The present disclosure relates to modifying a curvature of thin plates, and more particularly thin plate optical elements such as thin plate optical lenses, mirrors and other like components, and more particularly modifying a curvature of such elements and components using optical energy, to induce stress in the element which acts to modify a curvature of the element.
The statements in this section merely provide background information related to the present disclosure and may not constitute prior art.
Optical components with multiple lens elements are ubiquitous in optical assemblies including cameras, eye loupes, microscopes, etc. These types of lenses have a designated thickness, centering, and curvature which all work together to create a designed optical image/focal plane. Slight variations in these manufactured lenses can alter the focal plane image. To overcome this, higher tolerances are set for lens manufacturing. Unfortunately, this leaves a lower yield for production and higher cost. Another disadvantage is that process for polishing and form correcting such lenses currently requires material removal.
Wavefront deformation is a sub aperture specification designated by the waviness and roughness of the optic. It is quantified in terms of waves of the designed wavelength to be used. For reference, visible wavelengths are between 400 nm-700 nm. In this context, an optic designed for 400 nm would be commercially made within a 100 nm root mean squared (“rms”) roughness and 20 nm rms for high precision tolerances. The roughness is proportional to the abrasive size used when polishing. Additionally, the time required to achieve the roughness is exponential with decreased abrasive size. Once the desired roughness is achieved, the optical contour cannot be changed without major correction and repeating the polishing process.
Thickness variations are overcome by adding in air gaps using shims. However, refractive index in air and in the glass are different which cause problematic aberrations compounded through the system. Centering is accomplished by creating the optic with the correct curvature and then cutting around the sides of the optic with the curvature center at the center of the cut optic. Curvature is accomplished by using grinding and polishing with abrasives, which removes material at spatial locations. The process is repeated until the lens curvature is within tolerance. Because this process requires material removal, the thickness of the optic is affected during any correction.
In view of the foregoing, there remains a significant need for systems and methods that can more easily and economically adjust for, or correct for, the above-discussed types of manufacturing errors when making optical elements.
This section provides a general summary of the disclosure, and is not a comprehensive disclosure of its full scope or all of its features.
In one aspect the present disclosure relates to an apparatus for modifying a curvature of thin plate. The apparatus may comprising a support structure for supporting the thin plate about a perimeter thereof, and a laser. The laser may be configured to generate a beam having a predetermined energy (or fluence), with the beam being directed at one surface of the thin plate. The beam operates to heat and densify portions of the thin plate to create a force on the thin plate. The force causes a stress which induces a controlled deformation of the thin plate to at least one of modify a curvature of the thin plate or to correct a defect in the thin plate.
In another aspect the present disclosure relates to an apparatus for modifying a curvature of a thin plate optic. The apparatus may comprise an electronic controller, a support structure for supporting the thin plate optic about a perimeter thereof, a laser, an acousto-optic modulator, and a beam steering system. The laser may be configured to generate a beam having a predetermined energy, the beam being directed at one surface of the thin plate optic. The acousto-optic modulator is configured to assist in controlling a power of the beam received from the laser which is applied to the thin plate optic. The beam steering system is responsive to the electronic controller and configured to steer the beam in a circular path over at least one of an upper surface or a lower surface of the thin plate optic, to thus trace at least one substantially continuous line segment on at least one of the upper surface or the lower surface of the thin plate optic. The at least one substantially continuous line segment heats and densifies portions of the thin plate optic to create a line force on the thin plate optic. The line force induces a stress which produces a controlled deformation of the thin plate optic, to at least one of modify a curvature of the thin plate optic or to correct a defect in the thin plate optic.
In still another aspect the present disclosure relates to a method for modifying a curvature of a thin plate optic. The method may comprise supporting the thin plate optic about a perimeter thereof, and directing a laser beam having a predetermined energy at one of an upper surface or a lower surface of the thin plate optic. The method may further include using the predetermined energy of the laser beam to heat the thin plate optic to create a controlled force acting on the thin plate optic. The controlled force induces a deformation of the thin plate optic which causes a controlled deflection of a central portion or a portion of the thin plate optic. The controlled deflection acts to at least one of modify a curvature of the thin plate optic or to correct a defect in the thin plate optic.
Further areas of applicability will become apparent from the description provided herein. It should be understood that the description and specific examples are intended for purposes of illustration only and are not intended to limit the scope of the present disclosure.
The drawings described herein are for illustrative purposes only of selected embodiments and not all possible implementations, and are not intended to limit the scope of the present disclosure.
Corresponding reference numerals indicate corresponding parts throughout the several views of the drawings.
