Patent Publication Number: US-2022212314-A1

Title: Pitch layer pad for smoothing optical surfaces

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claim priority to U.S. Provisional Application No. 62/834,147, titled “PITCH LAYER PAD FOR SMOOTHING OPTICAL SURFACES,” filed on Apr. 15, 2019. The entire disclosure of the aforementioned application is incorporated by reference as part of the disclosure of this application. 
    
    
     TECHNICAL FIELD 
     This patent document relates to high-precision optical surfaces. 
     BACKGROUND 
     Various computer controlled optical surfacing (CCOS) processes have been developed since the 1960s. CCOS processes can provide good solutions for fabrication of precise optics because of their high convergence rate using deterministic removal processes. Among various key components of the CCOS process, a polishing tool is a component that provides physical contact with the optics and removes material from it. Polishing tool development for aspheric or freeform optics production has been a complex problem. 
     SUMMARY 
     Devices, systems and methods related to producing high-precision optical components and surfaces are disclosed. 
     In one example aspect, an apparatus for polishing an optical component having an aspheric or freeform surface is disclosed that includes a solid back plate, a container coupled to the solid plate, and a layer of viscoelastic polymer attached or otherwise coupled to the container. The container encloses a non-Newtonian material that exhibits a solid-like and a fluid-like behavior based on a stress frequency applicable to the non-Newtonian material. The layer of viscoelastic polymer positioned to provide physical contact with the optical component for polishing the optical component. The layer of viscoelastic polymer comprises one or more segments. 
     Another aspect of the disclosed embodiments relates to a method for producing a layer of viscoelastic polymer that includes melting a viscoelastic polymer into a liquid form, pouring the viscoelastic polymer between multiple substrates, and solidifying the viscoelastic polymer to obtain one or more viscoelastic polymer layers. The multiple substrates are separated by a plurality of spacers. 
     The above and other aspects and features of the disclosed technology are described in greater detail in the drawings, the detailed description and the claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a diagram illustrating a side view of a part of an example rigid polishing tool. 
         FIG. 2  is a diagram illustrating a side view of a part of an example compliant polishing tool. 
         FIG. 3  is a diagram illustrating a side view of a part of an example rigid-conformal polishing tool. 
         FIG. 4  illustrates smoothing of a local bump on a component using a non-Newtonian smoothing tool. 
         FIG. 5  a set of operations for producing a pitch layer pad in accordance with one or more example embodiments. 
         FIG. 6  illustrate an example segmented pattern of a pitch layer pad in accordance with one or more example embodiments. 
         FIG. 7  illustrate another example segmented pattern of a pitch layer pad in accordance with one or more example embodiments. 
         FIG. 8  illustrate yet another example segmented pattern of a pitch layer pad in accordance with one or more example embodiments. 
         FIG. 9  illustrates smoothing of a local bump on a workpiece using a pitch layer pad in accordance with one or more example embodiments. 
         FIG. 10  illustrates a configuration for a polishing tool in accordance with one or more example embodiments. 
         FIG. 11  illustrates a polishing tool and multiple segments of a polishing pad attached thereto in accordance with one or more example embodiments. 
     
    
    
