DETAILED ACTION
Notice of Pre-AIA or AIA Status
The present application, filed on or after March 16, 2013, is being examined under the first inventor to file provisions of the AIA .
Claim Interpretation
The following is a quotation of 35 U.S.C. 112(f):
(f) Element in Claim for a Combination. – An element in a claim for a combination may be expressed as a means or step for performing a specified function without the recital of structure, material, or acts in support thereof, and such claim shall be construed to cover the corresponding structure, material, or acts described in the specification and equivalents thereof.
The following is a quotation of pre-AIA 35 U.S.C. 112, sixth paragraph:
An element in a claim for a combination may be expressed as a means or step for performing a specified function without the recital of structure, material, or acts in support thereof, and such claim shall be construed to cover the corresponding structure, material, or acts described in the specification and equivalents thereof.
The claims in this application are given their broadest reasonable interpretation using the plain meaning of the claim language in light of the specification as it would be understood by one of ordinary skill in the art. The broadest reasonable interpretation of a claim element (also commonly referred to as a claim limitation) is limited by the description in the specification when 35 U.S.C. 112(f) or pre-AIA 35 U.S.C. 112, sixth paragraph, is invoked.
As explained in MPEP § 2181, subsection I, claim limitations that meet the following three-prong test will be interpreted under 35 U.S.C. 112(f) or pre-AIA 35 U.S.C. 112, sixth paragraph:
(A) the claim limitation uses the term “means” or “step” or a term used as a substitute for “means” that is a generic placeholder (also called a nonce term or a non-structural term having no specific structural meaning) for performing the claimed function;
(B) the term “means” or “step” or the generic placeholder is modified by functional language, typically, but not always linked by the transition word “for” (e.g., “means for”) or another linking word or phrase, such as “configured to” or “so that”; and
(C) the term “means” or “step” or the generic placeholder is not modified by sufficient structure, material, or acts for performing the claimed function.
Use of the word “means” (or “step”) in a claim with functional language creates a rebuttable presumption that the claim limitation is to be treated in accordance with 35 U.S.C. 112(f) or pre-AIA 35 U.S.C. 112, sixth paragraph. The presumption that the claim limitation is interpreted under 35 U.S.C. 112(f) or pre-AIA 35 U.S.C. 112, sixth paragraph, is rebutted when the claim limitation recites sufficient structure, material, or acts to entirely perform the recited function.
Absence of the word “means” (or “step”) in a claim creates a rebuttable presumption that the claim limitation is not to be treated in accordance with 35 U.S.C. 112(f) or pre-AIA 35 U.S.C. 112, sixth paragraph. The presumption that the claim limitation is not interpreted under 35 U.S.C. 112(f) or pre-AIA 35 U.S.C. 112, sixth paragraph, is rebutted when the claim limitation recites function without reciting sufficient structure, material or acts to entirely perform the recited function.
Claim limitations in this application that use the word “means” (or “step”) are being interpreted under 35 U.S.C. 112(f) or pre-AIA 35 U.S.C. 112, sixth paragraph, except as otherwise indicated in an Office action. Conversely, claim limitations in this application that do not use the word “means” (or “step”) are not being interpreted under 35 U.S.C. 112(f) or pre-AIA 35 U.S.C. 112, sixth paragraph, except as otherwise indicated in an Office action.