Example embodiments will now be described more fully with reference to the accompanying drawings.
The present disclosure makes use of well known “plate theory” to describe the deformation of a plate when it is subjected to lateral stress. The plate is described by two sides much larger than the third side. Its thickness is measured from the center of the shortest side. The assumptions for plate theory are that the deflections are small and they are only in the direction normal to the surface. For a plate initially flat with center plane on the x-y axis, the deformation is described by the point wd(x,y), which is the deviation from the x-y plane as shown in Error! Reference source not found.3.
In a plate with sufficiently small thickness, equivalent forces acting on the volume can be calculated by integrating through the thickness as shown in Error! Reference source not found.4a. For the present disclosure, the terminology “thin plate” can be understood to mean a plate with a length dimension (e.g., diameter) which is at least 8 times a thickness of the plate. The following discussion will make reference to a circular plate, but it will be appreciated that the present disclosure is not limited to only circular plates, but may be used to controllably change the shape of plates of virtually any shape (e.g., square, oval, etc.), provided the ratio of dimension to plate thickness is at least about 8:1 or greater.
For the following discussion, consider a force acting on a volume, the in-plane normal forces are shown to be:
where Nx and Ny are the normal forces per length acting along the plane. The force acting on the volume can vary through thickness creating moments. In-plane bending moments per length are described by an integral of the stress times the distance from the mid plane or:
In-plane shear force and twisting moment can be written as:
respectively. An out-of-plane shear stress may also act on the volume and is written as:
Using the definitions of the stress acting on a volume described above, the full aperture plate deflection can be calculated from sub-aperture stress concentration. The in-plane stresses acting on the plate are membrane forces that are applied if the volume is constricted in the x and y directions. Because the optic in this case is not being restricted, the membrane stress is considered negligible. The problem then can be reduced so there are only lateral forces acting on the surface of the optic, as shown in Error! Reference source not found.3, and the deformation of the originally flat plate is then wd(x,y). For this case where the force, Fzz, is acting in the −z direction, the governing equation can be written as the equation of Sophie Germain:
where wd is the deformation of the plate and
is the bending stiffness. In Equation Error! Reference source not found., E and v are the elastic modulus and Poisson's ratio of the material, respectively, and d is the thickness of the plate.
Full Aperture Bending
Plate theory as described above can be used to study the effect of stress on the full aperture optic. As an extension to the sub-aperture volumetric change, a known scenario with a solution in plate theory was tested by the co-inventors to observe and describe full aperture bending that occurs from laser polishing. The scenario with an already derived solution to plate theory is drawn in Error! Reference source not found.5a.
While the full circular track shown in
To describe the full aperture bending effect, an equivalent line force acting on the optic was derived using the bulk modulus. The volumetric change can be used in the bulk modulus equation, and when rearranged, becomes,
where, again, p is the hydrostatic pressure, K is the material bulk modulus, ΔV is the change in volume, and V; is the original volume. Assuming that no mass is lost through the process, the volume change, ΔV, can be written as:
where Vf and V; are the final and initial volume, respectively, of a volume element, m is the mass of the volume element, p0 is the initial density of the material, Tfi is the initial fictive temperature and Tf∞ is the final fictive temperature after the material has cooled. Δρ is the linear change in density with change in fictive temperature. For fused silica Δρ=9.33±0.2 g·m−3·K−1, and is constant with change in fictive temperature.
In Euclidean space, dividing by the initial volume, factoring out the mass and original density, and integrating over the initial volume element, Equation (84) can be rearranged to give:
The expression ΔV/V; is simply the integrand of Equation (85):
From this, Equation Error! Reference source not found. becomes:
The bulk modulus for Corning 7980 is 35.9 GPa.
The hydrostatic pressure, when applied to the surface area of a volumetric unit 20, is shown in Error! Reference source not found. The pressure, p, is applied to each surface equally. The stress in the z direction can be calculated as:
σzz=⅓p (Eq. 95)
In the elemental unit 20 volume of
The force described in Equation Error! Reference source not found. is illustrated as acting on a volume fraction in Error! Reference source not found.8 with equivalent cylindrical coordinates using the variable transformations r=√{square root over (x2+y2)} and tan(θ)=y/x. The volume fraction is in cylindrical coordinates and will be used to derive the equivalent line load acting on the surface of the optic O. The line load is depicted by arrows 32a in
The equivalent force distribution along the cross section of the beam 32 (from
where y is the width of the force distribution.
