Patent Publication Number: US-2022214163-A1

Title: Interference in-sensitive littrow system for optical device structure measurement

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit of pending U.S. Patent Application No. 63/134,442, filed Jan. 6, 2021, the contents of which are incorporated herein in their entirety. 
    
    
     BACKGROUND 
     Field 
     Embodiments of the present disclosure relate to devices and methods of measuring a pitch P of optical device structures and an orientation angle ϕ of the optical device structures. 
     Description of the Related Art 
     Virtual reality is generally considered to be a computer generated simulated environment in which a user has an apparent physical presence. A virtual reality experience can be generated in  3 D and viewed with a head-mounted display (HMD), such as glasses or other wearable display devices that have near-eye display panels as lenses to display a virtual reality environment that replaces an actual environment. 
     Augmented reality, however, enables an experience in which a user can still see through the display lenses of the glasses or other HMD device to view the surrounding environment, yet also see images of virtual objects that are generated for display and appear as part of the environment. Augmented reality can include any type of input, such as audio and haptic inputs, as well as virtual images, graphics, and video that enhances or augments the environment that the user experiences. As an emerging technology, there are many challenges and design constraints with augmented reality. 
     One such challenge is displaying a virtual image overlaid on an ambient environment. Optical devices are used to assist in overlaying images. Fabricating optical devices can be challenging as optical devices tend to have properties, such as optical device structure pitches and optical device structure orientations that need to be manufactured according to specific tolerances. Conventional systems will experience a decrease in accuracy and repeatability when measuring optical device structures on non-opaque substrates due to reflection and diffraction of light. Accordingly, what is needed in the art are improved devices and methods of measuring a pitch P of optical device structures and an orientation angle ϕ of the optical device structures with increased accuracy and repeatability. 
     SUMMARY 
     In one embodiment, a system is provided. The system includes a stage having a substrate support surface. The stage is coupled to a stage actuator configured to move the stage in a scanning path and rotate the stage about an axis. The system further includes an optical arm coupled to an arm actuator configured to scan the optical arm and rotate the optical arm about the axis. The optical arm includes a light source. The light source emits a light path operable to be diffracted to the stage. The optical arm further includes a first beam splitter and a second beam splitter positioned in the light path. The first beam splitter directs the light path through a first lens and the second beam splitter directs the light path through a first dove prism and a second lens. The optical arm further includes a first detector operable to detect the light path from the first lens and second detector operable to detect the light path from the second lens. 
     In another embodiment, a system is provided. The system includes a stage having a substrate support surface. The stage is coupled to a stage actuator configured to move the stage in a scanning path and rotate the stage about an axis. The system further includes an optical arm coupled to an arm actuator configured to scan the optical arm and rotate the optical arm about the axis. The optical arm includes a light source. The light source emits a light path operable to be diffracted to the stage. The optical arm further includes a dove prism positioned in the light path. The dove prism includes an actuator to rotate the dove prism. The optical arm further includes a first beam splitter positioned in the light path. The first beam splitter directs the light path through a first lens and a second beam splitter directs the light path through a second lens. The optical arm further includes a first detector operable to detect the light path from the first lens. 
     In yet another embodiment, a system is provided. The system includes a stage having a substrate support surface. The stage is coupled to a stage actuator configured to move the stage in a scanning path and rotate the stage about an axis. An optical arm coupled to an arm actuator is configured to scan the optical arm and rotate the optical arm about the axis. The optical arm includes a light source. The light source emits a light path operable to be diffracted to the stage. A first beam splitter and a second beam splitter are positioned in the light path. The first beam splitter directs the light path through a first lens and the second beam splitter directs the light path through a first dove prism. The optical arm further includes a first mirror operable to direct the light path to a second mirror and the second mirror directs the light path through the first lens. The optical arm further includes a first detector operable to detect the light path from the first lens. 
     In yet another embodiment, a method is provided. The method includes determining a fixed beam angle ϑ 0  and an initial orientation angle ϕ initial  of a first zone of optical device structures of a substrate. The method further includes rotating the substrate to position the initial orientation angle ϕ initial  perpendicular to light beams to be projected to the first zone of the substrate. The method further includes projecting light beams having a wavelength (λ laser ) to the first zone of the substrate at the fixed beam angle ϑ 0 . The method further includes measuring a reflected beam angle ϑ reflected  of the light beams reflected by the substrate. The reflected beam angle ϑ reflected  is obtained via a center of a symmetric beam profile. The symmetric beam profile is obtained from a combination of a first image and a second image of the light beams reflected by the substrate. The second image is rotated at a rotation angle different than the first image. The method further includes determining a pitch P of the optical device structures by a pitch equation P=λ laser /(sin ϑ 0 +sin ϑ reflected ). 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       So that the manner in which the above recited features of the present disclosure can be understood in detail, a more particular description of the disclosure, briefly summarized above, may be had by reference to embodiments, some of which are illustrated in the appended drawings. It is to be noted, however, that the appended drawings illustrate only exemplary embodiments and are therefore not to be considered limiting of its scope, and may admit to other equally effective embodiments. 
