DETAILED ACTION
Response to Remarks
1. Applicant’s filing of a terminal disclaimer on 03/18/2026 disclaiming the terminal part of any patent granted on the instant application which would extend beyond the expiration date of the full statutory term of any patent(s) granted on pending reference Application No. 18/271,838 has been reviewed, recorded, and is accepted.
2. Applicant’s remarks (see pgs. 18-22), filed 03/18/2026, regarding the prior art rejection of claims 1-5 under 35 U.S.C 101 have been fully considered but they are not persuasive.
Applicant appears to make arguments that “the applicant's claimed invention includes, for example, "a light source," "a mirror," and "reflecting surface of the mirror." Clearly, the inclusion of multiple necessary hardware are combined together and are made to function such that the applicant's claimed method functions; and thereby making it further clear that the applicant's invention is not to be regarded as an abstract idea, a law of nature, or a natural phenomenon; and should therefore fall within statutory patentable subject matter under 35 U.S.C. §101.” Applicant further asserts that “the applicant has amended independent claim 1, so as to amend the language "designing the mirror by using design formulas of the reflecting surface derived based on * * *," so as to include a more structural language recited within the claimed step of: "obtaining an equation (design equation) indicating a shape of the reflecting surface based on * * *.” (pg. 20 of Remarks). Examiner respectfully disagrees for the following reasons. The claims invention fails to positively recite any of the structures cited by Applicant such as "a light source," "a mirror," and "reflecting surface of the mirror”. In actuality, amended claim 1 recites “obtaining an equation (design equation) indicating a shape of the reflecting surface based on the coordinates and a condition that an optical path length from a light source position to a light collection position”, wherein the characterization of the coordinate system comprising optical axes, planes, intersection points of simulated light rays amount to parameters providing an input for the for the subsequent mathematical calculations of the reflecting surface design equation. See In re Grams, 888 F.2d 835, 839-40; 12 USPQ2d 1824, 1827-28 (Fed. Cir. 1989). Applicant’s statement that “the claim language is not merely about designing a mirror using an equation, but rather obtaining, as an equation, the shape of the mirror’s reflecting surface” fails to take into account that the claim(s) as a whole are directed to a mathematical formula wherein Applicant argues that one of the parameters of said formula is the claimed invention. Thus, the claimed mathematical relationships, within the design equation, between the parameters representative of "a light source," "a mirror," and "reflecting surface of the mirror" (as alleged by Applicant) do not result in the claimed method being directed to any physical processes, i.e., the recited design equation “indicating a shape of the reflected surface” does not amount to positively reciting the physical structure of the mirror (and its surface). The invention as a whole claims a method of design in which the design equation representing a surface is written in text format. Furthermore, such a generally recited design equation based on coordinate system transformations could easily be performed by the human mind, in addition to the mathematical calculations based on parameter conditions that are input into the design formula as recited in claims 2-8, which could be performed mentally or with pen and paper. See Parker v. Flook, 437 U.S. at 586, 198 USPQ at 196. Thus, Applicant’s amendments to claim 1 are insufficient to overcome the Examiner's factual findings that the claims remain directed to an ineligible abstract idea. Applicant’s arguments are not reflected in the present claim language in that the various hardware structures being referred to are not positively claimed. Therefore, Examiner maintains that the claimed method only encompasses mathematical calculations combined with mental processes as discussed supra, without significantly more.