The line load calculated in Equation Error! Reference source not found. can be used to calculate the center deflection, yc, using the solution,
Equations Error! Reference source not found.—Error! Reference source not found. are solutions to the plate theory scenario described above. In these equations, v is poisson's ratio of the material and
is the material stiffness function with h being the plate thickness.
Error! Reference source not found. 11 shows an average depth profile measured from the optic plotted, represented by curve 50, along with the calculated depth profile from plate theory, represented by curve 52. Discrepancies of the analytical solution and experimental measurement can be attributed to the decentering of the annular load as observed in Error! Reference source not found.a and that the track T was not uniform around the optic. This analysis also neglects any shear stress that may affect the moment sum acting on the plate. Further studies into full aperture bending may need to be done for even greater control of the optic shape using laser polishing.
Referring to
Beam Conditioning, Power Control and Gate Control
The laser 102 used in this embodiment of the system 100 is a CO2, continuous wave (CW) laser with a beam having 10.6 μm wavelength, and with the beam capable of a 30 W output (e.g., GEM series laser available from Coherent Inc., of Palo Alto, Calif.). The optical path for beam conditioning, power, and gate control is shown in
The amount of beam diffraction introduced by the AOM 104 depends on a magnitude of a drive signal (e.g., voltage signal) sent to a driver within the AOM 104. The beam portion 102a2 that is not diverted is sent to the initial power meter 106 which acts as a beam dump, removing the excess power from the system 100.
The beam 102a1 that is deflected by the AOM 104 is sent through two lenses, L1 and L2, with focal lengths in this example of 101.6 mm and 50.8 mm, respectively. These lenses L1 and L2 are used to reduce and collimate the beam 102a1 so that it is small enough to pass through the shutter aperture 114. The initial spot size of the beam 102a1 has a 10 mm diameter, and the resulting collimated beam 102a1 has a 5 mm diameter in this example.
The beam 102a1 is then separated to regulate the power using a closed loop control. The collimated beam 102a1 is sent to the wedged optic 108 with one side having an antireflective coating and the other side uncoated. The wedged optic 108 in this example diverts about 10% of the power (represented by beam portion 102a1″ toward the pickoff power meter 112. Although there is an antireflective coating on the back side of the wedged optic 108, the beam still reflects some of the power on that surface, as a ghost image. Because the optic 108 is wedged, the beams from each surface diverge at an angle to each other. It was found that the wedged optic 108 is highly advantageous in preventing interferometric effects on the pickoff power meter 112, which can change with the inevitable heating of the optic 108.
The pickoff beam 102a1″ is then sent through the focusing lens L3 to sufficiently reduce the size of the beam 112a1″ on the pickoff power meter 112 so that the full beam is on the sensor within the pickoff power meter. The ghost image is removed using the iris 110 to pass the pickoff beam 112a1″ and block the ghost image. The pickoff power meter 112 is preferably also not at the focus of the focusing lens L3 to prevent heating effects and damage from the focused beam 112a1″.
Power Calibration
The pickoff power meter 112 is used to monitor the power going into the system 100 and to adjust the voltage going to the AOM 104 for any fluctuations. The power going to the fused silica optic 128 was calibrated to the pickoff power meter 112 reading before each experiment. To calibrate the relationship between pickoff and actual power, an additional power meter 112a (shown in
During testing an open-loop voltage was sent to the AOM 104 and the power was read from the power pickoff meter 112 and the additional power meter 112a. Data from both meters was collected for 5 seconds after the power reading was stabilized. The average and standard deviation of the power from 1000 samples was calculated.
Closed Loop Power Control
It will be appreciated that the output of the laser 102 fluctuates with ambient temperature. For this reason, the system 100, in one preferred implementation, incorporates closed loop control to provide constant power and compensate for fluctuations.
Beam Steering and Imaging
Referring to
The heated chamber 126 in this example uses a top-down configuration, meaning, the beam needs to be aligned to enter through a top window of the heated chamber 126. For this, the beam 102a1′ was directed through L4, a spherical lens with focal length 508 mm. The beam 102a1′ then then is reflected by the mirror M8 to the pickoff mirror lens 122. The pickoff mirror lens 122 transmits 10.6 μm wavelength and reflects visible light used for the imaging device 130. The beam 102a1′ is then sent to the galvanometer 124 (e.g., available from NutField Technology (now Thorlabs, of Santa Barbara, Calif.) as model QS-30) which uses two mirrors 124a and 124b that rotate to scan the beam 102a1′ on the sample plane. After being directed by the galvanometer 104, the beam 102a1′ is sent to a meniscus lens (L5 in this example) with an effective focal length of 190 mm. The meniscus lens was used to flatten the focal plane as the beam is scanned by the galvanometer system. The combination focal lengths of L4 and L5 was chosen to create a slightly converging beam.