         FIG. 1  is a schematic view of a measurement system, according to embodiments. 
         FIGS. 2A-2F  are schematic views of a configuration of a measurement system, according to some embodiments. 
         FIGS. 3A-3C  are schematic views of a detector, according to embodiments. 
         FIG. 3D  is a schematic view of a dove prism, according to embodiments. 
         FIG. 3E  is a schematic view of a mirror assembly, according to embodiments. 
         FIG. 4  is a flow diagram of a method for measuring a pitch P of optical device structures and an orientation angle ϕ of the optical device structures, according to embodiments. 
     
    
    
     To facilitate understanding, identical reference numerals have been used, where possible, to designate identical elements that are common to the figures. It is contemplated that elements and features of one embodiment may be beneficially incorporated in other embodiments without further recitation. 
     DETAILED DESCRIPTION 
     Embodiments of the present disclosure relate to devices and methods of measuring a pitch P of optical device structures and an orientation angle ϕ of the optical device structures. In one embodiment, a system is provided. The system includes a stage having a substrate support surface. The stage is coupled to a stage actuator configured to move the stage in a scanning path and rotate the stage about an axis. The system further includes an optical arm coupled to an arm actuator configured to scan the optical arm and rotate the optical arm about the axis. The optical arm includes a light source. The light source emits a light path operable to be diffracted to the stage. The optical arm further includes a first beam splitter and a second beam splitter positioned in the light path. The first beam splitter directs the light path through a first lens and the second beam splitter directs the light path through a first dove prism and a second lens. The optical arm further includes a first detector operable to detect the light path from the first lens and second detector operable to detect the light path from the second lens. 
     The measurement system includes a stage, an optical arm, and a detector arm. Light projected from the optical arm reflects from a substrate disposed on the stage, and the reflected light from the substrate surface is incident on the detector and the optical arm. The deflection from the optical center of the focusing lens is used to determine the local non-uniformity of the optical device. Methods of diffracting light include measuring scattered light beams from the substrate surface, and local distortions are obtained from the measured values. Non-opaque substrates will cause interference due to diffraction of the light from other surfaces. The interferences will be diffracted to the optical arm and the detector arm. The interference causes the accuracy and the precision of the measurement results to decrease. 
       FIG. 1  is a schematic view of a measurement system  101 , according to one embodiment. As shown, the measurement system  101  includes a stage  102 , an optical arm  104 , and a detector arm  112 . The measurement system  101  is configured to diffract light projected by the optical arm  104 . The light projected by the optical arm  104  is directed at a substrate  103  disposed over the stage  102 . The light that is reflected and diffracted from the substrate  103  is incident on the detector arm  112  and the optical arm  104 . In one embodiment, which can be combined with other embodiments described herein, the measurement system  101  includes the optical arm  104  and the detector arm  112 . In another embodiment, which can be combined with other embodiments described herein, the measurement system  101  includes only the optical arm  104 . 
     As shown, the stage  102  includes a support surface  106  and a stage actuator  108 . The stage  102  is configured to retain the substrate  103  on the support surface  106 . The stage  102  is coupled to the stage actuator  108 . The stage actuator  108  is configured to move the stage  102  in a scanning path  110  along an x-direction and a y-direction, and rotate the stage  102  about a z-axis. The stage  102  is configured to move and rotate the substrate  103  such that light projected from the optical arm  104  is incident on different portions or gratings of the substrate  103  during operation of the measurement system  101 . 
     The substrate  103  includes one or more optical devices  105  having one or more gratings  107  of optical device structures  109 . Each of the gratings  107  includes regions of optical device structures  109 . The optical device structures  109  have an orientation angle ϕ and a pitch P. The pitch P is defined as a distance between adjacent points, such as adjacent first edges or adjacent center of masses of the optical device structures  109 . The pitch P and the orientation angle ϕ of the optical device structures  109  for a first grating  111  can be different than the pitch P and the orientation angle ϕ of the optical device structures  109  for a second grating  113  of the one or more gratings  107 . In addition, there can be local pitch P′ variations and local orientation angle ϕ′ variations of the optical devices structures  109  due to local warping or other deformation of the substrate  103 . The measurement system  101  can be utilized to measure the pitch P and the orientation angle ϕ of the optical device structures  109  for each of the gratings  107  of each of the optical devices  105 . The substrate  103  can be a single crystal wafer of any size, such as having a radius from about 150 mm to about 450 mm. 
