficient at the surface of the SPPR device 26. The optical vortex intensity profile of the reference beam 42 with low contrast interference fringes as imaged onto the camera 54 is shown in FIG. 6. In these figures, the shaded areas represent the vortex intensity peaks. The system 10 works well when implementing a device with high internal reflectivity in this embodiment, and the SPPR device 26 can face in either the forward or reverse direction.

[0024]

[0041] For high accuracy angle determination, the camera 54 is used to calibrate the system 10 as discussed above. From this measurement, a transfer function is obtained that in effect defines the calibration function of the optical system 10. This transfer function converts the change in laser frequency into an angle change, even in the presence of thermal effects of elements in the optical system 10. Ideally, for high accuracy measurements, materials with low thermal expansion coefficients are used in the optical system 10. However, the camera update from the calibration process before or during the measurement allows angle determination on a stationary surface, even in the presence of thermal effects and vibrations. For measurements made after focusing of the beam 42, the Gouy phase causes an extra shift in the rotation of the reference beam 42. It is easy to take this effect into account during the calibration of the optical system 10.

[0025]

[0042] System 10 allows the optical vortex beam to remain collimated over long distances for the purpose of illuminating platform 66. To determine the roll angle, the frequency of beam 18 is shifted to rotate the angular intensity profile. To measure pitch and yaw angles, the center of gravity of beam 40 is moved from one point to another. Using distance measuring devices such as LiDAR, RADAR, etc., distance can be estimated when measuring yaw and pitch angles.

[0026]

[0043] Processor 74 controls system 10 and adjusts laser source 12 to receive signals from cameras 54 and 70 and detector 62 and determine roll, yaw, and pitch angle measurements in accordance with the discussion herein. As discussed in more detail below, beam 40 is reflected from platform 66 when platform 66 is in a reference position to determine the distance between platform 66 and camera 70 and to identify the initial beam profile. A shift along the y-axis of the beam profile above or below the center point of the initial beam profile in the described direction is a measure of the pitch angle, as shown by the optical vortex intensity profile images in Figures 7 and 8. Additionally, a shift along the y-axis of the beam profile above or below the center point of the initial beam profile in the described direction is a measure of the pitch angle, as shown by the optical vortex intensity profile images in Figures 7 and 8. A shift along the x-axis of the beam profile to the left or right is a measure of the yaw angle, as shown by the optical vortex intensity profile images in Figures 9 and 10. Note that the distance to the platform 66 and the shift of the beam 40 on the camera 70 are used to measure the pitch and yaw angles. To measure the roll angle, as shown by the optical vortex intensity profile images in Figures 11 and 12, The beam 40 is rotated in a clockwise or counterclockwise direction relative to a reference (not shown) on the platform 66 .

[0027]

[0044] In system 10, measurement beam 40 reflected from SPPR device 26 is used to measure pitch, yaw, and roll angles to form high contrast interference fringes since device 26 has low internal reflectivity as discussed above. In an alternative embodiment, SPPR device 26 is configured as a 2 | 2=0.57, in which case the beam transmitted through device 26 becomes the measurement beam. FIG. 13 is a schematic block diagram of this type of optical system 80 for simultaneously measuring roll, pitch, and yaw angles, with similar elements to system 10 identified with the same reference numerals. In this embodiment, SPR device 26 is replaced with SPPR device 82, a custom device with high internal reflectivity that removes detector 24 and beam splitter 82 and provides a beam splitter 84 downstream of SPPR device 82 that splits the vortex beam from device 82 into reference beam 42 and measurement beam 40.

