# Transfer / transmission function in optical systems - reference needed

I'm dealing with a patent appeal and one of the main disputes is over something I would declare common knowledge. However, our patent attorney would like to have a publicly accessible reference to one of the equations that is used in the affected patent.

The equation describes the transfer of light from a light source by an optical system. Specifically, it is used to describe the behavior of a collimator. It looks like that:

$$E(x,y) = T(x,y)*I(x,y)$$

E... Irradiance (spatial light distribution after opt. system)
T... Transfer function
I... radiant intensity of light source

It's very similar to the matrix-method when dealing with optical systems, eg. in lenses or polarization. Unfortunately, 'very similar' doesn't cut it when you talk to attorneys.

So here is my question:
Does anybody know a reference to a similar equation in the context of irradiance/optics/optical systems that can be quoted.

• I am not a lawyer, but I would question the patenting of a physical law. That is explicitly ruled out by the law, at least in the US, if I am not mistaken. If, however, you are trying to patent an ad-hoc illumination function as part of e.g. a game or CGI effect design, then you are unfortunately in trouble. Algorithms can be patented if they relate to specific technical applications. Having said that, if two companies are fighting over the above expression, then it's like a bad divorce: the lawyers are getting rich over something that the parties should resolve calmly in a meeting. Jan 25 at 3:41
• I hear you. And I tried to explain that to our patent attorney. No luck.
– RaJa
Jan 25 at 6:22
• I can feel your pain. I was in a company that kept filing textbook chapters... what a waste of money. Jan 25 at 7:25
• I don't have any books on fourier optics handy, but that could do the trick en.wikipedia.org/wiki/… (or point spread functions, diffraction, etc) Jan 25 at 14:05
• Maybe you simply show that this equation is true at any individual position $(x,y)$ using absorption and then say an absorption profile is described by a general transfer function? Jan 26 at 13:21

• You are correct with respect to the units. But I've written that T can also stand for a transfer function that would take care of the units. And the specific geometry is actually an "inverted" parabolic mirror (plastic part with outside face in form of a parabolic mirror).
I found a book Introduction to Modern Optics (Fowles) page 140 that says $$U^\prime(\mu,\nu)=T(\mu,\nu)U(\mu,\nu)$$ for "spatial frequencies" $$\mu=kX/L$$ and $$\nu=kY/L$$, light of angular wavenumber $$k$$, focal length $$L$$, transfer function $$T$$, "optical disturbance" $$U$$, and $$^\prime$$ including the effects of the "finite size of the aperture at the $$\mu\nu$$ plane and including "lens defects, aberrations, and so forth."
• That's an interesting argument, but I suspect it's a little far stretched as it's basically Fourier optics (I guess from the spatial frequencies) and the patent is only dealing in geometrical optics. The problem is that you actually can convert physical properties into another with the right "transfer" function. And signal theory also says that OUT = T*IN with T the transfer function of your system. So it's common knowledge which just has to be "shown" in right context :\