This application includes one or more claim limitations that do not use the word “means,” but are nonetheless being interpreted under 35 U.S.C. 112(f) or pre-AIA 35 U.S.C. 112, sixth paragraph, because the claim limitation(s) uses a generic placeholder that is coupled with functional language without reciting sufficient structure to perform the recited function and the generic placeholder is not preceded by a structural modifier. Such claim limitation(s) is/are:
Claim 10 “a heat flux vector module configured to determine each heat flux vector based on a response matrix, a thermal deformation vector and each perturbation term;
a residual surface shape error module configured to determine each residual surface shape error based on the response matrix, and
a surface shape optimization module configured to apply a heat flux vector corresponding to a minimum value of each residual surface shape error to a heating sheet of the reflecting mirror to optimize the surface shape of the reflecting mirror” each recite a generic placeholder term, namely “module,” coupled with purely functional language. MPEP 2118 explains that terms such as “module for” are non-structural generic placeholders that my invoke 35 U.S.C. 112(f) when the claim does not recite sufficiently definite structure for performing the claimed function. Here, claim 10 does not recited sufficiently definite structure for performing the recited functions. Instead, the claim defined each “module” only by the result to be achieved. Accordingly, these limitations are construed as mean-plus-function limitations under 35 U.S.C. 112(f), and are interpreted to cover the corresponding structure, material, or acts described in the specification for performing the recited functions, and equivalents thereof. The corresponding disclosure appears, for example, in the specification’s algorithmic and system descriptions, including the flowchart of Fig. 4, the module diagram of Fig. 10, and the processor-based implementation of Fig. 11, together with the accompanying description of determining heat flux vectors, determining residual surface shape errors, and applying the selected heat flux vector.
Because this/these claim limitation(s) is/are being interpreted under 35 U.S.C. 112(f) or pre-AIA 35 U.S.C. 112, sixth paragraph, it/they is/are being interpreted to cover the corresponding structure described in the specification as performing the claimed function, and equivalents thereof.
If applicant does not intend to have this/these limitation(s) interpreted under 35 U.S.C. 112(f) or pre-AIA 35 U.S.C. 112, sixth paragraph, applicant may: (1) amend the claim limitation(s) to avoid it/them being interpreted under 35 U.S.C. 112(f) or pre-AIA 35 U.S.C. 112, sixth paragraph (e.g., by reciting sufficient structure to perform the claimed function); or (2) present a sufficient showing that the claim limitation(s) recite(s) sufficient structure to perform the claimed function so as to avoid it/them being interpreted under 35 U.S.C. 112(f) or pre-AIA 35 U.S.C. 112, sixth paragraph.
Claim Rejections - 35 USC § 103
The following is a quotation of 35 U.S.C. 103 which forms the basis for all obviousness rejections set forth in this Office action:
A patent for a claimed invention may not be obtained, notwithstanding that the claimed invention is not identically disclosed as set forth in section 102, if the differences between the claimed invention and the prior art are such that the claimed invention as a whole would have been obvious before the effective filing date of the claimed invention to a person having ordinary skill in the art to which the claimed invention pertains. Patentability shall not be negated by the manner in which the invention was made.
Claim(s) 1-4, 6, 10-13, 15 and 19 is/are rejected under 35 U.S.C. 103 as being unpatentable over Cocco et al. “Adaptive Shape Control of Wavefront-Preserving X-ray Mirrors with Active cooling and Heating 2020” in view of Vannoni et al. “An Error Function Minimization Approach for the Inverse Problem of Adaptive Mirrors Tuning 2014”.
Regarding claim 1, Cocco teaches a method for optimizing surface shape of a reflecting mirror (see abstract: “water-cooled, active optic mirror system (called “REAL: Resistive Element Adjustable Length”) that combines cooling with applied auxiliary heating” and “technique is theoretically capable of sub-nanometer surface figure error control even at high power density”), comprising:
determining each heat flux vector based on a response matrix (page 2 1st para: “The idea behind REAL is to compensate for the non-uniform heat load by introducing an external source of spatially adjustable heating, which will reduce thermal gradients that cause shape distortion” and see also page 3 5th para: “One of the first tests was the measurement of the effect of each individual heater on the mirror profile (i.e. the response function or influence function).”),
a thermal deformation vector (Cocco teaches measuring the beam-induced morror deformation and then computing correction values from that measured deformation, in particular see page 8 3rd para: “Once the thermal bump generated by the beam was measured, we used calculations based on the response functions to flatten the shape in situ. The power levels needed for each actuator to correct the deformation were calculated by linear regression and applied to the mirror”);
applying a heat flux vector corresponding to a minimum value of each residual surface shape error to a heating sheet of the reflecting mirror to optimize the surface shape of the reflecting mirror (page 8 3rd para. “The power levels needed for each actuator to correct the deformation were calculated by linear regression and applied to the mirror.” Cocco on page 4 last para and page 5 1st para: further teaches the resulting optimization of mirror shape, stating: “With the conventional water-cooling scheme … the measured residual height error was 12.9 nm rms” and after heater correction, “the residual shape error was measured to be 1.1 nm rms in the region illuminated by the beam”).