     The optical arm  104 , the detector arm  112 , and the stage  102  are coupled to a controller  130 . The controller  130  facilitates the control and automation of the method for measuring the pitch P and the orientation angle ϕ of optical device structures  109  described herein. The controller may include a central processing unit (CPU) (not shown), memory (not shown), and support circuits (or I/O) (not shown). The CPU may be one of any form of computer processors that are used in industrial settings for controlling various processes and hardware (e.g., motors and other hardware) and monitor the processes (e.g., transfer device position and scan time). The memory (not shown) is connected to the CPU, and may be a readily available memory, such as random access memory (RAM). Software instructions and data can be coded and stored within the memory for instructing the CPU. The support circuits (not shown) are also connected to the CPU for supporting the processor in a conventional manner. The support circuits may include conventional cache, power supplies, clock circuits, input/output circuitry, subsystems, and the like. A program (or computer instructions) readable by the controller determines which tasks are performable on the substrate  103 . The program may be software readable by the controller and may include code to monitor and control, for example, substrate position and optical arm position. 
       FIGS. 2A-2F  are schematic views of configurations  200 A- 200 F of a measurement system  101 . In embodiments where the substrate  103  is non-opaque, which can be combined with other embodiments described herein, reflections and diffractions of light from multiple surfaces of the substrate  103  will cause interference on the optical arm  104  and the detector arm  112 . The interference is non-symmetric i.e., the image of the light path diffracted or reflected off the substrate  103  is not circular or substantially circular on a first detector  208  and a plurality of second detectors  218 , as further described below, of the optical arm  104  and the detector arm  112 . To address this, the measurement system  101  utilizes prisms, such as a dove prism to rotate the image. Multiple images are combined to generate a symmetric beam i.e., a circular beam. The centroid of the beam is determined with image processing algorithms. The image processing algorithms may be at least partially executed by a controller  130 . 
       FIG. 2A  is a schematic view of a configuration  200 A of a measurement system  101 . The configuration  200 A includes a portion  202  of a section line  201  (shown in  FIG. 1 ) across a substrate  103 . The substrate  103  has one or more gratings  107  of optical device structures  109 . As shown, an optical arm  104  includes a light source  204 , a first beam splitter  206 , a second beam splitter  212 , a first detector  208 , a second detector  218 , a first dove prism  214 , a first lens  210 , and a second lens  216 . The optical arm  104  is in communication with the controller  130 . The optical arm  104  can include an arm actuator  203 . The arm actuator  203  is configured to rotate the optical arm  104  about the z-axis and scan the optical arm in a z-direction. The optical arm  104  can be fixed while the measurement is performed. 
     The first beam splitter  206  is positioned in a first light path  220  adjacent to the light source  204 . In one embodiment, which can be combined with other embodiments described herein, the first light path  220  has a circular or substantially circular cross-section. The light beams described herein can be laser beams. The light source  204  is operable to project light at a beam angle θ (shown in  FIG. 1 ) along the first light path  220  to the substrate  103 , according to one embodiment. The light source  204  is operable to project a collimated beam of light. The first light path  220  is incident on the substrate  103  and diffracts a second light path  222  back to the optical arm  104 . The optical arm  104  delivers the first light path  220  such that the light can be diffracted by the substrate  103  and form the second light path  222 . In one embodiment, which can be combined with other embodiments described herein, the second light path  222  is a first order diffraction. The second light path  222  is split by the second beam splitter  212  into the second light path  222 A and the second light path  222 B. 
     The first beam splitter  206  is operable to deflect the second light path  222 A diffracted by the substrate  103  to the first detector  208 . The first lens  210  is positioned between the first beam splitter  206  and the first detector  208 . The first lens  210  is configured to focus the second light path  222 A onto the first detector  208 . A first image of the second light path  222 A is projected on the first detector  208 . The first detector  208  is any optical apparatus used in the art to detect light, such as a charge-coupled device (CCD) array or an active-pixel sensor (CMOS array). 
     The second beam splitter  212  is operable to deflect the second light path  222 B diffracted by the substrate  103  to the second detector  218 . The second lens  216  is positioned between the second beam splitter  212  and the second detector  218 . The second lens  216  is configured to focus the second light path  222 B onto the second detector  218 . Prior to contacting the second detector  218 , the second light path  222 B passes through the first dove prism  214 . The first dove prism  214  rotates the image of the second light path  222 B on the second detector  218 . Therefore, a second image of the second light path  222 B is projected on the second detector  218 . The second image is at a rotation angle different than the first image. The first dove prism  214  is operable to rotate the second image at any angle. In one embodiment, which can be combined with other embodiments described herein, the second image is rotated 180° from the first image. The second detector  218  is any optical apparatus used in the art to detect light, such as a CCD array or a CMOS array. 