[0028]

[0045] The optical intensity profile of the beam transmitted through the SPPR device 82 is shown in FIG. 14. Similar to the system 10 discussed above, the beam 40 is reflected off the platform 66 when the platform 66 is in a reference position to determine the distance between the platform 66 and the camera 70 and to identify the initial beam profile. A shift of the beam profile along the y-axis above or below the center point of the initial beam profile in the described direction is a measure of the pitch angle, as shown by the optical vortex intensity profile images in FIGS. 15 and 16. Additionally, a shift of the beam profile along the x-axis above or below the center point of the initial beam profile in the described direction is a measure of the yaw angle, as shown by the optical vortex intensity profile images in FIGS. 17 and 18. Again, the distance to the platform 66 and the shift of the beam 40 on the camera 70 are to measure the pitch and yaw angles. To measure the roll angle, as shown by the optical vortex intensity profile images in FIGS. 19 and 20, the beam 40 is rotated in a clockwise or counterclockwise direction relative to a reference (not shown) on the platform 66.

[0029]

[0046] As previously explained, the confocal optical protractor (COP) of systems 10 and 80 can be a COTS SPPR device with low reflectivity at its surface or a custom-fabricated SPPR device with high reflectivity at its surface. In a COTS SPPR device, the reflectivity at the surface of the device is relatively low, i.e., |r 2 | 2 ~|0.219| 2 = 0.047. Thus, the number of photons that can be making rotational position measurements on the inner surface of the camera 70 and on the platform 66 of interest is Compared to the maximum number, the number of photon counts for rotation measurement is about 2 / 3 less. Depending on the albedo of the platform 66, even fewer light particles may be imaged on the camera 70. One of the main advantages of this confocal coupling of the optical protractor is that high contrast fringes (singleness) exist regardless of the reflectivity of the SPPR device. This allows for a high signal-to-noise ratio, especially for COTS SPPR devices. If the reflectivity of the SPPR device is |r 2 | 2 =|0.577| 2 = 0.33, the signal to noise ratio on the camera 70 is increased to maximize the number of light particles making the rotational position measurement in transmission coupling of the SPPR device.

[0030]

[0047] Equations describing the transmission amplitude of the SPPR device 26 and the reflection amplitude of the SPPR device 26 can be derived using matrix form. For purposes of clarity and simplicity, the transmission of the SPPR device 26 or 82 can be expressed as follows:

number

[0031]

[0048] Similarly, the reflection from the SPPR device 26 can be expressed as:

number

[0032]

[0049] The roll, pitch, and yaw angles are measured by tracking specific characteristics of the optical vortex beam reflected back from the exterior surface onto the camera 70. These characteristics include the centroids of the individual intensity peaks, the centroid of the entire optical vortex beam, and the rotational displacement of the optical vortex intensity profile. An example is shown in which four intensity peaks are projected onto the surface of the platform 66 where the angle is to be measured. The roll, pitch, and yaw angle measurement algorithm allows the location of the individual intensity peaks and the center of the optical vortex to be known with high precision and accuracy. For every four separate intensity peaks, the measurement accuracy is four times higher in the roll, pitch, and roll angle criteria compared to using one narrow intensity peak to determine the angle. Although this design uses four intensity peaks, there may be many more or fewer intensity peaks from the SPPR device 26.

[0033]

[0050] The roll angle is determined by tracking the rotation of the optical vortex, i.e., the rotational displacement (angular displacement) of the optical vortex beam on the camera 70. The resolution in determining the roll angle is non-linear. It maintains a high and wide range for measuring the roll angle. This angle can span the entire 360° measurement range. The pitch angle is determined by tracking the vertical displacement of the optical vortex beam centroid from the external platform on the camera 70. Similarly, the yaw angle is determined by tracking the horizontal displacement of the retro-reflected optical vortex beam from the external platform. The yaw and pitch angles are calculated from both the distance to the target and the displacement of the beam on the camera 70. Before the optical vortex beam is retro-reflected from the platform 66, the optical vortex beam is internally retro-reflected from the shutter 68 when the shutter 68 is closed to determine the initial position of the optical vortex beam 40. This includes the initial position of the beam centroid and the initial position of the angular intensity peak. This process is sequentially performed with other system calibration processes. Other system calibration processes include laser intensity calibration using the detector 24 and laser frequency calibration using the camera 54, and monitoring the internal rotation of the optical vortex beam 48 on the cameras 54 and 70 and the detector 62. In a different embodiment, for initial angle calibration, an initial position can be determined on an external plane of known angle. Additionally, a transfer function for converting the laser wavelength to the rotation of the optical vortex beam is stored. do.