However, Cocco fails: determining each heat flux vector base on each perturbation term; determining each residual surface shape error based on the response matrix, the thermal deformation vector and each heat flux vector satisfying constraint conditions.
In the same field of endeavor, Vannoni teaches: that the inverse problem of mirror tuning is solved by first measuring actuator responses and forming a matrix model. Specifically, Vannoni states: page 3 1st para: “we can created a matrix, classically names ‘interaction matrix’” and “if we have a given profile be …, we can solve the linear system Av= -b to find the needed voltages vector v … correct b in order to have at the end a flat profile.” Thus, Vannoni teaches determining a correction vector based on a matrix model and a deformation profile. More importantly, Vannoni expressly teaches the missing constrained residual-error determination. Vannoni explains that ordinary SVD may not provide an acceptable result because “These constraints are simply not considered by SVD mathematical approach, and this originated often a number of not acceptable results. See page 3 3rd para” Vannoni then teaches: “instead of computing a unique solution of the problem, we have to switch to "searching for the better solution" in a least squares fitting meaning. See page 3 4th para” Vannoni further teaches: “We build an error function, to be evaluated on the profile that we have, calculated as the root-mean-square of the difference between that profile and the profile that we want to obtain (in our case, a perfectly flat surface. In the function, we also consider the different constraints that we have, in terms of maximum amount of signal allowed and maximum amount of difference between adjacent benders signals. In case one of the constraints is violated, we assign an infinite value on the error function. We putted such an error function inside a general minimization algorithm, as Nelder-Mead simplex algorithm, Powell or Monte-Carlo. We start the minimization from a set of values that are inside the given constraints, in general even a zero set could be used, and we start the minimization algorithm. The algorithm runs for a certain number of iterations, depending on the precision that we need, and at the end we obtain a vector of voltage corrections that we can use to calculate the resulting profile). See page 3 last para and page 4 1st para” Thus, Vannoni teaches determining candidate correction vectors under constraint conditions and selecting the better solution based on residual error minimization, which Cocco does not expressly disclose. Accordingly, it would have been obvious to one of ordinary skill in the art before the effective filing date to modify the heater-based mirror optimization method of Cocco with the constrained error-function minimization approach of Vannoni, to predictably yield a method in which candidate heat flux vectors are determined from the response model and thermal deformation input, residual surface-shape error are evaluated for vectors satisfying contain conditions, and the selected correction vector is ten applied to the heating sheet of the reflecting mirror to optimize mirror surface shape.
Regarding claim 2, Cocco teaches the method for optimizing surface shape of a reflecting mirror according to claim 1, wherein the method further comprises: applying heat flux vectors sequentially to each heating sheet to obtain corresponding reflecting mirror heat flux deformation data (page 35th para: “One of the first tests was the measurement of the effect of each individual heater on the mirror profile (i.e. the response function or influence function)”) and further states that “The first step was to characterize the effect of each heater individually, measuring the response functions to be able to predict the proper setting to compensate arbitrary deformations” and “Each actuator was individually powered to 100% of its range, and the differential effect on the wavefront was measured with the wavefront sensors.” see page 5 7th para).
However, Cocco fails to teach determining the response matrix from the reflecting mirror heat flux deformation data. Vannoni teaches determining the response matrix from the reflecting mirror heat flux deformation data “we can create a matrix, classically named "interaction matrix", putting together the scaled M pulse profiles evaluated in N points” see page 3 1st para. It would have been obvious to one of ordinary skill in the art before the effective filing date to express Cocco’s individually measured heater response functions in the matrix form taught by Vannoni, because both Coccco and Vannoni address the same adaptive mirror inverse problem and Vannoni teaches the conventional way of organizing individual actuator response data into a matrix for correction calculations.