     DETAILED DESCRIPTION 
     Computer-controlled optical surfacing (CCOS) processes are widely used for fabrication of precise optics. Many CCOS processes are based on three main components: (1) a numerically controlled polishing machine, (2) process control intelligence to control the surfacing process, and (3) a polishing tool to polish the optics. 
     One of the key components for a CCOS process is the polishing tools, which provide physical contact with the workpiece and remove material from it. A tool influence function (TIF) is the shape of the wear function created by the polishing tool motion (e.g. spin or orbital motion) on the workpiece. In general, a dwell time map optimization approach can be used to achieve a given target removal map. Optimization intelligence (e.g., software programs) uses TIFs as building blocks to achieve the target removal map by spatially distributing and accumulating them. Having stable and deterministic TIFs is important in achieving successful CCOS processes. 
     The TIF is a function of tool properties, such as pressure distribution under the tool, polishing material at the contacting interface, contact area shape, tool motion, and so forth. For instance, developing a tool with a deterministic TIF for aspheric (or freeform) optics fabrication becomes a complex problem because local surface shape (e.g. curvature) of an aspheric surface varies as a function of position on a workpiece. Some flexibility in the tool is required to maintain intimate contact with the workpiece surface. However, rigidity of the tool is also desired to get natural smoothing effects, which removes mid-to-high spatial frequency errors on the workpiece. Thus, a well-behaved tool development is a balancing problem between flexibility and rigidity. 
     The smoothing effect becomes more important for large workpiece fabrications to correct mid-to-high spatial frequency errors smaller than the tool size. Based on the deterministic TIFs of CCOS processes, large errors (e.g., low spatial frequency surface errors compared to the tool size) can be corrected by increasing the dwell time on the high error areas. On the other hand, smaller tools require higher tool positioning accuracy to avoid residual tool marks, which is another source of mid-spatial frequency errors. Also, the use of small tools increases the total fabrication time. 
     Correcting these mid-to-high spatial frequency errors on optical surfaces is very important in some applications, including for the next generation of extremely large telescopes such as the Giant Magellan Telescope and for nuclear fusion energy plants using high power lasers (e.g. Laser Inertial Fusion Engine). Because the mid-to-high-spatial frequency errors are directly related to the sharpness of the point spread function (e.g. Airy disk radius) or the scattering characteristic of high-power laser application optics, the overall performance of those systems may be degraded due to those errors. 
     The most common polishing tools are rigid tools.  FIG. 1  is a schematic diagram illustrating an example side view of a part of a rigid polishing tool  100 . As shown in  FIG. 1 , the rigid polishing tool  100  has a solid back plate  101  and a polishing interface  103 . The back plate can, for example, be an aluminum back plate of a specific thickness. The polishing interface  103  includes a polishing material, such as pitch (a viscoelastic polymer) or polyurethane. The smoothing effects by a rigid tool can be understood in a simple way. If the tool does not fit to the surface irregularity under the tool (that is, infinite rigidity), and maintains its shape, the tool only rubs the high points on the surface. As the tool runs on the workpiece, it wears down the highs, and eventually the surface can be smoothed out. The spatial frequency of the final surface will be directly related to the tool size of the rigid tool. 
     A rigid polishing tool is suitable for spherical surface polishing, which has the same curvature everywhere on the optics (also referred to as the workpiece). However, rigid polishing tools have an intrinsic limitation in fabricating aspheric or freeform workpieces because they cannot follow the local curvature or shape changes as the tool moves on the workpiece. 
     Recent developments have introduced various tool structures to fit to the aspheric or freeform workpiece surfaces under fabrication.  FIG. 2  is a schematic diagram illustrating an example side view of a part of a compliant polishing tool  200 . The compliant tool  200  includes a solid back plate  201  such as an aluminum back plate. The compliant tool  200  utilizes compliant materials  205 , such as a liquid or air, that are often sealed in a container  207 . The compliant polishing tool  200  also often includes a polishing pad (e.g., a polyurethane pad) as the polishing interface  203 . A compliant polishing tool can conform to virtually any type of workpiece including aspheric and freeform surfaces. However, the compliant polishing tool has poor smoothing efficiency; its smoothing performance is limited by the polishing interface because the compliant material cannot exert much local pressure to the workpiece to remove surface bumps. 
     A rigid conformal (RC) polishing tool (also referred to as an RC lap) using a visco-elastic non-Newtonian fluid has been developed to take advantage from both rigid and compliant tools in two different time scales using a visco-elastic non-Newtonian fluid.  FIG. 3  is a schematic diagram illustrating an example side view of a part of a rigid-conformal polishing tool  300 . The rigid-conformal tool  300  includes a solid back plate  301  such as an aluminum back plate. The rigid-conformal polishing tool  300  includes a non-Newtonian material  305  enclosed in a container  307  and a polishing pad (e.g., polyurethane) as the polishing interface  303 . Non-Newtonian materials can resist deformation in a solid-like and/or a fluid-like manner depending on the applied frequencies of stress. For example, a visco-elastic non-Newtonian fluid can act like a solid for a short time period under stress. If stress is applied over a long time period, it flows like a liquid. The applied stress frequency can be both fast and slow at the same time, because there is the frequency associated with the spinning of the pad (high frequency) and a frequency of the pad as it is moving along the surface (low frequency). The non-Newtonian fluid behaves differently at the local point (where the non-Newtonian fluid is acting as a solid) than it does as the pad is moving slowly across the surface (where the non-Newtonian fluid is acting as a fluid). Both behaviors can happen at the same time, which allows the polishing head to grind down a bump while conforming to the overall surface figure of the surface. The use of the non-Newtonian materials allows the rigid-conformal polishing tool to conform to the aspheric or freeform surface shapes while maintaining a rigid behavior to preserve the natural smoothing abilities. 
     The flow characteristic of the RC lap depends on the frequency of applied stress. Because the tool motion (e.g. orbital motion) is usually fast (e.g. 60 RPM) relative to the local features (e.g. bumps or ripples) under the motion, the RC lap acts like a rigid tool with respect to that time scale. If the tool is orbiting at 60 RPM on a bumpy area, the tool quickly smoothes out the bumps with high local pressures on the bump peaks. However, the tool fits the overall local curvature changes on the workpiece since the RC lap moves slowly on the workpiece (e.g. ˜1 rpm workpiece rotation) along the tool path. 
     By the way of example, and not by limitation, in order to describe the smoothing effects by semi-flexible tools, the Bridging model can be used. As the tool moves on the workpiece, it continuously bends by different amounts to fit the local curvature, resulting in continuous changes in the pressure distribution under the tool. If a semi-flexible tool meets mid-spatial frequency ripples, the tool contacts the ridges of highs in the surface with higher pressure, and begins to smooth them out. The lap can be considered as to form a bridge across the ridges known as the bridging effect. For a semi-flexible tool, the strains induced from the thin plate bending influence the polishing pressure distribution. Kirchhoffs thin plate equations can be modified to include the effect of transverse shear strain. For the one-dimensional case, the polishing pressure distribution p(x) due to the sinusoidal error error(x) on the surface can be derived based on the theory of elasticity as: 
     