[0034]

[0051] Angular displacement to measure roll angle, as well as estimate yaw and pitch angles The displacements for the target are estimated from a non-linear fitting routine. The yaw and pitch angles are determined from the vertical and horizontal displacements of the centroids of the four intensity peaks on the x and y axes of the camera 70, respectively, and the distance to the target. The roll angle is determined by the rotational displacement of the intensity peaks. The four individual intensity peaks are captured by the camera 70 with unity contrast. As the beam is projected onto zero, these peak intensities are individually fitted. The location of the intensity peaks gives the centroid of the entire beam. Using the appropriate formula, the centroid is first calculated from the data, and then these values ​​are used as initial values ​​in a non-linear fitting routine to track the position of the object. Accurate determination of the beam centroid is the first step in determining the angular displacement of the retroreflected beam. If there is a speckle in the image, it is necessary to stitch together multiple images. By first taking the average, the effect of speckles can be reduced.

[0035]

[0052] Determining the roll, pitch, and yaw angles requires knowing the absolute center of the beam 40. For a vortex beam with a singularity, i.e., a very small vortex core (or no core) as generated by the SPPR device 26, the center of the beam 40 is defined as the point where all of the intensity peaks meet, which is equivalent to the beam's centroid. An algorithm for calculating the center of the beam 40 is discussed below. This algorithm works correctly for an even number of vortex intensity peaks, i.e., when β is even. Therefore, for this case only, we will assume β is 4. However, this algorithm can also be modified to work correctly for an odd number of intensity peaks. Two cases are discussed: A first case of an optical vortex intensity profile having high contrast fringes of beam 40 imaged on camera 70 will be discussed, and a second case of an optical vortex intensity profile having low contrast fringes of beam 40 imaged on camera 70 will be discussed. More specifically, depending on the selection of SPPR device 26 or 82, camera 70 can receive high contrast or low contrast fringes. When the SPPR device has low reflectivity, camera 70 produces an image with low contrast fringes, but with a moderate to high reflectivity SPPR device, i.e., a custom SPPR device, camera 70 produces an image with high contrast fringes. Camera 70 always has relatively high contrast fringes for systems 10 and 80.

[0036]

[0053] FIG. 21 is a flow chart diagram 90 illustrating a process for determining the center of an optical vortex intensity profile having high contrast fringes of beam 40 imaged onto camera 70. In box 92, shutter 68 is closed to block light from the exterior surface, although in some designs closing shutter 68 may not be necessary. Closing shutter 68 causes beam 40 to be reflected back from shutter 68 onto camera 70 in box 94. In box 96, the pixel screen on camera 70 is scanned with a number of pixels representing the number of intensity peaks in beam 40. quadrant In this example, there are four intensity peaks, i.e., β=4, and therefore four quadrant In box 98, on the x-axis and y-axis, quadrant In box 100, the collected data is used to quadrant The center of gravity and width of the intensity peak at are estimated, and these values ​​are divided into four quadrant In box 102, each quadrant A non-linear fitting routine is applied to the intensity peaks in . In box 100, initial values ​​in the fitting routine are estimated, and in one non-limiting embodiment, a Gaussian-like function is employed as the model in the fitting routine. In box 106, the fitting routine is used to estimate the x and y centroid location and width of each intensity peak. From the centroid location values ​​of each intensity peak, the center location of the beam 40 is calculated with sub-pixel accuracy and stored in box 108. One way to calculate the center location of the beam 40 is to find the diagonal quadrant The goal is to take the average of each x and y intensity peak at each quadrant The centroid and width values ​​of the individual intensity peaks in and the centroid of the entire beam form the initial positions in determining the angle when the shutter 68 is closed or open.