Regarding claim 3, the combination of Cocco teaches the method for optimizing surface shape of a reflecting mirror according to claim 1, and Cocco further teaches wherein the method further comprises: applying light source thermal power to light spots of the reflecting mirror to obtain thermal deformation data of the reflecting mirror (see page 3: “To simulate the thermal deformation, a class IV infrared Laser from IPG Photonics, able to deliver up to 100 W of polarized light at 1065-nm wavelength, was used. Variable absorbed power and laser beam footprint on the mirror were achieved by (1) controlling the power of the laser,”); and determining the thermal deformation vector based on the thermal deformation data of the reflecting mirror (see Fig. 4: “Measurement of the thermally induced deformation and subsequent correction using REAL. Left: from bottom to top: Thermal image of the mirror, 2D measurement and relative profile on the center line of the mirror while irradiated by the IR laser” and page 5 last para: “The plan for on-beamline tests was to create and measure a thermal bump arising from the HXR beam, and then correct the mirror deformation using the heaters.”).
Regarding claim 4, the combination of Cocco teaches the method for optimizing surface shape of a reflecting mirror according to claim 1, and Cocco further teaches wherein the determining each heat flux vector based on the response matrix, the thermal deformation vector (see page 8: “The measured response functions were used for the final test: increasing the power of the incident X-ray beam and compensating the thermal deformation with the heaters in a controlled way” and “Once the thermal bump generated by the beam was measured, we used calculations based on the response functions to flatten the shape in situ. The power levels needed for each actuator to correct the deformation were calculated by linear regression and applied to the mirror”) comprises:
Cocco fails to teach: determining each total deformation perturbation vector based on the thermal deformation vector, an initial deformation vector and each perturbation term; and determining each heat flux vector based on the response matrix and each total deformation perturbation vector.
Vannoni teaches beginning from an already existing measured mirror profile and using that profile in a matrix-based correction computation. Specifically, on page 3, Vannoni states: “First, we measure the mirror profile without any correction, and we store such profile as a reference baseline. We measure the resulting profile, and we calculate the difference between this profile and the stored baseline. The result is named ‘pulse profile’” and “we can create a matrix, classically names ‘interaction matrix’, putting together the scaled M pulse profiles evaluated in N points. Now, if we have a given profile b ε N, we can solve the linear system Av= -b to and the needed voltages vector v ε M to correct b in order to have at the end a flat profile.” Vannoni’s stored “reference baseline” corresponds to the claimed initial deformation vector, because it is the pre-correction mirror shape used as a reference in the subsequent optimization. Vannoni’s “given profile b” corresponds to a deformation vector used as the target for correction. And Vannoni’s matrix equation “Av = -b” teaches determining a correction vector from an interaction/response matrix and a deformation-profile vector. Vannoni also teaches that this vector need not be solved in only one rigid way, but instead may be searched through an optimization framework. Vannoni states that “instead of computing a unique solution of the problem, we have to switch to ‘searching for the better solution’ in a least squared fitting meaning.” Vannoni further states: “We build an error function” and “we also consider the different constraints that we have” and “we start the minimization from a set of values that are inside the given constraints” and “at the end we obtain a vector of voltage corrections.” Thus, Vannoni teaches generating correction vectors from a matrix model and deformation-profile input within an iterative optimization framework. Accordingly, it would have been obvious to one of ordinary skill in the art before the effective filing date to modify the heater-based mirror optimization method of Cocco with the matrix-based profile/baseline optimization method of Vannoni to predictably yield determining correction heat-flux vectors based on a response matrix and a total deformation input formed from the measured thermal deformation and the mirror’s initial profile state.