       
         
           
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     
                       error 
                       ⁡ 
                       
                         ( 
                         x 
                         ) 
                       
                     
                     = 
                     
                       PV 
                       ⁡ 
                       
                         ( 
                         
                           1 
                           - 
                           
                             sin 
                             ⁡ 
                             
                               ( 
                               
                                 2 
                                 ⁢ 
                                 
                                   π 
                                   · 
                                   ξ 
                                   · 
                                   x 
                                 
                               
                               ) 
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     1 
                     ) 
                   
                 
               
             
             
               
                 
                   
                     P 
                     ⁡ 
                     
                       ( 
                       x 
                       ) 
                     
                   
                   = 
                   
                     
                       P 
                       nominal 
                     
                     + 
                     
                       
                         error 
                         ⁡ 
                         
                           ( 
                           x 
                           ) 
                         
                       
                       
                         
                           1 
                           
                             
                               D 
                               plate 
                             
                             · 
                             
                               
                                 ( 
                                 
                                   2 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   π 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   ξ 
                                 
                                 ) 
                               
                               4 
                             
                           
                         
                         + 
                         
                           1 
                           
                             
                               D 
                               s_plate 
                             
                             · 
                             
                               
                                 ( 
                                 
                                   2 
                                   ⁢ 
                                   πξ 
                                 
                                 ) 
                               
                               2 
                             
                           
                         
                         + 
                         
                           1 
                           
                             K 
                             total 
                           
                         
                       
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     2 
                     ) 
                   
                 
               
             
           
         
       
     
     PV is the peak-to-valley magnitude of the sinusoidal error, ξ is the spatial frequency of the surface error, P nominal  is the nominal pressure under the tool, D plate  is the flexural rigidity of the plate, D s_plate  is the transverse shear stiffness of the plate, and K total  is the compressive stiffness of the whole tool including elastic material (e.g. pitch) and polishing interface material (e.g. polyurethane pad). The flexural rigidity and transverse shear stiffness of the flexible thin plate are defined as: 
         D   plate   =D   plate   ·t   plate   3 /12(1− v   plate   2 )  Eq. (3)
 
         D   s_plate   =E   plate   ·t   plate /2(1− v   plate )  Eq. (4)
 
     E plate  is the Youngs modulus of the plate material, t plate  is the plate thickness, and v plate  is the Poisson&#39;s ratio of the plate. 
     Although non-Newtonian materials are able to maintain a rigid behavior, the smoothing abilities are nonetheless affected when the stress is applied over a relatively long period of time, causing the non-Newtonian materials to behave more viscously.  FIG. 4  illustrates an example of smoothing a local bump on a workpiece using a non-Newtonian smoothing tool. In this example, the non-Newtonian smoothing tool  400  includes a back plate  401 , a non-Newtonian material  405  enclosed in a container (not shown), and a polyurethane pad as the polishing interface  403 . The non-Newtonian smoothing tool  400  is pressed against a workpiece  411  to smooth out a bump  413  (ΔL=˜1 μm). The non-Newtonian material is locally deformed by the bump  413 . Because the non-Newtonian material begins to act like a solid when the applied stress is oscillating at a higher frequency (e.g., &gt;1 Hz tool motion), there is additional local polishing pressure near the bump to wear down the bump. 
     By the way of example, and not by limitation, to quantitatively describe the smoothing action of polishing tools that use visco-elastic materials, a parametric smoothing model can be used. Quantifying the smoothing effect allows improvements in efficiency for finishing large precision optics. Dynamic modulus values can be used in the parametric smoothing model for the viscoelastic tools such as pitch or RC laps. Pitch can be regarded as an extreme of visco-elastic materials. It almost acts like a solid during the tool motion time period (e.g. ˜seconds). However, for very long time periods (e.g. ˜hours), it flows to fit the surface. The dynamic modulus quantitatively describes these time-dependent characteristics. It is defined as the ratio of the stress to strain under an oscillating stress condition. 
     Two dynamic modulus values, tensile storage modulus and loss modulus, are defined as Eq. (5) and (6). The storage modulus is related to the elastic deformation, and the loss modulus is related to the time-dependent viscous behavior of a non-Newtonian fluid. 
     