       FIG. 2B  is a schematic view of a configuration  200 B of a measurement system  101 . The configuration  200 B includes a portion  202  of a section line  201  (shown in  FIG. 1 ) across a substrate  103 . The substrate  103  has one or more gratings  107  of optical device structures  109 . As shown, the optical arm  104  includes a light source  204 , a first beam splitter  206 , a second beam splitter  212   a , . . .  212   n  (collectively referred to as the “plurality of second beam splitters  212 ”), a first detector  208 , a second detector  218   a , . . .  128   n  (collectively referred to as the “plurality of second detectors  218 ”), a first dove prism  214   a , . . .  214   n  (collectively referred to as the “plurality of first dove prisms  214 ”), a first lens  210 , and a second lens  216   a , . . .  216   n  (collectively referred to as the “plurality of second lenses  216 ”). The optical arm  104  is in communication with the controller  130 . The optical arm  104  can include an arm actuator  203 . The arm actuator  203  is configured to rotate the optical arm  104  about the z-axis and scan the optical arm in a z-direction. The optical arm  104  can be fixed while the measurement is performed. 
     The first beam splitter  206  is positioned in a first light path  220  adjacent to the light source  204 . The light source  204  is operable to project light at a beam angle θ (shown in  FIG. 1 ) along the first light path  220  to the substrate  103 , according to one embodiment. The first light path  220  is incident on the substrate  103  and projects a second light path  222  to the optical arm  104 . The optical arm  104  delivers the first light path  220  such that the light can be diffracted by the substrate  103  and form the second light path  222 . The second light path  222  is split by the plurality of second beam splitters  212  into the second light paths  222   a  . . .  222   n  (collectively referred to as the “plurality of second light paths  222 ”). 
     The first beam splitter  206  is operable to deflect the second light path  222 A diffracted by the substrate  103  to the first detector  208 . The first lens  210  is positioned between the first beam splitter  206  and the first detector  208 . The first lens  210  is configured to focus the second light path  222 A onto the first detector  208 . A first image of the second light path  222 A is projected on the first detector  208 . 
     The plurality of second beam splitters  212  are operable to deflect the plurality of second light paths  222 B, . . .  222   n  diffracted by the substrate  103  to the plurality of second detectors  218 . The plurality of second lenses  216  are positioned between the plurality of second beam splitters  212  and the plurality of second detectors  218 . The plurality of second lenses  216  are configured to focus the second light paths  222 B, . . .  212   n  onto the plurality of second detectors  218 . Prior to contacting the plurality of second detectors  218 , the second light paths  222 B, . . .  222   n  pass through the plurality of first dove prisms  214 . The plurality of first dove prisms  214  rotate the image of each of the second light paths  222 B, . . .  222   n  on the plurality of second detectors  218 . Therefore, a second image from of each of the second light paths  222 B, . . .  222   n  is diffracted on the plurality of second detectors  218 . The plurality of second images are at a rotation angle different than the first image. In one embodiment, which can be combined with other embodiments described herein, two second images are rotated 120° from the first image, such that the second images are at 120° and 240°. In another embodiment, which can be combined with other embodiments described herein, each second image of the plurality of second images is rotated 360°/n from the first image, where n is the number of images detected by the plurality of second detectors  218 . 
       FIG. 2C  is a schematic view of a configuration  200 C of a measurement system  101 . The configuration  200 C includes a portion  202  of a section line  201  across a substrate  103 . The substrate  103  has one or more gratings  107  of optical device structures  109 . As shown, the optical arm  104  includes a light source  204 , a first beam splitter  206 , a second beam splitter  212   a , . . .  212   n  (collectively referred to as the “plurality of second beam splitters  212 ”), a first detector  208 , a second detector  218   a , . . .  128   n  (collectively referred to as the “plurality of second detectors  218 ”), a first dove prism  214   a , . . .  214   n  (collectively referred to as the “plurality of first dove prisms  214 ”), a second dove prism  224 , a first lens  210 , and a second lens  216   a , . . .  216   n  (collectively referred to as the “plurality of second lenses  216 ”). The optical arm  104  is coupled to the controller  130 . The optical arm  104  can include an arm actuator  203 , and the arm actuator  203  is configured to rotate the optical arm  104  about the z-axis and scan the optical arm in a z-direction. The optical arm  104  can be fixed while the measurement is performed. 