Regarding claim 6, the combination of Cocco teaches the method for optimizing surface shape of a reflecting mirror according to claim 4, and Cocco further teaches wherein the determining each heat flux vector based on the response matrix (page 2 1st para: “The idea behind REAL is to compensate for the non-uniform heat load by introducing an external source of spatially adjustable heating, which will reduce thermal gradients that cause shape distortion” and see also page 3 5th para: “One of the first tests was the measurement of the effect of each individual heater on the mirror profile (i.e. the response function or influence function).”) comprises:
Cocco fails to teach: determining each heat flux vector based on an inverse matrix of a product of the response matrix and a transposition of the response matrix, the transposition of the response matrix and each total deformation perturbation vector.
Vannoni expressly teaches forming an “interaction matrix” from the individually measured actuator response, stating” “we can create a matrix, classically names ‘interaction matrix’, putting together the scaled M pulse profiles evaluated in N points, having at the end A ε NxM.” Vannoni further teaches using a deformation/profile vector as the input the correction computation, stating” “Now, if we have a given profile b ε N, we can solve the linear system Av = -b to find the needed voltages vector v ε M to correct b in order to have at the end flat profile.” It would have been obvious to one of ordinary skill in the art before the effective filing date to modify the heater based reflecting mirror optimization method of Cocco with the matrix inverse solution taught by Vannoni, as it predictably yielded determining the heat flux vector from the response matrix.
Regarding claim 10, Cocco teaches an apparatus for optimizing surface shape of a reflecting mirror (see abstract: “water-cooled, active optic mirror system (called “REAL: Resistive Element Adjustable Length”) that combines cooling with applied auxiliary heating” and “technique is theoretically capable of sub-nanometer surface figure error control even at high power density”), comprising:
a surface shape optimization module configured to apply a heat flux vector corresponding to a minimum value of each residual surface shape error to a heating sheet of the reflecting mirror to optimize the surface shape of the reflecting mirror (Cocco teaches: “An array of resistive heaters is bonded to the front of each blade” and that “The electric heaters are then wired through electrical feedthroughs and remotely controlled.” “Once the thermal bump generated by the beam was measured, we used calculations based on the response functions to flatten the shape in situ. The power levels needed for each actuator to correct the deformation were calculated by linear regression and applied to the mirror.” Cocco also teaches the optimization result, stating that “the height deformation was reduced from 15 nm rms to 1.5 nm rms” and that the system can “provide optimal power settings to the mirror heating channels and dynamically correct the thermal deformation.”).
Cocco fails teach: a heat flux vector module configured to determine each heat flux vector based on a response matrix, a thermal deformation vector and each perturbation term;
a residual surface shape error module configured to determine each residual surface shape error based on the response matrix, the thermal deformation vector and each heat flux vector satisfying constraint conditions.
With respect to “a residual surface shape error module configured to determine each residual surface shape error based on the response matrix, the thermal deformation vector and each heat flux vector satisfying constraint conditions” Vannoni teaches that, after mirror characterization, “we can create a matrix, classically named ‘interaction matrix’” and that “if we have a give profile b E N, we can solve the linear system Av = -b to find the needed voltage vector v E M to correct b in order to have at the end a flat profile.” More importantly, Vannoni expressly teaches constrained residual-error evaluation. Vannoni states: “We build an error function, to be evaluated on the profile that we have, calculated as the root-mean-square of the difference between that profile and the profile that we want to obtain” and “In the function, we also consider the difference constraints that we have, in terms of maximum amount of signal allowed and maximum amount of difference between adjacent benders signals. In case one of the constraints is violated, we assign an infinite value on the error function.” Vannoni further teaches that “The algorithm runs for a certain number of iterations … and at the end we obtain a vector of voltage corrections.” Accordingly, it would have been obvious to one of ordinary skill in the art before the effective filing date to modify the heater-based reflecting-mirror optimization apparatus of Cocco with the constrained error-function minimization approach of Vannoni, as it would have predictably yielded an apparatus having a heat flux vector determination function, a residual surface-shape error determination function and a surface shape optimization function as recited.