       
         
           
             
               
                 
                   
                     storage 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     modulus 
                     ⁢ 
                     
                       : 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       E 
                       ′ 
                     
                   
                   = 
                   
                     
                       
                         σ 
                         0 
                       
                       
                         ɛ 
                         0 
                       
                     
                     ⁢ 
                     cos 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     δ 
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     5 
                     ) 
                   
                 
               
             
             
               
                 
                   
                     Loss 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     modulus 
                     ⁢ 
                     
                       : 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       E 
                       ″ 
                     
                   
                   = 
                   
                     
                       
                         σ 
                         0 
                       
                       
                         ɛ 
                         0 
                       
                     
                     ⁢ 
                     sin 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     δ 
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     6 
                     ) 
                   
                 
               
             
           
         
       
     
     Where the oscillating stress and strain as expressed as 
       ε=ε 0  sin( t ω)  Eq. (7)
 
       σ=σ 0  sin( t ω+δ)  Eq. (8)
 
     The ε is the time dependent strain, ε 0  is magnitude of the strain, t is time, ω is angular frequency of the oscillation, a is the time dependent stress, σ 0  is magnitude of the stress, and δ is phase lag between the stress and strain. 
     The phase lag δ is a function of the angular frequency ω for the non-Newtonian fluid. For an ideal solid, the strain and stress are oscillating in phase (e.g., δ=0°). If the material is an ideal viscous fluid, the stress is 90° out of phase (e.g., δ=90°) with the strain. A loss tangent, which is the ratio between the storage and loss modulus, is a convenient measure of the relative contribution of the solid-like and fluid-like mechanical responses. The loss factor tan δ is defined as: 
     
       
         
           
             
               
                 
                   
                     tan 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     δ 
                   
                   = 
                   
                     
                       E 
                       ″ 
                     
                     
                       E 
                       ″ 
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     9 
                     ) 
                   
                 
               
             
           
         
       
     
     The polishing pressure distribution under the visco-elastic tools were derived based on the Bridging model. Because there is no flexible thin plate in the tool, the Bridging model in Eq. (2) can be simplified as: 
         P ( x )= P   nominal   +K   total ·error( x )  Eq. (10)
 
     Because the elastic material (e.g., visco-elastic material under the tan δ&lt;&lt;1 condition) is a part of the total compressive stiffness of the tool, the κtotal can be approximated by two springs connected in series as: 
     
       
         
           
             
               
                 
                   
                     1 
                     
                       K 
                       total 
                     
                   
                   = 
                   
                     
                       1 
                       
                         K 
                         elastic 
                       
                     
                     + 
                     
                       1 
                       
                         K 
                         others 
                       
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     11 
                     ) 
                   
                 
               
             
           
         
       
     
     K elastic  is the stiffness of the elastic material and K others  is the combined stiffness of all other structures including polishing pad, polishing compound fluid, wrapping material, and so forth. By combining Eq. (10) and (11) the pressure distribution under the RC lap is expressed as: 
     
       
         
           
             
               
                 
                   
                     P 
                     ⁡ 
                     
                       ( 
                       x 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         P 
                         nominal 
                       
                       + 
                       
                         
                           K 
                           total 
                         
                         · 
                         
                           error 
                           ⁡ 
                           
                             ( 
                             x 
                             ) 
                           
                         
                       
                     
                     = 
                     
                       
                         P 
                         nomial 
                       
                       + 
                       
                         
                           1 
                           
                             
                               1 
                               
                                 K 
                                 elastic 
                               
                             
                             + 
                             
                               1 
                               
                                 K 
                                 others 
                               
                             
                           
                         
                         · 
                         
                           error 
                           ⁡ 
                           
                             ( 
                             x 
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     12 
                     ) 
                   
                 
               
             
           
         
       
     
     The stiffness of the elastic material K elastic  can be expressed in terms of the storage modulus, which defines the local pressure caused by the deformation from a bump on the workpiece. If an elastic material with storage modulus E′ has a thickness L and is compressed by a ΔL tall bump, the compressive stiffness K elastic  is: 
     