     The first beam splitter  206  is positioned in a first light path  220  adjacent to the light source  204 . The light source  204  is operable to project light at a beam angle θ (shown in  FIG. 1 ) along the first light path  220  to the substrate  103 , according to one embodiment. The first light path  220  is incident on the substrate  103  and diffracts a second light path  222  to the optical arm  104 . The optical arm  104  delivers the first light path  220  such that the light can be diffracted by the substrate  103  and form the second light path  222 . The second light path  222  is split by the second beam splitter  212  i.e., into the plurality of second light paths  222 A,  222 B, . . .  222   n.    
     The first beam splitter  206  is operable to deflect the second light path  222 A diffracted by the substrate  103  to the first detector  208 . The first lens  210  is positioned between the first beam splitter  206  and the first detector  208 . The first lens  210  is configured to focus the second light path  222 A onto the first detector  208 . Prior to contacting the first detector  208 , the second light paths  222 A passes through the second dove prism  224 . The second dove prism  224  rotates the image of the second light path  222 A on the first detector  208 . Therefore, a first image of the second light path  222 A is projected on the first detector  208 . The first image of the second light path  22 A may be rotated to any angle by the second dove prism  224 . 
     The plurality of second beam splitters  212  are operable to deflect the plurality of second light paths  222 B, . . .  222   n  diffracted by the substrate  103  to the plurality of second detectors  218 . The plurality of second lenses  216  are positioned between the plurality of second beam splitters  212  and the plurality of second detectors  218 . The plurality of second lenses  216  are configured to focus the second light paths  222 B, . . .  212   n  onto the plurality of second detectors  218 . Prior to contacting the plurality of second detectors  218 , the second light paths  222 B, . . .  222   n  pass through the plurality of first dove prisms  214 . The plurality of first dove prisms  214  rotate the image of each of the second light paths  222 B, . . .  222   n  on the plurality of second detectors  218 . Therefore, a second image of each of the second light paths  222 B, . . .  222   n  is projected on the plurality of second detectors  218 . The plurality of second images are at a rotation angle different than the first image. In one embodiment, which can be combined with other embodiments described herein, two second images are rotated 120° from the first image, such that the second images are at 120° and 240°. In another embodiment, which can be combined with other embodiments described herein, each second image of the plurality of second images is rotated 360°/n from the first image, where n is the number of images detected by the second detector  218 . 
       FIG. 2D  is a schematic view of a configuration  200 D of a measurement system  101 . The configuration  200 D includes a portion  202  of a section line  201  across a substrate  103 . The substrate  103  has one or more gratings  107  of optical device structures  109 . As shown, an optical arm  104  includes a light source  204 , a first beam splitter  206 , a first detector  208 , a first dove prism  214 , and a first lens  210 . The optical arm  104  is coupled to the controller  130 . The optical arm  104  can include an arm actuator  203 , and the arm actuator  203  is configured to rotate the optical arm  104  about the z-axis and scan the optical arm in a z-direction. The optical arm  104  can be fixed while the measurement is performed. 
     The first beam splitter  206  is positioned in a first light path  220  adjacent to the light source  204 . In one embodiment, which can be combined with other embodiments described herein, the first light path  220  has a circular or substantially circular cross-section. The light source  204  is operable to project light at a beam angle θ (shown in  FIG. 1 ) along the first light path  220  to the substrate  103 , according to one embodiment. The first light path  220  is incident on the substrate  103  and diffracts a second light path  222  to the optical arm  104 . The optical arm  104  delivers the first light path  220  such that the light can be diffracted by the substrate  103  and form the second light path  222 . In one embodiment, which can be combined with other embodiments described herein, the second light path  222  is a first order diffraction. 
     The first beam splitter  206  is operable to deflect the second light path  222  diffracted by the substrate  103  to the first detector  208 . The first lens  210  is positioned between the first beam splitter  206  and the first detector  208 . The first lens  210  is configured to focus the second light path  222  onto the first detector  208 . A first image of the second light path  222 A is projected on the first detector  208 . Prior to contacting the first beam splitter  206 , the second light path  222  passes through the first dove prism  214 . The first dove prism  214  rotates the image of the second light path  222  on the first detector  208 . Therefore, a first image of the second light path  222  is diffracted on the first detector  208 . In one embodiment, which can be combined with other embodiments described herein, the first dove prism  214  is coupled to a dove prism actuator  226 . The dove prism actuator is operable to rotate the first dove prism  214  such that multiple images, such as a first image and a plurality of second images of the second light path  222  can be projected onto the first detector  208 . In one embodiment, which can be combined with other embodiments described herein, the plurality of second images are 90° from the first image, such that each of the second images are at 90°, 180°, and 270°. In another embodiment, which can be combined with other embodiments described herein, each second image of the plurality of second images is rotated 360°/n from the first image, where n is the number of images detected by the second detector  218 . 