[0037]

[0054] The contrast of the interference fringes is low when light is transmitted through the SPPR device 26, which has low reflectivity. This is the case for the optical hardware in system 10, and images / frames are typically monitored on camera 54 during dynamic calibration. Typically, finding the center of the optical vortex beam 40 is performed when system 10 is first constructed. This procedure is then used to monitor the center point to ensure that there is no statistically significant deviation in the center position during system operation.

[0038]

[0055] FIG. 22 is a flow chart diagram 112 showing a process of determining the center of an optical vortex intensity profile with low contrast fringes of beam 42 imaged on camera 54. In box 114, beam 42 is transmitted through SPPR device 26, and in box 116, integrated counts on the x and y axes are calculated. In box 118, the collected data is used to estimate the centroid and width of beam 42, and these values ​​are stored. In box 102, a non-linear fitting routine is applied to beam 42, where initial values ​​in the fitting routine are estimated in box 118, and in one non-limiting embodiment, a Gaussian-like function is adopted as a model in the fitting routine for the entire beam 42. In box 124, the x and y centroid positions and width of beam 42 are obtained from the non-linear fitting routine. The operations from boxes 116 to 124 are repeated for different rotation angles by changing the laser frequency of beam 42 to ensure consistency of the beam center (centroid) position in box 126. If a low reflectivity SPPR device is used, this value is compared to a previously stored value of the central position of beam 42 in box 128. During the initial calibration, there should not be any significant deviation from the stored value, in other words, the deviation should be less than a sub-pixel value.

[0039]

[0056] FIG. 23 is a flow chart 130 showing a process for calculating the pitch and yaw angles of the platform 66. In box 132, the shutter 68 is closed so that no light is coming from the external surface onto the camera 70. In box 134, the beam 40 is retroreflected from the shutter 68 (or an external calibration surface) and incident on the camera 70. In box 136, the center of gravity of the beam 40 is calculated as previously discussed in flow charts 90 or 112. In box 138, the shutter 68 is opened and in box 140, the center of gravity of the retroreflected beam is calculated. In box 142, the pitch angle is determined from the vertical displacement of the beam 40 on the camera 70, where each value of the vertical displacement corresponds to a measure of the pitch angle. In box 144, the yaw angle is determined from the horizontal displacement on the camera 70, where each value of the horizontal displacement corresponds to a measure of the yaw angle. If the pitch and yaw angles are continuously changing, successive measurements can be performed in box 146 to estimate the angles of change as a function of the position on the screen of the camera 70. In box 148, the pitch and yaw angles are stored.

[0040]

[0057] FIG. 24 is a flow chart diagram 150 showing a process for calculating the roll angle of the platform 66 with respect to a reference or between two or more points. In box 152, the shutter 68 is closed so that no light is incident on the platform 66. In box 154, the intensity of the laser source 12 is stabilized using the detectors 24 and 62 and the camera 54, and in box 156, the initial frequency of the laser source 12 is determined by the angular position of the intensity peak on the cameras 54 and 70. In box 158, the cameras 54 and 70 are synchronized to ensure that they receive image frames at the same time. In box 160, the center of gravity of the beam 40 on the cameras 54 and 70 is estimated as described in flow charts 90 or 112. The presence of background is subtracted from the value obtained by the nonlinear fitting routine. In box 162, the center of gravity of the beam 40 reflected back from the shutter 68 onto the camera 70 is estimated. In box 164, the roll angle on the camera 54 is calculated along a radial direction starting from the beam center of gravity position. , and in box 166, a non-linear fitting routine is used to estimate the location of the angular intensity peak and store these values. In box 168, starting from the beam centroid position, the tabulated count is calculated as a function of roll angle on camera 70 along the radial direction, and in box 170, a non-linear fitting routine is used to estimate the location of the angular intensity peak and store these values.

