The European Patent Office granted a software patent on a method for designing an optical system that satisfies a certain algebraic condition. Here are the practical takeaways of the decision T 0471/05 of 6.2.2007 of Technical Board of Appeal 3.4.02:
This European patent application relates to the activity of designing an optical system. This is done such that substantially all light rays imaged by the optical system between two predetermined points on the optical axis of the system satisfy an algebraic condition specified in the patent claim.
Here is how the invention is defined in claim 1 of the main request:
Claim 1 (main request)A method for designing an optical system having an optical axis and imaging a point P to a point P’, both on the optical axis, characterized in that the method comprises a step of making a design of the optical system, in which substantially all rays from P to P´ satisfy the condition
where alpha and alpha´ are the angles of one of the rays with the optical axis at P and P’ respectively, n and n´ are the refractive indices at P and P’ respectively, beta’ is the lateral magnification factor between P and P’, and q is a constant complying with 1 < q <2.
Is it technical?
Since claim 1 concerned a method for designing an optical system essentially such that a mathematical formula is satisfied, the question at hand was whether the claimed subject-matter is excluded from patentability per se. In this respect, the board noted:
Thus, the claim merely formulates a series of mathematical and optical abstract concepts without properly requiring a physical, technical implementation. In particular, neither the claimed design method nor the resulting “design” requires a technical activity or a technical entity – let alone a “physical” activity or entity within the meaning of decision T 453/91 (point 5.2 of the reasons). It follows that the subject-matter for which protection is sought (Article 84 EPC, first sentence) is the mere “design” of an optical system and encompasses purely abstract and conceptual implementations excluded from patent protection pursuant to Articles 52(1), (2) and (3) EPC. More particularly, the claimed method can be carried out as a purely mental act or as a purely mathematical design algorithm and, consequently, encompasses embodiments falling within the category of methods for performing mental acts as such and within the category of mathematical methods as such both expressly excluded from patent protection under Article 52(2)(a) and (c) in conjunction with Article 52(3) EPC.
The appellant argued that the claimed method defines an activity that requires the use of technical means, involves technical considerations, results in an optical system design and produces technical information in the form of the specifications of an optical system having predetermined technical characteristics, and pertains to the technical field of optical design. However, this did not convice the board:
However, this line of argument does not persuade the Board. The criteria for technical character of a claimed invention discussed in decision T 619/02 implicitly presuppose that the claimed subject-matter defining the matter for which protection is sought relates to a physical entity or a physical activity (see for instance point 2.1, first paragraph, and points 2.3.1, 2.4.1 of the decision). It cannot be denied that the method defined in claim 1 of the main request can be carried out using some physical means (e.g. a block of optical material to be gradually shaped into an optical system so as to satisfy the algebraic condition specified in the claim), or using some technical means (e.g. a computer to determine the optical specifications of the optical system design), or in the form of a physical activity that results in a physical entity (e.g. when the claimed step of “making a design of the optical system” is implemented by the manufacture of the design as actually claimed in claim 5), and that such implementations of the claimed method constitute physical, technical activities not excluded from patent protection (see for instance decisions T 914/02, point 2.3.3 of the reasons, and T 258/03, OJ EPO 2004, 575, point 4.7). Nonetheless, contrary to the appellant’s contention, the claimed method does not require the use of technical means and, as noted above, the method is not restricted to physical, technical implementations, and the fact that the claimed method encompasses non-excluded implementations such as those mentioned above does not overcome the fact that the claimed method also encompasses excluded subject-matter (T 914/02, points 2 and 3, and T 388/04, OJ EPO 2007, 16, point 3 of the reasons; see also T 453/91, point 5.2, and T 930/05, points 3.1 and 4.5). Thus, as long as the claimed design method is not confined to physical, technical implementations, the claimed subject-matter encompasses embodiments excluded from patentability under Articles 52(1) to 52(3) EPC and is not entitled to patent protection under the EPC.
Therefore, the board concluded that claim 1 of the main request is excluded from patent protection under Articles 52(1), (2) and (3) EPC.
In a second auxiliary request, the appellant added that the claimed method is carried out “using an optics design program”. This claim version overcame the exclusion:
Thus, claim 1 of the second auxiliary request defines an activity in which the design conditions defined in the claim are input into an optics design program to determine the design parameters of optical systems satisfying the design conditions expressed in the claim. In addition, the determination by the optics design program of the resulting design specifications requires implicitly that the optics design program is run in some form of hardware such as a computer. It follows that the claimed method defines an activity involving inherently and necessarily the use of such hardware fed with the optics design program and the claimed design conditions, i.e. defines a physical, technical activity.
By the way, if you are interested in a deeper look into how the European Patent Office examines software-related inventions, this 30-minute video gives a concise overview of the “two hurdle” approach with lots of examples:
Regarding inventive step, the board was apparently satisfied that the claimed subject-matter, including the mathematical formula, defines technical subject-matter, since it examined in detail whether these features were rendered obvious by the prior art at hand:
The Board, however, cannot follow the conclusion drawn by the examining division. First, the line of argument of the examining division relies on a parameter q algebraically interpolating between the Abbe and the Herschel conditions, i.e. relies on hindsight knowledge of the specific algebraic condition defined in the claimed invention and therefore on an ex post facto analysis. Second, even assuming that the skilled person would have considered the possibility of obtaining a compromise between the two antagonistic conditions different from that proposed in document D1, the Board notes that there is an infinite number of ways of reaching a compromise between the two conditions. In particular, there is an infinite number of mathematical functions interpolating between the two algebraic conditions  and ; even restricting such interpolating functions to parametric functions, there is an infinite number of such interpolating parametric functions, the one-parameter algebraic interpolations given by the appellant in the statement of grounds of appeal (see point V above) constituting just some examples. In fact, there are even infinite ways of compromising the two conditions with the algebraic function defined in the claim when – contrary to the requirements of the claimed design – the condition is only satisfied by some light rays, or by substantially all light rays but with different values of the parameter q.
In addition, the algebraic condition defined in the claimed invention does not constitute an arbitrary selection of just one from among infinite possibilities of mathematically interpolating between conditions  and , but, according to the disclosure of the invention, the claimed condition constitutes the selection of a specific mathematical interpolation that guarantees the achievement of an advantageous balance between field size and axial excursion (page 3, lines 15 to 25), thus allowing for a relatively large volume in image space where aberrations stay relatively low (pages 9 to 12 of the application).
In view of the above, neither the available prior art nor the general common knowledge in this field suggest the design requirements defined in claim 1 and the technical improvements achieved therewith.
Therefore, the Board decided that claim 1 of the second auxiliary request involves an inventive step.
You can read the whole decision here: T 0471/05 of 6.2.2007