       
         
           
             
               
                 
                   
                     K 
                     elastic 
                   
                   = 
                   
                     
                       
                         σ 
                         0 
                       
                       
                         Δ 
                         ⁢ 
                         L 
                       
                     
                     = 
                     
                       
                         
                           
                             
                               ɛ 
                               0 
                             
                             · 
                             
                               
                                 E 
                                 ′ 
                               
                               / 
                               cos 
                             
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           δ 
                         
                         
                           Δ 
                           ⁢ 
                           L 
                         
                       
                       = 
                       
                         
                           
                             
                               
                                 { 
                                 
                                   Δ 
                                   ⁢ 
                                   
                                     L 
                                     / 
                                     L 
                                   
                                 
                                 } 
                               
                               · 
                               
                                 
                                   E 
                                   ′ 
                                 
                                 / 
                                 cos 
                               
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             δ 
                           
                           
                             Δ 
                             ⁢ 
                             L 
                           
                         
                         = 
                         
                           
                             E 
                             ′ 
                           
                           
                             
                               L 
                               · 
                               cos 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             δ 
                           
                         
                       
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     13 
                     ) 
                   
                 
               
             
           
         
       
     
     The applied stress angular frequency ω is determined by the spatial frequency of the surface error ξ and the speed of the tool motion V tool_motion  as: 
     
       
         
           
             
               
                 
                   ω 
                   = 
                   
                     
                       
                         2 
                         ⁢ 
                         π 
                       
                       T 
                     
                     = 
                     
                       
                         
                           2 
                           ⁢ 
                           π 
                         
                         
                           ( 
                           
                             
                               1 
                               ξ 
                             
                             ⁢ 
                             
                               V 
                               
                                 tool 
                                 motion 
                               
                             
                           
                           ) 
                         
                       
                       = 
                       
                         2 
                         ⁢ 
                         
                           π 
                           · 
                           ξ 
                           · 
                           
                             V 
                             tool_motion 
                           
                         
                       
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     14 
                     ) 
                   
                 
               
             
           
         
       
     
     T is the time interval between a position under the tool sees two adjacent peaks in the sinusoidal ripple and V tool_motion  is the speed of the tool motion. 
     The speed of the smoothing action using the pressure distribution on a given ripple can be modeled by using the pressure distribution: 
       Δ z ( x )= R   Preston   ·P ( x )· V   tool     workpice   ( x )·Δ t ( x )  Eq. (15)
 
     Δz is the integrated material removal from the workpiece surface, R Preston  is the Preston coefficient (e.g., removal rate), P is the polishing pressure, V tool_workpiece  is the relative speed between the tool and workpiece and Δt is the dwell time. For a given initial sinusoidal ripple magnitude PV ini , the additional polishing pressure P add  on the peak is: 
     
       
         
           
             
               
                 
                   
                     P 
                     add 
                   
                   = 
                   
                     
                       P 
                       - 
                       
                         P 
                         nominal 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             1 
                             
                               K 
                               elastic 
                             
                           
                           + 
                           
                             1 
                             
                               K 
                               others 
                             
                           
                         
                       
                       · 
                       
                         PV 
                         ini 
                       
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     16 
                     ) 
                   
                 
               
             
           
         
       
     
     Then, for a dwell time Δt, the decrease in the ripple magnitude ΔPV is calculated as: 
       Δ PV=PV   ini   −PV   after   =R   Preston   ·P   add   ·V   tool_workpiece   ·Δt   Eq. (17)
 
     In order to normalize ΔPV, the nominal removal depth (e.g., removal depth from the nominal pressure) is used as: 
       nominal removal depth= R   Preston   ·P   nominal   ·V   tool_workpiece   ·Δt   Eq. (18)
 
     The smoothing factor SF is defined as: 
     
       
         
           
             
               
                 
                   SF 
                   = 
                   
                     
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         PV 
                       
                       
                         nominal 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         removal 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         depth 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             P 
                             nominal 
                           
                           · 
                           
                             ( 
                             
                               
                                 1 
                                 
                                   K 
                                   elastic 
                                 
                               
                               + 
                               
                                 1 
                                 
                                   K 
                                   others 
                                 
                               
                             
                             ) 
                           
                         
                       
                       · 
                       
                         PV 
                         ini 
                       
                     
                   
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
           
         
       