Applicant appears to make arguments that “With respect to our reliance on the applicant's specification in support of the requisite "practical application," we refer to the recent case of Ex parte Desjardins (Appeal No. 2024- 000567) decided by the U.S. PTO Appeals Review Panel of the Patent Trial and Appeal Board issued on September 26, 2025… Similarly, in the applicant's instant application, the applicant respectfully refers the Examiner to, for example, the applicant's paragraph [0018], which discusses the invention's advantages or benefits resulting in the requisite improvement of the applicant's claimed invention, in support of the claimed invention's requisite "practical application." (pg. 22 of Remarks). However, the Examiner notes that in Ex parte Desjardins, the claimed invention is directed to a method of training a machine learning model on a series of tasks, wherein the ARP determined that the specification identified improvements as to how the machine learning model itself operates, including training a machine learning model to learn new tasks while protecting knowledge about previous tasks to overcome the problem of “catastrophic forgetting” encountered in continual learning systems, thereby integrating the claims as a whole into a practical application at Step 2A Prong Two (italicized for emph.). In contrast, the instant application’s claims bear no relevance to training machine learning model or an integration of practical application at Step 2A by virtue of an improvement to the functioning of a computer (or other technology). Rather, the claims as a whole recite details directed to “obtaining an equation”, i.e., a design formula of a reflecting surface wherein a plurality of intersection points and displacements are expressed, followed by recitation of mathematical conditions correlating the optical path length with the simulated light collection and light source positions, wherein the properties of the simulated light beams such as incoming and outgoing light beams are inputted as parameter(s) into said formula. Thus, the present claims are not analogous to Ex parte Desjardins and the instant claimed invention fails to satisfy any practical applications outside the judicial exception (see MPEP § 2106.04). Furthermore, ¶0018 of the instant specification is directed to the advantages of employing a single mirror structure within the optical system (see ¶0018 stating “a light source position and a light collection position can be independently set in the vertical direction and the horizontal direction, and thereby a single mirror enabling free conversion of astigmatism can be manufactured”). However, ¶0018 of the specification is not reflected anywhere in the present claim language because the present claim language does not require the mirror structure nor do the claims recite any physical processes; rather, the claims recite a method of design by “obtaining a design equation” representing a reflecting surface (see claims filed 03/18/2026). Although the claims are interpreted in light of the specification, limitations from the specification are not read into the claims. See MPEP § 2145 Section VI, citing In re Van Geuns, 988 F.2d 1181, 26 USPQ2d 1057 (Fed. Cir. 1993) and Constant v. Advanced Micro-Devices, Inc., 848 F.2d 1560, 1571-72, 7 USPQ2d 1057, 1064-1065 (Fed. Cir.), cert. denied, 488 U.S. 892 (1988). The claimed invention as a whole encompasses a method of design which amounts to obtaining data followed by organizing and manipulating information through mathematical correlations, all of which can be performed mentally or by hand. See Parker v. Flook, 437 U.S. 584, 198 USPQ 193 (1978), wherein the Supreme Court noted that the "patent application does not purport to contain any disclosure relating to the chemical processes at work, the monitoring of process variables, or the means of setting off an alarm or adjusting an alarm system." 437 U.S. at 586, 198 USPQ at 195. The Court found this failure to explain any specifics of how to use the claimed formula informative when deciding that the additional elements in the claim were insignificant post-solution activity and thus not meaningful enough to render the claim eligible. 437 U.S. at 589-90, 198 USPQ at 197. Thus, the Examiner maintains that the claims provide no actual or practical applications, and recite the abstract idea of the mental processes of calculating a design formula for a mirror surface, without reciting any additional details. Therefore, Applicant fails to provide any factual basis for the conclusion that the claims are directed to an improvement to the functioning of a computer or to any other technology.
In conclusion, as explained above, none of Applicant’s arguments against the rejection of claims under 35 U.S.C. 101 are persuasive, and thus amended claims 1-8 remain rejected, as detailed below.
Claim Rejections - 35 USC § 101
35 U.S.C. 101 reads as follows:
Whoever invents or discovers any new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof, may obtain a patent therefor, subject to the conditions and requirements of this title.
Claims 1-8 are rejected under 35 U.S.C. 101 because the claimed invention is directed to an abstract idea in the form of mathematical calculations combined with mental processes, without significantly more. Claims 1-8 recite(s) a method of characterizing properties of light beams such as incoming and outgoing light beams, wherein the light beam(s) characterization is inputted as parameter(s) into a reflecting surface design formula. Furthermore, the method encompasses defining coordinate axes wherein a plurality of intersection points and displacements are expressed, followed by recitation of mathematical conditions correlating the optical path length with the light collection and light source positions comprised within a design formula. Specifically, the characterization of the coordinate system comprising optical axes, planes, intersection points of simulated light rays amounts to an extra-solution activity of mere data-gathering to provide an input for the for the subsequent mathematical calculations of the reflecting surface design formula i.e., “obtaining an equation (design equation) indicating a shape of the reflecting surface based on the coordinates and a condition that an optical path length from a light source position to a light collection position”, as recited in claim 1. See In re Grams, 888 F.2d 835, 839-40; 12 USPQ2d 1824, 1827-28 (Fed. Cir. 1989). Furthermore, such a generally recited design formula based on coordinate system transformations could easily be performed by the human mind, in addition to the mathematical calculations based on parameter conditions that are input into the design formula as recited in amended claims 2-8, which could be performed mentally or with pen and paper. See Electric Power Group v. Alstom, S.A., 830 F.3d 1350, 1353-54, 119 USPQ2d 1739, 1741-42 (Fed. Cir. 2016). See also MPEP § 2106.04(a)(2).1IL.B: “If a claim recites a limitation that can practically be performed in the human mind, with or without the use of a physical aid such as pen and paper, the limitation falls within the mental processes grouping, and the claim recites an abstract idea.”; see also Synopsys, 839 F.3d at 1139, 120 USPQ2d at 1474 (holding that claims to the mental process of "translating a functional description of a logic circuit into a hardware component description of the logic circuit" are directed to an abstract idea, because the claims "read on an individual performing the claimed steps mentally or with pencil and paper"). Thus, the instant claims 1-8 are directed to an ineligible abstract idea.
