I've been looking at some portraits taken with Petzval lenses after a friend turned me on to them. I quickly realized that the characteristics of these lenses make for some fantastic optical effects. I also determined that they cost a fortune and are in very "finite" supply.

I also read somewhere that Petzvals were created with a distinct formula - the Petzval equation, I think it was. I don't know how reliable the source is, but it would make sense. I mean it's all brass and glass, isn't it? It's science and not magic that produces these fantastic optics.

So I'm wondering whether there have been any lens designs in subsequent years that recreate the Petzval effect, only having more modern (and hopefully large-scale) productions. Surely someone knows the formula or equations, if they exist?