     
     The definition of the smoothing factor can be expressed as a linear function in SF vs. PVini space. For instance, the smoothing efficiency (e.g., the ripple magnitude decrease per unit nominal removal depth) can be easily calculated for a given initial ripple magnitude. Because the real smoothing effect may be affected by other complex factors such as polishing pads, wrapping materials and the fluid dynamics of polishing compounds, the theoretical smoothing model can be parameterized using two parameters, C 1  and C 2 , to fit the measured data. The first parameter C 1  represents K others  and other unknown effects which may change the slope of the linear SF function. As the PVini becomes smaller and smaller the fluid dynamics of the polishing compound may begin to limit the smoothing action. This can give a limiting minimum ripple magnitude PVmin of the ripple, which means no more smoothing occurs below PVmin. This can be represented as an x-intercept C 2  in SF vs. PVini space. The resulting parametric smoothing model is: 
     
       
         
           
             
               
                 
                   
                     S 
                     ⁢ 
                     F 
                   
                   = 
                   
                     
                       1 
                       
                         
                           P 
                           nominal 
                         
                         · 
                         
                           ( 
                           
                             
                               1 
                               
                                 
                                   K 
                                   elastic 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   ω 
                                   ) 
                                 
                               
                             
                             + 
                             
                               1 
                               
                                 c 
                                 1 
                               
                             
                           
                           ) 
                         
                       
                     
                     · 
                     
                       ( 
                       
                         
                           PV 
                           
                             i 
                             ⁢ 
                             n 
                             ⁢ 
                             i 
                           
                         
                         - 
                         
                           C 
                           2 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     20 
                     ) 
                   
                 
               
             
           
         
       