The Court has repeatedly determined in similar cases that such mathematical correlations are a judicial exception to patent eligibility and directed to an abstract idea. See Digitech Image Techs., LLC v. Electronics for Imaging, Inc., 758 F.3d 1344, 1350, 111 USPQ2d 1717, 1721 (Fed. Cir. 2014). In the present case, the judicial exception is not integrated into a practical application because the claims provide no actual or practical applications, and recite the abstract idea of the mental processes of calculating a formula based on coordinate transformations and characterization of simulated light beam(s), without reciting any additional details. Furthermore, the claims do not include additional elements that are sufficient to amount to significantly more than the judicial exception because those additional elements that do appear merely list the steps of the abstract idea. Specifically, the step of “weighting both a first formula fs(u, v, w) = 0 derived from a condition that an optical path length from a light source point to a light collection point is constant for the light collection in the sagittal direction, and a second formula fm(u, v, w) = 0 derived from a condition that an optical path length from the light source point to the light collection point is constant for the light collection in the meridional direction” does not positively require a reflecting surface and/or mirror, and amounts to obtaining data, organizing, inputting and manipulating information through mathematical calculations, all of which can be performed mentally or by hand. Similarly, the method further comprising “a plane that includes an intersection point Mo on the reflecting surface between the z1 axis and the z2 axis and is in contact with the reflecting surface is defined as a uv plane, a direction of a normal line passing through the Mo in the uv plane is defined as a w axis, av axis is a direction orthogonal to both the z1 axis and the z2 axis, and a u axis is a direction orthogonal to both the v axis and the w axis, an orthogonal coordinate system is defined based on a mirror” also does not add a meaningful limitation to the process of mere manipulating information through mathematical correlations in the form of defining intersection points and orthogonal coordinate axes, as recited and encompassed by the claims. Therefore, the claims do not include additional elements that are sufficient to amount to significantly more than the judicial exception.
Claims 2-8 are rejected as being dependent upon claim 1, and fail to cure the deficiencies of the rejected base claim, as claims 2-5 and newly amended claims 6-8 do not add any additional elements beyond method steps drawn to the abstract idea. As such, Claims 1-8 do not raise the abstract idea to the level of patentable subject matter.
Examiner’s Notes
Regarding claims 9-11, the Applicant is respectfully advised that “patentability of a product does not depend on its method of production. If the product in the product-by-process claim is the same as or obvious from a product of the prior art, the claim is unpatentable even though the prior product was made by a different process.” See MPEP § 2113, Section I, citing In re Thorpe, 777 F.2d 695, 698, 227 USPQ 964, 966. Nonetheless, the Examiner has considered the structure implied by the process steps. See also In re Nordt Dev. Co., 881 F.3d 1371,1375-76, 125 USPQ2d 1817, 1820 (Fed. Cir. 2018).
Allowable Subject Matter
Claims 9-11 would be allowable if the rejections set forth in this Office action are overcome.
The following is an examiner’s statement of reasons for the indication of allowable subject matter:
With respect to Claims 9-11, the prior art discloses various astigmatism control mirrors having a reflecting surface satisfying a design formula,
the astigmatism control mirror, which is manufactured by forming the reflecting surface on a plate surface, being designed by a method that is comprised of: defining an optical axis of an incoming beam to the mirror as a zi axis, and defining a cross section orthogonal to the zi axis as an x1y1plane; defining an optical axis of an outgoing beam from the mirror as a z2 axis, and defining a cross section orthogonal to the z2 axis as an x2y2plane; setting the xi axis and the x2 axis to be parallel to a sagittal direction of the reflecting surface; causing incoming beams to have a light source for light collection in the sagittal direction ((¶005: The radiation source may be operable to produce an astigmatic radiation beam; ¶0108, 000143-46: a concave toroidal-like mirror 350 may, for example, be paraboloidal, hyperboloidal, ellipsoidal or toroidal in this embodiment. mirror is arranged to decrease a divergence of the radiation beam; see FIG. 7 showing curvatures K1 and K2 of reflective surface 352 of mirror; ¶0156: The second mirror M2 increases the divergence of the radiation beam in the y- direction [incoming beam diverging at one point]; ¶00144-45: mirror 350 may have a first focal length in the u-v plane, which is related to the curvature of the reflective surface in the u-direction and the grazing incidence angle β of the radiation beam. toroidal third mirror M3 will therefore decrease the divergence of the radiation beam in the first and second directions in the x-y plane by different amounts; ¶00148: output radiation beam B.sub.out leaving the converging mirror M3 is collimated when the input radiation beam B.sub.in enters the radiation beam expander 200 along the nominal input path AB; ¶0156: The third mirror M3 reduces the divergence of the radiation beam in both the x and y directions such that the radiation beam is collimated; ¶0150; ¶0217: output radiation beam B.sub.out has a fixed position and direction; see FIG. 11 showing collection performance of output beam only in sagittal direction); and outgoing beams which are collected at one point are obtained from an incoming beam having astigmatism (¶0052, 0099: converging optic is astigmatic mirror [outgoing beam having astigmatism]; ¶0150; ¶00115: Such paraboloid, hyperboloid, ellipsoid extruded parabolic, extruded hyperbolic or extruded elliptical curved mirrors may be suitable for focusing radiation beams with a Gaussian intensity distribution).