Regarding claim 11, the combination of Cocco teaches the apparatus for optimizing surface shape of a reflecting mirror according to claim 10, wherein the apparatus further comprises: a heat flux vector application module configured to apply heat flux vectors sequentially to each heating sheet to obtain corresponding reflecting mirror heat flux deformation data (page 35th para: “One of the first tests was the measurement of the effect of each individual heater on the mirror profile (i.e. the response function or influence function)”) and further states that “The first step was to characterize the effect of each heater individually, measuring the response functions to be able to predict the proper setting to compensate arbitrary deformations” and “Each actuator was individually powered to 100% of its range, and the differential effect on the wavefront was measured with the wavefront sensors.” see page 5 7th para).
However, Cocco fails to teach a response matrix module configured to determine the response matrix from the reflecting mirror heat flux deformation data. Vannoni teaches determining the response matrix from the reflecting mirror heat flux deformation data “we can create a matrix, classically named "interaction matrix", putting together the scaled M pulse profiles evaluated in N points” see page 3 1st para. It would have been obvious to one of ordinary skill in the art before the effective filing date to express Cocco’s individually measured heater response functions in the matrix form taught by Vannoni, because both Coccco and Vannoni address the same adaptive mirror inverse problem and Vannoni teaches the conventional way of organizing individual actuator response data into a matrix for correction calculations.
Regarding claim 12, the combination of Cocco teaches the apparatus for optimizing surface shape of a reflecting mirror according to claim 10, and Cocco further teaches wherein the apparatus further comprises: a thermal power application module configured to apply light source thermal power to light spots of the reflecting mirror to obtain thermal deformation data of the reflecting mirror (see page 3: “To simulate the thermal deformation, a class IV infrared Laser from IPG Photonics, able to deliver up to 100 W of polarized light at 1065-nm wavelength, was used. Variable absorbed power and laser beam footprint on the mirror were achieved by (1) controlling the power of the laser,”); and a thermal deformation vector module configured to determine the thermal deformation vector based on the thermal deformation data of the reflecting mirror (see Fig. 4: “Measurement of the thermally induced deformation and subsequent correction using REAL. Left: from bottom to top: Thermal image of the mirror, 2D measurement and relative profile on the center line of the mirror while irradiated by the IR laser” and page 5 last para: “The plan for on-beamline tests was to create and measure a thermal bump arising from the HXR beam, and then correct the mirror deformation using the heaters.”).
Regarding claim 13, the combination of Cocco teaches the apparatus for optimizing surface shape of a reflecting mirror according to claim 10, and Cocco further teaches wherein the heat flux vector module see page 8: “The measured response functions were used for the final test: increasing the power of the incident X-ray beam and compensating the thermal deformation with the heaters in a controlled way” and “Once the thermal bump generated by the beam was measured, we used calculations based on the response functions to flatten the shape in situ. The power levels needed for each actuator to correct the deformation were calculated by linear regression and applied to the mirror”)
Cocco fails to teach: a total deformation perturbation vector unit configured to determine each total deformation perturbation vector based on the thermal deformation vector, an initial deformation vector and each perturbation term; and a heat flux vector unit configured to determine each heat flux vector based on the response matrix and each total deformation perturbation vector.