     
     C 1  is the slope correction parameter and C 2  is the x-intercept parameter. Because this is a linear function, these two parameters can be easily determined in practice by performing a few smoothing runs using a given polishing tool. 
     Experimental results have shown that, in some cases, the polishing ability of rigid polishing tools can be ˜7 times more efficient than the polishing ability of rigid-conformal polishing tools. The superb polishing efficiency in rigid polishing tools is at least partially attributed to the use of pitch. Since the days of Sir Isaac Newton, opticians have relied on the viscoelastic properties of pitch to create effective polishing tools. Under load, pitch exhibits an instantaneous elastic strain, a delayed elastic strain, and creep or permanent deformation. The ability of pitch to deform, albeit slowly, keeps it in constant uniform contact with the optical surface. 
     While the rigidity of a thick block of pitch prevents it from conforming to the aspheric or freeform surface of the workpiece (such as shown in  FIG. 1 ), a thin layer of pitch provides some flexibility. For example, a layer of pitch having a thickness of 1 mm can deform slightly in a range of 10 to 20 microns. A polishing interface formed using a thin layer of pitch (also referred to as a pitch layer pad) can be applied to the non-Newtonian material (or the container thereof) to provide both reasonable conformity to the workpiece and sufficient rigidity for efficient smoothing. Using a pitch layer pad as the polishing interface allows a polishing tool to polish a surface that has an arbitrary surface profile. 
     A pitch layer pad (PLP) can be manufactured in various ways.  FIG. 5  is a flowchart representation of a method  500  for producing a pitch layer pad in accordance with one or more example embodiments of the present technology. The method  500  includes, at operation  501 , melting a pitch material into the liquid form. In some example embodiments, the pitch material can include various amounts of the following elements: residues distilled from tar, oil, or wood; rosin; beeswax or linseed oil; asphalt; flake shellac; paraffin wax; wood flour; or walnut shell flour. Commercially available pitch materials such as Gugolz or Acculap can also be used. 
     The method  500  includes, at operation  503 , pouring the melted pitch material onto a substrate. The substrate can be a solid plate or a piece of wax paper. In some embodiments, the melted pitch material can be poured between multiple substrates separated by spacers. In some embodiments, the plurality of spacers has a size in a range of 0.1 mm to 5 mm. In some embodiments, the method comprises placing a matrix material between the multiple substrate to form a viscoelastic polymer compound after the viscoelastic polymer solidifies. In some embodiments, the matrix material includes a cloth or a polyurethane matrix. For example, spacers of various sizes (e.g., from 0.1 mm to 5 mm) can be placed between adjacent substrates to produce pitch layer pads having a thickness between 0.1 mm to 5 mm. In some embodiments, a matrix can be placed between adjacent substrates to produce a pitch compound matrix. For example, a piece of cloth, a polyurethane matrix, or other reinforcement structures can be used to compound pitch layer pad. 
     The method  500  also includes, at operation  505 , solidifying the pitch material. In some embodiments, a single PLP can be applied to the tool when the tool is relatively small (e.g., having a diameter of ˜3 cm). When the polishing tool has a larger size (e.g., 30 cm in diameter), it can be beneficial to have a PLP that is constructed to include multiple segments. For example, the solidified pitch material can be cut into different segments. A polishing compound (e.g., Hastilite or Rhodite) can be used in the polishing process. The channels formed between the segments can facilitate uniform polishing compound distribution under the polishing tool. In some embodiments, the method includes dividing each of the one or more viscoelastic polymer layers into multiple segments. In some embodiments, the multiple segments have random or pseudo-random boundaries. In some embodiments, the multiple segments include one or more slices or wedges to form a circular shape. In some embodiments, the multiple segments have a rectangular or square shape. 
       FIG. 11  illustrates an example polishing tool  1100  with multiple segments of a polishing pad attached to it. The polishing pad includes multiple segments  1101   a ,  1101   b  with channels  1103  in between.  FIGS. 6-8  illustrate three example multi-segment patterns of a pitch layer pad in accordance with one or more example embodiments of the present technology. For example, as shown in  FIG. 6 , a pizza-shaped segment pattern can be created for a circular polishing tool, where the pattern includes slices (or wedges)  601 . The spacings between the slides or wedges from multiple channels  603 . The example pattern in  FIG. 7  includes square (or generally rectangular) segments that can be used with square or rectangular-shaped polishing tools. Similarly, channels  703  are formed between the segments  701 . In another example, the segment pattern can be randomized or arbitrary, such as that pattern that is shown in  FIG. 8 , to accommodate various tool shapes. The boundaries of the segments can have random or pseudo-random boundaries. The channels  803  can also have random or pseudo-random shapes. 
     The solidified PLP (either a single pad or a pad having multiple segments) can be applied to the polishing tool using a pressure-sensitive adhesive or similar types of adhesive. The adhesive can allow easy replacement of the polishing pad for tool maintenance purposes. 
       FIG. 9  illustrates an example of smoothing a local bump on a workpiece using a pitch layer pad in accordance with one or more example embodiments of the present technology. In this example, a non-Newtonian smoothing tool  900  includes a back plate  901 , a non-Newtonian material  905  enclosed in a container (not shown), and a pitch layer pad (PLP) as the polishing interface  903 . The non-Newtonian smoothing tool  900  is pressed against a workpiece  911  to smooth out a bump  913 . While the non-Newtonian material and the polishing pad is still locally deformed by the bump  913 , the rigidity of the pitch layer pad provides a much higher local polishing pressure. As shown in  FIG. 9 , a much smaller deformity ΔL′ (e.g., 0.1 micron as compared to ˜1 μm in  FIG. 4 ) can be observed, indicating that the polishing tool is exerting more local pressure against the bump. The high local pressure allows the bump to be smoothed out in a much more efficient manner. For example, when the local pressure doubles, the smoothing rate also doubles accordingly. 
       FIG. 10  illustrates another example configuration of a polishing tool in accordance with one or more example embodiments of the present technology. In this example, the polishing tool  1000  includes a back plate  1001 , a non-Newtonian material  1005  enclosed in a container  1007 , and a pitch layer pad (PLP) as the polishing interface  1003 . The polishing tool  1000  also includes a driver pin  1009  configured to apply a drive force to drive the movement of the tool  1000 . The drive force allows the polishing tool  1000  to move against the workpiece  1011 . The polishing tool  1000  itself exerts a force against the workpiece  1011  due to its weight. An additional local polishing pressure (by the bumps) is also applied against the workpiece  1011  so that the polishing tool  1000  can smooth out any local bumps on the workpiece  1011 . The polishing tool  1000  can be used for regular polishing and smoothing process machines without major modifications to the existing machines. 
