PITCH LAYER PAD FOR SMOOTHING OPTICAL SURFACES
Methods, apparatus and systems for polishing an optical component having an aspheric or freeform surface are described. In one example aspect, a polishing device includes a solid plate and a container coupled to the solid plate. The container encloses a non-Newtonian material that exhibits a solid-like and a fluid-like behavior based on a frequency of a stress applicable to the non-Newtonian material. The device also includes a layer of viscoelastic polymer adhered to the container to polish the optical component. The layer of viscoelastic polymer comprises one or more segments positioned according to a shape of the solid plate.
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 FIELDThis patent document relates to high-precision optical surfaces.
BACKGROUNDVarious 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.
SUMMARYDevices, 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.
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.
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.
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.
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:
PV is the peak-to-valley magnitude of the sinusoidal error, ξ is the spatial frequency of the surface error, Pnominal is the nominal pressure under the tool, Dplate is the flexural rigidity of the plate, Ds_plate is the transverse shear stiffness of the plate, and Ktotal 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:
Dplate=Dplate·tplate3/12(1−vplate2) Eq. (3)
Ds_plate=Eplate·tplate/2(1−vplate) Eq. (4)
Eplate is the Youngs modulus of the plate material, tplate is the plate thickness, and vplate is the Poisson'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.
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.
Where the oscillating stress and strain as expressed as
ε=ε0 sin(tω) Eq. (7)
σ=σ0 sin(tω+δ) Eq. (8)
The ε is the time dependent strain, ε0 is magnitude of the strain, t is time, ω is angular frequency of the oscillation, a is the time dependent stress, σ0 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:
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)=Pnominal+Ktotal·error(x) Eq. (10)
Because the elastic material (e.g., visco-elastic material under the tan δ<<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:
Kelastic is the stiffness of the elastic material and Kothers 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:
The stiffness of the elastic material Kelastic 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 Kelastic is:
The applied stress angular frequency ω is determined by the spatial frequency of the surface error ξ and the speed of the tool motion Vtool_motion as:
T is the time interval between a position under the tool sees two adjacent peaks in the sinusoidal ripple and Vtool_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:
Δz(x)=RPreston·P(x)·Vtool
Δz is the integrated material removal from the workpiece surface, RPreston is the Preston coefficient (e.g., removal rate), P is the polishing pressure, Vtool_workpiece is the relative speed between the tool and workpiece and Δt is the dwell time. For a given initial sinusoidal ripple magnitude PVini, the additional polishing pressure Padd on the peak is:
Then, for a dwell time Δt, the decrease in the ripple magnitude ΔPV is calculated as:
ΔPV=PVini−PVafter=RPreston·Padd·Vtool_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=RPreston·Pnominal·Vtool_workpiece·Δt Eq. (18)
The smoothing factor SF is defined as:
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, C1 and C2, to fit the measured data. The first parameter C1 represents Kothers 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 C2 in SF vs. PVini space. The resulting parametric smoothing model is:
C1 is the slope correction parameter and C2 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
A pitch layer pad (PLP) can be manufactured in various ways.
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.
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.
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
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.
Claims
1. An apparatus for polishing an optical component having an aspheric or freeform surface, comprising:
- a solid back plate,
- a container coupled to the solid plate, wherein 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; and
- a layer of viscoelastic polymer attached or otherwise coupled to the container, the layer of viscoelastic polymer positioned to provide physical contact with the optical component for polishing the optical component, wherein the layer of viscoelastic polymer comprises one or more segments.
2. The apparatus of claim 1, wherein 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.
3. The apparatus of claim 1, wherein the layer of viscoelastic polymer has a thickness in a range 0.1 mm to 5 mm.
4. The apparatus of claim 1, wherein the layer of viscoelastic polymer further comprises a matrix material to form a compound matrix of viscoelastic polymer.
5. The apparatus of claim 4, wherein the matrix material includes a cloth or a polyurethane matrix.
6. The apparatus of claim 1, wherein the one or more segments of the layer of viscoelastic polymer form multiple channels for facilitating uniform distribution of a polishing compound.
7. The apparatus of claim 1, wherein the one or more segments of the layer of viscoelastic polymer have random or pseudo-random boundaries.
8. The apparatus of claim 1, wherein the one or more segments of the layer of viscoelastic polymer include one or more slices or wedges to form a circular shape.
9. The apparatus of claim 1, wherein the one or more segments of the layer of viscoelastic polymer have a rectangular or square shape.
10. The apparatus of claim 1, wherein the layer of viscoelastic polymer is adhered to the container using a pressure-sensitive adhesive.
11. The apparatus of claim 1, wherein the layer of viscoelastic polymer is adapted to polish a surface having an arbitrary surface profile.
12. The apparatus of claim 1, wherein 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.
13. A method for producing a layer of viscoelastic polymer, comprising:
- melting a viscoelastic polymer into a liquid form;
- pouring the viscoelastic polymer between multiple substrates, wherein the multiple substrates are separated by a plurality of spacers; and
- solidifying the viscoelastic polymer to obtain one or more viscoelastic polymer layers.
14. The method of claim 13, wherein the plurality of spacers has a size in a range of 0.1 mm to 5 mm.
15. The method of claim 13, comprising placing a matrix material between the multiple substrate to form a viscoelastic polymer compound after the viscoelastic polymer solidifies.
16. The method of claim 15, wherein the matrix material includes a cloth or a polyurethane matrix.
17. The method of claim 13, comprising:
- dividing each of the one or more viscoelastic polymer layers into multiple segments.
18. The method of claim 17, wherein the multiple segments have random or pseudo-random boundaries.
19. The method of claim 17, wherein the multiple segments include one or more slices or wedges to form a circular shape.
20. The method of claim 17, wherein the multiple segments have a rectangular or square shape.
Type: Application
Filed: Apr 14, 2020
Publication Date: Jul 7, 2022
Inventor: Dae Wook Kim (Tucson, AZ)
Application Number: 17/599,403