Vannoni teaches beginning from an already existing measured mirror profile and using that profile in a matrix-based correction computation. Specifically, on page 3, Vannoni states: “First, we measure the mirror profile without any correction, and we store such profile as a reference baseline. We measure the resulting profile, and we calculate the difference between this profile and the stored baseline. The result is named ‘pulse profile’” and “we can create a matrix, classically names ‘interaction matrix’, putting together the scaled M pulse profiles evaluated in N points. Now, if we have a given profile b ε N, we can solve the linear system Av= -b to and the needed voltages vector v ε M to correct b in order to have at the end a flat profile.” Vannoni’s stored “reference baseline” corresponds to the claimed initial deformation vector, because it is the pre-correction mirror shape used as a reference in the subsequent optimization. Vannoni’s “given profile b” corresponds to a deformation vector used as the target for correction. And Vannoni’s matrix equation “Av = -b” teaches determining a correction vector from an interaction/response matrix and a deformation-profile vector. Vannoni also teaches that this vector need not be solved in only one rigid way, but instead may be searched through an optimization framework. Vannoni states that “instead of computing a unique solution of the problem, we have to switch to ‘searching for the better solution’ in a least squared fitting meaning.” Vannoni further states: “We build an error function” and “we also consider the different constraints that we have” and “we start the minimization from a set of values that are inside the given constraints” and “at the end we obtain a vector of voltage corrections.” Thus, Vannoni teaches generating correction vectors from a matrix model and deformation-profile input within an iterative optimization framework. Accordingly, it would have been obvious to one of ordinary skill in the art before the effective filing date to modify the heater-based mirror optimization method of Cocco with the matrix-based profile/baseline optimization method of Vannoni to predictably yield determining correction heat-flux vectors based on a response matrix and a total deformation input formed from the measured thermal deformation and the mirror’s initial profile state.
Regarding claim 15, the combination of Cocco teaches the apparatus for optimizing surface shape of a reflecting mirror according to claim 13, but fail to teach wherein the heat flux vector unit is specifically configured to: determine each heat flux vector based on an inverse matrix of a product of the response matrix and a transposition of the response matrix, the transposition of the response matrix and each total deformation perturbation vector.
Vannoni expressly teaches forming an “interaction matrix” from the individually measured actuator response, stating” “we can create a matrix, classically names ‘interaction matrix’, putting together the scaled M pulse profiles evaluated in N points, having at the end A ε NxM.” Vannoni further teaches using a deformation/profile vector as the input the correction computation, stating” “Now, if we have a given profile b ε N, we can solve the linear system Av = -b to find the needed voltages vector v ε M to correct b in order to have at the end flat profile.” It would have been obvious to one of ordinary skill in the art before the effective filing date to modify the heater based reflecting mirror optimization method of Cocco with the matrix inverse solution taught by Vannoni, as it predictably yielded determining the heat flux vector from the response matrix.
Regarding claim 19, the combination of Cocco teaches method of claim 1, including measuring beam-induced thermal bump, characterizing the effect of each heater, and calculating/applying heater correction values (“The plan for on-beamline tests was to create and measure a thermal bump arising from the HXR beam, and then correct the mirror deformation using heaters.”) Cocco fails to teach: an electronic device, comprising a memory, a processor, and a computer program stored in the memory and runnable on the processor, wherein when executing the computer program, the processor implements steps of the method for optimizing surface shape of a reflecting mirror according to claim 1. Vannani teaches optimization was implemented as an algorithm run on a conventional computer, stating “The algorithm runs for a certain number of iterations” and the computation was performed on “a standard office notebook (1.7 Ghz speed processor, 4Gb RAM memory” see page 4). Accordingly, it would have been obvious to one of ordinary skill in the art before the effective filing date to implement Cocco’s mirror optimization method on the conventional processor-memory computer system as taught by Vannoni, since doing so merely used routine computer hardware to execute known optimization calculations.
Allowable Subject Matter
Claims 5, 7-9, 14 and 16-18 objected to as being dependent upon a rejected base claim, but would be allowable if rewritten in independent form including all of the limitations of the base claim and any intervening claims.
5. The method for optimizing surface shape of a reflecting mirror according to claim 4, wherein the determining each total deformation perturbation vector based on the thermal deformation vector, the initial deformation vector and each perturbation term comprises: determining each thermal deformation perturbation vector based on a maximum value of the thermal deformation vectors, and each perturbation term; and determining each total deformation perturbation vector based on the thermal deformation vector, the initial deformation vector and each thermal deformation perturbation vector.