     In one example aspect, an apparatus for polishing an optical component having an aspheric or freeform surface includes a solid back plate, a container coupled to the solid plate, and a layer of viscoelastic polymer attached or otherwise coupled to the container. The container encloses a non-Newtonian material that exhibits a solid-like and a fluid-like behavior based on a stress frequency applicable to the non-Newtonian material the layer of viscoelastic polymer positioned to provide physical contact with the optical component for polishing the optical component. The layer of viscoelastic polymer comprises one or more segments. 
     In some embodiments, the viscoelastic polymer includes at least one of: a residue distilled from tar, oil, or wood; a rosin; a beeswax or linseed oil; an asphalt; a flake shellac; a paraffin wax; a wood flour; or a walnut shell flour. In some embodiments, the layer of viscoelastic polymer has a thickness in a range 0.1 mm to 5 mm. In some embodiments, the layer of viscoelastic polymer further comprises a matrix material to form a compound matrix of viscoelastic polymer. In some embodiments, the matrix material includes a cloth or a polyurethane matrix. 
     In some embodiments, the one or more segments of the layer of viscoelastic polymer form multiple channels for facilitating uniform distribution of a polishing compound. In some embodiments, the one or more segments of the layer of viscoelastic polymer have random or pseudo-random boundaries. In some embodiments, the one or more segments of the layer of viscoelastic polymer include one or more slices or wedges to form a circular shape. In some embodiments, the one or more segments of the layer of viscoelastic polymer have a rectangular or square shape. 
     In some embodiments, the layer of viscoelastic polymer is adhered to the container using a pressure-sensitive adhesive. In some embodiments, the layer of viscoelastic polymer is adapted to polish a surface having an arbitrary surface profile. In some embodiments, the layer of viscoelastic polymer causes a smaller displacement of the non-Newtonian material and the polishing pad in polishing a surface protrusion as compared to a polishing arrangement that includes a polyurethane layer for contacting the surface protrusion. 
     At least parts of the disclosed embodiments, such as the motor and control system that drive the movement of the driver pin as shown in  FIG. 10 , can be implemented in digital electronic circuitry, or in computer software, firmware, or hardware. For example, electronic circuits can be used to control the operation of the detector arrays and/or to process electronic signals that are produced by the detectors. At least some of those embodiments or operations can be implemented as one or more computer program products, i.e., one or more modules of computer program instructions encoded on a computer-readable medium for execution by, or to control the operation of, data processing apparatus. The computer-readable medium can be a machine-readable storage device, a machine-readable storage substrate, a memory device, a composition of matter effecting a machine-readable propagated signal, or a combination of one or more of them. The term “data processing apparatus” encompasses all apparatus, devices, and machines for processing data, including by way of example a programmable processor, a computer, or multiple processors or computers. The apparatus can include, in addition to hardware, code that creates an execution environment for the computer program in question, e.g., code that constitutes processor firmware, a protocol stack, a database management system, an operating system, or a combination of one or more of them. A propagated signal is an artificially generated signal, e.g., a machine-generated electrical, optical, or electromagnetic signal, that is generated to encode information for transmission to suitable receiver apparatus. 
     A computer program (also known as a program, software, software application, script, or code) can be written in any form of programming language, including compiled or interpreted languages, and it can be deployed in any form, including as a stand-alone program or as a module, component, subroutine, or other unit suitable for use in a computing environment. A computer program does not necessarily correspond to a file in a file system. A program can be stored in a portion of a file that holds other programs or data (e.g., one or more scripts stored in a markup language document), in a single file dedicated to the program in question, or in multiple coordinated files (e.g., files that store one or more modules, sub programs, or portions of code). A computer program can be deployed to be executed on one computer or on multiple computers that are located at one site or distributed across multiple sites and interconnected by a communication network. 
     The processes and logic flows described in this specification can be performed by one or more programmable processors executing one or more computer programs to perform functions by operating on input data and generating output. The processes and logic flows can also be performed by, and apparatus can also be implemented as, special purpose logic circuitry, e.g., an FPGA (field programmable gate array) or an ASIC (application specific integrated circuit). 
     Processors suitable for the execution of a computer program include, by way of example, both general and special purpose microprocessors, and any one or more processors of any kind of digital computer. Generally, a processor will receive instructions and data from a read only memory or a random access memory or both. The essential elements of a computer are a processor for performing instructions and one or more memory devices for storing instructions and data. Generally, a computer will also include, or be operatively coupled to receive data from or transfer data to, or both, one or more mass storage devices for storing data, e.g., magnetic, magneto optical disks, or optical disks. However, a computer need not have such devices. Computer readable media suitable for storing computer program instructions and data include all forms of nonvolatile memory, media and memory devices, including by way of example semiconductor memory devices, e.g., EPROM, EEPROM, and flash memory devices. The processor and the memory can be supplemented by, or incorporated in, special purpose logic circuitry. 
     While this patent document contains many specifics, these should not be construed as limitations on the scope of any invention or of what may be claimed, but rather as descriptions of features that may be specific to particular embodiments of particular inventions. Certain features that are described in this patent document in the context of separate embodiments can also be implemented in combination in a single embodiment. Conversely, various features that are described in the context of a single embodiment can also be implemented in multiple embodiments separately or in any suitable subcombination. Moreover, although features may be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can in some cases be excised from the combination, and the claimed combination may be directed to a subcombination or variation of a subcombination. 
     Similarly, while operations are depicted in the drawings in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed, to achieve desirable results. Moreover, the separation of various system components in the embodiments described in this patent document should not be understood as requiring such separation in all embodiments. 
     Only a few implementations and examples are described and other implementations, enhancements and variations can be made based on what is described and illustrated in this patent document.