An imaging system comprised of the imaging device 130 was used to view the experiments in situ that were carried out using the system 100, and to ensure the sample surface (i.e., optic 128 upper surface) was in the correct plane before polishing. An illumination light (not shown) was placed to shine into one of the ports in the heated chamber 126. The illumination could not be co-linear with the beam 102a1′ because the ZnSe lens L5 and chamber 126 window (not shown) have reflective surfaces in the visible spectrum that would reflect any incident light. Additionally, the ZnSe lenses have a different focal distance in the visible spectrum than at the CO2 laser 102 wavelength. The meniscus lens L5 could not be placed at the focal distance of both wavelengths and distorted some of the visible light. Therefore, the light coming from the heated chamber 126 and going through L5 was reflected by the pickoff mirror 122 through lenses L6 and L7 to focus the image on the imaging device 130 camera as best as possible. Lens L6 in this example has a 200 mm focal length and is used as a field lens to garner more light from the system 100 due to decreased transmission through the ZnSe meniscus lens and chamber 126 window (not shown). Lens L7 in this example has a focal length of 100 mm and is used to focus the image on the imaging device 120.
The foregoing description of the embodiments has been provided for purposes of illustration and description. It is not intended to be exhaustive or to limit the disclosure. Individual elements or features of a particular embodiment are generally not limited to that particular embodiment, but, where applicable, are interchangeable and can be used in a selected embodiment, even if not specifically shown or described. The same may also be varied in many ways. Such variations are not to be regarded as a departure from the disclosure, and all such modifications are intended to be included within the scope of the disclosure.
The various embodiments and methods described herein of the system 100 as described herein.
Example embodiments are provided so that this disclosure will be thorough, and will fully convey the scope to those who are skilled in the art. Numerous specific details are set forth such as examples of specific components, devices, and methods, to provide a thorough understanding of embodiments of the present disclosure. It will be apparent to those skilled in the art that specific details need not be employed, that example embodiments may be embodied in many different forms and that neither should be construed to limit the scope of the disclosure. In some example embodiments, well-known processes, well-known device structures, and well-known technologies are not described in detail.
The terminology used herein is for the purpose of describing particular example embodiments only and is not intended to be limiting. As used herein, the singular forms “a,” “an,” and “the” may be intended to include the plural forms as well, unless the context clearly indicates otherwise. The terms “comprises,” “comprising,” “including,” and “having,” are inclusive and therefore specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. The method steps, processes, and operations described herein are not to be construed as necessarily requiring their performance in the particular order discussed or illustrated, unless specifically identified as an order of performance. It is also to be understood that additional or alternative steps may be employed.
When an element or layer is referred to as being “on,” “engaged to,” “connected to,” or “coupled to” another element or layer, it may be directly on, engaged, connected or coupled to the other element or layer, or intervening elements or layers may be present. In contrast, when an element is referred to as being “directly on,” “directly engaged to,” “directly connected to,” or “directly coupled to” another element or layer, there may be no intervening elements or layers present. Other words used to describe the relationship between elements should be interpreted in a like fashion (e.g., “between” versus “directly between,” “adjacent” versus “directly adjacent,” etc.). As used herein, the term “and/or” includes any and all combinations of one or more of the associated listed items.
Although the terms first, second, third, etc. may be used herein to describe various elements, components, regions, layers and/or sections, these elements, components, regions, layers and/or sections should not be limited by these terms. These terms may be only used to distinguish one element, component, region, layer or section from another region, layer or section. Terms such as “first,” “second,” and other numerical terms when used herein do not imply a sequence or order unless clearly indicated by the context. Thus, a first element, component, region, layer or section discussed below could be termed a second element, component, region, layer or section without departing from the teachings of the example embodiments.
Spatially relative terms, such as “inner,” “outer,” “beneath,” “below,” “lower,” “above,” “upper,” and the like, may be used herein for ease of description to describe one element or feature's relationship to another element(s) or feature(s) as illustrated in the figures. Spatially relative terms may be intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the figures. For example, if the device in the figures is turned over, elements described as “below” or “beneath” other elements or features would then be oriented “above” the other elements or features. Thus, the example term “below” can encompass both an orientation of above and below. The device may be otherwise oriented (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly.
The United States Government has rights in this invention pursuant to Contract No. DE-AC52-07NA27344 between the U.S. Department of Energy and Lawrence Livermore National Security, LLC, for the operation of Lawrence Livermore National Laboratory.