       FIG. 2E  is a schematic view of a configuration  200 E of a measurement system  101 . The configuration  200 E includes a portion  202  of a section line  201  across a substrate  103 . The substrate  103  has one or more gratings  107  of optical device structures  109 . As shown, an optical arm  104  includes a light source  204 , a first beam splitter  206 , a second beam splitter  212 , a first detector  208 , a first dove prism  214 , a first mirror  228 , a second mirror  230 , and a first lens  210 . The optical arm  104  is coupled to the controller  130 . The optical arm  104  can include an arm actuator  203 , and the arm actuator  203  is configured to rotate the optical arm  104  about the z-axis and scan the optical arm in a z-direction. The optical arm  104  can be fixed while the measurement is performed. 
     The first beam splitter  206  is positioned in a first light path  220  adjacent to the light source  204 . In one embodiment, which can be combined with other embodiments described herein, the first light path  220  has a circular or substantially circular cross-section. The light beams described herein can be laser beams. The light source  204  is operable to project light at a beam angle θ (shown in  FIG. 1 ) along the first light path  220  to the substrate  103 , according to one embodiment. The first light path  220  is incident on the substrate  103  and diffracts a second light path  222  to the optical arm  104 . The optical arm  104  delivers the first light path  220  such that the light can be diffracted by the substrate  103  and form the second light path  222 . In one embodiment, which can be combined with other embodiments described herein, the second light path  222  is a first order diffraction. The second light path  222  is split by the second beam splitter  212  i.e., into the second light path  222 A and the second light path  222 B. 
     The first beam splitter  206  is operable to deflect the second light path  222 A diffracted by the substrate  103  to the first detector  208 . The first lens  210  is positioned between the first beam splitter  206  and the first detector  208 . The first lens  210  is configured to focus the second light path  222 A onto the first detector  208 . A first image of the second light path  222 A is projected on the first detector  208 . 
     The second beam splitter  212  is operable to deflect the second light path  222 B diffracted by the substrate  103  to the first mirror  228 . The second light path  222 B reflects off the first mirror  228  to the second mirror  230 . The second light path  222 B diffracts to the first lens  210 . The first lens  210  is configured to focus the second light path  222 B onto the first detector  208 . Prior to contacting the first mirror  228 , the second light path  222 B passes through the first dove prism  214 . The first dove prism  214  rotates the image of the second light path  222 B on the first detector  208 . Therefore, a second image of the second light path  222 B is projected on the first detector  208  such that the first detector  208  detects the first image and the second image. In one embodiment, which can be combined with other embodiments described herein, the second image is rotated 180° from the first image. 
       FIG. 2F  is a schematic view of a configuration  200 F of a measurement system  101 . The configuration  200 F includes a portion  202  of a section line  201  across a substrate  103 . The substrate  103  has one or more gratings  107  of optical device structures  109 . 
     As shown, an optical arm  104  includes a light source  204 , a first beam splitter  206 , a second beam splitter  212 , a first detector  208 , a second detector  218 , a first dove prism  214 , a first lens  210 , and a second lens  216 . The optical arm  104  is coupled to the controller  130 . The optical arm  104  can include an arm actuator  203 , and the arm actuator  203  is configured to rotate the optical arm  104  about the z-axis and scan the optical arm in a z-direction. The optical arm  104  can be fixed while the measurement is performed. The configuration  200 F illustrates the optical arm  104  of the configuration  200 A of the measurement system  101 . Although the optical arm  104  of the configuration  200 A is shown in  FIG. 2F , any of the optical arms  104  of the configurations  200 A- 200 E can be included in the configuration  200 F. 
     The configuration  200 F further includes a detector arm  112 . The detector arm  112  is operable to measure a reflection light path  234 . The reflection light path  234  is a direct reflection of the first light path  220 . The first light path  220  is incident on the substrate  103  and diffracts the reflection light path  234  to the detector arm  112 . 
     In one embodiment, which can be combined with other embodiment described herein, the detector arm  112  includes a second beam splitter  212 , a first detector  208 , a second detector  218 , a first dove prism  214 , a first lens  210 , and a second lens  216 . The detector arm  112  can include a detector arm actuator  205 , and the detector arm actuator  205  is configured to rotate the detector arm  112  about the z-axis and scan the optical arm in a z-direction. The detector arm  112  can be fixed while the measurement is performed. The detector arm  112  can have similar configurations to the optical arms  104  of the configurations  200 A- 200 E. 