[0041]

[0058] The shutter 68 is opened in box 172 and the beam 40 is projected onto the platform 66 and imaged on the camera 70 in box 174. The initial frequency of the reflected beam 40 corresponds to the frequency when the direction of the beam 40 is aligned with a fiducial on the platform 66. In box 176, the center of gravity of the beam 40 imaged onto the platform 66 is determined using flow chart diagrams 90 or 112. Starting from the center of gravity of the beam 40, a radial tally count is calculated as a function of roll angle in box 178. In box 180, the position of the intensity peak is obtained from a non-linear optimization fitting routine. In a calibration process, the beam 40 is reflected back from the shutter 68 and in box 182, the initial positioning of the intensity peak from the calibration process is stored for the non-linear fitting routine. When the platform 66 is rotated, The optical vortex beam rotates, tracking the rotation by the change in laser beam frequency, rotating the direction of the optical vortex intensity profile. In box 184, the roll angle is estimated. If the platform 66 is rotated in incremental steps, the optical vortex pattern of the beam 40 can be rotated incrementally to determine the roll angle. If there is a smooth continuous rotation of the platform 66 at the first velocity, the rotational Doppler shift can be used to obtain the roll angle.

[0042]

[0059] The foregoing discussion discloses and describes merely exemplary embodiments of the present disclosure, and those skilled in the art will readily recognize that various changes, modifications, and variations can be made from such discussion and the accompanying drawings and claims without departing from the spirit and scope of the present disclosure, as set forth in the following claims.

Claims

1. 1. A method for measuring pitch of an element, comprising: providing a frequency tunable laser beam; directing the laser beam into a spiral phase plate resonator (SPPR) device, the SPPR device including opposing reflective surfaces that reflect the laser beam back and forth within the device, one of the opposing reflective surfaces including a spiral step index, combining a plurality of reflected amplitudes having different phases to generate an optical vortex intensity pattern defined by the phases of the plurality of reflected amplitudes, the optical vortex intensity pattern including a singularity centroid and a radial optical peak; reflecting a laser beam off the element after propagation through the SPPR device to direct the laser beam onto a camera that produces an image of the optical vortex intensity pattern; determining a pitch angle of the element by a shift of the optical vortex intensity pattern relative to a plane of an image produced by the camera; A method comprising:

2. 2. The method of claim 1, wherein the SPPR device is a device having a medium to high internal reflectivity, and wherein the laser beam is transmitted through the SPPR device and the radial light peak has high contrast interference fringes.

3. 2. The method of claim 1, wherein the SPPR device is a device with low internal reflectivity, and wherein the laser beam reflects off the SPPR device and the radial light peak has low contrast interference fringes.

4. 10. The method of claim 1, further comprising stabilizing the intensity of the laser beam using a beam intensity detector and a pattern direction detector.

5. The method of claim 1 , wherein the optical vortex intensity pattern comprises four radial optical peaks.

6. 1. A method for measuring the yaw angle of an element, comprising: providing a frequency tunable laser beam; directing the laser beam into a spiral phase plate resonator (SPPR) device, the SPPR device including opposing reflective surfaces that reflect the laser beam back and forth within the device, one of the opposing reflective surfaces including a spiral step index, combining a plurality of reflected amplitudes having different phases to generate an optical vortex intensity pattern defined by the phases of the plurality of reflected amplitudes, the optical vortex intensity pattern including a singularity centroid and a radial optical peak; reflecting a laser beam off the element after propagation through the SPPR device to direct the laser beam onto a camera that produces an image of the optical vortex intensity pattern; determining the yaw angle of the element by a shift in the optical vortex intensity pattern in a plane orthogonal to a plane in an image produced by the camera; A method comprising:

7. 7. The method of claim 6, wherein the SPPR device is a device having a medium to high internal reflectivity, and wherein the laser beam is transmitted through the SPPR device and the radial light peak has high contrast interference fringes.

8. 7. The method of claim 6, wherein the SPPR device is a device with low internal reflectivity, and the laser beam reflects off the SPPR device and the radial light peak has low contrast interference fringes.

9. 7. The method of claim 6, further comprising stabilizing the intensity of the laser beam using a beam intensity detector and a pattern direction detector.

10. The method of claim 6 , wherein the optical vortex intensity pattern includes four radial optical peaks.

Images