7. The method for optimizing surface shape of a reflecting mirror according to claim 4, wherein determining each heat flux vector by an equation comprises the following equation:
H=(M.sup.T(x)M(x)).sup.−1M.sup.T(x)(−C(x)−K(x)+(max(K(x))+ε)I); where, M(x) denotes the response matrix, H denotes the heat flux vector, C(x) denotes the initial deformation vector; K(x) denotes the thermal deformation vector, ε denotes the perturbation term, and −C(x)−K(x)+(max(K(x))+ε)I denotes the total deformation perturbation vector.
8. The method for optimizing surface shape of a reflecting mirror according to claim 1, wherein determining each residual surface shape error based on the response matrix, the thermal deformation vector and each heat flux vector satisfying constraint conditions comprises: determining each thermal deformation perturbation vector based on a maximum value of the thermal deformation vectors, and each perturbation term; and determining each residual surface shape error based on the response matrix, the thermal deformation vector, an initial deformation vector, each thermal deformation perturbation vector and each heat flux vector satisfying constraint conditions.
9. The method for optimizing surface shape of a reflecting mirror according to claim 8, wherein determining each residual surface shape error by an equation comprises the following equation:
e=M(x)H′+C(x)+K(x)−((max(K(x))+ε)I); where, e denotes the residual surface shape error, M(x) denotes the response matrix, H′ denotes the heat flux vector satisfying constraint conditions, C(x) denotes the initial deformation vector; K(x) denotes the thermal deformation vector, and (max(K(x))+ε)I denotes the thermal deformation perturbation vector.
14. The apparatus for optimizing surface shape of a reflecting mirror according to claim 13, wherein the total deformation perturbation vector unit comprises: a thermal deformation perturbation vector sub-unit configured to determine each thermal deformation perturbation vector based on a maximum value of the thermal deformation vectors, and each perturbation term; and a total deformation perturbation vector sub-unit configured to determine each total deformation perturbation vector based on the thermal deformation vector, the initial deformation vector and each thermal deformation perturbation vector.
16. The apparatus for optimizing surface shape of a reflecting mirror according to claim 13, wherein the heat flux vector module is specifically configured to: determine each heat flux vector an equation comprises the following equation:
H=(M.sup.T(x)M(x)).sup.−1M.sup.T(x)(−C(x)−K(x)+(max(K(x))+ε)I); where, M(x) denotes the response matrix, H denotes the heat flux vector, C(x) denotes the initial deformation vector; K(x) denotes the thermal deformation vector, ε denotes the perturbation term, and −C(x)−K(x)+(max(K(x))+ε)I denotes the total deformation perturbation vector.
17. The apparatus for optimizing surface shape of a reflecting mirror according to claim 10, wherein the residual surface shape error module comprises: a thermal deformation perturbation vector unit configured to determine each thermal deformation perturbation vector based on a maximum value of the thermal deformation vectors, and each perturbation term; and a residual surface shape error unit configured to determine each residual surface shape error based on the response matrix, the thermal deformation vector, an initial deformation vector, each thermal deformation perturbation vector and each heat flux vector satisfying constraint conditions.
18. The apparatus for optimizing surface shape of a reflecting mirror according to claim 17, wherein the residual surface shape error module is specifically configured to: determine each residual surface shape error by an equation comprises the following equation:
e=M(x)H′+C(x)+K(x)−((max(K(x))+ε)I); where, e denotes the residual surface shape error, M(x) denotes the response matrix, H′ denotes the heat flux vector satisfying constraint conditions, C(x) denotes the initial deformation vector; K(x) denotes the thermal deformation vector, ε denotes the perturbation term, and (max(K(x))+ε)I denotes the thermal deformation perturbation vector.
Conclusion
The prior art made of record and not relied upon is considered pertinent to applicant's disclosure.
Veldman et al. “Optimal thermal actuation for mirror temperature control” (2022): teaches The obtained actuation heat load shapes and their corresponding intensities provide insights for the design of a thermal actuation layout for mirror heating.
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/EPHREM Z MEBRAHTU/Primary Examiner, Art Unit 2872
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