     The reflection light path  234  is split by the second beam splitter  212  i.e., into the reflection light path  234 A and the reflection light path  234 B. The reflection light path  234 A diffracted by the substrate  103  is diffracted to the first detector  208 . The first lens  210  is positioned between the first beam splitter  206  and the first detector  208 . The first lens  210  is configured to focus the reflection light path  234 A onto the first detector  208 . A first image of the reflection light path  234 A is projected on the first detector  208 . The first detector  208  is any optical apparatus used in the art to detect light, such as a CCD array or a CMOS array. 
     The second beam splitter  212  is operable to deflect the reflection light path  234 B diffracted by the substrate  103  to the second detector  218 . The second lens  216  is positioned between the second beam splitter  212  and the second detector  218 . The second lens  216  is configured to focus the reflection light path  234 B onto the second detector  218 . Prior to contacting the second detector  218 , the reflection light path  234 B passes through the first dove prism  214 . The first dove prism  214  rotates the image of the reflection light path  234 B on the second detector  218 . Therefore, a second image of the reflection light path  234 B is projected on the second detector  218 . The second detector  218  is any optical apparatus used in the art to detect light, such as a CCD array or a CMOS array. 
       FIG. 3A  illustrates a detector  302  as a position sensitive detector  301 A, i.e., a lateral sensor, according to one embodiment. The detector  302  can be any detector such as the first detector  208  and the second detector  218  of the configurations  200 A- 200 F.  FIG. 3B  illustrates the detector  302  as a quadrant sensor  301 B, according to one embodiment.  FIG. 3C  illustrates the detector  302  as an image sensor array  301 C, such as a CCD array or a CMOS array, according to some embodiments. 
       FIG. 3D  is a schematic view of a dove prism  304 , such as the first dove prism  214  and the second dove prism  224 . A light path  306  such as the plurality of second light paths  222 A,  222 B, . . .  222   n  and the reflection light path  234 B can pass through the dove prism  304 . The light path  306  travels through the dove prism  304  such that the light path  306  is rotated as desired. 
       FIG. 3E  is a schematic view of a mirror assembly  308 . In one embodiment, which can be combined with other embodiments described herein, the mirror assembly  308  can replace the dove prism  304 . The mirror assembly  308  includes a plurality of mirrors  310 . The light path  306  travels through the mirror assembly  308  such that the light path  306  is rotated by reflecting between the plurality of mirrors  310 . 
       FIG. 4  is a flow diagram of a method  400  for measuring a pitch P of optical device structures  109  and an orientation angle ϕ of optical device structures  109 . To facilitate explanation, the method  400  will be described with reference to the measurement system  101  of  FIG. 1  and a first configuration  200 A of the measurement system  101  shown in  FIG. 2A . A controller  130  is operable to facilitate the operations of the method  400 . 
     At operation  401 , a fixed beam angle ϑ 0  and an initial orientation angle ϕ initial  of a plurality of optical device structures  109  are determined. The fixed beam angle ϑ 0  is the initial angle of light beams to be projected to a substrate  103 . The initial orientation angle ϕ initial  is the desired orientation angle of each of the plurality of optical device structures  109 . In one embodiment, which can be combined with other embodiments described herein, the fixed beam angle ϑ 0  and the initial orientation angle ϕ initial  are determined by a predetermined specification of the optical device structures  109  for each of the gratings  107  of the optical devices  105  on the substrate  103  prior to fabricating the optical devices  105 . In another embodiment, which can be combined with other embodiments described herein, the fixed beam angle ϑ 0  and the initial orientation angle ϕ initial  are determined by estimation. 
     At operation  402 , the stage  102  is rotated about the z-axis to positon the initial orientation angle ϕ initial  of the optical device structures  109 , of the first zone  115 , perpendicular with light beams to be projected to the first zone  115  of the substrate  103 . The first zone  115  corresponds to the first region of the optical device structures  109  to be measured. At operation  403 , the light beams from an optical arm  104  having a wavelength (λ laser ) are projected to the substrate  103  at the fixed beam angle ϑ 0 . 
     At operation  404 , a reflected beam angle ϑ reflected  of first order mode beams (R_1 st ) reflected by the optical device structures  109  is determined. In one embodiment, which can be combined with other embodiments described herein, the method  400  utilizes the configuration  200 A of the optical arm  104  of the measurement system  101 . A first image of a second light path  222 A is detected by a first detector  208 . A second image of a second light path  222 B is detected by a second detector  218 . The second image is rotated by a first dove prism  214  such that the second image is rotated 180° from the first image. 
     In another embodiment, which can be combined with other embodiments described herein, the method  400  utilizes the configuration  200 B of the optical arm  104  of the measurement system  101 . A first image of a second light path  222 A is detected by a first detector  208 . A plurality of second images of a second light path  222 B, . . .  222   n  is detected by a plurality of second detectors  218 . Each second image of the plurality of second images is rotated 360°/n from the first image, where n is the number of images detected by the second detector  218 . 