Specifically, the best prior art of Nienhuys et al. (WO 2016/150612 A2) discloses and/or teaches an astigmatism control mirror satisfying the claimed conditions as recited above.
However, the best prior art of record fails to teach or reasonably suggest:
causing incoming beams to have a light source for light collection in the sagittal direction at a position displaced by L1s in a z1-axis direction from an intersection point Mo on the zi axis on the reflecting surface between the zi axis and the z2 axis, and a light source for light collection in a meridional direction at a position displaced by L1m in the z1-axis direction from the intersection point Mo on the zi axis; causing outgoing beams to be collected at a position displaced by L2s in a z2-axis direction from the intersection point Mo on the z2 axis for light collection in a sagittal direction, and to be collected at a position displaced by L2m in the z2-axis direction from the intersection point Mo on the z2 axis for light collection in a meridional direction; causing all incoming light rays passing through the mirror to pass through both a sagittal light source ray and a meridional light source ray, the sagittal light source ray passing through a position of the light source in the light collection in the sagittal direction and extending in a direction orthogonal to both the x1 axis and the z1 axis, the meridional light source ray passing through a position of the light source in light collection in the meridional direction and extending in a direction orthogonal to both the y1 axis and the zi axis; causing all outgoing light rays emitted from the mirror to pass through both a sagittal collected light ray and a meridional collected light ray, the sagittal collected light ray passing through a collecting position in the light collection in the sagittal direction and extending in a direction orthogonal to both the x2 axis and the z2 axis, the meridional collected light ray passing through a collecting position in the light collection in the meridional direction and extending in a direction orthogonal to both the y2 axis and the z2 axis; representing any point on the reflecting surface of the mirror by M, expressing coordinates of an intersection point between the sagittal light source ray and an incoming light ray to the M point and an intersection point between the meridional light source ray and the incoming light ray to the M point by using the L1s and the L1m, and expressing coordinates of an intersection point between an outgoing light ray from the M point and the sagittal collected light ray and an intersection point between the outgoing light ray from the M point and the meridional collected light ray by using the L2s and the L2m; and obtaining the reflecting surface having a shape represented by an equation based on the coordinates and a condition that an optical path length from a light source position to a light collection position is constant with respect to any point on the reflecting surface for both the light collection in the sagittal direction and the light collection in the meridional direction, wherein: values of the L1s and the L1m are different from each other, and values of the L2s and the L2m are equal to each other; wherein: values of the L1m and the L2m are positive or negative infinity, and each of the L1s and the L2s has a predetermined value (where Lis + L2s ≠ 0), wherein: values of the L1s and the L1m are equal to each other, and values of the L2s and the L2m are different from each other
The best prior art of Nienhuys, fails to teach or reasonably suggest the cumulative details of newly-amended Claims 9-11 in a single embodiment. Moreover, given the complex nature of optical systems, one of ordinary skill in the art at the time the invention was filed would not have found it obvious to modify the optical system of Nienhuys to satisfy the claimed conditions as recited supra, as such a modification would have unpredictable results.
Conclusion
Applicant's amendment necessitated the new ground(s) of rejection presented in this Office action. Accordingly, THIS ACTION IS MADE FINAL. See MPEP § 706.07(a). Applicant is reminded of the extension of time policy as set forth in 37 CFR 1.136(a).
A shortened statutory period for reply to this final action is set to expire THREE MONTHS from the mailing date of this action. In the event a first reply is filed within TWO MONTHS of the mailing date of this final action and the advisory action is not mailed until after the end of the THREE-MONTH shortened statutory period, then the shortened statutory period will expire on the date the advisory action is mailed, and any extension fee pursuant to 37 CFR 1.136(a) will be calculated from the mailing date of the advisory action. In no event, however, will the statutory period for reply expire later than SIX MONTHS from the mailing date of this final action.
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/SAMANVITHA SRIDHAR/Examiner, Art Unit 2872
/BUMSUK WON/Supervisory Patent Examiner, Art Unit 2872
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