     In another embodiment, which can be combined with other embodiments described herein, the method  400  utilizes the configuration  200 C of the optical arm  104  of the measurement system  101 . A first image of a second light path  222 A is detected by a first detector  208 . The first image is rotated by a second dove prism  224 . A plurality of second images of a second light path  222 B, . . .  222   n  are detected by a plurality of second detectors  218 . Each second image of the plurality of second images is rotated 360°/n from the first image, where n is the number of images detected by the second detector  218 . 
     In another embodiment, which can be combined with other embodiments described herein, the method  400  utilizes the configuration  200 D of the optical arm  104  of the measurement system  101 . A first dove prism  214  includes a dove prism actuator  226  that rotates the first dove prism  214 . Multiple images, such as a first image and a plurality of second images are detected by a first detector  208 . Each second image of the plurality of second images is rotated 360°/n from the first image, where n is the number of images detected by the first detector  208 . 
     In another embodiment, which can be combined with other embodiments described herein, the method  400  utilizes the configuration  200 E of the optical arm  104  of the measurement system  101 . A first image of a second light path  222 A is detected by a first detector  208 . A second image of a second light path  222 B is detected by the second detector  218 . The second image is rotated by a first dove prism  214  and reflected by a first mirror  228  and a second mirror  230  such that the second image is rotated 180° from the first image. 
     In another embodiment, which can be combined with other embodiments described herein, the method  400  utilizes the configuration  200 F of the optical arm  104  and the detector arm  112  of the measurement system  101 . The optical arm  104  can be any of the configurations  200 A- 200 E. A first detector  208  of the detector arm  112  can detect a first image of a reflection light path  234 A. A second image of a reflection light path  234 B is detected by the second detector  218 . The second image is rotated by a first dove prism  214  and reflected by a first mirror  228  and a second mirror  230  such that the second image is rotated 180° from the first image. 
     In one embodiment, which can be combined with other embodiments described herein, at least the first image and the second image are combined to generate a symmetric beam profile. In another embodiment, which can be combined with other embodiments described herein, a plurality of second images are combined with the first image to generate a symmetric beam profile. An image processing algorithm (via an image processing software) is applied to the symmetric beam profile to calculate a center of the symmetric beam profile. The image processing algorithm is at least partially executed by the controller  130 . 
     Utilizing the measurement system  101  described herein allows for the combination of multiple images to determine the center of the symmetric beam profile. When non-opaque substrates  103  are utilized, interference due to multi-surface reflection may occur, which will alter the intensity profile projected to the detector. The measurement system  101  allows for the projection of the second images rotated at different angles to the plurality of second detectors. The rotated second images compensate for the non-symmetric interference by allowing for the center of the symmetric beam profile to be determined reliably with the additional images. By combining the second images with the first image, a center of the symmetric beam profile is obtained reliably despite the interference. 
     The reflected beam angle ϑ reflected  of the first order mode beams (R_1 st ) reflected by the optical device structures  109  is calculated based one the center of the symmetric beam profile. A final orientation angle ϕ final  corresponding to the orientation angle ϕ of the optical device structures  109  is calculated based on the center of the symmetric beam profile. 
     In one embodiment, which can be combined with other embodiments described herein, during operations  401 - 404 , the detector arm  112  having the first detector  208  and the second detector  218  measures a zero order mode beam (R_0), such as the reflection light path  234  (shown in  FIG. 2F ) reflected by the optical device structures  109  to determine an inverse reflected beam angle ϑ reflected . The inverse reflected beam angle ϑ reflected  is compared to the reflected beam angle ϑ reflected  to account for warpage of the substrate  103 . 
     At operation  405 , the pitch P is determined by the equation P=λ laser /(sin ϑ 0 +sin ϑ reflected ). At operation  406 , the stage  102  is scanned along a scanning path  110  and operations  401 - 405  are repeated for subsequent zones of the one or more gratings  107  of the one or more optical devices  105 . 
     In summation, devices and methods of measuring a pitch P of optical device structures and an orientation angle ϕ of the optical device structures are provided herein. The devices and method provide for a more accurate reading of the pitch P and the orientation angle ϕ by combining a first image and a second image in a measurement system. The combination of the first image and the second image increases the accuracy and repeatability of the measurements by compensating for the non-symmetric interference by allowing for the center of the symmetric beam profile to be determined reliably with the additional images. The devices and methods described herein account for the interference when measuring non-opaque substrates. 
     While the foregoing is directed to embodiments of the present disclosure, other and further embodiments of the disclosure may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow.